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Optics Express

Analytical study of pulse amplification in silicon Raman amplifiers

Ivan D. Rukhlenko, Malin Premaratne, Ivan L. Garanovich, Andrey A. Sukhorukov, Govind Prasad Agrawal

Published Aug 12, 2010• 10 citations

Abstract

The nonlinear process of stimulated Raman scattering is important for silicon photonics as it enables optical amplification and lasing. To understand the dynamics of silicon Raman amplifiers (SRAs), a numerical approach is generally employed, even though it provides little insight into the contribution of different SRA parameters to the signal amplification process. In this paper, we solve the coupled pump-signal equations analytically under realistic conditions, and derive an exact formula for the envelope of a signal pulse when picosecond optical pulses are amplified inside a SRA pumped by a continuous-wave laser beam. Our solution is valid for an arbitrary pulse shape and fully accounts for the Raman gain-dispersion effects, including temporal broadening and group-velocity reduction (a slow-light effect). It can be applied to any pumping scenario and leads to a simple analytic expression for the maximum optical delay produced by the Raman dispersion in a unidirectionally pumped SRA. We employ our analytical formulation to study the evolution of optical pulses with Gaussian, exponential, and Lorentzian shapes. The ability of a Gaussian pulse to maintain its shape through the amplifier makes it possible to realize soliton-like propagation of chirped Gaussian pulses in SRAs. We obtain analytical expressions for the required linear chirp and temporal width of a soliton-like pulse in terms of the net signal gain and the Raman-dispersion parameter. Our results are useful for optimizing the performance of SRAs and for engineering controllable signal delays.

DOI: 10.1364/oe.18.018324

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The theory of transient stimulated Raman scattering has been extended to include an arbitrary shape of the laser pump pulse. It is shown that the maximum Stokes gain depends on the total energy content per unit area of the pump pulse, and not on the instanteous intensity for an exciting pulse of short duration. The Stokes pulse has a leading edge which rises sharply to a maximum, where the maximum occurs with some delay with respect to the maximum of the pump pulse. The trailing edge follows the decay of the pump. In a nondispersive medium, the gain is not reduced by frequency broadening of the laser output, while in a dispersive medium, considerable gain reduction is expected. Numerical results for various laser-pulse shapes and spectral distributions are presented.

Group-velocity mismatch between the pump and Stokes pulses and the inertia of optical nonlinearity are shown to modify scenarios of slow-light evolution of laser pulses accompanying stimulated Raman and Brillouin scattering (SRS and SBS) of light. In the transient regime of SRS and SBS, the inertia of nonlinear polarization of a medium shifts the peak of an amplified Stokes field envelope relative to the input Stokes pulse. This shift is sensitive to the shape of input laser pulses and is controlled by the SRS and/or SBS gain, the damping time of the optical phonon wave, and the delay time between the input pump and Stokes pulses. In the regime where both the inertia of nonlinear polarization of an SRS medium and group-delay effects are significant, stationary modes of the Stokes field may exist in the frame of reference propagating with the group velocity of the pump field. The maximum group delay attainable for such modes of the Stokes field is limited, similar to the steady-state regime, by the ratio of the steady-state SRS gain to the Raman gain bandwidth.

We experimentally investigated optical pulse propagation through an amplifying ring resonator, in which a semiconductor optical amplifier was used as a loss or gain medium. Initially, the transmission intensity showed resonance dips as a function of laser frequency. These dips were gradually filled and transformed into resonance peaks as the amplification gain increased. A Gaussian-shaped temporal pulse was either advanced by −7.3 ns at low amplification gain or delayed up to 45 ns at high gain. System operation was classified into a complete set of the four regions depending on the gain parameter, and experimental delay times were analyzed based on relevant system dispersion.

We propose and demonstrate the use of narrow band optical parametric amplification for tunable slow and fast light propagation in optical fibers. The parametric gain is coupled to the Raman process which changes the gain value moderately but modifies the gain spectral shape. Consequently, the delay is enhanced at short wavelengths while it is moderated at long wavelengths. The maximum delay and tuning range can be optimized with respect to each other considering saturation effects in long fibers. The proposed scheme offers tunable delay in the presence of gain and with a bandwidth which is sufficiently wide to process digital data streams at tens of Gbit/s rates as well as picoseconds pulses.

Slow and fast light (SFL) in nonlinear media has attracted considerable interest for several years and has been observed in plenty of configurations. It generally requires a sharp spectral resonance which in turn results in a strong change of the group velocity at the resonance, thus leading to optical delaying or advancement. SFL has also been observed in optical fibres by taking advantage of the parametric gain, stimulated Brillouin or Raman scattering, leading to the development of all-optical tunable fiber-based delay lines at telecommunication wavelengths. But the implications of SFL go well beyond pulse delaying or advancement. As the group and phase velocities have to be distinguished one from another in a slow-light medium, this can have other important implications, in particular on the pulse walk-off or on the frequency chirp. We recently demonstrated in a Raman medium with normal dispersion that pulse walk-off between the pump and the signal can be cancelled out despite the large frequency detuning, leading to an increasing interaction length and enhancement Raman conversion efficiency.

Narrowband fiber parametric amplification is known to provide slow and fast light capabilities. Here, an analytical expression of the maximum slow light time delay achievable in ideal, isotropic fibers is derived. Then, the effects of random birefringence on the slow and fast light ability are numerically investigated by integrating the governing equations over a large number of statistical realizations of the fiber. The different polarization rotation along the fiber for the signal, the idler, and the pump reduces the amplifier mean gain and the mean time delay. For small random birefringence, the decrease of the mean delay can be directly imputed to the reduction of the mean gain. For large random birefringence, severe pulse distortion occurs, the mean delay is further reduced and the delay uncertainty highly enhanced. The influence of the stimulated Raman scattering is finally addressed.