**2. Theoretical Background**

SRS can be obtained by irradiating a sample with two simultaneous light sources: a light wave at frequency ω*<sup>L</sup>* (the pump laser wave) and a light wave at frequency ω*<sup>S</sup>* = ω*<sup>L</sup>* − ωυ (the Stokes Raman wave), where *h*¯ωυ corresponds to a vibrational energy. In SRS phenomenon, when the frequency difference between the pump and the Stokes laser beams matches a given molecular vibrational frequency of the sample under test, there is a transfer of energy from the high power pump beam to the probe beam, which can be co-propagating or counter-propagating. The SRS effect occurs in the form of a gain for the Stokes beam power (stimulated Raman gain, SRG) and a loss for the pump beam power (stimulated Raman loss, SRL), see Figure 1a. It is worth noting that in SRS, because of its coherent nature, the molecular bonds oscillate with a constant phase relation (see Figure 1b) and interfere constructively within a certain macroscopic area (e.g., inside the focus area of laser beam), therefore the SRS signal can be orders of magnitude more sensitive than spontaneous Raman scattering [9–12].

In SRS, high-order Raman sidebands can be produced by a field propagating through a medium optically polarizable. Many Stokes frequencies can be generated at the output when the pump power exceeds the threshold value, thus Stokes frequencies at ω*<sup>P</sup>* − ων, ω*<sup>P</sup>* − 2ων and of anti-Stokes frequencies at ω*<sup>P</sup>* + ων, ω*<sup>P</sup>* + *2*ων can be observed. If the intensity of the first-Stokes wave is enough high, it can generate a "second-Stokes" beam (see Figure 2). By iterating this process, higher Stokes order can be generated, leading to the so-called "cascaded" SRS. The intensity of the *i*th Stokes order thus depends on the conversion rate from the (*i* − 1)th Stokes order (proportional to *g*·*Ii*·*Ii*−1) and loss rate to the (*i* + 1)th order (proportional to *g*·*Ii*·*Ii*+1) where *g* is the Raman gain of material. We note that frequency conversion can be obtained over a wide range of output wavelengths (visible and UV) within a single Raman laser system. For example, it is possible to use standard diode-pumped crystalline solid-state lasers to generate several Stokes order by cascading effect [9–14].

**Figure 1.** Stimulated Raman-Scattering (SRS) principle. (**a**) Pump–probe modalities associated with the SRS process are pointed out: SRG, stimulated Raman gain; SRL, stimulated Raman loss. (**b**) Stimulated Raman scattering occurs through inelastic scattering of probe photons off from vibrationally excited molecules that interfere coherently.

**Figure 2.** Cascaded Raman scattering principle. An input frequency ω*<sup>P</sup>* (green) can cause the spontaneous emission of frequencies ω*<sup>P</sup>* ± ων*,* [Stokes (blue) and anti-Stokes (orange)]. This initial spontaneous event provides the seed photons necessary for subsequent first-order SRS (**left**). The first-order Stokes and anti-Stokes photons then can cause second-order Raman scattering (**right**) to produce new frequencies ω*<sup>P</sup>* ± 2ων (red and violet) and so on through propagation, resulting in a broadband ladder of frequencies ω*<sup>P</sup>* ± *n*ων.

Optical fibers are an excellent medium for utilizing SRS. There are two key parameters for performances optimization of Raman fiber amplifier and laser. The first, linear losses are fundamentals for enabling long interaction lengths. We note that different types of fibers have different low-loss wavelength windows. For example, the silica fibers, which are used in the majority of optical fiber applications, have extremely low losses (<1dB/km) in the near-IR region, whereas they are very lossy in the mid-IR region. The second, effective area: Because of their small core diameter <10 μm, single-mode fiber has the ability to confine light to small mode areas, which significantly enhances nonlinearity. We note that in silica glass, in spite of intrinsically small values of the third-order nonlinear coefficients, which are smaller by a factor of 100 or more compared to many crystals and liquids, nonlinear effects in optical fibers can be observed at relatively low power levels.

In the past century, fused silica has been the main material used for long and short-haul transmission of optical signals, because of its good optical properties and attractive figure of merit (trade-off between Raman gain and losses). Since in amorphous materials, molecular vibrational frequencies spread out into bands that overlap and create a continuum, in silica fibers, the Raman gain (gR(Ω)) spectrum extends over a large frequency range (up to 40 Thz). The maximum of the Raman gain spectrum in silica fibers is downshifted from the pump frequency by about 13.2 THz (440 cm<sup>−</sup>1), corresponding to 100 nm in the telecom window. Therefore, being the signal wavelength usually around 1550 nm, the pump light wavelength has to be about 1450 nm. We note that at high enough powers there can be lasing at all frequencies with sufficient Raman gain [21–27], though the peak gain is at a specific frequency shift. The following fundamental properties of Raman gain are critical for designing Raman fiber amplifiers and lasers:

(1) Raman gain has a spectral shape that depends primarily on the frequency separation between a pump and signal, not on their absolute frequencies. This follows from energy conservation: Their frequency separation must be equal to the frequency of the created optical phonon;

(2) Since Raman gain does not depend on the relative direction of propagation of pump and signal, SRS occurs almost uniformly for all the orientations between the pump and signal propagation direction, as a consequence FRAs can work for both the copropagating, counter-propagating or bidirectional pumps with respect to the signal;

(3) SRS is a fast process, response time of fused Silica is evaluated to be less than 100 fs [28,29]. For most applications, this appears instantaneous, and especially in relation to the application as Raman amplifiers in optical communications systems;

(4) Raman gain is polarization dependent. Raman gain coefficients are usually quoted for parallel linearly polarized pump and Stokes fields. For perpendicular polarizations the gain is more than an order of magnitude smaller than the parallel one. In typical long fibers, which do not maintain linear polarization, the Raman gain will assume some average value which is approximately half of the polarized gain [30,31];

(5) Peak Raman gain in a specific fiber can be different based upon the material composition. For example, in phosphosilicate fiber the peak gain is at 1330 cm<sup>−</sup>1. This larger Raman shift is attractive for many applications, since fewer Stokes shifts are needed to reach the final desired wavelength.

Concerning materials, two problems are of great interest: (1) Development of glasses with a higher Raman gain coefficient; (2) increase of Raman gain bandwidth [32–36]. The increase of dopant content in Ge- and P-doped silica fibers with a simultaneous reduction of optical losses seems the most straightforward solution to the first problem. The second option is to use multicomponent glasses, including heavy-metal oxides-doped glasses, which also permits the development of glasses with the Raman gain bandwidth of several hundreds of cm−<sup>1</sup> [37–42]. However, in multicomponent glass approach the current limitation is to obtain low-loss fibers.

In fiber communication systems, two basic issues are related to SRS. First, pump-to-Stokes coupling provides a mechanism for crosstalk from short- to long-wavelength channels, which is more efficiently when the channel frequency spacing is close to the one associated with the maximum Raman gain [43]. In wavelength division multiplexed (WDM) systems, within the 1.53- to 1.56-μm erbium-doped fiber amplifier window, channel spacings on the order of 100 GHz are used, thus due to the Raman gain peak at approximately 500 cm<sup>−</sup>1, Raman gain is considerably reduced, but is still sufficient to cause appreciable crosstalk, which can lead to system penalties depending on the number of channels [44]. Second, the conversion to Stokes power from the original signal—a mechanism by which signal power can be depleted. A related problem is walkoff [45] occurring between the signal and Stokes pulses, since these will have different group delays. If pulses are of sub-picosecond widths, additional complications arise due to the increased importance of SPM and cross-phase modulation (XPM) [6].
