Nonlinear Band Gap Transmission in Optical Waveguide Arrays

Abstract

The effect of nonlinear transmission in coupled optical waveguide arrays is theoretically investigated and a realistic experimental setup is suggested. The beam is injected in a single boundary waveguide, linear refractive index of which (n(0)) is larger than refractive indexes (n) of other identical waveguides in the array. Particularly, the effect holds if omega(n(0)-n)/c>2Q, where Q is a linear coupling constant between array waveguides, omega is a carrier wave frequency, and c is a light velocity. Numerical experiments show that the energy transfers from the boundary waveguide to the waveguide array above a certain threshold intensity of the injected beam. This effect is due to the creation and the propagation of gap solitons in full analogy with a similar phenomenon in sine-Gordon lattice [Phys. Rev. Lett. 89, 134102 (2002)]].

Light Detectors Bistable Nonlinear Waveguide Arrays

“…Another consequence of the attenuation is the existence of a second (nonzero) threshold input amplitude where the solution bifurcates back from the regime I to the regime III. For a vanishing attenuation, this second threshold would be exactly zero according to the analytical solution (16). The existence of this lower end threshold is clearly of importance in view of experimental realization but, as being directly related to attenuation, it depends on the precise physical context.…”

“…In order to avoid an initial shock, the coupling Q 0 is actually smoothly set by using Q 0 (1 − e −z/5 ). The input-output dependence resulting from of (14), (17) and (20) is plotted on fig.3 and the profiles of the different exact solutions (16), (19) and (22) corresponding to the different output amplitudes are presented in fig.4.…”

“…We shall make use of the possibility to drive a waveguide array, in the forbidden band gap, through directional coupling by boundary waveguides, which results in the generation of (discrete) gap solitons [16], produced by nonlinear supratransmission [17], and used to conceive resonators with nonlinear eigenstates [18].…”

Nonlinear Dynamics of a 2d Array of Coupled Pendulums Under Parametric Excitation

“…The sine-Gordon model and its discrete analog are ubiquitous models in mathematical physics with a wide range of applications extending from chains of coupled pendulums [1] and Josephson junction arrays [2] to gravitational and high-energy physics models [3,4]. For instance, Ikeda et al investigated the behavior of intrinsic localized modes (ILMs) for an array of coupled pendulums subjected to horizontal [5] and verical [6] sinusoidal excitation.…”

Bistability in the sine-Gordon equation: The ideal switch

“…This process, quite generic, has been experimentally realized on a chain of coupled pendula [8], and applies for instance in discrete systems of coupled waveguide arrays [9] where the forbidden gap results from discreteness, or else in Bragg media (periodic dielectric structures) under constant micro-wave irradiation in the photonic band gap [10]. In Josephson junctions arrays, submitted to microwave excitation, the boundary u x (0, t) = f (t) induces the threshold B s = 2(1 − Ω 2 ) [8].…”