Abstract
Electromagnetic waves at grazing incidence onto a planar medium are analogous to zero energy quantum particles incident onto a potential well. In this limit waves are typically completely reflected. Here we explore dielectric profiles supporting optical analogues of ‘half–bound states’, allowing for zero reflection at grazing incidence. To obtain these profiles we use two different theoretical approaches: supersymmetric quantum mechanics, and direct inversion of the Helmholtz equation, showing that discretized approximations to these profiles exhibit low reflectivity close to grazing incidence.
Highlights
At grazing incidence, a wave is nearly always completely reflected from a surface
In this work we investigate the problem of designing graded dielectric materials that do not reflect at grazing incidence
Surprisingly there are permittivity profiles (and analogous graded sound speeds in acoustics, or potentials V(x) in quantum mechanics) that do not act as perfect reflectors at grazing incidence
Summary
A wave is nearly always completely reflected from a surface. The effect can be observed optically for almost any surface viewed at a shallow angle, where it behaves as a mirror. As the stone’s momentum becomes close to parallel to the surface, only a small impulse is required to reverse the stone’s motion normal to the surface Despite this general behaviour, surprisingly there are permittivity profiles (and analogous graded sound speeds in acoustics, or potentials V(x) in quantum mechanics) that do not act as perfect reflectors at grazing incidence. Requiring that the ‘lowering’ operator of this factorization has a zero eigenvalue we obtain a permittivity profile that does not reflect grazing incidence waves This approach connects with recent work on analogues of supersymmetric quantum mechanics (SUSY) in optics [22,23,24,25,26,27], to design complex potentials [28, 29] and optical fibres [30] amongst other things, and where the same factorization is leads to isospectral structures.
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