定义：由受激拉曼散射导致的光学增益

拉曼增益是由受激拉曼散射产生光学增益。当具有高光强的泵浦光入射时，不论在透明固体介质（如光纤）还是在液体或气体介质中都有可能发生。利用这个可以用来制作拉曼放大器和拉曼激光器。增益的大小依赖于泵浦光和信号光之间的频率偏移，泵浦的波长以及材料的性质。和稀土掺杂增益介质相比，拉曼增益需要更高的泵浦强度和更长的相互作用距离，并且具有不一样的饱和特性和依赖于泵浦光的波长的增益谱。
由受激拉曼散射导致的的窄带泵浦波和斯托克斯位移波（具有较低的光学频率）之间的相互作用可以通过以下方程来描述：

其中 和 是光强（以W/m2的单位）， 和 的两个光的频率， 是拉曼增益系数（对于石英光纤为10-13m/ W的量级）。这两个光束假定是完全重叠并且在z方向上传播的。当然，其他方面的影响也需要根据情况被被添加到等式中，如自发拉曼散射和线性传播损耗。
该方程表明，斯托克斯波经历了增益系数为 的放大，而泵浦光失去了更多的能量。这是因为，一个泵浦光子被转换成一个斯托克斯光子（低能量）和一个声子。声子能量对应于光子能量的差异。这个丢失的光能量被转换成热能。
拉曼增益系数主要取决于在光频率的差，但也受到泵浦波长和偏振方向的影响。图1示出了石英的拉曼增益对于频率差的函数，假设两个光束的具有相同的线性偏振。当频率偏移为13.2THz时拉曼增益具有最大值。例如，一个波长为1064nm的泵浦光会在1116nm处具有最大的拉曼增益。在拉曼光谱中的峰对应于石英材料本身的某些振动模式。

图 1 石英光纤的拉曼增益谱。横轴为信号光相对于泵浦光的相对频率偏移。
对于宽带激光特别是超短脉冲，受激拉曼散射会更加显著。它可以利用一个拉曼响应函数h（t）来表述，该函数描述了电场的非线性极化的延迟时间响应。
光纤中的拉曼增益会十分显著，因为在光纤中激光可以在很长的距离内保持很高的光强。当某个波长的拉曼增益高于70dB时，即使入射光中没有斯托克斯光，还是将会有相当大的功率被转换为斯托克斯波。这种效应限制了高功率光纤激光器和放大器的性能。

Definition: optical gain arising from stimulated Raman scattering

Categories: nonlinear optics, physical foundations

Formula symbol: g_R

Units: %, dB

Raman gain is optical gain (amplification) arising from stimulated Raman scattering. It can occur in transparent solid media (e.g. optical fibers), liquids and gases under the influence of intense pump light, and is used in Raman amplifiers and Raman lasers. Its magnitude depends on the optical frequency offset (in the terahertz region) between pump and signal wave, to some smaller extent on the pump wavelength, and on material properties. Compared with laser gain e.g. in rare-earth-doped laser gain media, Raman gain requires higher pump intensities and/or longer interaction lengths, has substantially different saturation characteristics, and a gain spectrum which depends on the wavelength of the pump light.

The quasi-continuous interaction between some narrow-band pump wave and a Stokes-shifted wave (with a lower optical frequency) via stimulated Raman scattering can be described with the following coupled differential equations:

where I_p and I_s are the optical intensities (with units of W/m²), ν_p and ν_s the optical frequencies of the two beams, and g_R is the Raman gain coefficient, which is e.g. of the order of 10⁻¹³ m/W for silica fibers for the optimum frequency offset of roughly 13 THz. It is assumed that both beams fully overlap and propagate in the z direction. Of course, additional terms can be added to the equations, e.g. in order to include spontaneous Raman scattering and linear propagation losses.

The equations show that the Stokes waves experiences a local gain coefficient g_R I_p, whereas the pump wave loses some more energy than is transferred to the Stokes wave. This is because one pump photon is converted into one Stokes photon (with lower energy) and a phonon. The phonon energy corresponds to the difference of photon energies. This lost optical energy is effectively converted into heat.

Due to the rather low value of the Raman gain coefficients e.g. of typical silica fibers, strong Raman conversion requires many meters of fiber if the optical powers are limited to a few watts. For optical pulses, e.g. with nanosecond pulse durations, where the peak powers can be much higher (many kilowatts), strong Raman conversion may occur even within short lengths of fiber (see Figure 1).

Figure 1: A case study for Raman amplification in a fiber shows that strong Raman conversion is possible within a short fiber length, if substantial peak powers occur e.g. in nanosecond pulses.

The Raman gain coefficient depends mainly on the difference in optical frequencies, but also to some extent on the pump frequency and the polarization directions. Figure 2 shows the Raman gain for fused silica as a function of the frequency difference, assuming equal linear polarizations of both beams. There is a maximum Raman gain for a frequency offset of 13.2 THz. For example, a pump wave at 1064 nm leads to the largest Raman gain at a signal wavelength of 1116 nm. The peaks in the Raman spectrum correspond to certain vibration modes of the silica structure.

Figure 2: Raman gain spectrum of fused silica, as used e.g. in silica fibers. The quantity on the horizontal axis is the frequency offset of the signal wave with respect to the pump wave. The data are based on Ref. [4].

The modeling of stimulated Raman scattering for broadband beams and particularly for ultrashort pulses is significantly more involved. It can be based on, e.g., a Raman response function h(t), describing the delayed temporal response of the nonlinear polarization to the electric field [2, 4, 6].

The Raman gain can be fairly strong in optical fibers, where substantial optical intensities can be maintained over long lengths. When the Raman gain corresponding to some optical wave exceeds the order of 70 dB, substantial power is transferred to a Stokes wave, even if there is no Stokes input to the fiber. This effect can limit the performance of high-power fiber lasers and amplifiers.

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