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Updated: Jun 5, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

Iterative nonlinear beam propagation using Hamiltonian ray tracing and Wigner distribution function.

Hanhong Gao¹, Lei Tian, Baile Zhang

¹Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA. gaohh87@mit.edu

|December 18, 2010

Summary

This summary is machine-generated.

We developed an iterative Hamiltonian ray tracing method to simulate nonlinear beam propagation. This approach offers intuitive optical engineering interpretations and matches split-step methods for accuracy.

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Area of Science:

Nonlinear optics
Computational physics
Optical engineering

Background:

Simulating beam propagation in nonlinear media is crucial for understanding light-matter interactions.
Traditional methods like split-step beam propagation can be computationally intensive.
Interpreting simulation results in traditional optical engineering terms remains a challenge.

Purpose of the Study:

To present an iterative Hamiltonian ray tracing method for simulating beam propagation in nonlinear media.
To demonstrate the method's applicability to phenomena like self-focusing and spatial solitons.
To highlight the interpretability of ray tracing in optical engineering terms.

Main Methods:

Computing the Wigner distribution function at the entrance plane.
Using the Wigner distribution function as initial conditions for solving Hamiltonian equations.
Iterative simulation of beam propagation in Kerr-effect media.

Main Results:

The method accurately simulates periodic self-focusing, spatial solitons, and Gaussian-Schell model beams.
Simulation results show good agreement with the established split-step beam propagation method.
The Hamiltonian ray tracing approach provides intuitive ray diagrams.

Conclusions:

Hamiltonian ray tracing is a viable and accurate method for simulating nonlinear beam propagation.
The method offers advantages in interpretability, aligning with traditional optical engineering concepts.
This technique enhances the understanding of complex nonlinear optical phenomena.