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‘There are also those who don’t mind anything. It is as if they could say to supervisors “Do your job quickly and let us do our usual businesses”. … This happens mostly to people who are unhappy about their leadership or leaders, they are the ones who think that supervisors just come to disturb them or make them waste their time.’ (S2, male, A0 degree)
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other
| 99.94 |
Some supervisors described a more externalised coping strategy, such as providers trying to influence evaluations through inappropriate negotiations or persuasions. This could be by asking or begging for better marks or a form of bribing such as offering a beer at bar. Some providers believed supervisors expected this. In the mixed FGD, a provider described it could be by using gender attributes: ‘Another colleague … told me “you do not know how to talk to him!”. S/he said, “you get close to him, smile to him and tell him ‘forgive me’”. He is a man – and then he gives you all your marks [best marks in PBF].’ (P1, female, A2 degree)
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other
| 99.9 |
All FGDs had suggestions about how the supervisory relationship may be improved. Respectful and friendly forms of communication were generally found essential. Some providers explained that pleasant communication and a humble attitude of the supervisor would compensate the negative experience of a low performance mark, changing it instead into a constructive experience.
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other
| 99.94 |
Several providers suggested training of supervisors in interpersonal skills is needed. Supervisors also found training relevant. Yet, a supervisor in the mixed FGD thought training in communication might not solve interpersonal problems related to attitudes or values of supervisors: ‘It’s about conscience of everyone. … Training itself is not enough. … In fact, when you do not put your conscience on it, you feel that it [supervision] does not mean anything even. You notice that it has become a game rather than something formative.’ (S7, male, degree not reported)
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other
| 99.94 |
‘It’s about conscience of everyone. … Training itself is not enough. … In fact, when you do not put your conscience on it, you feel that it [supervision] does not mean anything even. You notice that it has become a game rather than something formative.’ (S7, male, degree not reported)
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other
| 99.94 |
Providers too talked about changes in attitude and not simply communication skills, as in FGD5: ‘Supervisors should change: they should come with disposal for mutual understanding with those whom they supervise, and with humility so that these [supervisees] feel comfortable with them and vice versa. This will facilitate teaching and correcting each other, as well as mutual empowerment.’ (P8, female, A2 degree)
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other
| 99.9 |
‘Supervisors should change: they should come with disposal for mutual understanding with those whom they supervise, and with humility so that these [supervisees] feel comfortable with them and vice versa. This will facilitate teaching and correcting each other, as well as mutual empowerment.’ (P8, female, A2 degree)
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other
| 99.94 |
Several said providers should be trained in what to expect from formative and evaluative supervision visits. Further, providers expressed a need for a channel of feedback to supervisors as in FGD4: ‘What I suggest is that people [supervisors and providers] should sit and have a discussion whereby they [supervisors] ask us “Do you think that we do the supervision well?” … in order that there isn’t any favoritism.’ (P3, female, A1 degree)
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other
| 99.9 |
Drawing on Weberian theory of social action, our data are used to propose an ideal type model of how poor supervisory relationships develop and may be addressed in our study domain.35 This is illustrated in Figure 1 as a vicious cycle, depicting potential linkages of problematic social phenomena in supervision as described in our material.
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other
| 99.44 |
We use these negative perceptions, instead of, for instance, positive or appreciative accounts, as they emerged abundantly and appear useful for pointing to three main entries for improvement of the supervisory relationship, as illustrated in Figure 1 and described in the following with supporting references.
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other
| 99.9 |
Firstly, our study suggests that a supervision structure relying heavily on performance evaluations may induce substantial anxiety among providers and exacerbate the inherent power imbalance. The supervisory encounter in our material appeared to revolve around the performance indicators that supervisors mark, much like students may focus on subjects that are to be assessed in examinations.36 This may limit attention on the vastness of activities and work problems not included in evaluation checklists.37 Suggestions for structural changes were given in another paper,14 such as pre-announcing the date of evaluations and reducing the monthly frequency of evaluation visits to give supervisors time to offer formative encounters.
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other
| 99.9 |
Another approach is to introduce a formal structure for feedback from providers to supervisors,17 particularly on aspects relating to building the supervisory relationship. Providers are the direct beneficiaries of supervision, and their feedback on supervision quality is essential to improving it. Similarly, as reported,14 HC managers share a responsibility for the outcome of supervision and may too benefit from a feedback channel.
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other
| 99.9 |
Finally, in addition to the results presented our data had massive complaints about shortage of transport vehicles for supervision, high provider turnover, absenteeism and stressful work demands indicating precarious structural and organisational conditions that themselves may impair the supervision encounter and its supportive content. These structural challenges must be dealt with on policy and implementation levels.
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other
| 99.9 |
Secondly, our material suggests that the quality of the interpersonal communication between external supervisors and providers is essential to the quality of the supervisory relationship and outcome of supervision. For instance, providers appear to benefit more from supervisors with a humble approach when correcting or advising, in spite of inherent power differentials.
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other
| 99.9 |
External supervisors work in a conflict-prone environment, and the very process of evaluation is an occasion for disagreement, where controversy may be the rule rather than the exception.37 Anxiety may be expected and is to some extent beneficial in evaluation, yet in our data we find signs of so-called excessive evaluation anxiety, including conflict, avoidance, resistance, shame and anger,17,18 which may all inhibit performance. While this is unpleasant for providers, such environment may also wear down evaluators in their aspirations for objective evaluations and respectful professional relations. Over time, objectivity and the supervisory relationship may begin to come apart.17
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other
| 99.75 |
In our data, several supervisors described providers’ feelings of anxiety and discomfort in reasonable proportion with the attention they received from providers, suggesting supervisors do not have problems interpreting providers’ emotional state. The better supervisors are prepared to take account of providers’ anxiety by involving them in the supervision process and purposes, acknowledging their feelings of discomfort,38 listening, providing useful feedback and encouraging them as part of critique, the more likely providers will be enabled to improve practice.4,18
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other
| 99.44 |
Also, the more mindful supervisors are of the availability and use of power sources, the less is the risk of power misuse.39 This may help make the power relation as transparent as possible, whereas well-intended aims to simply shift the terminology of activities in favour of mentorship and support may conceal an inescapable power differential in the supervisory relationship.14,40 It may also promote the use of less formal power forms known from non-managerial supervision where supervisors hold no formal authority over the supervisee,41 but exert power through their professional expertise or the capacity to provide information perceived as useful by supervisees.13
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other
| 99.9 |
Third, our data indicate that poor supervisory relationships often develop with providers perceived as insufficiently skilled. Providers performing poorly may experience low marks and negative feedback, which by itself does not seem to induce a change in practice. A notable reaction from some providers is to avoid supervision. A dilemma of supervision inequity may emerge, where those most in need of supervision are those most unlikely to benefit from it. This indicates that at least for a group of providers, rewards (which in their absence may be perceived as punishment) may be an ineffective power source and evoke fear and experiences of repeated failure. Our data imply that these providers often perceive the support system to oppose rather than meet their need for meaningful supervisory relations to guide their professional development, so that their competence and autonomous motivation remain unstrengthened.9 In response, any supervisee indeed has the power to reject the role as learner.15 Constructive attention towards providers with performance difficulties thus appears necessary for facilitating improved practice.
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other
| 86.25 |
The restrictive power of rewards is inherent to PBF. Applying promotive sources of power by engaging in non-judgemental interaction with providers to understand their needs and problems at work seems necessary to facilitate meaningful collaboration and sustainable improvements in practice.21 One approach would be to engage providers and supervisors in developing a supervisory contract to clarify roles, expectations and intentions.16,18 A supervisory contract should include ethical aspects concerning the supervisory relationship with reference to confidentiality, providers’ fear and welfare as well as proper communication.18 This may also address gender equality in the supervisory relationship because the majority of primary healthcare providers are female as opposed to the majority of supervisors being male, and also because female providers in one FGD shared experiences of supervisors using gender discriminating terms (such as saying ‘those women’ in a derogatory way). In the mixed FGD, male supervisors agreed that such terms were unacceptable. This together with the fact that other FGDs did not raise the issue of gender discrimination may indicate that such discrimination is the exception rather than the rule.
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other
| 99.8 |
The supervisory role and responsibility must also be clear at a structural level. Role theory suggests individuals may act in ways they believe are socially expected from the roles they acquire.42 From this lens, it is important that required supervisory attitudes and behaviour are clear at policy and implementation level, so supervisors are informed and influenced from within their organisation rather than for example solely from traditional or cultural concepts of a supervisor.
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other
| 99.94 |
Apart from a contract, we suggest to institutionalise open, provider-oriented conversations and mutual feedback channels in evaluative supervision visits. Although a dual role of evaluator and supporter may be difficult to fill, studies indicate it is possible for supervisors who develop an effective relationship with supervisees.20,43
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other
| 99.9 |
As part of PBF, external and managerial supervision takes up substantial resources in Rwanda, which should be spent in ways that best help improve practice. We see a need for further studies on supervision, PBF and the problem of excessive evaluation anxiety in the Rwandan context. Questions to explore include how best to identify excessive evaluation anxiety, who are affected and how and the effect of strategies to prevent it. Further research is needed to explore reactions and optimal support of providers who experience multiple mediocre evaluations. Appropriate tools to measure external supervision quality should be locally validated and might serve as specific supervisor feedback. Interventional studies on supervision, PBF, alternative models and excessive evaluation anxiety should be in a controlled design with rigorous methods to quantify single intervention components using validated indicators.3 Finally, it has been suggested that medical doctors with a specialisation in primary healthcare, such as family physicians, play a role in the supervisory support of primary care providers in Africa.29 This could help ensure that supervision effectively addresses providers’ needs for developing their skills in response to the population’s needs for high-quality primary healthcare and should be a topic for further study.
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other
| 99.75 |
Our study design does not simply allow transfer of results to other districts or HCs. It is theoretically possible that critique presented is unique to our sample. To explore transferability, we presented our findings on several occasions (latest in October 2016) to providers and supervisors from participating and non-participating facilities to request their critique and modifications. This confirmed and refined our findings and interpretation and brings confidence that results are still relevant and not representing isolated cases. Still, our data do not allow quantification of problems revealed, such as inappropriate use of power among supervisors and excessive evaluation anxiety among providers. They may be the exception rather than the rule, yet we are confident they are harmful and significant enough to require attention and action. Other studies would be needed to estimate their magnitude.
