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

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Does the nonlinear Schrödinger equation correctly describe beam propagation?

N Akhmediev, A Ankiewicz, J M Soto-Crespo

|October 6, 2009

Summary

This study reconsiders the standard parabolic equation for nonlinear beam propagation. An additional term accounting for propagation constant changes is introduced, impacting self-focusing dynamics.

Area of Science:

Nonlinear optics
Wave propagation physics

Background:

The standard parabolic equation, specifically the nonlinear Schrödinger equation, is widely used for modeling stationary nonlinear beam propagation.
Self-focusing phenomena in nonlinear media are typically analyzed using this approximation.

Purpose of the Study:

To re-examine the validity of the standard parabolic equation in nonlinear beam propagation.
To introduce and analyze an additional term that accounts for variations in the propagation constant along the direction of propagation.
To explore the physical implications of this refined model compared to the standard approximation.

Main Methods:

Theoretical reconsideration of the parabolic equation for nonlinear beam propagation.
Inclusion of a novel term representing changes in the propagation constant.

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Numerical simulations to compare the outcomes of the new approach with the standard nonlinear Schrödinger equation.

Main Results:

An additional term involving changes of the propagation constant along the propagation direction is identified as crucial.
The departure from the standard parabolic equation approximation leads to significant physical consequences.
Numerical simulations demonstrate a clear difference between the results obtained from the new approach and the standard nonlinear Schrödinger equation.

Conclusions:

The standard parabolic equation (nonlinear Schrödinger equation) requires modification for accurate modeling of stationary nonlinear beam propagation.
Accounting for the changing propagation constant is essential for understanding self-focusing dynamics.
The proposed refined model offers a more accurate description of nonlinear beam propagation phenomena.