Optimal Control for Optical Solitons in Nematic Liquid Crystals

We study an optimal control problem for a coupled Schrödinger-elliptic evolution system that describes the propagation of a laser beam in nematic liquid crystals. We consider a bilinear control related to an electric field depending on the optical axis acting on the sample. This problem arises from...

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Bibliographic Details
Published in:Applied mathematics & optimization 2024-10, Vol.90 (2), p.31, Article 31
Main Authors: Sánchez de la Vega, Constanza, Borgna, Juan Pablo, Rial, Diego
Format: Article
Language:English
Subjects:
Applied mathematics
Bias
Calculus of Variations and Optimal Control
Optimization
Control
Control systems
Electric fields
Laser beams
Lasers
Liquid crystals
Mathematical and Computational Physics
Mathematical functions
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Nematic crystals
Numerical and Computational Physics
Optimal control
Optimization
Parameter modification
Simulation
Solitary waves
Systems Theory
Theoretical
Well posed problems
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Summary:We study an optimal control problem for a coupled Schrödinger-elliptic evolution system that describes the propagation of a laser beam in nematic liquid crystals. We consider a bilinear control related to an electric field depending on the optical axis acting on the sample. This problem arises from the study of an optimal way to transform the input signal into a target signal by modifying a system parameter related to the bias electric field. We prove well-posedness, existence and first order necessary conditions for an optimal solution.
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-024-10173-y