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study
| 99.94 |
Social desirability bias is a risk to consider in any study that involves social interaction in generating data. We believe the low-moderator-involvement approach helped reduce this. In all FGDs, except the mixed FDG, participants already knew each other well. Participants frequently expressed their agreement and disagreement with others and related their points to something others said. Extreme positions were often modified or contested. Also, discussion topics were designed for open discussion allowing any polarity of views.14 We thus believe the data give a balanced and trustworthy picture of supervisors’ and providers’ positive and negative perceptions concerning the supervisory relationship.
|
study
| 99.7 |
We found several signs of the so-called excessive evaluation anxiety among Rwandan primary healthcare providers, the scope of which should be further investigated. It appears to pose challenges for establishing a supervisory relationship appropriate for generating professional development among providers. A recommendation is for supervisors to adapt a style of communication and behaviour that acknowledges structural evaluation pressures and derived anxiety, and addresses it constructively. This may include the engagement in mutually developed supervisory contracts defining expected and intended roles and functions of all supervision forms and actors. Providers most in need of supervision to improve performance may be most unlikely to benefit from it. Particular efforts to encourage and support providers with performance difficulties are needed, as are structural changes to make the supervision scheme more responsive to providers’ context of challenges at individual facilities.
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other
| 99.9 |
External supervision appeared driven by evaluation requirements of PBF with the potential to both improve and damage motivation of providers. The risk of harm calls for careful attention to factors that influence the supervisory relationship. The available forms of power should be recognised by supervisors, and used with caution. Rewards, which in their absence may be experienced as punishment, is a power form inherent to PBF in Rwanda, shaping the supervisory relationship. Promotive power sources that account for experienced and actual needs of providers appear decisive for desirable supervision outcomes.
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other
| 99.9 |
While our study demonstrates that negative supervisory relationships may be detrimental to supervision outcomes and provider motivation thus aligning with reviews of supervision interventions in resource-constrained settings that did not confirm its effectiveness,1,2,3,44 this is not evidence against the assumption that constructive exchange between a provider and a supervisor has a crucial role to play for the continuous skill development and motivation of African primary care providers.
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review
| 62.0 |
Osteoarthritis (OA) is a multifactorial, progressive, and painful disease. OA is influenced by genetic and environmental factors, including mechanical stress . To overcome difficulties in studying osteoarthritis in humans, a variety of animal models have been developed [2–4]. The use of strenuous running helps simulate long-term stress on weight-bearing joints. This model does not require surgical procedures; therefore it can detect subtle symptoms of osteoarthritis without surgical modification. Running protocols for rats usually require 30 km in 6 weeks (Table 1), but a proportion of rats often drop off the protocol because of foot problems, and quantitative data for this dropout rate have not been reported [5, 6]. We previously used 30 km of running protocol and experienced drop out problems. Here, we first examined the dropout rate of rats during a forced 30-km running protocol.Table 1Reports on the effects of running exercise on articular cartilage in Wistar ratsStudyRunning distanceRunning periodOA inducedMethodEffectSekiya et al. 200930 km6 weeksNoHarmfulSiebelt et al. 201131.8 km6 weeksNoHarmfulBeckett et al. 201230 km / 55 km3 / 6 weeksNoHarmfulPap et al. 199830 km12 weeksYesIntracranial self stimulationHarmfulSiebelt et al. 201415 km6 weeksYesPapain injectionHarmfulSaito et al. 201515 km3 weeksYesMIA 0.1 mg injectionHarmfulGalois et al. 200415 km4 weeksYesACLTBeneficialCifuentes et al. 201015 km8 weeksYesMIA 1.2 mg injectionBeneficial Abbreviations: ACLT anterior cruciate ligament transection, MIA mono-iodoacetate
|
study
| 99.94 |
OA progression is also influenced by inflammation, which is possibly affected by mechanical stress . Acute inflammation is one of the triggers for OA. Intra-articular injection of mono-iodoacetate (MIA) induces arthritis and 1 mg MIA is often used to induce arthritis in rats. However, in this condition, both cartilage and bone are rapidly destructed [8–10]. Therefore, the use of this amount seems to be inappropriate for analyzing OA progression in OA models. It is still debated whether strenuous running in the inflammatory phase produces beneficial or harmful effect in rat knees (Table 1). We hypothesized that it is possible to reduce the running distance required to make OA in combination with another OA inducer as MIA. If both strenuous running and low amounts of MIA induce OA in an additive manner, this will be a good model for mimicking OA in rats. Secondly, we examined the influences of strenuous running and/or low amounts of MIA injection on cartilage.
|
study
| 100.0 |
It is widely accepted that synovial inflammation is a feature of OA [11–13]. Clinically, exercise is effective in improving symptoms of OA in the chronic phase [14, 15]. On the other hand, it is well known that exercise in the inflammatory phase leads to exacerbation of symptoms . However, it is still unknown how exercise affects synovitis. Thirdly, we examined if low amounts of MIA injection induced synovitis and how strenuous running affected synovitis, if at all.
|
study
| 99.94 |
All animal care and experiments were conducted in accordance with the institutional guidelines of the Animal Committee of Tokyo Medical and Dental University. Thirty-six wild type male Wistar rats (Charles River Laboratories Japan, Kanagawa, Japan) from the ages of ten to eleven weeks were used for the experiments. The weight ranged between 294-342 g. Rats were housed under a 12-h light–dark cycle and allowed food and water ad libitum.
|
study
| 99.94 |
For strenuous running, we used a rodent treadmill machine (MK-680R5; ME Service, Tokyo, Japan), in which electrical shocks were applied to the grid behind the lane to stimulate the rats that failed to run spontaneously (Fig. 1a). Rats were forced to run with a 5% incline [5, 6]. Healthy rats were forced to run 30 km (20 m/min for 50 min, 5 days a week) over 6 weeks (Fig. 1b), and we examined the completion rate every week. Rats were observed during the running, and rats which stopped running in the grid over one minute despite electric stimulation were defined as drop out.Fig. 1Relationship between the number of rats that could continue to run and the distance rats run during strenuous running. a Treadmill for rats. b Protocol of strenuous running for 30 km for 6 weeks. c Survival rate of rats during the strenuous running
|
study
| 100.0 |
MIA (Sigma-Aldrich, St. Louis, MO, USA) was dissolved in phosphate-buffered saline (PBS). 0.1 mg MIA in 50 μl PBS was injected once into the right knee and PBS was injected into the left knee with a 27-gauge needle in a 1.0 ml syringe through the lateral infrapatellar area toward the inter condylar space of the femur in a deep knee flexed position (Fig. 2a). Seven days after the injection, rats were forced to run 15 km (20 m/min for 50 min, 5 days a week) over 21 days and were then evaluated. Rats were also kept without running for 21 days and evaluated (Fig. 2b).Fig. 2Outline of the study. a Schema to show the grouping of knee injection and running. b Protocol for injection of mono-iodoacetate (MIA), running, and evaluation
|
study
| 100.0 |
First, 7 days after PBS injection, rats were forced to run 15 km over 21 days. Synovium was evaluated in rats before and after 15 km running (Fig. 5a). Second, 7 days after MIA injection, rats were forced to run 15 km over 21 days. Synovium was evaluated in rats before, after 15 km running, and after 21 days without running (Fig. 5d).
|
study
| 100.0 |
Femoral and tibial condyles were dissected separately without damaging the cartilage surface, and then stained with India ink to assess cartilage degeneration. Quantification of macroscopic images was evaluated by the area of macroscopic cartilage degeneration. Macroscopic pictures were taken using a ZEISS Stimi 2000C microscope (Carl Zeiss, Oberkochen, Germany) on a dedicated medical photography platform. The degeneration area of the medial tibial plateau was measured using AxioVision Rel software version 4.8 (Carl Zeiss, Oberkochen, Germany). Macroscopic assessment was performed separately by two examiners and the average values were recorded.
|
study
| 99.94 |
The distal femur, proximal tibia and whole knee joints were fixed in 4% paraformaldehyde for 7 days, decalcified in 20% EDTA solution for 21 days, and then embedded in paraffin wax. The specimens were sectioned in the sagittal plane at 5 μm and stained with safranin-o/fast green. Each section was evaluated with the Osteoarthritis Research Society International histological grading system (OARSI score: 0 to 24) for articular cartilage degeneration . For evaluation of synovium, 7 days after MIA injections, before and after 15 km of running, whole knee joints were sectioned in a sagittal plane and stained with hematoxylin-eosin (HE). Each section was evaluated with Krenn’s synovitis grading system (Synovitis score: 0 to 9) for infrapatellar fat pad (IFP) synovitis . Histologic sections were visualized using an Olympus BX53 microscope (Olympus, Tokyo, Japan). Microscopic assessment was performed separately by two examiners and the average values were recorded.
|
study
| 100.0 |
We searched articles published in January, 1980 to May, 2016 by PubMed. The key words were “running”, “osteoarthritis”, and “rats”. 26 articles were hit and 7 articles were finally selected as “reports on the effects of running exercise on articular cartilage in Wistar rats”.
|
review
| 98.75 |
First, rats were forced to run for 30 km over 6 weeks without MIA injections (Fig. 1a, b). Even though all rats run up to 15 km, the number of rats that could not complete the running increased after 20 km. 50% of rats completed 30 km of running (Fig. 1c).
