Advances in OptoElectronics

Volume 2016, Article ID 5843636, 7 pages

http://dx.doi.org/10.1155/2016/5843636

## Noise Gain Features of Fiber Raman Amplifier

Taras Shevchenko National University of Kyiv, 4g, Academician Glushkov Prospect, Kyiv 03022, Ukraine

Received 21 April 2016; Accepted 14 June 2016

Academic Editor: Somenath N. Sarkar

Copyright © 2016 Georgii S. Felinskyi and Mykhailo Y. Dyriv. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The formation dynamics of the optical noise in a silica single mode fiber (SMF) as function of the pump power variation in the counter pumped fiber Raman amplifier (FRA) is experimentally studied. The ratio between the power of amplified spontaneous emission and the power of incoherent optical noise is quantitatively determined by detailed analysis of experimental data in the pump powers range of 100–300 mW within the full band of Stokes frequencies, including FRA working wavelengths over the C + L transparency windows. It is found out the maximum of Raman gain coefficient for optical noise does not exceed ~60% of corresponding peak at the gain profile maximum of coherent signal. It is shown that the real FRA noise figure may be considerably less than 3 dB over a wide wavelength range (100 nm) at a pump power of several hundreds of mW.

#### 1. Introduction

The fiber optic amplifiers based on the effect of stimulated Raman scattering were the first practical devices of nonlinear optics widely used in the high-speed and long distance telecommunication [1, 2].

It is commonly accepted in digital communication systems to use the bit error rate (BER) as a generalized quality parameter to describe the statistical probability of the bit errors occurrence [3]. In the fiber line it is clearly expressed by the optical signal to noise ratio (OSNR) , where and are the optical powers of signal and noise waves, respectively. The OSNR should be changed at the simultaneous gain of the signal and noise optical waves from at FRA input to at amplifier output. of the standard configuration consisting of the optical link and the FRA is a function of [4] and reads as follows:where is the complementary error function and is noise figure of FRA. can significantly change . For example, if dB then and the +1 dB or −1 dB at this OSNR level leads to reduction or increasing by one order of its value.

The phenomenological noise theory [5–7] establishes the lower “quantum limit” of at the level of 3 dB in any optical amplifiers. However, the almost complete absence of FRA effect on the degradation is observed [8] just at the start of FRA application. It is shown in the early 2000s [3, 4, 9] that one can really achieve without any additional methods for error correction in the terabit telecommunication over the distance of many hundred kilometers. Therefore the analysis of reasons for the apparent mismatch between actual noise theory and its application has great practical interest. The additional experimental studies are also required to clarify the FRA noise gain features.

In general, the linear approach to electronic equivalent circuits used in the phenomenological theory is unacceptable to the description of such nonlinear processes as Raman light scattering. Unfortunately this conventional theory results in too much overstated estimations of the FRA own noise because of photon-phonon interaction and nonlinear nature of the stimulated light scattering that are not taken into account. So, we will consider two fundamental reasons of FRA low noise. Firstly, it is the optical noise formation due to spontaneous Raman scattering. Secondly, the stimulated light scattering results to the nonlinear amplification of noise and signal waves exponentially increased with pumping power .

#### 2. Fundamentals of the Spontaneous and Stimulated Light Scattering

The common basis for both signal fiber gain and optical noise amplification is the fundamental physical processes of elastic and inelastic light scattering. Coherent signal wave is effectively amplified in a single mode fiber by stimulated Raman scattering using the relatively small pump power. Backward part of elastic Rayleigh scattering can lead to the signal distortion due to strong interference of delayed signal wave reflections. The main source of amplifier optical noise is initially formed by spontaneous Raman scattering (SRS) from the pump.

Rayleigh scattering cross section and SRS cross section do not depend on their excitation wave intensities. Thus both these effects are referred to as linear optical effects [1, 3, 9]. The absolute value is in comparison to the excitation wave intensity and the corresponding value for SRS is .

Rayleigh scattering is elastic; therefore it resulted in coherent wave with , where and are frequencies of the scattered wave and the pumping wave, respectively. Scattered wave in the Stokes Raman scheme is inelastic and it appears with shifted frequency , where is the phonon frequency, that is, the own vibration frequency of molecules in the fiber core.

Stokes wave at SRS process is not coherent since it is formed involving the thermal phonons with arbitrary phase of vibration frequency . Thus spontaneous Stokes waves are obtained with random phase distribution at the frequency . Therefore, the intensity of Stokes spectrum components at SRS process is directly proportional to phonon population factor (); here that is depended on vibration frequency and temperature .

The stimulated Raman amplification occurred at the same Stokes frequency as SRS. It is independent of the phonon population density. Therefore it is independent of the temperature. Practically, this means that only nonequilibrium phonons affect the stimulated Raman gain. One can assume that that leads to . As a result, the spectral response of stimulated amplification, that is, the Raman gain profile , repeats the SRS spectrum at [1]:where is well known as zero Kelvin cross section.

The spontaneous Raman cross section and Raman gain profile for standard silica fiber are shown in Figure 1. The essential difference between spontaneous Raman spectrum and Raman gain profile according to (2) and the data on Figure 1 should be observed in the frequency region of Stokes shift less than 6 THz = 200 cm^{−1}. In more high-frequency area the thermal density factor of Stokes phonon numbers (>400 cm^{−1}) loses its frequency dependence, practically not differing from unit. Consequently, the spontaneous Raman spectrum coincides with the Raman gain profile.