Supersymmetric Optical Structures

Abstract

We show that supersymmetry can provide a versatile platform in synthesizing a new class of optical structures with desired properties and functionalities. By exploiting the intimate relationship between superpatners, one can systematically construct index potentials capable of exhibiting the same scattering and guided wave characteristics. In particular, in the Helmholtz regime, we demonstrate that one-dimensional supersymmetric pairs display identical reflectivities and transmittivities for any angle of incidence. Optical SUSY is then extended to two-dimensional systems where a link between specific azimuthal mode subsets is established. Finally we explore supersymmetric photonic lattices where discreteness can be utilized to design lossless integrated mode filtering arrangements.

Supersymmetry-generated one-way-invisiblePT-symmetric optical crystals

“…Moreover, the unidirectional * bikash.midya@gmail.com invisibility is ambiguous for a crystal with length L > 2π 3 /b 2 a 3 [22]. Thus, at the PT -symmetry breaking point the sinusoidal crystal appears to be one-way invisible solely for a shallow grating which indeed is realized by recent experiments on a PT -synthetic photonic lattice [24,25].On the other hand, nonrelativistic supersymmetry (SUSY) transformations are shown [26][27][28][29][30][31][32] to be useful in the framework of optics to synthesize new optical structures. In particular, SUSY has provided a method to generate an optical medium with defects that can not be detected by an outside observer [30], to obtain transparent interface separating two isospectral but different crystals [29], and to create a family of isospectral potentials to optimize quantum cascade lasers [31].…”

“…On the other hand, nonrelativistic supersymmetry (SUSY) transformations are shown [26][27][28][29][30][31][32] to be useful in the framework of optics to synthesize new optical structures. In particular, SUSY has provided a method to generate an optical medium with defects that can not be detected by an outside observer [30], to obtain transparent interface separating two isospectral but different crystals [29], and to create a family of isospectral potentials to optimize quantum cascade lasers [31].…”

Supersymmetric mode converters

“…The optical potential V ¼ 2k 2 0 n 0 ÁDnðxÞ is then determined by the refractive index profile n(x) ¼ n 0 þ Dn(x). A SUSY partner potential can be found by factorizing the operator H ¼ q 2 /qX 2 þ V in the eigenvalue problem Hc ¼ mc by means of the superpotential method 14 (see Supplementary Fig. 1).…”

“…This operation is fully reversible, that is, the same element can be employed to demultiplex the superposition of modes after transmission. We would also like to emphasize that, even though the experimental results presented here are of qualitative nature and were obtained in discrete onedimensional settings, the fundamental principle of SUSY-MDM is equally applicable to continuous arrangements and can even be extended to optical fibres, where whole subsets of modes may be selectively manipulated according to their specific optical angular momenta 14 . Along these lines, detailed simulations of supersymmetric mode conversion in continuous refractive index landscapes, and its robustness with respect to dispersion, are provided in the Supplementary Discussion (see also Supplementary Figs 6 and 7).…”

“…While evidence for supersymmetric behaviour in any physical setting, whether natural or artificial, has so far remained elusive, its fundamental ideas can in principle be adopted in other areas of physics 13 . In its optical manifestation, SUSY can potentially establish close relationships between seemingly different dielectric structures 14 . For example, two refractive index profiles interrelated via supersymmetric transformations share identical scattering characteristics 15 and therefore can become virtually indistinguishable to an external observer, even in the presence of losses 16,17 .…”