Effect of free carriers on pump-to-signal noise transfer in silicon Raman amplifiers

Abstract

We study noise transfer from pump to signal in silicon Raman amplifiers, with particular emphasis on the regimes of strong cumulative free-carrier absorption and heavy pump depletion. We calculate the relative intensity noise (RIN) transfers in copumped and counterpumped amplifiers and provide intuitive explanations for RIN peculiarities. We show that noise transfer at low frequencies may be suppressed by carefully choosing the pump intensity, effective free-carrier lifetime, or amplifier length, but only at the expense of a rise in noise at high frequencies. © 2010 Optical Society of America OCIS codes: 190.4360, 230.0230, 230.4480, 250.4390. Despite several experimental demonstrations of net Raman gain in silicon-on-insulator (SOI) waveguides [1][2][3], the problem of efficient Raman amplification in silicon is far from being fully solved. The main reason for this is the need to minimize nonlinear optical losses, caused by two-photon absorption (TPA) and free-carrier absorption (FCA), while avoiding excessive signal noise. The noise performance is especially important for silicon Raman amplifiers (SRAs), because they operate at high pump powers that result in enhanced transfer of the relative intensity noise (RIN) from pump to the signal. Unlike the challenge of nonlinear losses, which has been much investigated in recent years [4][5][6], the physics of RIN transfer in SRAs is poorly understood. The results of a few recent theoretical studies on this phenomenon [7,8] are not widely applicable, for they are based on strong simplifying assumptions, which may not be met in practice. Specifically, in order to estimate the impact of RIN transfer on the noise figure in SRAs, Sang et al.[7] assumed instantaneous FCA and employed the undepleted-pump approximation. While the first assumption is valid for low-frequency noise components, the second holds only when the signal power remains much smaller than the pump power all along the amplifier. In our recent work [8], we abandoned the undepleted-pump approximation and analytically calculated the low-frequency RIN in copumped SRAs. Although the results allowed us to qualitatively predict the possibility of zero noise transfer under certain conditions, a precise quantitative assessment of this phenomenon is still required. In this Letter, we present a general study of the RIN-transfer problem in SRAs. In our work, we consider both the depletion of the pump and the cumulative nature of FCA, draw an intuitive picture of the physics behind the noise transfer, and present guidelines for RIN minimization.The starting point for our study is the set of partial differential equations that describe the interaction of two cw fields (pump and signal) propagating through an SOI waveguide of constant cross section. These equations relate the pump intensity I p ðz; tÞ, the signal intensity I s ðz; tÞ, and the density Nðz; tÞ of free carriers as [8,9]

Engineering optical nonlinearities in silicon–nanocrystal waveguides

“…Without loss of generality, we consider a 1.434 μm pump amplifying a signal at 1.55 μm, so that the pump-signal frequency detuning is exactly equal to the Raman shift in silicon of 15.6 THz [20,28,29,34]. Figure 3(a) shows how the corresponding four mode overlap factors (calculated using COM-SOL Multiphysics 4.3b) vary with waveguide width for h 100 nm.…”

“…Our theory employs an analytic expression for the effective third-order susceptibility of a silicon-nanocrystal composite derived using the effective medium approximation and assuming an arbitrary orientation of the nanocrystals in space [1]. Much like the common models of nonlinear optical phenomena developed for silicon [20,[24][25][26][27][28][29][30][31][32][33][34], our theory predicts that the efficiency of nonlinear effects due to the evolution of optical fields inside a silicon-nanocrystal waveguide critically depends on the overlap factors and effective refractive indices of the interacting modes, which, in turn, are the functions of the composition and geometric parameters of the waveguide.…”

Maximization of Gain in Slow-Light Silicon Raman Amplifiers

“…The examples below illustrate the peculiarities of SRA optimization in the regime of heavy pump depletion, in which signal gain is calculated numerically from (1). Figure 2 shows the contour plots of the net signal gain in an 8 mm long SRA for I p0 = 30 MW/cm 2 and I s0 = 0.1 MW/cm 2 ; the depletion [37] of the pump beam at the amplifier output equals 76%. It is seen that the maximum gain of approximately 17.7 dB is achieved for the slow-down factors S s ≈ 7.8 and S p ≈ 3.4.…”

Analytical study of pulse amplification in silicon Raman amplifiers

“…In other words, even though the dynamics of a signal pulse inside a SRA differ for the forward-and backward-pumping configurations, the output signal pulse profiles do not. The backward-pumping geometry is preferable though, as it enables better noise performance by lowering noise transfer from the pump to the signal [48]. Second, Eq.…”