Design of a reflectionless optical amplifier through broken-supersymmetry

Abstract

A very interesting class of metamaterials is characterized by supersymmetry (SUSY). What makes SUSY very attractive for the design of new optical devices is the possibility to define different spatial refractive index distributions (superpartners) having the same scattering spectra (angularly and spectrally). In this study we explore the possibilities offered by the generation of superpartners of vacuum, being reflectionless and possessing unit transmission by definition. In particular, broken-SUSY is used to define a reflectionless active cavity capable of amplifying electromagnetic radiation in the visible. The approach is analytical through the use of the Darboux transform (a type of supersymmetric transformation) for the generation of the optical potential and the calculation of the field, while the transmission/reflection spectra evaluation is done with the Transfer Matrix method. Interestingly, we show that the Darboux transform allows to define 1D materials that are reflectionless for a continuum of frequencies. Moreover, the proposed device behaves as a dynamic optical filter amplifying radiation arriving at large angles while for other directions is almost completely transparent. Thus, simply by rotation different functionalities can be obtained. In addition, the active filter is reflectionless for all wavelengths and angles of incidence.