Perturbative unidirectional invisibility

Abstract

We outline a general perturbative method of evaluating scattering features of finite-range complex potentials and use it to examine complex perturbations of a rectangular barrier potential. In optics, these correspond to modulated refractive index profiles of the form n(x) = n0 + f (x), where n0 is real, f (x) is complex-valued, and |f (x)| ≪ 1 ≤ n0. We give a comprehensive description of the phenomenon of unidirectional invisibility for such media, proving five general theorems on its realization in PT -symmetric and non-PT -symmetric material. In particular, we establish the impossibility of unidirectional invisibility for PT -symmetric samples whose refractive index has a constant real part and show how a simple scaling transformation of a unidirectionally invisible PT -symmetric index profile with n0 = 1 may be used to generate a hierarchy of unidirectionally invisible PT -symmetric index profiles with n0 > 1. The results pertaining unidirectional invisibility for n0 > 1 open up the way for the experimental studies of this phenomenon in a variety of active material. As an application of our general results, we show that a medium with n(x) = n0 + ζe iKx , ζ and K real, and |ζ| ≪ 1 can support unidirectional invisibility only for n0 = 1. We then construct unidirectionally invisible index profiles of the form n(x) = n0 + ℓ z ℓ e iK ℓ x , with z ℓ complex, K ℓ real, |z ℓ | ≪ 1, and n0 > 1.

Unidirectional reflectionlessness and invisibility in the TE and TM modes of aPT-symmetric slab system

“…But notice that not all values of g satisfying (27) gives rise to a left (right) reflectionless configuration. One must account for the excluded points arising from the invalidity of the counter-direction reflectionlessness in (19).…”

“…(Color online) Plots of gain coefficient g as a function of wavelength λ corresponding to TE and TM wave solutions of a PT -symmetric bilayer in (27), which gives the uni/bi-directionally reflectionless potential configurations at incident angle of 30…”

“…This approach employs the truth that object being invisible is to be concealed behind an artificially manufactured material [26]. The complication in the process of fabrication on account of geometrical requirements and challenges in the applicability process highlights the second approach benefited from interferometric methods heading the transfer matrix, which has found a growing interest in recent years [19][20][21][22][27][28][29][30][31][32][33][34][35].…”

Floquet exceptional points and chirality in non-Hermitian Hamiltonians

“…In the slow cycling limit ω → 0, the adiabatic approximation basically corresponds to disregard the rapidly-oscillating terms exp(±iΩt) and exp(±i2Ωt) in Eqs. (31)(32)(33) that couple the amplitudes of different adiabatic states (rotating-wave approximation). This yields…”

“…They have been predicted and observed in a wide variety of physical systems, including atomic and molecular systems [13,14,15], microwave cavities and waveguides [16,17,18], electronic circuits [19], optical structures [20,21], Bose-Einstein condensates [22,23], acoustic cavities [24], non-Hermitian Bose-Hubbard models [25], exciton-polariton billiards [26], opto-mechanical systems [27] and many others. Besides of their theoretical interest, EPs can find important applications, for example in the design and realization of unidirectionally invisible media [28,29,30,31,32], for asymmetric mode switching [18,33] and topological energy transport [27], for the design of novel laser devices [34,35,36,37,38], for optical sensing [39] and polarization mode conversion [40]. The dynamical properties associated to the encircling of an EP and the chirality of EPs arising from breakdown of the adiabatic theorem have received a great attention in recent years [16,17,18,27,40,41,42,43,44,45].…”