JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 26, NO. 7, APRIL 1, 2008 847 Noise Figure of Silicon Raman Amplifiers Dimitrios Dimitropoulos, Daniel R. Solli, Ricardo Claps, Ozdal Boyraz, Member, IEEE, and Bahram Jalali, Fellow, OSA Abstract—The noise figure of silicon Raman amplifiers in the presence of nonlinear losses is calculated. The impact of two- photon absorption (TPA) and free-carrier scattering on the noise figure is quantified using the quantum formulation of the Langevin approach. It is found that TPA-induced free-carrier loss degrades the noise figure by an amount that depends on the carrier lifetime. For example, in a 1-cm-long waveguide pumped at 200 MW/cm , the noise figure is 5.2 dB for a lifetime of ns and is reduced to 3.7 dB for ns. The reduction in the noise figure along with a concomitant increase in Raman gain from 2 to 8 dB suggests that lifetimes on the order of 0.1 ns or less are needed to create a useful silicon Raman amplifier that operates in the con- tinuous-wave mode. It is also shown that in devices that use a p-n junction for carrier sweep-out, the screening of the junction field by generated free carriers results in a sharp increase in the noise figure at high-pump intensities. These results apply to operation in the near-infrared communication wavelengths. For mid-infrared wavelengths above the two photon absorption band-edge (2.3 nm), the absence of TPA and pump-induced free-carrier absorption ensures that the amplifier has a low-noise figure. Index Terms—Amplifier noise, optical noise, silicon, silicon on insulator technology. I. INTRODUCTION T HE recent observations of high Raman gain [1]–[3] in bulk silicon along with demonstrations of Raman lasers [4], [5] have opened up new possibilities for low-cost photonic compo- nents that, in some cases, may be amenable to integration with CMOS electronics. For operation in the technologically impor- tant 1300–1550 nm wavelength range, the main challenge is the nonlinear optical loss that competes with the Raman gain. This loss is caused by absorption from free carriers that are created in the medium because of two-photon absorption (TPA) induced by the high-intensity pump beam (Fig. 1). The free-carrier ab- sorption loss is proportional to the lifetime of the carriers in the amplifying medium. In this paper, we show, for the first time, how the nonlinear losses affect the signal-to-noise ratio of a Raman amplifier. We use the model to determine the minimum noise figure of the silicon Raman amplifier as a function of the carrier lifetime, waveguide losses, and pump intensity. Manuscript received March 13, 2007; revised August 8, 2007. This work was supported by the MTO office of the Defense Advanced Research Project Agency (DARPA). D. Dimitropoulos, D. R. Solli, and B. Jalali are with the Department of Elec- trical Engineering at the University of California, Los Angeles, CA 90095 USA (e-mail: ddimitr@ee.ucla.edu; solli@ucla.edu; jalali@ucla.edu). R. Claps was with the University of California, Los Angeles, CA 90095 USA. He is now with Neptec Optical Solutions, Fremont, CA 94539 USA (e-mail: ricardoc@nepopt.com). O. Boyraz was with the University of California, Los Angeles, CA 90095 USA. He is now with the University of California, Irvine, CA 92697 USA (e-mail: oboyraz@uci.edu). Digital Object Identifier 10.1109/JLT.2007.915211 Fig. 1. Illustration of two-photon absorption and the resulting free carrier ab- sorption when silicon is illuminated with a high-intensity pump beam. II. DERIVATION OF THE NOISE FIGURE A. Propagation Equation for the Stokes Signal In a single-mode silicon waveguide Raman amplifier, the Stokes wave evolves according to the equation (1) where is the photon annihilation operator for the Stokes field and is the position along the length of the waveguide. The operator is normalized according to the commutation relation , where is the creation operator for the Stokes field. The gain parameter is given by , where is the pump intensity and is the Raman gain coeffi- cient. The incident pump wave amplitude is treated as a classical field (c-number) and its propagation is described later (5). The Stokes wave experiences losses determined by the coefficient . The first term characterizes the linear propagation loss, the second term includes loss from two-photon absorption (TPA), and the third term incorporates optical absorption from free-carriers generated from the TPA process. Although the linear loss is independent of the nonlinear terms, the coefficients of the two nonlinear loss terms above are dependent on each other. This connection can be demonstrated by examining the characteristics of the free-carriers created by TPA. The number density of TPA-generated electron-hole (e-h) pairs equals , where is the number of pairs generated per unit time per unit volume, is the photon energy, and is the “effective” lifetime of the pairs. Given the optical absorption cross section of an electron-hole pair, we 0733-8724/$25.00 © 2008 IEEE