Nonlinear multicore waveguiding structures with balanced gain and loss

Abstract

Artículo de publicación ISIWe study existence, stability, and dynamics of linear and nonlinear stationary modes propagating in radially symmetric multicore waveguides with balanced gain and loss.We demonstrate that, in general, the system can be reduced to an effective PT -symmetric dimer with asymmetric coupling. In the linear case, we find that there exist two modes with real propagation constants before an onset of the PT -symmetry breaking while other modes have always the propagation constants with nonzero imaginary parts. This leads to a stable (unstable) propagation of the modes when gain is localized in the core (ring) of the waveguiding structure. In the case of nonlinear response, we show that an interplay between nonlinearity, gain, and loss induces a high degree of instability, with only small windows in the parameter space where quasistable propagation is observed. We propose a novel stabilization mechanism based on a periodic modulation of both gain and loss along the propagation direction that allows bounded light propagation in the multicore waveguiding structures.Fondo Nacional de Ciencia y Tecnología (Grant 1120123), Programa Iniciativa Científica Milenio (Grant P10-030-F), Programa de Financiamiento Basal (Grant FB0824) and the Australian Research Council; Comisión Nacional de Investigación Científica y Tecnológica (Fellowship BCH72130485/2013

Nonlinear switching and solitons in PT‐symmetric photonic systems

“…The nonlinear effects in PT-symmetric systems can be utilized for an efficient control of light including all-optical low-threshold switching and unidirectional invisibility [24,56,57]. The possibility to engineer PT-symmetric oligomers, which may include nonlinearity, triggers a broad variety of studies on both the few-site systems and entire PT-symmetric lattices, including onedimensional PT-symmetric dimer [35,58], trimer [58,59], quadrimer [58,60], 2D PT-symmetric plaquettes [60,61], PT-symmetric finite/infinite chains [62][63][64][65], necklaces [66] and multicore fibers [67].…”

“…This offers an opportunity to explore the multicore waveguide systems with PT-symmetry in the presence of gain and loss. Existence, stability, and dynamics of both linear and nonlinear stationary modes propagating in radially symmetric multicore waveguides with balanced gain and loss have recently been studied [67]. A multicore waveguide array of N identical waveguides arranged in a circular geometry with the central one being gain (loss) and all peripheral ones being loss (gain), as shown in Fig.…”

“…Modulation of structure parameters along the propagation direction of coupled optical waveguides with gain and loss can open new opportunities for optical signal control in both linear [178][179][180] and nonlinear [67,82,[181][182][183][184][185] regimes.…”

“…31(a). Linear beam evolution in such arrays is described by the coupled-mode equations, i da n dz = −κ(a n−1 + a n+1 ) + i(−1) n (t)a n , (67) where n is the waveguide number, a n are the mode amplitudes, t is the propagation coordinate, κ is the coupling between the neighboring waveguides, and (t) = 0 square(ωt + θ ) is a square modulation profile of gain and loss. Solutions of this system can be found analytically in Fourier space, characterized by the transverse wavenumber q.…”

Revisiting the Optical PT-Symmetric Dimer

“…The second one dealt with composite systems, where a mature mode coupling theory produced a theory of coupled optical P T -symmetric structures [9]. In the ten years following those first proposals for an optical realization of P T -symmetry, work has been reported on slab waveguides [10,11], Bragg scatterers [12][13][14][15][16][17], as well as linear [18][19][20][21][22][23][24][25][26] and nonlinear [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] coupled waveguides, to mention just a few. Research in this field is slowly getting to information technologies applications with recent proposals of all-optical P T -symmetric logic gates [46] and amplitude-to-phase converters [47].…”