Nonlinear Fourier transform for characterization of the coherent structures in optical microresonators

2020 ◽  
Vol 45 (11) ◽  
pp. 3059
Author(s):  
Sergei K. Turitsyn ◽  
Igor S. Chekhovskoy ◽  
Mikhail P. Fedoruk
Keyword(s):  
Fourier Transform ◽  
Coherent Structures ◽  
Optical Microresonators ◽  
Nonlinear Fourier Transform

scholarly journals Characterization of coherent structures in dissipative systems using nonlinear Fourier transform

2020 ◽  
Author(s):  
Igor Chekhovskoy ◽  
Olga Shtyrina ◽  
Mikhail P. Fedoruk ◽  
Sergey Medvedev ◽  
Sergei Turitsyn
Keyword(s):  
Fourier Transform ◽  
Coherent Structures ◽  
Dissipative Systems ◽  
Nonlinear Fourier Transform

scholarly journals Nonlinear Fourier Transform for Analysis of Coherent Structures in Dissipative Systems

2019 ◽  
Vol 122 (15) ◽  
Author(s):  
I. S. Chekhovskoy ◽  
O. V. Shtyrina ◽  
M. P. Fedoruk ◽  
S. B. Medvedev ◽  
S. K. Turitsyn
Keyword(s):  
Fourier Transform ◽  
Coherent Structures ◽  
Dissipative Systems ◽  
Nonlinear Fourier Transform

scholarly journals Analysis of laser radiation using the Nonlinear Fourier transform

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Srikanth Sugavanam ◽  
Morteza Kamalian Kopae ◽  
Junsong Peng ◽  
Jaroslaw E. Prilepsky ◽  
Sergei K. Turitsyn
Keyword(s):  
Fourier Transform ◽  
Laser Radiation ◽  
Coherent Structures ◽  
Probability Distributions ◽  
Fourier Method ◽  
Mathematical Methods ◽  
Dispersive Waves ◽  
Full Field ◽  
Rich Diversity ◽  
Nonlinear Fourier Transform

AbstractModern high-power lasers exhibit a rich diversity of nonlinear dynamics, often featuring nontrivial co-existence of linear dispersive waves and coherent structures. While the classical Fourier method adequately describes extended dispersive waves, the analysis of time-localised and/or non-stationary signals call for more nuanced approaches. Yet, mathematical methods that can be used for simultaneous characterisation of localized and extended fields are not yet well developed. Here, we demonstrate how the Nonlinear Fourier transform (NFT) based on the Zakharov-Shabat spectral problem can be applied as a signal processing tool for representation and analysis of coherent structures embedded into dispersive radiation. We use full-field, real-time experimental measurements of mode-locked pulses to compute the nonlinear pulse spectra. For the classification of lasing regimes, we present the concept of eigenvalue probability distributions. We present two field normalisation approaches, and show the NFT can yield an effective model of the laser radiation under appropriate signal normalisation conditions.

Infrared Spectroscopy Characterization of Marine Shells

2001 ◽  
Vol 711 ◽  
Author(s):  
Octavio Gomez-Martinez ◽  
Daniel H. Aguilar ◽  
Patricia Quintana ◽  
Juan J. Alvarado-Gil ◽  
Dalila Aldana ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Infrared Spectroscopy ◽  
Crassostrea Virginica ◽  
Thermal Treatments ◽  
Vibration Modes ◽  
Lattice Vibrations ◽  
Vibration Frequencies ◽  
Mussel Shells ◽  
Carbonate Lattice

ABSTRACTFourier Transform infrared spectroscopy has been employed to study the shells of two kind of mollusks, American oysters (Crassostrea virginica) and mussels (Ischadium recurvum). It is shown that it is possible to distinguish the different calcium carbonate lattice vibrations in each case, mussel shells present aragonite vibration frequencies, and the oyster shells present those corresponding to calcite. The superposition, shift and broadening of the infrared bands are discussed. Changes in the vibration modes due to successive thermal treatments are also reported.

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