1190 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 25, NO. 5, MAY2007 Dispersion-Compensating Fiber Raman Amplifiers With Step, Parabolic, and Triangular Refractive Index Profiles Andrew Che On Chan and Malin Premaratne, Senior Member, IEEE Abstract—This paper presents a comprehensive analysis of the performance of a gain-flattened coaxial fiber Raman amplifier with respect to the refractive index profile. The variation of the dispersion coefficient and the end–end gain spectrum of the coaxial fiber Raman amplifier against the core structure as a function of the step, parabolic, and triangular profiles are analyzed. The analysis shows that the dispersion coefficient is sensitive to the variation of the core structure of the fiber, whereas the effective Raman gain coefficient remains nearly constant as the structure changes. Simulations of transmissions employing the coaxial fiber Raman amplifier with the three different structures are carried out individually, and the results show that the parabolic and trian- gular profiles perform better than the step profile, where the par- abolic profile gives the best performance over 80 km of G.652 fiber, with a transmission rate of 20 Gb/s and a gain ripple of ±1 dB. In addition, the analysis shows that the maximum negative disper- sion wavelength of the fiber exhibits a linear relationship with the normalized core radius. Hence, a coaxial fiber Raman amplifier providing a possible operation over the L-band is proposed. Index Terms—Dispersion compensation, gain flattening, Raman amplifiers, refractive index profile (RIP). I. I NTRODUCTION W AVELENGTH division multiplexing technology offers a cost-effective way to increase the transmission capac- ity by transmitting closely spaced multiple wavelength channels over a single fiber [1]. However, the number of wavelength channels that can be launched into the transmission systems is limited by the bandwidth (30 nm between 1530–1560 nm) of the erbium-doped fiber amplifiers employed to compensate for the fiber loss. Therefore, widening the gain bandwidth of the amplifier is a reasonable way to partially resolve the problem of limited transmission capacity [2]–[6]. Raman amplifiers have been studied extensively to provide a widened and flattened gain bandwidth over the commonly used transmission windows. They have the ability to provide a gain of over 40 THz bandwidth. Even though a single pump- based Raman amplifier bandwidth reaches its peak at around 13.2 THz away from the pump frequency, properly positioned multiple pumps can be used to get a flattened broadband gain. For example, Miyamoto et al. [7] reported a gain-flattened Manuscript received October 23, 2006; revised January 19, 2007. The authors are with the Advanced Computing and Simulation Labora- tory (AXL), Department of Electrical and Computer System Engineering, Monash University, Clayton, 3800 VIC Australia (e-mail: andrew.chan@ eng.monash.edu.au; malin@ieee.org). Digital Object Identifier 10.1109/JLT.2007.893033 TABLE I ALLOWABLE ACCUMULATED DISPERSION OF VARIOUS DATA RATES discrete Raman amplifier consists of two forward and five backward pumps with a 3-dB bandwidth of 100 nm. However, it is a difficult and nontrivial task to configure pump wavelengths and powers in flattening the gain bandwidth. By using a unique coaxial fiber design, Thyagarajan and Kakkar [8] reported a single pump-based gain-flattened Raman amplifier with a gain spectrum spanning over 90 nm. Within the operating wavelength region, their coaxial fiber was designed in such a way that both the Raman gain coefficient g R and the effective area A eff change in a manner in which their ratio is not changed. Because the effective Raman gain is determined as the ratio of g R to A eff , this design will render a flattened effective Raman gain spectrum (i.e., end–end gain spectrum) within the operating wavelength region. Moreover, their coaxial fiber design has the ability to provide a dispersion coefficient in the range -300–-600 ps/nm/km, thus providing the ability to compensate the accumulated dispersion without the additional dispersion-compensating modules. Based on the above design, a subsequent study in [9] reported an S-band gain-flattened Raman amplifier with the ability to compensate dispersion in a 10-Gb/s system with five 80-km spans. Table I lists the allowable accumulated dispersion limit that a receiver can tol- erate at various data rates [10], [11]. However, the transmission possibility of the coaxial fiber having a parabolic or triangular core structure rather than a simple step core structure has not yet been considered. In this paper, the performance of a gain-flattened coaxial fiber Raman amplifier as a function of the refractive index profile (RIP) parameters is investigated in detail. Based on the findings of this analysis, the simulation study of a transmis- sion over 80 km of G.652 fiber shows that a parabolic core coaxial fiber Raman amplifier achieved the best performance at 20 Gb/s, with a gain ripple of ±1 dB. Our analysis indicates that a maximum negative dispersion wavelength exhibits a linear relationship with the normalized core radius. We exploited this relationship to design an L-band coaxial fiber Raman amplifier with a superior performance. 0733-8724/$25.00 © 2007 IEEE