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Regularized differential evolution for a blind phase retrieval problem in ultrashort laser pulse characterization.

D Gerth¹, E Escoto², G Steinmeyer²

¹Faculty of Mathematics, Chemnitz University of Technology, Chemnitz 09107, Germany.

The Review of Scientific Instruments

|May 3, 2019

Summary

Researchers improved ultrashort laser pulse measurement using a modified Differential Evolution (DE) algorithm. This enhanced method accurately reconstructs temporally varying pulse shapes, determining both average and coherence lengths.

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Area of Science:

Ultrafast Optics and Photonics
Nonlinear Optics
Computational Physics

Background:

Characterizing ultrashort laser pulses is crucial for many scientific applications.
Dispersion scan (d-scan) is a common method, but it involves solving a nonlinear inverse problem.
Measuring temporally varying pulse shapes adds significant complexity to the d-scan method.

Purpose of the Study:

To develop a robust method for measuring the temporal shape of unstable ultrashort laser pulse trains.
To simultaneously infer the average and coherence lengths of laser pulses.
To compare the effectiveness of different regularization techniques for pulse reconstruction.

Main Methods:

Utilized a Differential Evolution (DE) algorithm, a metaheuristic optimization technique.
Modified the standard DE algorithm to retrieve two independent functions for improved accuracy.
Implemented and evaluated three distinct regularization methods to stabilize the inverse problem.

Main Results:

The enhanced DE algorithm successfully reconstructed temporally varying ultrashort laser pulse shapes.
The method allowed for the simultaneous determination of both average pulse length and coherence length.
Spline-based regularization demonstrated superior performance compared to two other investigated methods.

Conclusions:

The modified DE algorithm with regularization is effective for characterizing unstable ultrashort laser pulse trains.
This approach provides a reliable way to measure key pulse parameters, including coherence length.
Spline-based regularization is the recommended approach for this type of nonlinear inverse problem.