Resonant-state-expansion Born approximation for waveguides with dispersion

The resonant-state expansion (RSE) Born approximation, a rigorous perturbative method developed for electrodynamic and quantum mechanical open systems, is further developed to treat waveguides with a Sellmeier dispersion. For media that can be described by these types of dispersion over the relevant frequency range, such as optical glass, I show that the perturbed RSE problem can be solved by diagonalizing a second-order eigenvalue problem. In the case of a single resonance at zero frequency, this is simplified to a generalized eigenvalue problem. Results are presented using analytically solvable planar waveguides and parameters of borosilicate BK7 glass, for a perturbation in the waveguide width. The efficiency of using either an exact dispersion over all frequencies or an approximate dispersion over a narrow frequency range is compared. I included a derivation of the RSE Born approximation for waveguides to make use of the resonances calculated by the RSE, an RSE extension of the well-known Born approximation.Comment: BEST VERSION OF THIS ARTICL

Resonant state expansion applied to planar open optical systems

The resonant state expansion (RSE), a novel perturbation theory of Brillouin-Wigner type developed in electrodynamics [Muljarov, Langbein, and Zimmermann, Europhys. Lett., 92, 50010(2010)], is applied to planar, effectively one-dimensional optical systems, such as layered dielectric slabs and Bragg reflector microcavities. It is demonstrated that the RSE converges with a power law in the basis size. Algorithms for error estimation and their reduction by extrapolation are presented and evaluated. Complex eigenfrequencies, electro-magnetic fields, and the Green's function of a selection of optical systems are calculated, as well as the observable transmission spectra. In particular we find that for a Bragg-mirror microcavity, which has sharp resonances in the spectrum, the transmission calculated using the resonant state expansion reproduces the result of the transfer/scattering matrix method

Resonant state expansion applied to two-dimensional open optical systems

The resonant state expansion (RSE), a rigorous perturbative method in electrodynamics, is applied to two-dimensional open optical systems. The analytically solvable homogeneous dielectric cylinder is used as unperturbed system, and its Green's function is shown to contain a cut in the complex frequency plane, which is included in the RSE basis. The complex eigenfrequencies of modes are calculated using the RSE for a selection of perturbations which mix unperturbed modes of different orbital momentum, such as half-cylinder, thin-film and thin-wire perturbation, demonstrating the accuracy and convergency of the method. The resonant states for the thin-wire perturbation are shown to reproduce an approximative analytical solution

Resonant state expansion applied to planar waveguides

The resonant state expansion, a recently developed method in electrodynamics, is generalized here to planar open optical systems with non-normal incidence of light. The method is illustrated and verified on exactly solvable examples, such as a dielectric slab and a Bragg reflector microcavity, for which explicit analytic formulas are developed. This comparison demonstrates the accuracy and convergence of the method. Interestingly, the spectral analysis of a dielectric slab in terms of resonant states reveals an influence of waveguide modes in the transmission. These modes, which on resonance do not couple to external light, surprisingly do couple to external light for off-resonant excitation

Resonant-state expansion applied to three-dimensional open optical systems

The resonant-state expansion (RSE), a rigorous perturbative method in electrodynamics, is developed for three-dimensional open optical systems. Results are presented using the analytically solvable homogeneous dielectric sphere as unperturbed system. Since any perturbation which breaks the spherical symmetry mixes transverse electric (TE) and transverse magnetic (TM) modes, the RSE is extended here to include TM modes and a zero-frequency pole of the Green's function. We demonstrate the validity of the RSE for TM modes by verifying its convergence towards the exact result for a homogeneous perturbation of the sphere. We then apply the RSE to calculate the modes for a selection of perturbations sequentially reducing the remaining symmetry, given by a change of the dielectric constant of half-sphere and quarter-sphere shape. Since no exact solutions are known for these perturbations, we verify the RSE results by comparing them with the results of state of the art finite element method (FEM) and finite difference in time domain (FDTD) solvers. We find that for the selected perturbations, the RSE provides a significantly higher accuracy than the FEM and FDTD for a given computational effort, demonstrating its potential to supersede presently used methods. We furthermore show that in contrast to presently used methods, the RSE is able to determine the perturbation of a selected group of modes by using a limited basis local to these modes, which can further reduce the computational effort by orders of magnitude

