Light localization induced by a random imaginary refractive index

Abstract

We show the emergence of light localization in arrays of coupled optical waveguides with randomness only in the imaginary part of their permittivity and develop a one-parameter scaling theory for the normalized participation number of the Floquet-Bloch modes. This localization introduces a new length scale in the decay of the autocorrelation function of a paraxial beam propagation. Our results are relevant to a vast family of systems with randomness in the dissipative part of their impedance spatial profile.PACS numbers: 42.60.Da, 42.25.Bs Wave propagation in random media is of great fundamental and applied interests. It covers areas ranging from quantum physics and electromagnetic wave propagation to acoustics and atomic-matter wave systems. Despite this diversity, the underlying wave character of these systems provides a unified framework for studying mesoscopic transport and, in many occasions, points to new research directions and applications. A celebrated example of this universal behavior of wave propagation is the so-called Anderson localization phenomenon associated with a halt of transport in a random medium due to interference effects originating from multiple scattering events [1]. In recent years a number of experiments with classical [2-10] and matter waves [11,12] have confirmed the validity of this prediction. In all these cases, however, the wave localization originates from randomness pertaining the spatial profile of the reactive part of the impedance.In the present paper we show the emergence of localization phenomena in a new setting, namely a class of systems, whose the spatial impedance profile has random dissipative part. Realizations of this class includes Bose-Einstein condensates in randomly leaking opticalThe Floquet-Bloch modes of an array of N = 50 waveguides with random imaginary index of refraction taken from a box distribution with width W = 5. All modes are exponentially localized at various localization centers corresponding to gain (red stripes) or loss (green stripes) waveguides alike.

Metal-insulator phase transition in a non-Hermitian Aubry-André-Harper model

“…Several non-Hermitian models with disorder or incommensurate potentials have been investigated, in which non-Hermiticity is introduced by considering either complex on-site potentials, phenomenologically describing dissipation and/or amplification with the surrounding enviroment, or asymmetric hopping amplitudes, such as in systems with synthetic imaginary gauge fields. In systems with on-site complex disorder (non-Hermitian Anderson model), it was shown that a purely imaginary disorder can induce localization like in the Hermitian Anderson localization problem, with a duality between dissipation and amplification [21,22,27,30,34]. On the other hand, for real-energy on-site potential disorder a non-Hermitian delocalization transition is observed * stefano.longhi@polimi.it by application of an imaginary gauge field (Hatano-Nelson-Anderson model [23-26, 29, 33, 39, 46, 47, 49]).…”

Anderson attractors in active arrays

“…Noteworthy, dissipation in ordered lattices have proved to be destructive for the originally ballistic transport. Namely, it evokes the mobility transition towards diffusive light propagation, when introduced homogeneously 27 , and exponential localization, when randomized 28 . Instructively, the dissipation introduced at the boundaries of passive chains (or mimicked by semi-infinite propagating leads) organizes non-trivial transitions in the scaling of relaxation 29 , transparency 30 , and arising asymmetry of wave propagation 31 , depending on the levels of disorder and nonlinearity.…”

Observation of Poynting’s vector reversal in an active photonic cavity

“…We note that the phenomenon we described here relies on providing coherent gain in a cavity, and thus they may also be observed in other non-Hermitian platforms for propagating waves, including acoustics [39,40] and phononics [41], and potentially even electronics [42] and magnonics [43]. Furthermore, we have considered only deterministic systems here, and it remains an open question what the impact of Poynting's threshold is in disordered active structures, especially when the disorder leads to Anderson localization [44].…”