Analysis of laser radiation using the Nonlinear Fourier transform

Area of Science:

• Nonlinear dynamics
• Laser physics
• Optical signal processing

Background:

• Modern lasers display complex nonlinear dynamics, involving both dispersive waves and coherent structures.
• Classical Fourier methods are insufficient for analyzing time-localized or non-stationary laser signals.
• Developing methods for simultaneous characterization of localized and extended fields is crucial.

Purpose of the Study:

• To demonstrate the application of the Nonlinear Fourier Transform (NFT) for analyzing laser dynamics.
• To utilize the Zakharov-Shabat spectral problem for signal processing of coherent structures in dispersive radiation.
• To establish NFT as a viable tool for laser signal analysis.

Main Methods:

• Employed the Nonlinear Fourier Transform (NFT) based on the Zakharov-Shabat spectral problem.
• Utilized full-field, real-time experimental measurements of mode-locked laser pulses.
• Computed nonlinear pulse spectra and introduced eigenvalue probability distributions for regime classification.

Main Results:

• Successfully applied NFT to represent and analyze coherent structures within dispersive laser radiation.
• Demonstrated the computation of nonlinear pulse spectra from experimental data.
• Presented two field normalization approaches for effective laser radiation modeling using NFT.

Conclusions:

• The Nonlinear Fourier Transform (NFT) provides a powerful signal processing tool for complex laser dynamics.
• NFT enables simultaneous characterization of localized and extended fields in laser radiation.
• Appropriate signal normalization allows NFT to effectively model laser output.