**5. Raman Soliton Laser**

Nonlinear effects are usually favored when pulsed operation are used, since high peak powers can be achieved with modest average powers. During their propagation inside optical fibers, short optical pulses (less than 10 ps) are affected by combination of chromatic dispersion and by the nonlinear effects [2–4], giving rise to a variety of phenomena, such as supercontinuum generation and soliton formation.

In the simplest situation, a single input pulse at the carrier frequency ω<sup>0</sup> excites a single mode of the fiber. Each spectral component of the input field propagates as a plane wave and acquires a slightly different phase shift because of the frequency dependence of the propagation constant βω. For this reason, it is useful to expand βω in a Taylor series around the carrier frequency ω0, and, depending on the pulse bandwidth, the second-order dispersion term (group velocity dispersion (GVD)) can be considered or third- or higher-order dispersion terms can be included. The GVD parameter (called β2) can be positive or negative with values in the range of 0.1–20 ps2/km, depending on how close the pulse wavelength is to the zero-dispersion wavelength of the fiber. When the dispersive term can be neglected, spectral changes induced by SPM are a direct consequence of the time dependence of nonlinear phase shift. The time dependence of δω is referred to as frequency chirping. The chirp induced by SPM increases in magnitude with the propagated distance. In other words, new frequency components are generated continuously as the pulse propagates down the fiber. The situation changes drastically when both the GVD and SPM are equally important and must be considered simultaneously inside the fiber. In the case of normal dispersion (β<sup>2</sup> > 0), both the pulse shape and spectrum change as the pulse propagates through the fiber and the combined effects of GVD and SPM can be used for pulse compression.

An interesting situation occurs for anomalous dispersion (β<sup>2</sup> < 0), where the generation of optical solitons can be obtained. Solitons are special types of optical wavepackets formed by the balance between nonlinearity (positive SPM) and dispersion (and/or diffraction). This could be surprising, since GVD affects the pulse in the time domain while the SPM effect is in the frequency domain. However, a small time-dependent phase shift added to a Fourier transform-limited pulse does not change the spectrum to first-order. If this phase shift is cancelled by GVD in the same fiber, the pulse does not change its shape or its spectrum as it propagates. In the context of optical fibers, the use of solitons for optical communications was, for the first time, suggested in 1973 [98] and observed in an experiment in 1980 [99]. Temporal solitons have recently been observed in optical fiber waveguides [98–100] in laser resonators [101], and in dielectric microcavities [102]. In each of these cases nonlinear compensation of GVD is provided by the Kerr effect.

Optical communication systems are often limited by fiber dispersion that broadens the pulse and by fiber losses. The use of fundamental solitons as an information bit solves the prolem of dispersion, because in a fiber channel, nonlinear phase modulation can compensate for linear group dispersion leading to pulses that propagate without changing temporal shape and spectrum. This mutual

compensation of dispersion and nonlinear effects takes place continuously with the distance in the case of "classical" solitons and periodically with the so-called dispersion map length in the case of dispersion-managed solitons. Due to the fiber losses, soliton width begins to increase because of a decrease in the peak power during propagation inside the fiber, so amplification is required in order to recover original width and peak power. A proposed scheme makes use of SRS [103–106]. Figure 9 showes the basic idea. Solitons are launched into a fiber link consisting of many segments of length L. At the end of each segment, pump lasers inject CW light, upshifted in frequency from the soliton carrier frequency by about 13 THz, in both directions through wavelength dependent directional couplers. Since the Raman gain is distributed over the entire fiber length, the soliton can be adiabatically amplified.

**Figure 9.** Schematic illustration of a soliton communication system. Solitons are amplified through SRS by injecting continuous wave (CW) pump radiation periodically.

During their propagation in optical fiber, soliton pulses are affected by SRS. The Intrapulse Stimulated Raman Scattering is a phenomenon that appears for short pulses with a relatively wide spectrum, in which Raman gain can amplify the low-frequency components of a pulse by transferring energy from the high-frequency components of the same pulse. As a result, the pulse spectrum shifts continuously toward the red side as the pulse propagates through the fiber [107,108]. This shift, called Raman-induced frequency shift (RIFS), was experimentally observed in 1986 [109], its Raman origin was also pointed out soon after [110], while a more general theory was developed later [7]. With the advent of microstructured fibers, much larger values of the RIFS (>50THz) were observed [111]. The RIFS is useful to generate Raman solitons whose carrier wavelength can be tuned by changing fiber length or input peak power. The effects of intrapulse Raman scattering can be dramatic in the context of solitons, where they lead to new phenomena such as decay and self-frequency shift of solitons.

Besides the Kerr nonlinearity, a secondary effect associated with soliton propagation is caused by Raman interaction. Equations describing SRS can be solved by inverse scattering methods and are found to have solutions. The so called Raman soliton was experimentally observed for the first time in 1983 [112]. When the wavelength of the pump pulse is close to or inside the anomalous dispersion region of an optical fiber, the Raman pulse should experience the soliton effects, i.e., under suitable conditions, almost all of the pump-pulse energy can be transferred to a Raman pulse that propagates undistorted as a fundamental soliton. We note that the soliton pulse is a bright soliton, while the Stokes pulse is a dark soliton and it has been demonstrated that quantum fluctuaction can induce them [113,114]. Raman solitons have also been generated by using a conventional fiber with the zero-dispersion wavelength near 1.3 μm led to 100-fs Raman pulses near 1.4 μm [115].

An interesting application of the soliton effects has led to the development of Raman soliton laser [116–121]. Such lasers provide their output in the form of solitons of widths 100 fs, but at a wavelength corresponding to the first-order Stokes wavelength., which can be tuned over a considerable range (10 nm). A ring-cavity configuration is commonly employed (see Figure 10). A dichroic beamsplitter, highly reflective at the pump wavelength and partially reflective at the Stokes wavelength, is used to couple pump pulses into the ring cavity and to provide the laser output. In a 1987 experimental demonstration of the Raman soliton laser [122], 10 ps pulses from a mode-locked color-center laser operating near 1.48 μm were used to pump the Raman laser synchronously. Even though Raman soliton lasers are capable of generating femtosecond solitons useful for many applications, they suffer from a noise problem that limits their usefulness [123]. The performance of Raman soliton lasers can be significantly improved if the Raman-induced frequency shift can somehow be suppressed [124].

**Figure 10.** Schematic representation of the ring-cavity geometry implemented for Raman soliton lasers. BS is a dichroic beamsplitter, M1 and M2 are mirrors of 100% reflectivity, L1 and L2 are microscope objective lenses.
