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Fractional order integration using a fiber Fabry-Pérot interferometer.

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Title: Fractional order integration using a fiber Fabry-Pérot interferometer.
Authors: Tendela, Lucas1,2 (AUTHOR) tendela@ifir-conicet.gov.ar, Cuadrado-Laborde, Christian1 (AUTHOR), Cruz, José Luis3 (AUTHOR), Chen, Xianfeng4 (AUTHOR), Andrés, Miguel V.3 (AUTHOR) miguel.andres@uv.es
Source: Optical & Quantum Electronics. Apr2026, Vol. 58 Issue 4, p1-20. 20p.
Subjects: Fractional integrals, Fabry-Perot interferometers, Photonics, Transfer matrix, Optical information processing, Fiber Bragg gratings, Light filters
Abstract: The theoretical, numerical, and experimental demonstration of optical fraction-al-order integration is presented using a Fabry-Pérot interferometer made up of two fiber Bragg gratings. A spectral filtering behavior consistent with fractional-order integration is demonstrated by modeling the interferometer using the transfer matrix method and de-riving analytical expressions. It is shown that, under appropriate design conditions, the output light pulse corresponds to the mathematical result of applying a fractional integration operator to the input light pulse. This behavior is confirmed through numerical simulations and validated experimentally by fabricating a customized Fabry-Pérot interferometer, in which two fiber Bragg gratings are recorded in a photosensitive optical fiber. Analytical expressions relating the integration order to the reflectivity of a fiber Bragg grating are also derived, together with an analysis of the bandwidths that this optical de-vice can process. To the best of our knowledge, this is the first experimental demonstration of all-fiber fractional-order integration. The transmission of the fiber interferometer is experimentally characterized. Its performance as a photonic fractional integrator is demonstrated using light pulses as input. The results indicate that fractional-order operators can be implemented in an all-optical manner using fiber-optic technology. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract:The theoretical, numerical, and experimental demonstration of optical fraction-al-order integration is presented using a Fabry-Pérot interferometer made up of two fiber Bragg gratings. A spectral filtering behavior consistent with fractional-order integration is demonstrated by modeling the interferometer using the transfer matrix method and de-riving analytical expressions. It is shown that, under appropriate design conditions, the output light pulse corresponds to the mathematical result of applying a fractional integration operator to the input light pulse. This behavior is confirmed through numerical simulations and validated experimentally by fabricating a customized Fabry-Pérot interferometer, in which two fiber Bragg gratings are recorded in a photosensitive optical fiber. Analytical expressions relating the integration order to the reflectivity of a fiber Bragg grating are also derived, together with an analysis of the bandwidths that this optical de-vice can process. To the best of our knowledge, this is the first experimental demonstration of all-fiber fractional-order integration. The transmission of the fiber interferometer is experimentally characterized. Its performance as a photonic fractional integrator is demonstrated using light pulses as input. The results indicate that fractional-order operators can be implemented in an all-optical manner using fiber-optic technology. [ABSTRACT FROM AUTHOR]
ISSN:03068919
DOI:10.1007/s11082-026-08722-6