Optical pulse differentiation based on a resonant slow & fast light system

Abstract

We experimentally demonstrate that temporal differentiation of optical pulses can be realized in a slow & fast light system based on a resonance. The waveform of a 13 ns Gaussian pulse was experimentally first-order differentiated.OCIS codes: (060.4370) Nonlinear optics, fibers; (290.5900) Scattering, stimulated Brillouin; (070.6020) Signal processing Development of basic mathematical operations in all-optical signal processing circuits -such as differentiators, integrators and logic gates -is attracting an increasing interest in the optical community, since they are key functions required for all-optical computing and networks. All-optical temporal differentiators and integrators have been experimentally realized in optical fibers, based on a single uniform long-period fiber grating (LPG) and a phaseshifted fiber Bragg grating. In this paper, we propose a new technique that can provide a first-order derivative of an arbitrary optical waveform, using a resonance-based slow & fast light system. Sharp spectral resonances can generate a strong dispersion leading to a substantial change of the effective group velocity at the center of the resonance. Neglecting the higher order dispersion terms, the spectral distribution of the pulse exiting from such a system E out (ω) is well approximated by [1]:where e G is the net signal power gain, ω o is the central frequency of the resonance, Γ B is the resonance FWHM width and E in (ω) is the pulse input spectrum. According to the Fourier transform properties, it can be simply anticipated that the output pulse will be temporal shifted by an amount of G/Γ B and the effective delay can be tuned by varying G, which is essentially the principle of resonance-based slow & fast light. For small frequency detunings ω−ω o , the phase shifts satisfies the condition G/Γ B (ω−ω o ) ‹‹ 1 and the transfer function can be further simplified as:It is interesting to point out that the second term in the transfer function is the required spectral response for a firstorder differentiator and the output signal in the time domain can be simply expressed by this sum.The output signal is formed by the sum of the input signal plus its derivative weighted by the gain factor. For large gains the derivative term can be strongly dominant and leads to a simple visual interpretation of the delay/advancement effect and of the signal temporal shapes, as illustrated by the experimental traces shown in Fig. 1 for a fast light system. The sign of the derivative is simply reversed for a slow light system. + + + Fig. 1. Time traces of an optical pulse exiting from a Brillouin fast light system for different pump powers (black line represents the input pulse). The insert depicts the sum given by Equ.3 to interpret the experimental traces squared (thus rectified) by the power-dependent photodetection.

An ultra-high-speed photonic temporal differentiator using cascaded SOI microring resonators

“…Now we discuss another phenomenon in our experimental results, that is, the two lobes of the differential signals are sometimes asymmetric to the left but sometimes to the right. In fact, when the microring deviates from the critical coupling state, the output pulse is formed by the vector sum of an ideal differential signal plus an input signal weighted by some factor [3,20]. If the factor is a positive number, which corresponds to under-coupling of the resonator, the left lobes will be larger than the right ones.…”

“…It is interesting to point out that there is a phenomenon of nonreturn-to-zero in the middle of the two lobes of the differentiated results, which is particularly obvious in the 10 Gbit s −1 result. In fact, a microring has a slow or fast light function; according to [20], the output signal from a microring-based device can be attributed to the sum of the input signal and the derivative weighted by a gain (or loss) factor. While the detuning between the operation wavelength of the pulse laser and the center wavelength of the resonance becomes larger, the slow light effect may be decreased so that the input weight becomes larger.…”