Abstract
We study the effects of weak two-photon absorption on two-dimensional (2D) solitons interaction in a silicon-based waveguide under a framework of coupled perturbed D nonlinear Schrödinger equations with a pure Kerr nonlinearity and a nonstationary potential. We extend the perturbative analysis for collisions of two one-dimensional solitons in silicon waveguides to derive the theoretical expressions for the amplitude evolution of a single perturbed soliton and for the abrupt amplitude downshift of a colliding soliton due to a fast interaction between two 2D solitons in silicon lattices. The theoretical calculations are then validated by the extensive simulations of the coupled perturbed D nonlinear Schrödinger model with periodic and non-periodic potentials. The simulations are implemented by using the accelerated imaginary-time evolution scheme and the split-step Fourier method. These results allow us to accurately capture the abrupt energy downshift of a colliding soliton in silicon-based two-dimensional waveguides.
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