Calculated threshold of supratransmission phenomena in waveguide arrays with saturable nonlinearity

Abstract

In this work, we consider a semi-infinite discrete nonlinear Schrödinger equation with saturable nonlinearity driven at one edge by a driving force. The equation models the dynamics of coupled photorefractive waveguide arrays. It has been reported that when the frequency of the driving force is in the forbidden band, energy can be transmitted along the lattices provided that the driving amplitude is above a critical value. This nonlinear tunneling is called supratransmission. Here, we explain the source of supratransmission using geometric illustrations. Approximations to the critical amplitude for supratransmission are presented as well.

arXiv comment7 pages, 2 figures, presented at the 6th International Symposium on Modern Optics and Its Applications (ISMOA) 2007

References in corpus (8)

• Energy transmission in the forbidden bandgap of a nonlinear chain
• Radiationless Travelling Waves In Saturable Nonlinear Schrödinger Lattices
• Nonlinear Band Gap Transmission in Optical Waveguide Arrays
• Nonlinear supratransmission as a fundamental instability
• On the propagation of binary signals in damped mechanical systems of oscillators
• An application of nonlinear supratransmission to the propagation of binary signals in weakly damped, mechanical systems of coupled oscillators
• Nonlinear energy transmission in the gap
• An energy-based computational method in the analysis of the transmission of energy in a chain of coupled oscillators

Cited by in corpus (6)

• Boundary driven waveguide arrays: Supratransmission and saddle-node bifurcation
• Surge of power transmission in flat and nearly flat band lattices
• Nonlinear bandgap transmission by discrete rogue waves induced in a pendulum chain
• Nonlinearity-induced Band Gap Transmission in Dispersive and Flat Band Photonic Lattices
• In-band supratransmission in nonlinear flat band lattices
• Supratransmission of rogue wave-like breathing solitons