Age shall not weary us: Deleterious effects of self-regulation depletion are specific to younger adults

Self-regulation depletion (SRD), or ego-depletion, refers to decrements in self-regulation performance immediately following a different self-regulation-demanding activity. There are now over a hundred studies reporting SRD across a broad range of tasks and conditions. However, most studies have used young student samples. Because prefrontal brain regions thought to subserve self-regulation do not fully mature until 25 years of age, it is possible that SRD effects are confined to younger populations and are attenuated or disappear in older samples. We investigated this using the Stroop color task as an SRD induction and an autobiographical memory task as the outcome measure. We found that younger participants (<25 years) were susceptible to depletion effects, but found no support for such effects in an older group (40–65 years). This suggests that the widely-reported phenomenon of SRD has important developmental boundary conditions casting doubt on claims that it represents a general feature of human cognition

A brief early intervention for adolescent depression that targets emotional mental images and memories: protocol for a feasibility randomised controlled trial (IMAGINE trial)

This is the final version of the article. Available from BioMed Central via the DOI in this record.Background: Adolescent depression is common and impairing. There is an urgent need to develop early interventions to prevent depression becoming entrenched. However, current psychological interventions are difficult to access and show limited evidence of effectiveness. Schools offer a promising setting to enhance access to interventions, including reducing common barriers such as time away from education. Distressing negative mental images and a deficit in positive future images, alongside overgeneral autobiographical memories, have been implicated in depression across the lifespan, and interventions targeting them in adults have shown promise. Here, we combine techniques targeting these cognitive processes into a novel, brief psychological intervention for adolescent depression. This feasibility randomised controlled trial will test the feasibility and acceptability of delivering this imagery-based cognitive behavioural intervention in schools. Methods/design: Fifty-six adolescents (aged 16-18) with high symptoms of depression will be recruited from schools. Participants will be randomly allocated to the imagery-based cognitive behavioural intervention (ICBI) or the control intervention, non-directive supportive therapy (NDST). Data on feasibility and acceptability will be recorded throughout, including data on recruitment, retention and adherence rates as well as adverse events. In addition, symptom assessment will take place pre-intervention, post-intervention and at 3-month follow-up. Primarily, the trial aims to establish whether it is feasible and acceptable to carry out this project in a school setting. Secondary objectives include collecting data on clinical measures, including depression and anxiety, and measures of the mechanisms proposed to be targeted by the intervention. The acceptability of using technology in assessment and treatment will also be evaluated. Discussion: Feasibility, acceptability and symptom data for this brief intervention will inform whether an efficacy randomised controlled trial is warranted and aid planning of this trial. If this intervention is shown in a subsequent definitive trial to be safe, clinically effective and cost-effective, it has potential to be rolled out as an intervention and so would significantly extend the range of therapies available for adolescent depression. This psychological intervention draws on cognitive mechanism research suggesting a powerful relationship between emotion and memory and uses imagery as a cognitive target in an attempt to improve interventions for adolescent depression. Trial registration: ISRCTN85369879.This study represents independent research from a Clinical Doctoral Research Fellowship (Dr Victoria Pile, ICA-CDRF-2015-01-007) supported by the National Institute for Health Research and Health Education England

The development of cross-cultural recognition of vocal emotion during childhood and adolescence

Humans have an innate set of emotions recognised universally. However, emotion recognition also depends on socio-cultural rules. Although adults recognise vocal emotions universally, they identify emotions more accurately in their native language. We examined developmental trajectories of universal vocal emotion recognition in children. Eighty native English speakers completed a vocal emotion recognition task in their native language (English) and foreign languages (Spanish, Chinese, and Arabic) expressing anger, happiness, sadness, fear, and neutrality. Emotion recognition was compared across 8-to-10, 11-to-13-year-olds, and adults. Measures of behavioural and emotional problems were also taken. Results showed that although emotion recognition was above chance for all languages, native English speaking children were more accurate in recognising vocal emotions in their native language. There was a larger improvement in recognising vocal emotion from the native language during adolescence. Vocal anger recognition did not improve with age for the non-native languages. This is the first study to demonstrate universality of vocal emotion recognition in children whilst supporting an “in-group advantage” for more accurate recognition in the native language. Findings highlight the role of experience in emotion recognition, have implications for child development in modern multicultural societies and address important theoretical questions about the nature of emotions