Supersymmetry-Inspired Non-Hermitian Optical Couplers

Abstract

Supersymmetry has been shown to provide a systematic and effective framework for generating classes of isospectral optical structures featuring perfectly-phase-matched modes, with the exception of one (fundamental) mode which can be removed. More recently, this approach has been extended to non-Hermitian scenarios characterized by spatially-modulated distributions of optical loss and gain, in order to allow the removal of higher-order modes as well. In this paper, we apply this approach to the design of non-Hermitian optical couplers with higher-order mode-selection functionalities, with potential applications to mode-division multiplexing in optical links. In particular, we highlight the critical role of the coupling between non-Hermitian optical waveguides, which generally induces a phase transition to a complex eigenspectrum, thereby hindering the targeted mode-selection functionality. With the specific example of an optical coupler that selects the second-order mode of a given waveguide, we illustrate the aforementioned limitations and propose possible strategies to overcome them, bearing in mind the practical feasibility of the gain levels required.

Instantaneous modulations in time-varying complex optical potentials

“…Such an extension of the concept of spacetime reflection into the classical domain stems from the works of El-Ganainy et al [18] and Makris et al [19,20], who have employed the similarity between the Schrödinger and a scalar approximation of Maxwell's equations to describe the dynamics of light beams in  -symmetric optical lattices. There have been further theoretical [21][22][23][24] and experimental [25][26][27] studies dealing with the implementation of the parity-time reversal symmetry in optics especially relevant for the development of new artificial structures and materials (see also the recent review paper [28] and references cited therein).…”

PT-symmetric spectral singularity and negative-frequency resonance

“…(18a) and (18b) together, we conclude that the Hamiltonian is PT -symmetric ifĤ em (z, ω) = H * em (−z, ω). This means that the condition of PTsymmetry on dielectric function, as obtained from equation (16), is the well known condition [8] ǫ(−z, ω) = ǫ * (z, ω).…”

“…A major consequence of this extension of quantum mechanical framework to nonHermitian systems, is a new class of optical structures [4] with spatially distributed loss and gain profiles [5][6][7]. Such PT -symmetric non-Hermitian optical systems with complex dielectric profiles find promising applications in optical components ranging from couplers [8] and waveguides [9] to microresonators [10,11] and lasers [12][13][14][15][16][17][18].…”

Topological state engineering via supersymmetric transformations

“…In recent years, the field of photonics has shed light on a plethora of phenomena stemming from topological phases (See [15,16] and references therein), and photonic lattices have been established as a versatile experimental platform [17][18][19][20]. In a similar vein, SUSY notions have been introduced to photonics [8] to tackle the long-standing challenge of systematically shaping the modal content of highly multi-moded structures [21][22][23][24][25][26][27][28], controlling scattering characteristics [29][30][31], designing laser arrays [32,33], creating band gaps in extremely disordered potentials [34] and robust mid-gap states [35]. To elucidate how SUSY enables the manipulation of topological properties, we apply discrete SUSY transformations to photonic lattices embodying the simplest system with non-trivial topological properties, the Su-Schrieffer-Heeger (SSH) model [36].…”