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Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping
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In-fiber all-optical fractional differentiator.

C Cuadrado-Laborde1, M V Andrés

  • 1Departamento de Física Aplicada y Electromagnetismo, Institut Universitari de Ciència dels Materials, Universidad de Valencia, Valencia, Spain. claborde@ciop.unlp.edu.ar

Optics Letters
|March 14, 2009
PubMed
Summary

We developed an all-optical fractional differentiator using an asymmetrical pi phase-shifted fiber Bragg grating. This device accurately calculates fractional time derivatives of optical waveforms, offering a novel approach in optical signal processing.

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Area of Science:

  • Photonics and Optical Engineering
  • Nonlinear Optics
  • Fiber Optics

Background:

  • Fractional calculus extends traditional calculus, enabling modeling of complex systems.
  • All-optical signal processing offers high speed and bandwidth advantages over electronic methods.
  • Fiber Bragg gratings (FBGs) are versatile components in optical systems.

Purpose of the Study:

  • To demonstrate an all-optical fractional differentiator.
  • To investigate the use of asymmetrical pi phase-shifted fiber Bragg gratings for this purpose.
  • To develop analytical expressions for relating differentiator order to grating parameters.

Main Methods:

  • Designing and simulating an asymmetrical pi phase-shifted fiber Bragg grating.
  • Utilizing the grating's spectral response for differentiation.

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  • Deriving analytical relationships between grating parameters and fractional order.
  • Performing numerical simulations to validate performance with arbitrary optical waveforms.

    • Main Results:

    • An asymmetrical pi phase-shifted FBG was shown to provide the necessary spectral response for an all-optical fractional differentiator.
    • Analytical expressions were derived to link fractional differentiator order with grating design parameters.
    • The device demonstrated high accuracy in calculating fractional time derivatives of complex optical fields.
    • Numerical simulations confirmed the effectiveness of the proposed concept.

    Conclusions:

    • Asymmetrical pi phase-shifted fiber Bragg gratings are suitable for implementing all-optical fractional differentiators.
    • The derived analytical expressions facilitate the design of such devices.
    • This approach offers a promising method for all-optical computation of fractional derivatives.