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Fractional Fourier transform for quasi-periodic Bloch functions.

C C Chong1, A Vourdas, C Bendjaballah

  • 1Department of Electrical Engineering and Electronics, The University of Liverpool, UK.

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|October 5, 2001
PubMed
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This study extends the fractional Fourier transform (FRFT) to quasi-periodic Bloch functions. The research establishes an isomorphism to apply FRFT properties and presents numerical examples for this novel application.

Area of Science:

  • Mathematical Physics
  • Quantum Mechanics
  • Signal Processing

Background:

  • The fractional Fourier transform (FRFT) is a generalization of the traditional Fourier transform.
  • Quasi-periodic Bloch functions are crucial in solid-state physics for describing electron behavior in crystals.

Purpose of the Study:

  • To investigate and extend the fractional Fourier transform (FRFT) to the domain of quasi-periodic Bloch functions.
  • To establish a mathematical framework for applying FRFT properties to these specialized functions.

Main Methods:

  • Utilizing an isomorphism between square-integrable functions and quasi-periodic Bloch functions.
  • Extending established FRFT methodologies from real line functions to quasi-periodic Bloch functions.

Related Experiment Videos

Main Results:

  • Successfully extended the fractional Fourier transform (FRFT) to quasi-periodic Bloch functions.
  • Characterized the fundamental properties of the FRFT within this new function space.
  • Demonstrated the applicability through various numerical examples.

Conclusions:

  • The fractional Fourier transform (FRFT) can be effectively applied to quasi-periodic Bloch functions.
  • This extension opens new avenues for analyzing complex periodic systems using FRFT techniques.