Perturbative analysis of generally nonlocal spatial optical solitons

Area of Science:

• Nonlinear Optics
• Mathematical Physics
• Soliton Theory

Background:

• The nonlocal nonlinear Schrödinger equation (NNLSE) models complex optical phenomena.
• Accurate analytical solutions are crucial for understanding NNLSE soliton dynamics.
• Perturbed harmonic oscillator analogies offer a framework for soliton analysis.

Purpose of the Study:

• To calculate fundamental and higher-order soliton solutions for the NNLSE in the generally nonlocal case.
• To improve the accuracy of soliton descriptions using a second approximation.
• To investigate the behavior of nonlocal solitons under different nonlocal response functions.

Main Methods:

• Analytical calculation of soliton solutions using a second approximation.
• Comparison of analytical results with numerical simulations.
• Investigation of soliton properties in the strongly nonlocal limit.

Main Results:

• Second approximation soliton solutions provide more accurate descriptions of nonlocal soliton states than zeroth approximation.
• Gaussian-function-like soliton solutions fail to accurately describe nonlocal states for exponential-decay type nonlocal responses.
• In the strongly nonlocal limit, soliton power and phase constant exhibit specific inverse power-law relationships with beam width, dependent on the nonlocal response type.

Conclusions:

• The second approximation significantly enhances the accuracy of analytical soliton solutions for the NNLSE.
• The choice of nonlocal response function critically affects the applicability of specific soliton solution forms.
• Understanding these properties is vital for controlling and utilizing NNLSE solitons in applications.