New Publication: Supersymmetry, half-bound states, and grazing incidence reflection

Congratulations to third year PGR Dean Patient, whose paper ‘Supersymmetry, half-bound states, and grazing incidence reflection’ was published in Journal of Optics.

Dean explains his findings:

Any wave that approaches a material at grazing incidence will almost always completely reflect, this effect can be seen all around us: we can see the reflection of the horizon off of the sea or a lake (where it looks like you’re looking into a mirror), we can see glare in the road when you’re trying to drive, and you can even create this effect when you skim a stone along the surface of water. However from a technical standpoint, this effect can become an unwanted inconvenience – an effect that naturally manifests despite efforts to remove it.


Here, we theoretically explore ways to ensure that a wave approaching a material at grazing incidence will not reflect at all. We first do this by taking inspiration from Quantum Mechanics, and apply their theoretical frameworks to the world of optics, to design bespoke material parameters that do not reflect grazing incidence waves. We further design materials that when placed above a mirror (which reflects all waves at any angle), will absorb grazing incidence waves entirely, such that there is no reflection.


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.

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