We propose a low-cost
INTRODUCTIONCoarse wavelength division multiplexing (CWDM) [1] is an attractive solution for medium capacity communication systems. CWDM technology is less complex than DWDM (dense wavelength division multiplexing) [2] technology, therefore less expensive. CWDM systems are widely deployed in metro networks. Optical channels in CWDM systems are 20 nm apart, therefore a 4-channels CWDM system requires approximately 80 nm of optical bandwidth. If a CWDM system requires amplification, conventional Erbium doped fiber amplifiers cannot be used due to their limited bandwidth, typically less than 40 nm. Consequently, a broadband low-cost amplification system is needed in order to allow the upgrade of CWDM systems to higher bit rates or to extend its reach. In this article, we show that Raman amplification can indeed provide low-cost optical gain over a large bandwidth, and therefore can be a suitable solution for CWDM systems. One of the characteristics of the Raman gain is its flexibility to enlarge the gain bandwidth using multiple pumps [3][4][5][6]. It was demonstrated that with multiple pumps a Raman amplifier can provide gain over more than 100 nm [3, 4]. This flexibility can also allow future upgrades of the systems by extending the bandwidth as needed.The main purpose of this work is to prove that Raman amplification is a suitable solution for CWDM systems. We also present and validate a simple mathematical model that can be used in the design, analyze and optimization of Raman amplification systems.This work is organized in the following way. Initially we present the theoretical model, after we validate the model using experimental results, subsequently the model is used to design an amplifier for a CWDM system. Finally, in the last section we discuss the results and present the main conclusions.
MATHEMATICAL MODELTo model a Raman amplification system the interactions between all optical signals presented in the fiber must be considered. These signals can be optical channels, containing data, or just pump signals, used to provide Raman gain. The mathematical model used in this work comprises a set of coupled differential equations to model these interactions [7],where the signal "ϩ" and "Ϫ", in the left-hand side of expression (1), accounts for forward and backward propagation, respectively. The symbol N accounts for the total number of interacting signals in the fiber, P j (z) and P k (z) are the optical powers of the jth and kth signal at position z, respectively, ␣ is the attenuation coefficient, and g kj is related to the Raman gain coefficient bywhere A eff is the fiber effective area [8], and g R ( m Ϫ n ) is the Raman gain coefficient. The coefficient g R ( m Ϫ n ) is a function that has as argument the difference between the frequencies m and n , of the mth and nth signal, respectively. There are different possible ways of obtaining g R ( m Ϫ n ), one is from the theoretical impulse response of the fiber [9] and another option is by measuring g R ( m Ϫ n ) directly. We t...