|
study
| 100.0 |
Secondly, we examined the influences of forced running and MIA injection on cartilage (Fig. 2a, b). All rats completed 15 km of running even after MIA injection. Macroscopically, 15 km of strenuous running affected neither the femoral nor tibial articular cartilage (Fig. 3a). Intra-articuar injection of 0.1 mg MIA did not affect the femoral articular cartilage surface, but induced erosion at the tibial cartilage irrespective of the forced 15 km of running (Fig. 3b).Fig. 3Macroscopic observation for articular cartilage. a Macroscopic images of the femoral and tibial articular cartilages stained with India ink. Cartilage erosion is surrounded by a yellow dotted line. b Quantification of degenerated area of the tibial cartilage (n =4, * p < 0.05 by Steel-Dwass test)
|
study
| 100.0 |
Macroscopic observation for articular cartilage. a Macroscopic images of the femoral and tibial articular cartilages stained with India ink. Cartilage erosion is surrounded by a yellow dotted line. b Quantification of degenerated area of the tibial cartilage (n =4, * p < 0.05 by Steel-Dwass test)
|
study
| 99.94 |
Histologically, no changes in articular cartilage was found in rat knee joints forced to run 15 km. MIA injection did clearly induced a loss of sulphated-glycosaminoglycans (sGAG) in both femoral and tibial cartilages (Fig. 4a). On the tibial side, cartilage degeneration induced by MIA was observed around the apex part of the tibia, which was not covered with the meniscus. Though the forced running did not affect the femoral cartilage, the forced running further exacerbated the sGAG loss of the cartilage affected by MIA in the tibial cartilage (Fig. 4b). OARSI score for histology was significantly higher in the MIA-treated groups than in the MIA untreated groups both in the femoral and tibial cartilages (Fig. 4b). Interestingly, in the tibial cartilage, OARSI score was significantly higher in the running group than in the non-running group in the MIA-treated condition. This difference was attributed not to stage (area volume) but to grade (tissue reaction); in the MIA treated non-running group, the tibial grade was 2 (cartilage matrix depletion into upper 1/3) or 3 (cartilage matrix depletion into lower 2/3), while in the MIA treated running group, the tibial grades had risen to 3 or 4 (cartilage matrix loss).Fig. 4Histological observation for articular cartilage. a Femoral and tibial sections stained with safranin-o in the sagittal plane. b OARSI scores for femoral and tibial cartilage (n =4, * p < 0.05 by Steel-Dwass test)
|
study
| 100.0 |
Thirdly, we examined the influences of forced running and MIA injection on synovium. In the PBS injected knee (Fig. 5a), thickness of the synovial cell layer at the infrapatellar fat pad did not increase after 7 days, the synovial thickness appeared to be unchanged after 15 km of running (Fig. 5b) and synovitis scores were similar between rats not forced to run and rats subjected to forced running (Fig. 5c). In MIA treated knees (Fig. 5d), even though the thickness of the synovial cell layer at the infrapatellar fat pad increased 7 days after MIA injection, the synovial thickness decreased irrespective of running at 21 days (Fig. 5e). The synovitis score in rats injected with MIA at 21 days with or without running was significantly lower than that in rats injected with MIA at 0 days (Fig. 5f). There was no difference between synovitis scores with running and without running in MIA treated knees.Fig. 5Analyses for synovitis of the knee. a Protocol for running without MIA injection. b Synovial sections stained with HE. Whole knee joints were sectioned in the sagittal plane for synovium of infrapatellar fat pad. c Quantification of synovitis evaluated by Krenn’s synovitis scoring system (n = 4). d Protocol for running with MIA injection. e Synovial sections stained with HE. Synovial cell layer is indicated by arrows. f Quantification of synovitis evaluated by Krenn’s synovitis scoring system (n = 4, * p < 0.05 by Steel-Dwass test)
|
study
| 100.0 |
Analyses for synovitis of the knee. a Protocol for running without MIA injection. b Synovial sections stained with HE. Whole knee joints were sectioned in the sagittal plane for synovium of infrapatellar fat pad. c Quantification of synovitis evaluated by Krenn’s synovitis scoring system (n = 4). d Protocol for running with MIA injection. e Synovial sections stained with HE. Synovial cell layer is indicated by arrows. f Quantification of synovitis evaluated by Krenn’s synovitis scoring system (n = 4, * p < 0.05 by Steel-Dwass test)
|
study
| 99.94 |
In this study, we revealed that only 50% of the rats completed 30 km of running. 0.1 mg MIA induced cartilage matrix depletion at the tibial cartilage and 15 km of running further exacerbated, even though 15 km running did not affect the cartilage in the PBS injected knee. Synovitis caused by MIA improved with time whether or not rats were forced to run.
|
study
| 100.0 |
As an OA model in rats, 15 km of running was insufficient and 30 km of running induced OA but only 50% of the rats completed the regimen. This is the first report to reveal dropout rate in 30 km of running. To induce OA in rats, 30 km of running in 6 weeks is currently popular but some modifications are required to reduce the dropout rate. Beckett et al. reported that over 30 km running distances were required to induce OA progression in 3 weeks . Even though the drop off rate was not mentioned in this paper, it might increase because 30 km of running in 3 weeks seems more stressful.
|
study
| 100.0 |
The influence of strenuous running on OA remains a matter of controversy. There are 8 reports (including this one) describing the influence of strenuous running on articular cartilage in Wistar rats (Table 1) [5, 19–24]. Thirty km of strenuous running was harmful without other OA inductions in all four papers [5, 19, 20, 24]. Fifteen km of strenuous running with other OA inductions was also harmful in two papers in addition to this one; two other papers reported running as beneficial. Cifuentes et al. reported that 15 km of running over 8 weeks was beneficial in the knee injected with 1.2 mg MIA . The difference between the study by Cifuentes et al. and ours was the time from MIA injection to the start of strenuous running. Cifuentes et al. started strenuous running just after MIA injection, while we did 1 week after injection at which time synovitis was already induced.
|
review
| 99.44 |
According to another study of ours, 0.1 mg MIA induced punctate depressions on the surface of cartilage and cartilage erosion proceeded with time in Wistar rats . In our current results, additional running advanced cartilage degeneration induced by 0.1 mg MIA in only the tibial cartilage, not in the femoral cartilage. In the tibial side, cartilage degeneration induced by MIA was observed around the apex part of the tibia, which was not covered with the meniscus. Therefore, the apex part of the tibia cartilage was possibly sensitive to the mechanical stress induced by strenuous running. In the femoral side, while cartilage degeneration by MIA was observed in the posterior part, mechanical stress would affect an extensive area, not a focal area, of the femoral condyle cartilage. This might reduce the influence of mechanical stress in the femoral cartilage.
|
study
| 100.0 |
0.1 mg MIA induced cartilage degeneration and 15 km of running further exacerbated this at the tibial cartilage. However, this was due to increased proteoglycan loss, which might be reversible and is not necessarily attributable to OA. To make an irreversible OA model, the amount of MIA and the distance of strenuous running must be adjusted in more detail.
|
study
| 99.94 |
Synovitis caused by MIA was observed 7 days after injection; however, synovitis was reduced after 3 weeks with or without 15 km of strenuous running. Additionally, only 15 km of running did not induce synovitis. This means that the strenuous running did not exacerbate and influence synovitis in this model. However, we cannot exclude qualitative or quantitative effects of running that might not be detected by Krenn's score (e.g. changes in cytokine expression, macrophage subtypes, etc.)
|
study
| 100.0 |
To examine the effect of MIA, we tested both treatments (0.1 mg MIA and PBS alone) in the same animal, with each knee receiving a different treatment, because we wished to exclude inter-animal variability. This matched analyses enabled to examine the effect of MIA in more strict manner. However, the use of the contralateral knee as a control is potentially problematic. Gait abnormalities could lead to abnormal stresses on the saline-injected contralateral knee which therefore might not be normal.
|
study
| 100.0 |
Mechanical stress is an important factor that regulates cartilage metabolisms . Appropriate mechanical stress maintains or increases the amount of sGAG, while excessive mechanical stress decreases it. MIA induces inflammation, inhibits glycolytic system, reduces viability of chondrocytes, and results in degeneration of the cartilage . In this low dosage of the MIA-induced model, forced running further progressed cartilage degeneration in an inflammatory condition. Both mechanical stress and inflammation are the most important factors affecting OA progression, and even though some modifications are required, this is a good model for mimicking OA in rats.
|
study
| 100.0 |
Men who have sex with men (MSM) are the group at highest risk of acquiring HIV in the UK, and an estimated one in five HIV‐positive MSM is undiagnosed 1. Mathematical modelling suggests that increasing the uptake of HIV testing and its frequency combined with antiretroviral treatment could reduce the incidence of HIV infection 2, 3, 4. Testing those at high risk every 3 months is cost saving when compared with annual testing 5. However, in the UK, HIV incidence is not decreasing 1, 6 and high proportions of newly diagnosed men have not previously tested 7, 8. Increases in the uptake of HIV testing in high‐income countries have been widely reported 9, 10, 11, 12, 13, 14, 15, but we have demonstrated a stabilization in recent HIV testing among MSM in Scotland, which suggests that the current opt‐out testing approach (whereby all patients are offered a test regardless of symptoms or risk factors) has reached its limit in maximizing routine uptake 16. Innovative methods of increasing the uptake of testing are required 4. Investigations of the psychosocial, sociocultural and technological aspects of testing will enable interventions to be developed which reduce barriers to testing, and promote frequent testing among high‐risk MSM 17.
