Abstract
In exact analogy with their electronic counterparts, photonic temporal integrators are fundamental building blocks for constructing all-optical circuits for ultrafast information processing and computing. In this work, we introduce a simple and general approach for realizing all-optical arbitrary-order temporal integrators. We demonstrate that the N(th) cumulative time integral of the complex field envelope of an input optical waveform can be obtained by simply propagating this waveform through a single uniform fiber/waveguide Bragg grating (BG) incorporating N pi-phase shifts along its axial profile. We derive here the design specifications of photonic integrators based on multiple-phase-shifted BGs. We show that the phase shifts in the BG structure can be arbitrarily located along the grating length provided that each uniform grating section (sections separated by the phase shifts) is sufficiently long so that its associated peak reflectivity reaches nearly 100%. The resulting designs are demonstrated by numerical simulations assuming all-fiber implementations. Our simulations show that the proposed approach can provide optical operation bandwidths in the tens-of-GHz regime using readily feasible photo-induced fiber BG structures.
Highlights
The cumulative time integral of a given waveform is a fundamental signal processing functionality with a wide range of potential applications, e.g. in communications, information processing and computing
We demonstrate that an Nth-order temporal integrator can be realized using a design based on a single-unit uniform Bragg grating (BG) incorporating N π-phase-shifts along its grating profile, i.e. multiple-phase-shifted BG (MPS-BG)
In contrast to the original design proposed in [3], we show that the required π phase-shift in a first-order integrator does not have to be necessarily located at the middle of the uniform grating; we show that the required π phase-shift may be located at any arbitrary position along the grating profile provided that each uniform grating section in the BG structure is sufficiently long so that the peak reflectivity associated with each of these uniform sections reaches nearly 100%
Summary
The cumulative time integral of a given waveform is a fundamental signal processing functionality with a wide range of potential applications, e.g. in communications, information processing and computing. These detrimental FP effects are pronounced due to the required high reflectivity of the uniform gratings in the concatenated π-phase-shifted BGs [3], which effectively behaves like bandwidth-limited strong-reflection mirrors These difficulties could be avoided by use of optical isolators between the concatenated BG integrators; this would translate into an increased complexity, longer devices, and a higher cost. In this manuscript, we demonstrate that an Nth-order temporal integrator can be realized using a design based on a single-unit uniform BG incorporating N π-phase-shifts along its grating profile, i.e. multiple-phase-shifted BG (MPS-BG). The resulting grating profiles are remarkably simple and could be readily realized with present technologies (e.g. using photoinduced phase-shifted fiber BGs [8], [10])
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