# Calculated threshold of supratransmission phenomena in waveguide arrays with saturable nonlinearity

## TL;DR

This paper investigates the threshold for supratransmission in waveguide arrays with saturable nonlinearity, providing geometric insights and approximations for the critical driving amplitude in photorefractive systems.

## Contribution

It introduces a geometric explanation and analytical approximations for the supratransmission threshold in nonlinear waveguide arrays with saturable nonlinearity.

## Key findings

- Derived approximations for critical amplitude of supratransmission
- Provided geometric interpretation of nonlinear tunneling
- Validated threshold conditions for photorefractive waveguides

## Abstract

In this work, we consider a semi-infinite discrete nonlinear Schr\"odinger 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.