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study
| 99.94 |
Current British HIV Association/British Association of Sexual Health and HIV and Centers for Disease Control and Prevention guidelines recommend at least annual HIV testing for MSM 18, 19, with more frequent testing (up to every 3 months) recommended for individuals at risk of HIV acquisition 18. Critically, there is no consensus regarding the definition of those “at risk” or how to measure HIV testing frequency.
|
review
| 99.75 |
Frequent testing is likely to be central to the success of biomedical prevention approaches such as pre‐exposure prophylaxis (PrEP) and treatment as prevention (TasP) 20, 21, 22, 23, and in order to meet their challenges it is important that we are able to measure testing frequency. Self‐testing kits for HIV have been approved by the US Food and Drug Administration 4, and in the UK regulations outlawing their sale were repealed in April 2014 and commercial products became available in April 2015. However, it remains to be seen whether self‐testing kits can increase HIV testing and antiretroviral therapy uptake, particularly among those who would benefit most from it. While an international systematic review of research regarding self‐testing has demonstrated its acceptability 24, there are problems concerning the generalizability of its findings; many of the contributing studies focus upon developing countries and MSM are under‐represented. Moreover, most studies relate to an earlier era in the HIV epidemic when PrEP and TasP were unavailable 25, 26. In this paper we explore the frequency of, and reasons for, HIV testing among three community‐based samples of MSM in the UK, presenting estimates of annual and more frequent testing for the first time. We examine the factors associated with frequency of testing to assess the implications for future HIV prevention efforts.
|
study
| 99.9 |
The Medical Research Council (MRC) Gay Men's Sexual Health Survey in Glasgow and Edinburgh collected anonymous, self‐complete questionnaires and oral fluid specimens (using OraSure® Oral Specimen Collection Devices; OraSure Technologies, Inc., Bethlehem, PA, USA) in 17 gay commercial venues in May 2011, using a form of time and location sampling 9. Overall, 1515 men participated [65% response rate (RR)] and 1218 provided oral fluid samples (52% RR).The Glasgow Caledonian University (GCU) Social Media, MSM & Sexual Health Survey was a Scotland‐wide online survey carried out from November 2012 to February 2013. Pop‐up message blasts and/or banner adverts invited men using gay‐specific social media websites (Gaydar, Recon and Squirt), smartphone apps (Grindr and Gaydar) and Facebook to participate. In total, 1326 men completed useable questionnaires (given the nature of online surveys it is not possible to calculate a response rate).The University College London/Public Health England (UCL/PHE) Gay Men's Survey in London was conducted between March and June 2011 in 31 gay social venues including bars, clubs and saunas. Overall, 1216 men participated (RR 62%) and 1005 provided an oral fluid specimen using OraSure® (RR 51%).
|
study
| 99.94 |
The Medical Research Council (MRC) Gay Men's Sexual Health Survey in Glasgow and Edinburgh collected anonymous, self‐complete questionnaires and oral fluid specimens (using OraSure® Oral Specimen Collection Devices; OraSure Technologies, Inc., Bethlehem, PA, USA) in 17 gay commercial venues in May 2011, using a form of time and location sampling 9. Overall, 1515 men participated [65% response rate (RR)] and 1218 provided oral fluid samples (52% RR).
|
study
| 99.94 |
The Glasgow Caledonian University (GCU) Social Media, MSM & Sexual Health Survey was a Scotland‐wide online survey carried out from November 2012 to February 2013. Pop‐up message blasts and/or banner adverts invited men using gay‐specific social media websites (Gaydar, Recon and Squirt), smartphone apps (Grindr and Gaydar) and Facebook to participate. In total, 1326 men completed useable questionnaires (given the nature of online surveys it is not possible to calculate a response rate).
|
study
| 62.84 |
The University College London/Public Health England (UCL/PHE) Gay Men's Survey in London was conducted between March and June 2011 in 31 gay social venues including bars, clubs and saunas. Overall, 1216 men participated (RR 62%) and 1005 provided an oral fluid specimen using OraSure® (RR 51%).
|
study
| 99.9 |
Ethical approval was granted by the University of Glasgow College of Social Sciences Ethics Committee (Glasgow/Edinburgh survey), the Health and Community Science subcommittee, the School of Health and Life Sciences Ethics Committee, Glasgow Caledonian University (Scotland‐wide online survey), and the University College London Hospital Research Ethics Committee (London survey).
|
other
| 99.94 |
The surveys included comparable data on demographics (age, area of residence and education), HIV/sexually transmitted infection (STI) testing, and sexual behaviour in the previous 12 months [numbers of sexual, anal intercourse (AI) and unprotected anal intercourse (UAI) partners]. Number of sexual and AI partner variables were dichotomized (< 10 vs ≥ 10 partners). A measure of UAI with higher risk for HIV infection was derived to include men who reported UAI with at least two partners, casual partners and/or unknown/discordant partners in the previous 12 months (compared with men reporting UAI with fewer than two partners, regular partners or known/concordant partners only).
|
study
| 100.0 |
Participants were asked how often they tested for HIV as described below, from which we calculated a measure of testing frequency indicative of annual and more frequent HIV testing. In the Glasgow/Edinburgh and London surveys, the number of HIV tests in the last 2 years was categorized into fewer than two, two or three and at least four tests. Testing regularity was sought in the Scotland‐wide online survey, so men who indicated that they tested “every 3/6 months” were categorized as having at least four tests, and those indicating testing “every year/every few years” were categorized as having had two or three tests; those remaining were categorized as having fewer than two tests. The latter category includes men who had never tested (who were a small proportion of the overall sample).
|
study
| 100.0 |
Participants were also asked the reasons for their last HIV test. Testing as a result of an episode of unprotected sex, condom error/accident, and/or sexual partner change was attributed to a perceived risk event, while testing as a result of a regular/routine sexual health check or offer from a health professional was coded as part of a regular sexual health check. Other reasons (e.g. visa requirements, blood donation, in vitro fertilization/sperm donation, other medical treatment, or life insurance applications) were coded as “other”. Categories were complicated by multiple responses, but our measure is hierarchical in that testing as a result of a risk event was prioritized over routine testing, and the latter was prioritized over “other”.
|
study
| 99.94 |
We excluded: HIV‐positive men (n = 134); men who did not provide an OraSure® test in the Glasgow/Edinburgh/London surveys and did not therefore have confirmed HIV status (n = 297); men with missing data on the HIV status question in the Scotland‐wide online survey (n = 185); men who did not identify as gay or bisexual, because of the small number of responses (n = 59); and men who did not answer the question on when was their last HIV test and/or how often they tested for HIV (n = 599). Data were analysed using IBM spss 19.0 for Windows (IBM United Kingdom Limited, Portsmouth Hampshire, UK). χ 2 tests were used for bivariate comparisons. Multinomial logistic regression was conducted to compare the frequency for testing categories and binary logistic regression was used to compare men tested as part of a regular sexual health check and those tested in response to a perceived risk event. We adjusted for factors significant at the bivariate level (P < 0.05) and for demographic and behavioural differences between the surveys.
|
study
| 100.0 |
The total sample was 2409. The mean age of participants was 34.2 years [range 18–83 years; standard deviation (SD) 11.1 years]. Most identified as gay (as opposed to bisexual) and reported education after age 16 years (Table 1). Just 9.8% had never had an HIV test, while 57.2% had tested in the previous 12 months; 14.3% reporting having an STI in the previous 12 months. Most reported sexual contact in the previous 12 months and 37.8% reported higher risk UAI in the previous 12 months (i.e. UAI with at least two partners, casual partners and/or unknown/discordant partners).
|
study
| 100.0 |
Significant differences in the age patterning of the three surveys were apparent, with the highest proportion of young men (aged < 25 years) in the Glasgow/Edinburgh survey and the highest proportion of older men (aged ≥ 46 years) in the Scotland‐wide online survey. Participants in the latter survey had the highest mean age (37.8 years; SD 12.6 years), followed by the London survey (33.4 years; SD 9.5 years), while the participants in Glasgow/Edinburgh had the lowest mean age (32.3 years; SD 10.7 years) f(2) = 52.64; P < 0.001. The Scotland‐wide online survey also included a higher proportion of bisexual men. Men in the Glasgow/Edinburgh survey were least likely to report that they were employed, although the proportion with no education after age 16 years was highest in the Scotland‐wide online survey. Men in the Scotland‐wide online survey were more likely to have never tested for HIV, while testing in the previous 12 months was highest in the London survey. Significantly lower proportions of men in the Glasgow/Edinburgh survey reported ≥ 10 sexual or AI partners in the previous 12 months, but the difference in the proportions reporting any UAI between the surveys was borderline significant. The London survey sample was most likely to report having had an STI in the previous 12 months, but the proportion reporting higher risk UAI was highest in the Scotland‐wide online sample.
|
study
| 100.0 |
Overall, 510 men (21.2%) reported having at least four HIV tests, 812 (33.7%) reported having two or three tests, and 1087 (45.1%) reported having zero or one test in the last 2 years, and we estimate that 54.9% (n = 1322) had at least one test per year. Table 2 compares the characteristics of men reporting fewer than two tests, two or three tests, and at least four tests in the last 2 years. The Scotland‐wide online sample included the highest proportions of men reporting two or three tests and at least four tests in the last 2 years. Significantly higher proportions of older men (aged ≥ 36 years) reported zero or one test in the last 2 years, while reporting at least four tests was most common among younger men (aged ≤ 25 years). There was less age variation in the proportions reporting two or three tests. Men reporting higher risk behaviours (STI, ≥ 10 sexual partners, ≥ 10 AI partners and/or higher risk UAI in the previous 12 months) were consistently more likely to report at least four tests in the last 2 years than men who did not report these behaviours. Other demographic and behavioural variables showed no significant relationship with testing frequency.
|
study
| 99.94 |
Multinomial logistic regression analysis was used to compare the three testing groups (Table 3). First we considered the comparison between men reporting zero or one test and those reporting two or three tests in the last 2 years. The two groups differed significantly on survey location and age. Those reporting two or three tests were more likely to come from the Scotland‐wide online survey and they were less likely to be aged > 36 years than ≤ 25 years. Those reporting two or three tests were also more likely to have had ≥ 10 sexual partners in the previous 12 months. Next we compared men reporting zero or one test and at least four tests in the last 2 years. Those reporting at least four tests were more likely to come from the Scotland‐wide online survey and less likely to come from the London survey or to be aged > 36 years. There were additional differences with respect to sexual behaviour: men reporting at least four tests were more likely to report having ≥ 10 sexual partners, ≥ 10 AI partners and an STI in the previous 12 months. There was no significant association with higher risk UAI. Finally, when comparing men reporting two or three tests and at least four tests, those reporting at least four tests were less likely to come from the London survey or be aged > 36 years and more likely to report ≥ 10 AI partners in the previous 12 months. Those reporting at least four tests were more likely to have higher risk UAI in the previous 12 months but this was of borderline statistical significance (P = 0.05).
