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

Abstract

We report the first experimental demonstration of single transmissive fiber Bragg grating implementation of a first-order optical differentiation. The device has been designed and fabricated, and the experimental results show a good performance over an operational bandwidth of ∼2 nm. © 2013 Optical Society of America OCIS codes: 060.3735, 200.4740, 230.1150, 320.5540, 320.7080. Optical differentiators were first proposed by Ngo and Binh [1], and constitute a basic device to analogue alloptical signal processing [2][3][4][5]. 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. 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]. 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]. 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].The spectral response of the ideal first-order differentiator is H diff ω F out ω∕F in ω jω, where ω is the base-band angular pulsation, i.e., ω ω opt − ω 0 , ω opt is the optical angular pulsation, ω 0 is the central angular frequency of the signals, and j is the imaginary unit. This spectral response presents a π-phase shift at ω 0.As it was demonstrated in [13], an FBG in transmission can simultaneously obtain the amplitude and pha...

Fiber Bragg Grating-Based Optical Signal Processing: Review and Survey

“…Several approaches for first-and high-order optical differentiators have been proposed in the literature based on FBGs, providing either different operation bandwidth or spectral resolution, still within the practical limitations of the technology [52][53][54][55][56][57][58][59][60][61][62][63]. First approaches proposed multiple-phase-shifts FBGs operating in reflection for first-and high-order differentiation, but with a limited bandwidth around 20 GHz [54,55].…”

“…First approaches proposed multiple-phase-shifts FBGs operating in reflection for first-and high-order differentiation, but with a limited bandwidth around 20 GHz [54,55]. Afterwards, an alternative design approach based on the use of especially apodized linearly-chirped FBG operated in transmission (following the space-to-frequency-to-time mapping design method) were proposed and experimentally demonstrated increasing the operation bandwidths to a few hundreds of GHz [56,57,60].…”

Reconfigurable photonic temporal differentiator based on a dual-drive Mach-Zehnder modulator

“…Meanwhile, the field differentiator is used to differentiate the optical complex field (including the amplitude and phase) and can be used for pulse reshaping, ultrashort pulse generation, and achieving the odd-symmetric Hermite-Gaussian (OS-HG) pulses [16]. Many approaches have been proposed to realize the field differentiation, such as using the microring resonator [17], apodized fiber Bragg gratings (FBGs) [18][19][20], and long period fiber gratings (LPGs) [21].…”

Compact in-line optical notch filter based on an asymmetric microfiber coupler

“…Fiber gratings based optical differentiators have been widely investigated [12]. However, this device usually needs a special design and requires highly precise control in the fabrication process [13,14]. In 2012, differentiation of 25 THz optical signals based on this ultrawideband notch filter was experimentally demonstrated [6].…”