Design of an ultrafast all-optical differentiator based on a fiber Bragg grating in transmission

Abstract

We propose and analyze a first-order optical differentiator based on a fiber Bragg grating (FBG) in transmission. It is shown in the examples that a simple uniform-period FBG in a very strong coupling regime (maximum reflectivity very close to 100%) can perform close to ideal temporal differentiation of the complex envelope of an arbitrary-input optical signal.

Experimental demonstration of an optical differentiator based on a fiber Bragg grating in transmission

“…However, the FBG approaches proposed in [9-12] inevitably require one or more additional optical elements, such as an optical circulator, coupler, or additional fiber grating to obtain a first-order differentiator. An extremely simple, single optical-element FBG approach was proposed in [13] for first-order differentiation. It is well-known that the amplitude and phase of an FBG in transmission are related by the logarithmic Hilbert transform relation [14].…”

“…It is well-known that the amplitude and phase of an FBG in transmission are related by the logarithmic Hilbert transform relation [14]. Using this relationship in the design process, it was theoretically and numerically demonstrated that a single FBG in transmission can be designed to simultaneously approach the amplitude and phase of a first-order differentiator spectral response, without the need for any additional elements.In this Letter, we design, numerically simulate, and fabricate a first-order optical differentiator based on an FBG in transmission, using the ideas introduced in [13]. To prove the concept, we characterized the FBG with an optical vector analyzer, and performed an experiment of optical pulse differentiation where the signals were characterized using an optical spectrum analyser (OSA) and a second harmonic generation (SHG) frequency resolved optical gating (FROG) system [15].…”

“…They perform a temporal differentiation of the complex field envelop (both amplitude and phase) of an arbitrary optical input signal at operation speeds several orders of magnitude higher than is possible using electronics. Many different schemes have been previously proposed [6][7][8][9][10][11][12][13]. Overall, fiber grating approaches [8][9][10][11][12][13], both fiber Bragg grating (FBG) and long period grating (LPG), are simple all-fiber approaches with interesting advantages, such as low cost, low insertion losses, and full compatibility with fiber optic systems.…”

“…Many different schemes have been previously proposed [6][7][8][9][10][11][12][13]. Overall, fiber grating approaches [8][9][10][11][12][13], both fiber Bragg grating (FBG) and long period grating (LPG), are simple all-fiber approaches with interesting advantages, such as low cost, low insertion losses, and full compatibility with fiber optic systems. Although the LPG approach proposed in [9] have been proved to have a good performance in a regime of huge bandwidths (up to 19 nm), FBGs may be preferred in applications with a bandwidth up to a few nm, because of the extreme sensitivity of LPGs to environmental fluctuations [9].…”

“…An extremely simple, single optical-element FBG approach was proposed in [13] for first-order differentiation. It is well-known that the amplitude and phase of an FBG in transmission are related by the logarithmic Hilbert transform relation [14].…”