|
study
| 99.94 |
We explored the reasons that men who had ever tested provided for having their most recent HIV test (n = 2009). Overall, 1140 (56.7%) tested as part of a regular sexual health check, 714 (35.5%) reported testing in response to a perceived risk event, and 155 (7.7%) tested for other reasons. In comparing the characteristics of the three groups (Table 4), we found that the Glasgow/Edinburgh survey had the highest proportion tested as part of a sexual health check, the London survey had the highest proportion tested after a perceived risk event, and the Scotland‐wide online sample had the highest proportions tested for other reasons (this survey also included the most alternative testing options). Reasons for testing varied with age, with the highest proportion tested after a perceived risk event in the youngest age category (≤ 25 years). Men reporting higher risk UAI in the previous 12 months were more likely to report testing in response to a perceived risk event, although little variation in other sexual risk behaviours was observed. As would be expected, the proportion reporting testing as part of a regular check‐up increased with the frequency of HIV testing.
|
study
| 100.0 |
Factors associated with reasons for last HIV test among gay and bisexual men who have had an HIV test in the UK: n, row %, unadjusted and multivariate logistic regression comparing men tested as part of a regular test or sexual health check‐up and men tested in response to a risk event (n = 2009)
|
study
| 99.75 |
Binary logistic regression was used to compare men tested as part of a regular sexual health check and those tested in response to a perceived risk event (Table 4). The odds of having had an HIV test because of a perceived risk event remained significantly higher among the London survey sample compared with Glasgow/Edinburgh, and among men reporting higher risk sexual behaviour than among men not reporting this behaviour. The adjusted odds were significantly lower among men aged ≥ 46 years and men aged 26–35 years, than among those aged ≤ 25 years, and among those reporting more frequent HIV testing in the previous 2 years. All variables remained significant in the multivariate model.
|
study
| 100.0 |
This is the first study to explore the frequency of HIV testing amongst MSM in the UK. Half reported at least two HIV tests in the last 2 years, suggestive of annual testing, the minimum recommended in current UK guidelines 18. However, fewer than one in five reported having four or more tests in the last 2 years, which suggests that 6‐monthly testing is less common. The guidelines recommend that all men test annually and those at “higher risk” test up to every 3 months, but our findings suggest neither recommendation is being met. Among the HIV testers, more than half reported that their most recent test was part of a regular sexual health check and over one‐third tested in response to a perceived risk event. Regional, demographic and behavioural differences are worthy of attention and each will be considered in turn.
|
study
| 99.94 |
Regional differences in HIV testing behaviour are not new and we are among those who have previously reported on such, particularly between the large urban centres of the UK 27, 28, 29. When compared with the Glasgow/Edinburgh survey, we found evidence of higher testing frequency in the Scotland‐wide online survey and lower frequency in the London survey. This was the case despite higher rates of recent testing in the Glasgow/Edinburgh and London samples, demonstrating the limitations of the recency measure and the different survey methods and sample characteristics. However, testing as a result of a perceived risk event was higher in the London survey. While between‐survey differences should be treated with caution, they suggest the need to consider regional differences in the roll‐out, uptake and potential impact of HIV testing interventions. For example, the promotion of frequent, regular testing was a particular focus of Scottish HIV prevention efforts (particularly on‐scene) 30, which could account for the higher levels of this behaviour. However, it is also possible that the variations reflect the demographic and behavioural differences evident between the samples.
|
study
| 100.0 |
Our results suggest that the frequency of HIV testing decreases with age and that there are differential patterns of risk among age groups. When comparing infrequent (zero or one test in the last 2 years) and annual testers (two or three tests in the last 2 years), there was a significant association with the number of sexual, but not AI, partners in the previous 12 months. When comparing annual and frequent testers (at least four tests in the last 2 years), the reverse pattern was observed in that there was a significant association with the number of AI partners but not the total number of sexual partners. Both number of sexual partners and number of AI partners were significant when comparing infrequent and frequent testers. Having an STI in the previous 12 months was only significantly different between infrequent and frequent testers. Although somewhat complicated and inconsistent, this does suggest a patterning by sexual risk behaviour similar to findings from elsewhere, albeit using different measures of frequency (studies in the USA and Australia have measured inter‐test intervals, and repeat and return testing) 31, 32, 33. However, higher risk UAI was not associated with testing frequency. Indeed, only one‐quarter of men reporting higher risk UAI also reported the frequent testing recommended (up to every 3 months) for those at high risk of HIV infection. This difference between guidelines and actual practice has also been reported in Australia, where only 34% were found to meet the comprehensive STI and HIV testing recommendations for sexually active gay and bisexual men 13. In another Australian study, 6‐monthly re‐testing rates were only 15% among higher risk MSM 33.
|
study
| 99.94 |
A strong association between frequent and regular testing has been reported elsewhere 31, and the lack of association between higher risk UAI and testing frequency could indicate that episodes of higher risk UAI are less frequent events, albeit reported by over one‐third of our sample. Furthermore, higher risk UAI was associated with testing after a perceived risk event (when compared with testing as part of a regular sexual health check), which suggests that men reporting higher risk UAI could be aware of the HIV‐related risk inherent in their behaviour and are testing accordingly. HIV prevention requires men to incorporate increasingly complex understandings of transmission risks and sero‐adaptive behaviours into their sexual lives 34, 35, 36. The extent to which men are able to do so and the level of sexual health literacy required to fulfil this task are largely unknown and worthy of further research. Furthermore, given that current guidelines suggest that individuals at risk of HIV test as frequently as every 3 months (as well as after a risk event) 18, and that men newly diagnosed with HIV are known to have been less frequent testers 1, 31, 37, 38, there is a clear need to promote frequent testing as a distinct and routinized behaviour through behaviour change interventions and to address barriers to frequent testing accordingly.
|
study
| 99.94 |
Most men who attend for a sexual health screen will have an HIV test 39. An audit of sexual health clinics in England found that almost all MSM reported one or more HIV tests in a 12‐month period 40, which does suggest that clinic attenders are meeting the minimum annual testing recommendations 18. Yet in our varied community samples, this recommendation was consistently not being met and it is likely that not all men are attending clinics for regular sexual health screening. Our data suggest subtle differences in the risk profiles of regular vs “risk event” testers, who are at potentially greatest risk for HIV infection. Accessing services remains a key opportunity for intervention and frequent testing for HIV and STIs should be promoted to those men only testing after a risk event. Annual testing should be conducted at a population level with MSM to reduce undiagnosed HIV infection and regular sexual health screening should be offered to all men at risk of STI/HIV transmission.
|
study
| 99.94 |
Caution should be adopted in generalizing our findings beyond the respective survey populations or to the wider population of MSM in the UK. All three surveys provide cross‐sectional data and causality cannot be inferred, and while the reliance on self‐report data could be subject to bias, this has been minimized by their anonymous, self‐complete nature; the surveys also have comparability and consistency over time. While the Glasgow/Edinburgh and London surveys included a biological measure of HIV status, the Scotland‐wide online survey could not and is reliant on self‐reported HIV status, which is therefore likely to include undiagnosed HIV‐positive participants. Possible underreporting of this should be noted, particularly as one‐quarter of the HIV‐positive men in the Glasgow/Edinburgh survey population are known to be undiagnosed 41. Minor differences in the wording of questions could have affected interpretations and the figures presented could be over‐ or under‐estimates of actual HIV testing rates. For the testing frequency measure, we assumed that two tests in the last 2 years was indicative of an annual test, but this may not be the case (i.e. both tests could have been in the last year). Further work is required to refine the measure of testing frequency. Similarly, the between‐survey differences, while of interest, should not be overemphasized in case they are in some part reflective of subtle variations in the mode of questioning or data collection methodologies, particularly between online and venue‐based samples 42. However, combining samples from different locations allows us to present a broader picture of men's experiences and HIV testing behaviours. As social and sexual mixing patterns change, and the use of online networking sites and other social media as a means of identifying and meeting sexual partners increases 43, 44, behavioural research will need to incorporate such multiple recruitment strategies.
|
study
| 99.94 |
HIV testing is a core component of current HIV prevention, but despite substantial increases in HIV testing in recent years, our results suggest that MSM in the UK do not test frequently enough. Evidence‐based behaviour change interventions are needed to increase the frequency of testing among those at risk for HIV infection. Such interventions will prove essential to facilitating the effectiveness of PrEP (PrEP requires individuals to have accurate knowledge of their HIV status) 45. Innovative means of increasing uptake are being tested 46, 47, 48, 49, 50, 51, but it is not yet clear if any of these approaches will increase testing frequency in the medium to longer term or in the subpopulations that matter. It is also unknown whether the availability of self‐testing, or even self‐sampling, kits will increase the frequency of testing, particularly in those at higher risk. The regional, demographic and behavioural differences, and the subtle variations in the risk profiles of testers described here make it unlikely that a “one size fits all” approach to increasing the frequency of testing will be successful. Our analysis suggests that targeted and tailored behaviour change interventions may well offer purchase to this complex problem. Moreover, additional efforts to reduce the known barriers to HIV testing remain important 52, 53, particularly if we are to optimize the potential of biomedical interventions.
|
study
| 99.5 |
Temporary storage of light, by means of its slowing down which leads to increase of the local intensity of slow light, has been the subject of intensive research, since many useful optical phenomena rely on strong interaction between light and matter1. Initial attempts to substantially reduce the speed of light were based on quantum effects such as electromagnetic induced transparency2 and optical coherent effects3, where restrictions like the usage of ultracold gases or the narrow operational bandwidth limited their practical implementations. More recently the on-chip realizations of slow light schemes have become possible, such as coupled resonator optical waveguides4, 5, which can lead to low group velocities with negligible distortion. However a fundamental limit, limiting such structures is the so-called delay-bandwidth product, which imposes a trade-off between the factor of slowing-down and the bandwidth in which the slowing, exists6. One way to alleviate this limitation is to adiabatically tune (or chirp) the structure, meaning that one or several structural parameters are gradually varied along the direction of propagation. In particular, it has been shown that in a tapered metamaterial heterostructure, light can be slowed down and trapped at specific locations depending on its frequency using negative Goos–Hänchen shift7. This phenomenon, termed as the “Trapped Rainbow” effect, can also be considered as the spatial separation of the frequency components of the propagating wave, and has been demonstrated in dielectric8 and plasmonic9–18 gratings or waveguides, in one-19 and two-dimensional20–22 photonic crystals (2D PhCs), in a hyperbolic metamaterial waveguide23, in sonic crystals24, and in a waveguide under a tapered magnetic field25. While significant steps have been taken towards the slowing down and “trapping” of the light, one still needs to cope with extrinsic losses while implementing such schemes. It has been debated whether material absorption that is reminiscent of metallic structures can give large propagation losses and prevent the light stopping mechanism in metamaterials26. Although it is possible to overcome the material losses in metamaterials by employing absorption-free dielectric 2D PhCs in their negative refraction regime27 instead of metallic components, it still remains unclear whether other extrinsic loss mechanisms such as out-of-plane radiation losses can be compensated and overcome in such structures. Yet some attempts to reduce the losses in 2D PhCs have been undertaken28, 29, the inevitable relation between the group velocity of the light and its interaction time with the medium still leads to considerable amount of scattering loss enhancement, as one approaches the band edge region (where most of the slow light behavior occurs)27, 30–33.
