Supersymmetry, half-bound states, and grazing incidence reflection

Patient, Dean A.; Horsley, S. A. R.

doi:10.1088/2040-8986/ac01b1

Cited by 4 publications

(7 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Unlike the isotropic multilayers that were the focus of our previous study [9], for anisotropic multilayers the two Helmholtz equations for TE and TM polarisations can be simultaneously factorised into the form â † â' ¼ 0; the same factorisation used in the formalism of supersymmetric quantum mechanics. This procedure builds on the novel method for designing non-reflecting optical materials that was explored in [9]: a new application of quantum mechanical techniques to the design of optical materials. This can be done provided the principal values of the permittivity are of the form given in equations ( 9) and (10).…”

Section: Discussionmentioning

confidence: 99%

“…In previous work [9] we gave a method for designing materials where there is zero reflection for one polarisation at grazing incidence (k y ! ffiffiffiffi e b p k 0 ).…”

Section: Factorisation At Grazing Incidencementioning

confidence: 99%

“…These arise when the potential well supports a so-called half-bound state (HBS) [7], allowing the particle to transmit with certainty [8]. Isotropic permittivity profiles can support analogues of these states [9]. In previous work we designed such media using the factorisation method [10] to decompose the Helmholtz equation into 'raising' and 'lowering' operators.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Reflectionless anisotropic multilayers for both polarisations at grazing incidence

Patient

Horsley

2022

EPJ Appl. Metamat.

Self Cite

View full text Add to dashboard Cite

We find a method for designing anisotropic multilayer profiles that are reflectionless at grazing incidence, for both electromagnetic polarisations. The Helmholtz equation for grazing incidence propagation through an anisotropic multilayer can be factorised into a pair of equations of the form [see formula in PDF]. Solutions of [see formula in PDF] then determine two of the three principal values of the permittivity. Imposing the additional constraint of uniaxial anisotropy, we find a pair of coupled equations for the profile of both permittivity components such that neither polarisation is reflected.

show abstract

Section: Discussionmentioning

confidence: 99%

“…In previous work [9] we gave a method for designing materials where there is zero reflection for one polarisation at grazing incidence (k y ! ffiffiffiffi e b p k 0 ).…”

Section: Factorisation At Grazing Incidencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Reflectionless anisotropic multilayers for both polarisations at grazing incidence

Patient

Horsley

2022

EPJ Appl. Metamat.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In general, time modulation in photonic structures can give rise, among others, to topological effects, [ 11–14 ] formation of exceptional points, [ 15 ] optical isolation, [ 16,17 ] non‐hermiticity, [ 18–20 ] temporal cloaking, [ 21 ] breaking of Lorentz reciprocity, [ 22–25 ] optical‐wave‐based machine learning, [ 26 ] and temporal supersymmetry. [ 27–29 ] Though many of the aforementioned phenomena are typical for magnetic, non‐linear, or active materials, modulation in the time domain makes them possible to realize with ordinary linear, passive, and non‐magnetic materials.…”

Section: Introductionmentioning

confidence: 99%

Optical Transitions and Nonreciprocity in Spatio‐Temporally Periodic Layers of Spherical Particles

Panagiotidis

Almpanis

Papanikolaou

et al. 2023

Advanced Optical Materials

View full text Add to dashboard Cite

temporalcloaking, [21] breaking of Lorentz reciprocity, [22][23][24][25] optical-wavebased machine learning, [26] and temporal supersymmetry. [27][28][29] Though many of the aforementioned phenomena are typical for magnetic, non-linear, or active materials, modulation in the time domain makes them possible to realize with ordinary linear, passive, and non-magnetic materials.The simplest realization is a temporal slab [30][31][32][33][34] which can exhibit nonreciprocal effects. Furthermore, by arranging such temporal slabs in a multilayer architecture, it is possible to build generalized Bragg reflectors or hyperbolic media. [12,[35][36][37][38] Apart from these 1D configurations, novel architectures based on dynamic particles, that is, particles with time-dependent material or geometrical parameters, [39][40][41][42] and periodic or quasiperiodic arrangements of such, offer further possibilities for more sophisticated designs, for example, space-time varying metamaterials [8,11] and metasurfaces, [43][44][45] which expand the boundaries in light control.What is more, optical transitions, which occur in time-varying environments, can give rise to interesting and potentially useful effects, such as frequency conversion and filtering. Photonic transitions, similar to electronic transitions, have been anticipated in time-modulated photonic crystals by Winn et al. [46] using coupled mode theory. Such transitions through a temporal modulation can take place in different photonic configurations, such as ring resonators [47,48] or linear waveguides, [49] while the modulation in time can be achieved, for example, through an electrically driven change of the permittivity, [50] acoustic or spin waves. However, despite the previous studies that assume discrete optical modes, the problem of optical transitions between leaky modes in open systems, due to the temporal variation of the material properties, did not receive much attention so far.It is the purpose of the present paper to study, by means of full-wave dynamic calculations, the optical transitions between finite-Q modes in arrays of dielectric particles with a periodically varying permittivity. Such collective optical modes originate from the interaction between multipolar Mie resonances of the individual spheres. [51][52][53][54][55] Although for interacting dipolar (ℓ = 1) modes in a periodic lattice physically elucidating semi-analytical models can be employed, this is not the case for collective modes of higher multipolar order (ℓ > 1), which manifest themselves in high-finesse (high-Q) optical resonances in the reflection and/or transmission spectra, [54,56,57] where a fully electrodynamic approach must be undertaken. Here, we An extension of the photonic layer multiple scattering methodology to dynamic spherical scatterers, which exhibit a periodic time-varying response, is presented. The applicability of the method is demonstrated on specific examples of single-and bi-layers of periodically modulated high-refractiveindex spherical particles arranged on a squar...

show abstract

“…10 The optical equivalent of the HBS is a grazing incidence wave that is transmitted through a dielectric profile without reflection. 11 The field of an optical HBS outside of the dielectric is a non-zero constant everywhere. In this way, the mode is 'bound' to the dielectric profile, but it cannot be normalised.…”

Section: Introductionmentioning

confidence: 99%

Removing grazing incidence reflection with half-bound states and non-Hermitian systems

Patient¹,

Horsley²

2022

Metamaterials XIII

View full text Add to dashboard Cite

Supersymmetry, half-bound states, and grazing incidence reflection

Cited by 4 publications

References 45 publications

Reflectionless anisotropic multilayers for both polarisations at grazing incidence

Reflectionless anisotropic multilayers for both polarisations at grazing incidence

Optical Transitions and Nonreciprocity in Spatio‐Temporally Periodic Layers of Spherical Particles

Removing grazing incidence reflection with half-bound states and non-Hermitian systems

Contact Info

Product

Resources

About