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Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

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Published on: January 28, 2019

Spatial periodic forcing can displace patterns it is intended to control.

Yair Mau¹, Aric Hagberg, Ehud Meron

¹Physics Department, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel.

Physical Review Letters

|August 7, 2012

Summary

Spatial periodic forcing controls patterns in one dimension but destabilizes them in two dimensions. This study reveals how forcing induces rectangular and oblique patterns in 2D systems, unlike 1D reinforcement.

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Area of Science:

Physics
Complex Systems
Nonlinear Dynamics

Background:

Spatial periodic forcing is an underutilized technique for pattern control.
It can influence amplitude, wave number, stability, and induction of patterns in systems.

Purpose of the Study:

To investigate the effects of spatial periodic forcing on pattern-forming systems.
To compare the behavior of forcing in one-dimensional versus two-dimensional systems.

Main Methods:

Theoretical analysis of pattern-forming systems under spatial periodic forcing.
Mathematical modeling to predict system responses.

Main Results:

In one spatial dimension, forcing reinforces existing periodic patterns.
In two dimensions, forcing destabilizes or displaces patterns.
Forcing induces two-dimensional rectangular and oblique patterns in 2D systems.

Conclusions:

Spatial periodic forcing exhibits contrasting effects in 1D and 2D pattern-forming systems.
The dimensionality significantly alters the response to spatial periodic forcing, leading to complex pattern formation in 2D.