|
review
| 99.75 |
In contrast to their 2D counterparts, three-dimensional (3D) PhCs are capable of providing complete photonic bandgaps (PBGs) in all three directions. Among them, the layer-by-layer (or namely the woodpile) PhCs have been intensively studied due to their flexible micro- or nanofabrication requirements and their robustness against fabrication imperfections34, 35. Such a structure consists of layers of parallel rods or logs, where the rods in each consecutive layer are rotated by 90°. Additionally, each layer with the same orientation of rods is shifted relative to each other by a half of the in-plane period (a), forming a 3D PhC of the symmetry of a face-centered tetragonal lattice. In this study, we propose a woodpile PhC with gradually varied longitudinal periods in the stacking direction, to gradually slow down and stop the incident wave. We first present the local dispersion analysis of such a configuration which suggest the choice of structural parameters. We then evaluate the intensity enhancement factors and calculate the spatial positions where the wave stops and the maximal field enhancement occurs, by means of instantaneous and steady-state field distribution analysis. Finally we verify the principle experimentally in the microwave regime, by comparing the numerically calculated and experimentally measured field profiles and the intensity enhancement factors.
|
study
| 100.0 |
We note that various “trapped rainbow” guiding schemes have been already experimentally demonstrated at microwave12–14 or even at visible16, 18, 36, 37 frequencies. However in such waveguide or grating based structures, the modal volume of the localized wave is inevitably restricted by the volume of the defect waveguide or the width of the tapered grating. Such a limitation impose severe constraint onto the local field intensity and the available volume at which the spectrally resolved wave can be efficiently harvested. In this manuscript, on the other hand, we show that the “trapped rainbow” effect occurring in a defect free bulk structure can lead to considerable higher local field intensities by employing 3D PhC bulk modes with large modal volumes.
|
study
| 100.0 |
We consider a 3D woodpile PhC composed of cylindrical alumina (Al2O3) rods with a radii and height equal to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r=\frac{\sqrt{2}}{8}a$$\end{document}r=28a and h = 8.463a, respectively, where a is the in-plane period. The Al2O3 rods have a dielectric constant equal to ε rod = 9.8 at microwave frequencies. The general schematics and the main operational principle of the proposed configuration is shown in Fig. 1(a). As mentioned above, the period in the stacking direction is continuously varied. We consider a slow (adiabatic) variation of the PhC period, which allows to consider local dispersion relation of it at every layer24. In result, the frequency of the PBG becomes smoothly varying along the propagation direction, as shown in Fig. 1(b). Therefore, a wave entering the structure will gradually slow down inside the PhC as its frequency will progressively approach the edge of the local PBG. Once the PBG is reached, the wave will “stop”, i.e. become temporarily localized, and afterwards will propagate back. Since the local PBG is distinct for every spatial position, each frequency component will be localized at different positions along the PhC, as illustrated in the left inset of Fig. 1(a).Figure 1Proposed 3D PhC configuration for rainbow trapping. (a) Schematic illustration of the chirped woodpile PhC structure. For better visualization the number of periods of the illustrated PhC structure is reduced. The lower inset depicts the cross sectional view of the structure in the yz- plane. (b) The variation of the PBG along the propagation direction is representatively depicted. Due to the gradual variation of the layer-to-layer distances, the incident wave will be spatially separated into its frequency components along the propagation direction, thus forming a “trapped rainbow”, as it is representatively shown as a cross sectional view on the lower left of (a). The upper right inset in (b) representatively shows the change of the dispersion curves in the propagation direction, where the layer-to-layer distance of the solid black dispersion curve is smaller than that of the dashed blue dispersion curve. The black arrows reveal the propagation direction of the incoming wave.
|
study
| 100.0 |
Proposed 3D PhC configuration for rainbow trapping. (a) Schematic illustration of the chirped woodpile PhC structure. For better visualization the number of periods of the illustrated PhC structure is reduced. The lower inset depicts the cross sectional view of the structure in the yz- plane. (b) The variation of the PBG along the propagation direction is representatively depicted. Due to the gradual variation of the layer-to-layer distances, the incident wave will be spatially separated into its frequency components along the propagation direction, thus forming a “trapped rainbow”, as it is representatively shown as a cross sectional view on the lower left of (a). The upper right inset in (b) representatively shows the change of the dispersion curves in the propagation direction, where the layer-to-layer distance of the solid black dispersion curve is smaller than that of the dashed blue dispersion curve. The black arrows reveal the propagation direction of the incoming wave.
|
study
| 99.3 |
A detailed numerical analysis is performed to deduce the structure parameters. Preliminary, for a periodical woodpile PhC with a constant layer-to-layer distance \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d=\frac{\sqrt{2}}{4}a$$\end{document}d=24a (i.e. the rods from the consecutive layers just touch one another) the local band structure is numerically calculated with the plane-wave expansion method38 and the result is shown in Fig. 2(a). The calculated band structure reveals a complete PBG with a gap/mid-gap ratio (the ratio of gap width to the central frequency of the gap) of 11%, while the gap/mid-gap ratio of the partial PBG in the propagation direction Γ-X′ (stacking direction) is equal to 39%. Moreover, the frequencies at the bottom and top of this partial PBG are defined as the lower and upper cut-off frequencies and their variation with respect to the layer-to-layer distance is plotted in Fig. 2(b). Despite their similarity in terms of their layer-to-layer distance relations, the two cut-off regions differ in an important respect: To obtain a local PBG at the lower/upper bands, the layer-to-layer distance should be increased/decreased; respectively (see upper left inset of Fig. 1(b)). Consequently, the direction of the gradual layer-to-layer distance variation (whether it decreases or increases along the propagation direction) depends on the operational frequency region: The upper/lower cut-off regions require a decreasing/increasing layer-to-layer distance, respectively (indicated by red and green arrows in Fig. 1(b)). Apart from this apparent distinction, another difference between the two cut-off regions becomes evident if the partial PBGs in other directions are examined. The PBGs in the Γ-K direction, which corresponds to the direction along the rod axes are superimposed on Fig. 2(b). Unlike the Γ- X′ direction, the wave propagation in the Γ-K direction is nondegenerate for modes with polarization vectors along the rod axis and along the stacking direction, which we will refer to as the transverse electric-like (TE-like) and transverse magnetic-like (TM-like) modes, respectively. As can be seen from Fig. 2(b), the TM-like PBG comprises the whole upper cut-off region in the examined layer-to-layer distance range, whereas the TE-like PBG encloses only a portion of the examined range. On the other hand, for all utilized layer-to-layer distances, the lower cut-off region lies outside the coverage of both PBGs, which indicates that in the case of vertically scattered light, the corresponding structure based on the lower cut-off operation will be vulnerable to radiation losses. Furthermore, the PBG variations in the same range for propagation directions corresponding to the X, U, U′, K′, W, W’, W″, and L symmetry points35, whose positions in the Brillouin zone are shown on the lower right inset of Fig. 2(a), are calculated and given in Fig. 2(c). For directions with nondegenerate modes, the complete PBGs comprising simultaneously both TE-like and TM-like PBGs have been taken into account. Consequently, the local dispersion analyses in Fig. 2(b) and (c) imply that a complete confinement is not possible, since modifying the layer-to-layer distances will further break the low rotational symmetry of the lattice structure39, which in turn will increase the structural anisotropy. Nevertheless, a close inspection of the PBG variations reveals that for the layer-to-layer distance range \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{1.15,1.35\}\ast \frac{\sqrt{2}}{4}a$$\end{document}{1.15,1.35}∗24a, the localized mode near the cut-off region is still confined in most directions.Figure 2Bandstructure analysis of the woodpile PhC structure. (a) Numerically calculated band structure of the woodpile PhC with Al2O3 rods. The lower right inset depicts the first Brillouin zone of the woodpile structure. (b) The dependency of the layer-to-layer distance onto the longitudinal and transverse cut-off frequencies. The TM-like and TE-like PBGs in the transverse directions are highlighted with light green and red colored areas. (c) The PBG variations for other directions. The dashed white line indicates the upper cut-off frequencies in the Γ- X′ direction.
|
study
| 100.0 |
Bandstructure analysis of the woodpile PhC structure. (a) Numerically calculated band structure of the woodpile PhC with Al2O3 rods. The lower right inset depicts the first Brillouin zone of the woodpile structure. (b) The dependency of the layer-to-layer distance onto the longitudinal and transverse cut-off frequencies. The TM-like and TE-like PBGs in the transverse directions are highlighted with light green and red colored areas. (c) The PBG variations for other directions. The dashed white line indicates the upper cut-off frequencies in the Γ- X′ direction.
