Localization of light in evanescently coupled disordered waveguide lattices: Dependence on the input beam profile

Optical waveguide arrays: quantum effects and PT symmetry breaking

“…In real samples, disorder is always present through variations in the tunneling amplitudes C j,j+1 or on-site potentials β j in the tight-binding Hamiltonian, equation (1). The effect of such disorder on the transport properties of lattices was first investigated in the context of electronic systems [61,62], and then extended to classical waves [17][18][19]. In one dimension, all eigenstates of a disordered Hamiltonian are exponentially localized in the limit of an infinite system size, N → ∞ irrespective of the strength of the disorder v d .…”

“…A variation in the index of refraction or the tunneling amplitude, both of which can be introduced easily, permit the modeling of a tight-binding Hamiltonian with site or bond disorders respectively. Due to this versatility, many quantum and condensed matter phenomena -Bloch oscillations [12,13], Dirac zitterbewegung [14], and increased intensity fluctuations [15,16] of light undergoing Anderson localization [17][18][19] -have been theoretically predicted to occur or experimentally observed in waveguide arrays. They have been used to investigate solitonic solutions that arise due to nonlinearities in the dielectric response [20,21].…”

Lattice topology dictates photon statistics

“…We consider coupled identical waveguides with nearestneighbor-only interactions arranged on two different lattice topologies: the linear lattice and the closed ring lattice ( Fig. 1(a)), the former of which has been studied extensively 20,[23][24][25][26][27][37][38][39][40][41][42][43][44][45][46] . The complex envelope A = {A x (z)} x of a coherent monochromatic field at lattice site x evolves according to the matrix equation 20 idA/dz +ĤA = 0, whereĤ is the coupling matrix or the system's Hamiltonian ( Fig.…”

Confinement of Light in Disordered Photonic Lattices: A New Platform for Waveguidance

“…We consider an evanescently coupled waveguide array (as photonic lattice) consisting of a large number (N) of unit cells, and in which all the waveguides spaced equally apart are buried inside a medium of constant refractive index n 0 [5,7]. The overall structure is homogeneous in the longitudinal (z) direction along which the incident optical beam is assumed to propagate.…”

“…1b from which it can be seen that above a threshold value of C the beam mimics a waveguide-like channel through the lattice and get localized at the output end with no variation (as one of its signatures) in its beam width. Incorporating the statistical nature of the disorder (over 100 ensembles of same disorder level) we have estimated the localization length [5]. Thus, the disordered photonic lattice structure effectively behaves like a guiding geometry for the incident light, a phenomenon which has also recently been demonstrated in a cylindrical waveguiding geometry, which led to the concept of an Anderson localized fiber (self-averaging must be strong enough to ensure that the localization can be observed in one particular sample rather than through ensemble averaging) [6,8,9].…”