This paper reviews recent work on the design, experimental implementation, and application of two fundamental all-optical analog signal processing functionalities, namely, photonic temporal differentiation and photonic temporal integration, using customized grating devices directly written in optical fibers.

Ultrafast Analog All-Optical Signal Processors Based on Fiber-Grating Devices

Since the discovery of the Bragg’s law in 1913, Bragg gratings have become important optical devices and have been extensively used in various systems. In particular, the successful inscription of a Bragg grating in a fiber core has significantly boosted its engineering applications. However, a conventional grating device is usually designed for a particular use, which limits general-purpose applications since its index modulation profile is fixed after fabrication. In this article, we propose to implement a fully reconfigurable grating, which is fast and electrically reconfigurable by field programming. The concept is verified by fabricating an integrated grating on a silicon-on-insulator platform, which is employed as a programmable signal processor to perform multiple signal processing functions including temporal differentiation, microwave time delay, and frequency identification. The availability of ultrafast and reconfigurable gratings opens new avenues for programmable optical signal processing at the speed of light.

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A fully reconfigurable waveguide Bragg grating for programmable photonic signal processing

Parabolic pulses in optical fibers have stimulated an increasing number of applications. We review here the physics underlying the generation of such pulses as well as the results obtained in a wide range of experimental configurations.

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Optical Parabolic Pulse Generation and Applications

We show that general-form optical cavities are able to perform the temporal differentiation of optical signals. Analytical relationships to account for the scattering losses for such a cavity’s characteristics are deduced on the basis of temporal coupled-mode theory. A compact nanocavity-aided differentiator based on a ridge photonic crystal waveguide is designed.

Use of photonic crystal cavities for temporal differentiation of optical signals

We report the fabrication of a pi -phase-shifted long-period fiber grating (LPFG) capable of operating as a terahertz-bandwidth second-order temporal differentiator. We demonstrate its operation experimentally by differentiating subpicosecond long optical pulses. A new scheme for achieving high-order photonic temporal differentiation based on LPFG filters is also proposed and demonstrated. In particular, we prepared a LPFG based first-order differentiator that was frequency and bandwidth matched to the second-order device and demonstrated the cascadability of these devices leading to the implementation of a third-order differentiator. By also employing these devices in reflection, up to the fifth-order differentiation is demonstrated experimentally.

Terahertz-bandwidth high-order temporal differentiators based on phase-shifted long-period fiber gratings

We show that long-period fiber grating (LPG) incorporating N−1π-phase shifts can serve as an Nth order temporal differentiator that operates in transmission. Due to the inherent large bandwidth provided by LPGs, subpicosecond (terahertz-bandwidth) optical signals may be processed with centimeters-length devices. Design parameters for up to fifth-order differentiators are given.

Design of terahertz-bandwidth arbitrary-order temporal differentiators based on long-period fiber gratings.

We demonstrate high quality pulse compression at high repetition rates by use of spectral broadening of short parabolic-like pulses in a normally-dispersive highly nonlinear fiber (HNLF) followed by linear dispersion compensation with a conventional SMF-28 fiber. The key contribution of this work is on the use of a simple and efficient long-period fiber grating (LPFG) filter for synthesizing the desired parabolic-like pulses from sech2-like input optical pulses; this all-fiber low-loss filter enables reducing significantly the required input pulse power as compared with the use of previous all-fiber pulse re-shaping solutions (e.g. fiber Bragg gratings). A detailed numerical analysis has been performed in order to optimize the system’s performance, including investigation of the optimal initial pulse shape to be launched into the HNLF fiber. We found that the pulse shape launched into the HNLF is critically important for suppressing the undesired wave breaking in the nonlinear spectral broadening process. The optimal shape is found to be independent on the parameters of normally dispersive HNLFs. In our experiments, 1.5-ps pulses emitted by a 10-GHz mode-locked laser are first reshaped into 3.2-ps parabolic-like pulses using our LPFG-based pulse reshaper. Flat spectrum broadening of the amplified initial parabolic-like pulses has been generated using propagation through a commercially-available HNLF. Pulses of 260 fs duration with satellite peak and pedestal suppression greater than 17 dB have been obtained after the linear dispersion compensation fiber. The generated pulses exhibit a 20-nm wide supercontinuum energy spectrum that has almost a square-like spectral profile with >85% of the pulse energy contained in its FWHM spectral bandwidth.

Nonlinear pulse compression of picosecond parabolic-like pulses synthesized with a long period fiber grating filter

We present a rigorous theoretical and experimental analysis of signal propagation along a long-period fiber grating (LPFG) made in an Erbium-doped amplifying fiber (EDF). First, numerous effects that influence amplifying process in Erbium-doped fibers were considered. These are clustering of Er ions and subsequent upconversion and change of fiber refractive index due to the optical pumping. Subsequently, LPFG-assisted interaction between the amplified fiber core mode and a cladding mode is described combining rate equations that describe propagation through the EDF and coupled-mode equations that describe propagation through the LPFG. While this implementation is relatively straightforward for the signal and pump, it requires particular attention when dealing with spontaneous emission and amplified spontaneous emission (ASE) that are incoherent (described purely by amplitude), but have to diffract on the LPFG (that is amplitude and phase sensitive). This issue is carefully addressed here. As a result, we were able to rigorously describe the propagation of pump, signal, and ASE through the LPFG-amplifying diffractive structure considering effects such as pump depletion, shift of the coupling wavelength due to the pump power, and ASE formation along the structure. Forward pumping (pump copropagating with the signal) and backward pumping (pump counterpropagating to the signal) were both considered. The theoretical analysis was fully verified by carried-out experiments.

Theoretical and Experimental Analysis of Long-Period Fiber Gratings Made Directly Into Er-Doped Active Fibers

An active-fiber-based all-optical first-order temporal differentiator with power efficiency surpassing 100% is demonstrated experimentally. It is based on a long-period fiber grating (LPFG) inscribed into a piece of highly-doped Erbium-doped fiber (EDF). The performed theoretical analysis considers effects like relative position of the LPFG with respect to the input end of the EDF and influence of the input signal power. In the design, parameters like noise characteristics and level of non-linear interaction are taken into account. The advantages of such an implementation over the setup using concatenation of a passive LPFG with an amplifier lies in reducing the unwanted nonlinearities and reducing the amplified spontaneous emission (ASE).

First-order loss-less differentiators using long period gratings made in Er-doped fibers

A novel configuration of all-fiber photonic differentiator optimized for tens-of-gigahertz processing speeds is suggested. This device covers the gap in terms of processing speeds between fiber Bragg grating based differentiator ( 100-200 GHz).

David Krcmarík

Papers

Design of terahertz-bandwidth arbitrary-order temporal differentiators based on long-period fiber gratings.

Nonlinear pulse compression of picosecond parabolic-like pulses synthesized with a long period fiber grating filter

Theoretical and Experimental Analysis of Long-Period Fiber Gratings Made Directly Into Er-Doped Active Fibers

First-order loss-less differentiators using long period gratings made in Er-doped fibers

Fast photonic temporal differentiator based on fiber Mach-Zehnder interferometer