Analysis of Mode-Dependent Gain in Raman Amplified Few-Mode Fiber R. Ryf, R.-J. Essiambre, J. von Hoyningen-Huene, P. J. Winzer Bell Laboratories, Alcatel-Lucent, 791 Holmdel-Keyport Rd, Holmdel, NJ, 07733, USA. Roland.Ryf@alcatel-lucent.com Abstract: We present a theory for Raman amplification in few-mode fibers based on the real (non LP) waveguide modes of the fiber. The condition for minimal mode-dependent gain is analyzed and reported for a few-mode fiber supporting 12 polarization- and spatial modes. The results are in agreement with recent experimental demonstrations. OCIS codes: 060.4510, 060.2320, 060.2280, 060.4230. 1. Introduction Recent demonstrations of long-distance transmission over few-mode fiber (FMF) [1, 2] clearly show the potential of mode multiplexing to expand the capacity of a single optical fiber. However extending the benefits of optical amplifi- cation to mode-mixed systems has significant challenges. One notable advantage of mode multiplexing compared to space-division multiplexing using non-overlapping transmission paths [3] is the strong intensity overlap of the mul- tiplexed channels, which enables sharing a single pump mode across multiple signal modes, in similarity to optical amplification in wavelength-division multiplexed (WDM) systems, where a single pump is shared across multiple WDM channels. Optical amplification in multimode fibers has been reported in [4], however no effort to minimize the mode dependent gain (MDG) had been undertaken. Minimizing the MDG for in-line amplification is important because of its direct impact on the achievable mode multiplexed capacity [5]. A scheme to reduce the MDG in a FMF based Erbium doped fiber amplifier (EDFA) has been proposed in [6] and experimentally investigated in [7], and Ra- man amplification in a FMF with low MDG has been reported in [1]. In this work we present a theory for distributed Raman amplification in FMF. In contrast to recent work on FMF-EDFAs [6], our work is based on the real waveguide modes (WGM) of the FMF (and not on the linearly polarized (LP) pseudomodes), which is particularly relevant for the case of distributed Raman amplification. The MDG dependence on the launch configuration of the Raman pumps are then investigated in detail for the case of a FMF supporting 12 polarization- and spatial modes (PSMs). The con- dition for minimum MDG are reported and compared with our recent experimental demonstration [1], confirming the validity of our approach. 2. Raman amplification in multi-mode fiber In Raman amplification [8], the power of a pump laser at λ P = 1455 nm is transferred to a signal wavelength at λ S = 1560 nm. This process is phase insensitive but polarization dependent. The use of a depolarized pump allows to remove the polarization dependency of the gain. In a FMF both pump and signal power can be coupled into any mode supported by the fiber. The signal power S m present in mode m at position z along the fiber is described by dS m dz = −α S S m + γ R  ∑ n f n,m (P + n + P − n )  S m , and (1) dP ± n dz = ∓α P P ± n ∓ λ S λ P γ R  ∑ n f n,m S m  P ± n , (2) where P ± n is the power at the pump wavelength in mode n, P + n and P − n denote co-propagating and counter-propagating pump, respectively, γ R is related to the cross section of spontaneous Raman scattering, and α S and α P are the absorption coefficients at wavelengths λ S and λ P , respectively. The intensity overlap integrals are defined as f n,m = +∞  −∞ I n (x, y)I m (x, y)dxdy +∞  −∞ I n (x, y)dxdy +∞  −∞ I m (x, y)dxdy , (3) here we assume that the wavelength dependence of the mode profile I n (x, y) is negligible. Note that in general the superposition of different modes at the same wavelength will produce a spatial interference pattern commonly referred OFC/NFOEC Technical Digest © 2012 OSA