A fourth-order Runge-Kutta in the interaction picture method for numerically solving the coupled nonlinear...

Area of Science:

• Optics and Photonics
• Computational Physics
• Nonlinear Optics

Background:

• Light propagation in optical fibers is governed by the coupled nonlinear Schrödinger equation (CNLSE).
• Randomly varying birefringence in communication fibers complicates accurate modeling.
• Existing methods like split-step approximations are limited by step size, impacting computational efficiency.

Purpose of the Study:

• To present a novel fourth-order Runge-Kutta in the interaction picture (RK4IP) method.
• To accurately solve the CNLSE for light propagation in optical fibers with random birefringence.
• To improve computational efficiency by allowing larger step sizes compared to traditional methods.

Main Methods:

• Developed and implemented a fourth-order Runge-Kutta algorithm in the interaction picture (RK4IP).
• Applied the RK4IP method to solve the CNLSE for optical fibers with general local birefringence.
• Treated Kerr nonlinearity without approximation.

Main Results:

• The RK4IP method demonstrates computational errors stemming from the Runge-Kutta algorithm, outperforming split-step approximations.
• RK4IP enables step sizes comparable to dispersion and nonlinear lengths for small birefringence.
• For random birefringence, RK4IP step sizes can exceed correlation and beating lengths, depending on linear and nonlinear interactions.

Conclusions:

• The RK4IP method provides a robust and efficient approach for simulating light propagation in birefringent optical fibers.
• Results from RK4IP align well with the Manakov-PMD approximation under conditions of sufficient polarization mixing.
• This method offers a valuable tool for analyzing nonlinear fiber optics with complex birefringence.