|
study
| 98.9 |
Following this approach, it is reasonable to vary the layer-to-layer distances of the PhC structure from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.35\ast \frac{\sqrt{2}}{4}a$$\end{document}1.35∗24a to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.15\ast \frac{\sqrt{2}}{4}a$$\end{document}1.15∗24a. However, one must take into account that the direct coupling into the slow light mode from the air region is problematic due to the mode mismatch at the air- PhC interface40, 41. Furthermore, in order to avoid photon tunneling into the air cladding, one needs additional layers at the end of the structure. These two requirements can be both satisfied by increasing the layer-to-layer distance interval further including \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{1.00,1.50\}\ast \frac{\sqrt{2}}{4}a$$\end{document}{1.00,1.50}∗24a. In this way, the wave enters the structure with a wave vector away from the slow light region and the leakage due to the large penetration depth of the slow light modes is suppressed. On the other hand, since the operational frequency region is at the upper cut-off region, the layer-to-layer distance should decrease along the propagation direction, as discussed previously. Moreover, the number of rods in each layer is chosen to be 7, as it is restricted by the length of the Al2O3 rods (h = 8.463a). The number of layers, on the other hand, is chosen to be 30, to create a smoothly varying chirp function. In this case, the local layer-to-layer distance between the nth and (n + 1)th layer is equal to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${a}_{z}(n)=[(42.5-0.5n)\ast \frac{\sqrt{2}}{4}a]/28$$\end{document}az(n)=[(42.5−0.5n)∗24a]/28. Here, we note that an important criterion that should be satisfied in adiabatic structures (to reduce the back-reflections) is the Wentzel-Kramers-Brillouin approximation18, which requires1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\delta }_{n}=\frac{{k}^{-1}(n+1)-{k}^{-1}(n)}{{a}_{z}(n)}\ll 1$$\end{document}δn=k−1(n+1)−k−1(n)az(n)≪1where δ n is the adiabatic parameter between the nth and (n + 1)th layer and k(n) is the local wave vector at the nth layer. To reveal whether the adiabaticity condition is satisfied for the proposed PhC structure, the local wave vector distribution was obtained numerically for the frequency 7.91 GHz (which is predicted numerically to localize at the 24th layer), by calculating the dispersion curve for all intermediate periods. By inserting the obtained wave vector variation and the a z(n) variation into equation (1), the adiabatic parameter has been evaluated to be in the range of 0.005 and 0.009, which already satisfies equation (1). Possible solutions to further decrease the adiabatic parameter (and, thus, to decrease the back-reflections) could be increasing the number of layers or decreasing the chirping interval. However, the mode coupling mismatch at the slow light regime40, 41 should be further taken into account when tailoring the latter one, as was discussed above.
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To verify the propagation characteristics, the proposed structure was modeled in a 3D grid by employing commercially available software42 based on the finite-difference time-domain (FDTD) method. Perfectly matched layer (PML) boundary conditions were used to terminate the computational domain and a TM polarized (electric field is in the y- direction) Gaussian pulse with a pulse length equal to ct/a = 30 in normalized time units was launched. The source was placed at a distance of 0.2a in front of the structure. Fig. 3(a–c) show the electric field intensities, calculated along the propagation (z-) direction, at the center point of the xy- plane at each time frame for normalized central frequencies a/λ = 0.450, 0.468 and 0.496, respectively. Figures 3(a–c) suggest that the PhC exhibits distinct localization regions for each frequency. More precisely, the incoming wave is slowed down until it reaches its localization region (or turning point) and is then trapped for a finite time interval before it starts propagating backwards. If the trapping time is defined as the time duration of the electric field intensity decaying from its maximum value until its 1/e 19, then the normalized trapping times for Figs 3(a–c) would be obtained as ct/a = 18.9, 20.3 and 24.1; respectively. Further inferences can be made from the time evolution of the pulses, if one pays attention to the change of the magnitude of the field intensity. At the localization region the intensity increases, since the local energy density is expected to be inversely proportional to the group velocity20, 21, 43. Furthermore, to obtain a broadband analysis of the field enhancement, the steady-state electric field intensity was numerically calculated at the same region (along the z- propagation direction, at the center of the xy- plane), and is shown in Fig. 3(d). If the turning point is defined as the spatial position where the intensity becomes maximum, then a nearly linear increase of the position of the turning point is observed, which originates from both facts that the upper cut-off region is nearly linearly dependent on the layer-to-layer distance (see Fig. 1(b)) and that the chirp function is varying linearly. One interesting observation from Fig. 3(d) is that the intensity enhancement is highly sensitive to the operation frequency. In particular, for the normalized operation frequency range a/λ = {0.42, 0.50} the maximum normalized intensities occurring at the localization regions deviate between 8 and 132. We attribute this deviation to the oscillations occurring between the turning point and the entrance of the structure. For instance, Fig. 3(a–c) suggest that the intensity enhancement is nearly equal for these frequencies, which is expected since the nearly linear cut-off variation will induce similar slowdowns for different frequencies, even though their steady-state intensity enhancements are much diversified, as indicated with white arrows in Fig. 3(d). The main difference between these two cases is that the steady state analysis is the response of a continuous source excitement, which comprises multiple enhancement factors such as slowing down and multiple interferences of the reflected waves from the turning point and at the entrance of the structure; whereas the time evolution analysis is the response of a source with a finite temporal pulse width, which includes only the slowing mechanism in terms of the intensity enhancement. We therefore believe that the oscillatory behavior of the intensity enhancement stems from the peculiar relation between the optical path and the local wave vector distribution. In this regard, for a specific frequency, the local wave vector distribution leads to such a local wavelength distribution that it will encounter constructive interferences within the optical path (which is also unique to the operational frequency). In other words, the slowing down of the wave will be accompanied by a structural resonance, which in result give rise to an additional enhancement factor. Such frequencies correspond to the narrowband peaks in Fig. 3(d) and one can infer from this figure that the spectral distance between these peaks decreases as the operational frequency increases. This is also reasonable, since increasing the frequency will cause the wave to localize and reflect further away from the entrance of the structure and to enter the structure with a wave vector away from the cut-off region, compared to lower operation frequencies. This will have the consequence that the wavelength distribution will initiate with lower spatial wavelengths as the wave enters the structure21, in which case it will be enough to increase the operational frequency less compared to lower frequencies, to match up the next constructively interfered frequency.Figure 3Instantaneous and steady-state field analysis. Time evolution of a Gaussian pulse propagating inside the 3D PhC (along the z- propagation direction, at the center of the xy- plane), for three frequencies: (a) a/λ = 0.450, (b) a/λ = 0.468 and (c) a/λ = 0.496. (d) Broadband steady-state field intensity distributions at the same propagation line. Steady-state field distributions obtained at the xz- plane of the center of the y- direction for the normalized operational frequencies equal to (e) a/λ = 0.450, (f) a/λ = 0.468 and (g) a/λ = 0.496. The magnitude of the field intensities are normalized by dividing the calculated intensities to the intensity produced by the source at the specific frequencies. The distances in the z- propagation direction are given with respect to the position of the source.
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Instantaneous and steady-state field analysis. Time evolution of a Gaussian pulse propagating inside the 3D PhC (along the z- propagation direction, at the center of the xy- plane), for three frequencies: (a) a/λ = 0.450, (b) a/λ = 0.468 and (c) a/λ = 0.496. (d) Broadband steady-state field intensity distributions at the same propagation line. Steady-state field distributions obtained at the xz- plane of the center of the y- direction for the normalized operational frequencies equal to (e) a/λ = 0.450, (f) a/λ = 0.468 and (g) a/λ = 0.496. The magnitude of the field intensities are normalized by dividing the calculated intensities to the intensity produced by the source at the specific frequencies. The distances in the z- propagation direction are given with respect to the position of the source.
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Furthermore, the steady state electric field intensities along the xz- plane at the middle of the structure in the y- transverse direction were calculated and are shown in Fig. 3(e–g) for the normalized operation frequencies equal to a/λ = 0.450, 0.468 and 0.496; respectively. It follows from these figures that the intensity enhancements differentiate that from the pulse excitations, as expected. Furthermore, additional localization regions occur apart from the localization region at the turning point, since the abovementioned resonator effect will give rise to a standing wave within the respective optical path. Nevertheless, the local energy density at the turning points will be higher than at the additional localization regions, as the slowing down will become maximum at these points21.
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To quantitatively evidence our interpretation regarding the additional enhancement mechanism described above, we calculated the phase of the different frequency components at a particular position. Figure 4 shows the unwrapped phase of the electric field in the y- direction at the longitudinal position equal to 10.55a with respect to the front face of the structure. Moreover, the normalized intensity spectrum at the same spatial position is shown in Fig. 4. It follows that for the frequencies, at which the intensities are locally maximum, the phases are integer multiples of π. This is in accord with our abovementioned interpretation of the large enhancement factors, since a constructive interference between a specific path requires also the same amount of phase shift44.Figure 4Accumulated phase and intensity enhancement relation. Superimposed phase and normalized intensity spectrum. The unwrapped phases are calculated with respect to the phase at the entrance of the structure. The gray cross markers indicate the locations of the intensity peaks.
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Accumulated phase and intensity enhancement relation. Superimposed phase and normalized intensity spectrum. The unwrapped phases are calculated with respect to the phase at the entrance of the structure. The gray cross markers indicate the locations of the intensity peaks.
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Further numerical analyses were carried out to reveal the quantitative amount of propagation losses, which occur due to the finite transverse dimensions of the structure. The propagation losses were characterized by calculating the reflected power, by taking into consideration that in the case of a lossless propagation all incident power should be eventually reflected back after it is localized. The calculated reflected power is then normalized to the incident source power to give quantitative information about the loss spectra. Strictly speaking, since every frequency component will travel a different distance, it is more physically meaningful to normalize the loss to the distance travelled by the wave for every frequency component. The travelling distance has estimated as the twofold of the distance between the entrance of the structure and the turning point, by taking into account the forward and backward propagation distances. Therefore, for a more accurate analysis one must take this fact into account. However, in the present calculations we ignore this fact and define the travelling distance as an effective distance travelled by the wave, excluding the additional round trips. Following this direction, the loss spectra is calculated for 7 (original structure) and 12 (extended structure) transverse periods and are superimposed in Fig. 5. It can be observed from this figure that for the normalized frequency interval a/λ = {0.44, 0.48} the propagation losses are lower than the rest of the operational frequency spectrum, which is expected as the TE-like transverse PBG does not compromise outside this interval, as was discussed. Another conclusion that can be drawn from Fig. 5 is that increasing the number of the transverse periods reduces the losses, as expected. It is worth noticing that the narrowband enhancement peaks in Fig. 3(d) matches well with the loss peaks in Fig. 5. As above discussed, the narrowband enhancement peaks arises from multiple roundtrips inside the structure, which lies also in the origin of the enhanced losses.Figure 5Lateral loss analysis. Superimposed loss spectra of the PhC structure, with 7 and 12 transverse periods is shown. Note the oscillatory behavior, which is a direct consequence of the resonant propagation of the wave between the localization region and the input side of the structure.
