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Fractional Fourier transform for partially coherent Gaussian-Schell model beams
Optics Letters
|November 23, 2007
Summary
This study introduces a new formula for the fractional Fourier transform (FRT) of partially coherent twisted anisotropic Gaussian-Schell model (GSM) beams. The findings offer a powerful tool for analyzing beam transformations in optical systems.
Area of Science:
- Optics and Photonics
- Wave Phenomena
- Mathematical Physics
Background:
- Partially coherent beams exhibit complex spatial correlations.
- Gaussian-Schell model (GSM) beams are widely used to model partially coherent light.
- Anisotropic and twisted beam structures introduce additional complexities in propagation.
Purpose of the Study:
- To derive an analytical formula for the cross-spectral density of partially coherent twisted anisotropic GSM beams after a fractional Fourier transform (FRT).
- To establish a tensor ABCD law for FRT systems applied to these beams.
- To explore the relationship between the derived FRT formula and the generalized Collins formula.
Main Methods:
- Application of the fractional Fourier transform (FRT) directly to the cross-spectral density.
- Utilizing the tensor method for deriving propagation formulas.
- Analysis of beam characteristics in the FRT system.
Main Results:
- An analytical and concise formula for the cross-spectral density of partially coherent twisted anisotropic GSM beams undergoing FRT was derived.
- A tensor ABCD law specific to FRT was obtained.
- The connection between the FRT formula and the generalized Collins formula was discussed.
Conclusions:
- The derived formulas provide a robust analytical tool for calculating and analyzing the FRT of partially coherent beams.
- This work simplifies the understanding of how complex partially coherent beams transform under FRT.
- The results are significant for applications involving beam shaping and propagation in optical systems.
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