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Lateral loss analysis. Superimposed loss spectra of the PhC structure, with 7 and 12 transverse periods is shown. Note the oscillatory behavior, which is a direct consequence of the resonant propagation of the wave between the localization region and the input side of the structure.
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To verify the propagation characteristics experimentally in the microwave regime, the proposed structure was constructed from absorption free Al2O3 rods (see Fig. 6). Prior to performing the experimental analyses, the coupling efficiency has been numerically estimated to be in the range of 65–71% and experimentally in the range of 62–74%. The numerical estimation was based on the termination of the simulations at the specific time step where the initial reflections due to air-PhC coupling mismatch have been completely gone through the reflection monitor. Experimentally, on the other hand, a strong microwave absorber was placed inside the PhC structure to similarly avoid the chirping reflections and to account only for the reflections arising from the coupling mismatch. The discrepancy between the experimental and numerical estimations stems mainly from the additional reflections and interferences inside the receiver antenna’s metallic aperture and to the non-ideal absorption (approximately 95%) of the microwave absorber. In contrast to the calculations, in our experimental setup (see Fig. 6) we could scan the electric field distribution only at the top surface of the structure. The monopole antenna was kept parallel to the y- axis and the tip of the antenna was placed 2 mm above the top of structure. A motorized linear stage was used to move the monopole antenna with 1 mm lateral resolutions in the x- and z- directions, as shown in Fig. 6. In this way, the y- component of the electric field at the top surface of the structure was measured and shown in Fig. 7(a–c) for frequencies equal to 7.52 GHz (a/λ = 0.450), 7.80 GHz (a/λ = 0.467) and 7.91 GHz (a/λ = 0.473), respectively. On the other hand, the electric field distribution was numerically calculated at the same surface and is in Fig. 7(d–f) for frequencies equal to 7.52 GHz, 7.80 GHz and 7.91 GHz, respectively. Comparing Fig. 7(a) with Fig. 7(d), Fig. 7(b) with Fig. 7(e) and Fig. 7(c) with Fig. 7(f), we note that the turning points in the numerical and experimental cases are in good agreement. We attribute the discrepancy in the field distributions between the two cases to the difference of the experimental and numerical source beam shapes.Figure 6Microwave experimental setup. Schematic illustration of the experimental setup is shown. The lower left inset depicts the photographic view of the constructed woodpile PC. Figure 7Steady-state field and group index measurements. (a–c) Experimentally measured and (c–e) numerically calculated steady state electric field distributions at the top xz- surface of the structure for frequencies (a–d) 7.52 GHz, (b–e) 7.80 GHz and (c–f) 7.91 GHz are shown. Experimentally measured average group indices for frequencies (g) 7.52 GHz, (h) 7.80 GHz and (i) 7.91 GHz are given. The colored areas denote the localization regions. The upper left insets show the calculated bandstructure for layer indexes equal to 16, 20 and 24; which are determined as the localized positions of the frequencies 7.52 GHz, 7.80 GHz and 7.91 GHz, respectively. The dashed red lines reveal the operational frequencies.
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Steady-state field and group index measurements. (a–c) Experimentally measured and (c–e) numerically calculated steady state electric field distributions at the top xz- surface of the structure for frequencies (a–d) 7.52 GHz, (b–e) 7.80 GHz and (c–f) 7.91 GHz are shown. Experimentally measured average group indices for frequencies (g) 7.52 GHz, (h) 7.80 GHz and (i) 7.91 GHz are given. The colored areas denote the localization regions. The upper left insets show the calculated bandstructure for layer indexes equal to 16, 20 and 24; which are determined as the localized positions of the frequencies 7.52 GHz, 7.80 GHz and 7.91 GHz, respectively. The dashed red lines reveal the operational frequencies.
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To experimentally evidence that the group velocity of the propagating wave converges to zero towards the localization regions, we performed a series of time delay measurements45. Figure 7(g–i) show the measured average group indices \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bar{n}}_{g}$$\end{document}n¯g for the frequencies equal to 7.52 GHz, 7.80 GHz and 7.91 GHz, respectively. We find that in all three cases \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bar{n}}_{g}$$\end{document}n¯g gradually increases towards the localization region. At these regions, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bar{n}}_{g}$$\end{document}n¯g varies between 90 and 110, which verifies the slow light originating localizations20. We should note that in theory one expects to obtain zero group velocity at the localization regions, however there are two major factors that prevent obtaining such a measurement. The first one is the lateral losses occurring at the localization region, which impose an additional decay rate to the system and cause deviation of the group velocity from zero. The second one, which is rather a practical issue, is the difficulty to obtain the time delay measurements continuously along the longitudinal direction. As was said above, due to the 3D periodicity of the structure, the time delay measurements had to be taken at discrete positions which transforms the τ d = ∂φ/∂ω differential relation into a finite difference approximation. To further reveal that the localized modes approach the band edge regions, the bandstructure in the propagation Γ-X′ direction for the instantaneous az periods at the localization regions were numerically calculated (see upper left insets of Fig. 7(g–i)). One can infer from these figures that the localized modes are indeed close to the band edge region and, thus, are expected to be slowed down and be localized.
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In view of the fact that the field distribution obtained at the top surface of the structure would not give any implication about the intensity enhancement, we further measured the electric field intensity spectrum at single points inside the structure (see Fig. 8(a)) to estimate the enhancement factors. Accordingly the normalized intensities were obtained at the center of the structural heights in the x- and y- directions and at a distance in the propagation z- direction equal to 5.15a = 9.25 cm and 9.55a = 17.15 cm with respect to the input side of the structure, and are superimposed with the regarding numerical calculations in Fig. 8(b,c), respectively. One can infer from these figures that the experimentally measured maximum intensities are around 72–74 for both cases, whereas the numerically calculated intensities are around 88–89. Moreover, one can observe that there are some spectral peak shifts and intensity differences between the numerical and experimental cases. We attributed these discrepancies to the structural fabrication errors, the non-uniform detection efficiency of the monopole antenna, the modified component of the detected electric field due to antenna tilting and the positional error of the detected area. Nevertheless, the experimental results verified that the wave can be enhanced and localized at various positions depending on its frequency.Figure 8Field enhancement measurements. (a) Schematic description of the measurement of the electric field intensity inside the structure. The numerically calculated and experimentally measured electric field intensity spectra, obtained at the center of the xy- plane and at a distance equal to (b) 9.25 cm and (c) 17.15 cm in the z- direction with respect to the input of the structure are superimposed.
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Field enhancement measurements. (a) Schematic description of the measurement of the electric field intensity inside the structure. The numerically calculated and experimentally measured electric field intensity spectra, obtained at the center of the xy- plane and at a distance equal to (b) 9.25 cm and (c) 17.15 cm in the z- direction with respect to the input of the structure are superimposed.
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In summary, a chirped woodpile PhC, whose layer-to-layer distances are gradually decreased along the propagation direction, has been numerically and experimentally demonstrated to slow down and finally to trap and enhance different frequency components at different spatial positions. It has been argued that the Fabry-Perot interferences occurring between the turning points and the entrance of the structure together with the adiabatic slowing mechanism can lead to intensity enhancements close to two orders of magnitude. An experimental realization at the microwave regime verified the operation principle, and we further note that the proposed structure is also feasible for current nanofabrication technologies, such as electron-beam lithography46 or direct laser writing techniques47, 48, due to its simple layer-by-layer architecture and its robustness against fabrication disorders34, 35. Furthermore we showed that the propagation losses can be suppressed, owing to the 3D periodicity of the structure. Such a phenomenon could be exploited to realize nonlinear optical devices, broadband photon harvesting systems, wavelength division multiplexing devices and optical buffers. We should note however, that the light enhancement phenomenon in the proposed configuration should not be considered as a permanent storage of a ‘trapped rainbow’7, but rather a temporary localization, due to the finite trapping time caused by the reflection at the turning points25, 49. It should be also noted that although high group indices up to 110 have been measured, a zero group velocity near the localization region could not be obtained due to additional out-of-plane losses and experimental limitations.
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Plates made of Plexiglas were employed to embody the constructed 3D PhC structure. By employing a laser engraving machine, holes were drilled inside the Plexiglas plates at the exact positions where the Al2O3 rods should be placed. The refractive index of Plexiglas has been measured via Bragg condition50 to be equal to 1.59 and numerical analyses revealed that placing the Plexiglas plates does not change the results significantly. The structural parameters are same as in the numerical calculations, where the in-plane period is set equal to a = 17.96 mm. The experimental setup (see Fig. 6), consists of a standard horn antenna, a monopole coaxial antenna and a vector network analyzer (Agilent 5071 C ENA). The horn antenna has an aperture size of 12.5 cm and 9.5 cm in the x- and y- directions, respectively, and is used to inject electromagnetic waves into the structure with electric field polarized in the y- direction, whereas the monopole antenna is used to detect the radiated electromagnetic waves. Furthermore, the experimental setup was covered with microwave absorbers to minimize the noise due to environmental reflections.
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The time delay is a measure of the photon transit time and is defined as τ d = ∂φ/∂ω, where φ is the phase difference between the input and output port of the vector network analyzer and ω is the operational angular frequency. Since the 3D periodicity of the woodpile PhC structure prevents to take a continuous spatial measurement along the longitudinal z- direction, we injected the receiver antenna inside the PhC structure with a tilting angle of 16° with respect to the y- axis until the center of the structural height at specific points. The difference of the time delays measured at these points have been divided to the corresponding point-to-point spatial distance to obtain the average group velocity, which is then divided to the speed of light in free space to estimate the average group index \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bar{n}}_{g}$$\end{document}n¯g.
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| 99.8 |
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