Raman Gain Media

Stimulated Raman scattering is a nonlinear interaction with a delayed nonlinear response of a χ⁽³⁾ nonlinearity. When a signal photon meets a pump photon at an appropriate wavelength within a Raman gain medium, it can occur that the pump photon is converted into another signal photon, and a phonon is emitted into the medium, the energy of which is the difference in photon energies. This process can be exploited for amplifying optical signals in Raman amplifiers and Raman lasers. Raman gain media may be operated with continuous-wave or pulsed radiation; a high Raman gain is easier to achieve in pulsed operation.

Raman-active optical media can be of different types:

• There are Raman crystals, i.e., transparent optical crystals (typically used as single crystals) with a suitable Raman response.
• Alternatively, one can use optical glasses.
• In some cases, one uses a gas in some gas cell, or a liquid.

One may have freely propagating laser beams in a solid Raman medium or in a gas. Alternatively, or one may use a waveguide structure to guide the light – for example, an optical fiber (utilizing the glass of the fiber core) or a hollow-core fiber filled with a Raman-active gas.

Relevant Properties of Raman Gain Media

The crucial properties of a Raman gain medium can be described as follows:

• A simplified description of the amount of obtained Raman gain can be done based on equations which consider the steady state of pump and signal with slowing varying optical powers and narrow bandwidth during the vibronic phase relaxation time:

• The Raman gain coefficient <$g_\textrm{R}$> has fundamental units of m/W; multiplied with the pump intensity, it delivers the gain coefficient (gain per unit length) in units of m⁻¹ at the signal wavelength. It depends on the difference in optical frequency between pump and signal. One may specify that quantity just for the optimum frequency difference, or fully as a function of frequency difference, or a peak value together with some bandwidth. Instead of the frequency difference, one more commonly specifies the Stokes shift (i.e., the difference in inverse wavelengths) in units of cm⁻¹.
• Note that Raman gain media usually have multiple vibrational modes resulting in multiple peaks of the nonlinear gain spectrum.
• A more comprehensive and general description requires the nonlinear index <$n_2$>, the Raman factor <$f_\textrm{R}$> and the Raman response function <$h(t)$> to fully describe the Raman amplification of a time-dependent complex amplitude <$A$> of a light beam:

• The imaginary part of the Fourier transform of the Raman response function is related to the nonlinear gain spectrum. The Raman gain is also proportional to the nonlinear coefficient <$\gamma$> (which in turn is proportional to the nonlinear index) and the Raman factor <$f_\textrm{R}$>. (For more details, read the article on delayed nonlinear response.) This type of description is required e.g. for ultrashort pulses of light, being shorter than the vibronic relaxation time of the medium.

A number of further properties of a Raman gain medium can be relevant for its application:

• Some Raman crystals are optically isotropic – for example, based on a cubic crystal structure. Others with a lower crystal symmetry exhibit birefringence and direction- and polarization-dependent Raman gain.
• The refractive index can be relevant in various ways.
• High transparency in the relevant spectral range can be important to minimize optical losses and also parasitic heating. One may specify a coefficient of parasitic absorption, or more generally a loss coefficient.
• The damage threshold intensity for laser-induced damage can be relevant for operation at high laser intensities. It often applies to the surface, and can be strongly dependent on the methods of surface preparation.
• The chemical durability may be limited; in particular, some Raman crystals are hygroscopic.
• Thermo-optic properties, including the thermal conductivity the temperature derivative of the refractive index and the thermal expansion coefficient, can be important for operation with high average powers, where one may have thermal lensing and other effects. Note that some heating is unavoidable in operation, since there is some quantum defect between pump and signal.

Raman Crystals and Glasses

Barium Nitrate Crystals

Barium nitrate (Ba(NO₃)₂) has been used for Raman amplifiers and lasers since the 1980s. Its Raman gain spectrum has multiple peaks; the dominant one (around 1049 cm⁻¹) is related to the symmetric stretching mode of the nitrate ion. The peak Raman gain is 47 cm/GW for pumping at 532 nm, which is quite high, but the bandwidth is relatively narrow. Both quantities result from the relatively weak damping of the mentioned vibration mode.

Barium nitride exhibits a wide transparency range from 330 nm to 1.8 μm. Thermal properties are not particularly good, with a low thermal conductivity (1,17 W / m K), a high thermal expansion coefficient (13 · 10⁻⁶ / K) and a strongly negative <$\partial n/\partial T$> of −20 · 10⁻⁶ / K.

Ba(NO₃)₂ crystals are relatively soft and hygroscopic, thus need to be treated with care.

Tungstate Crystals

Various tungstate materials, such as potassium gadolinium tungstate KGd(WO₄)₂ (in short, KGW), are also frequently used as Raman gain media. With their monoclinic crystal structure, they are birefringent. Compared with barium nitride, it is substantially more robust, with high laser damage threshold and much better thermal properties. It delivers substantially less Raman gain (peak: 11 cm/GW at 532 nm with 901 cm⁻¹ Stokes shift), but with a substantially larger bandwidth due to the small vibronic relaxation time. The transparency region is quite wide, from 0.3 μm to 5 μm. A variant with similar properties and an even broader transparency range (up to 5.5 μm) is potassium yttrium tungstate (KY(WO₄)₂, KYW).

Besides KGW, other tungstates can be used, such as barium tungstate (BaWO₄) and strontium tungstate (SrWO₄). These single tungstates have a tetragonal crystal structure.

Tungstate crystals can also be doped with laser-active ions such Yb³⁺ or Nd³⁺. They can then be used as laser gain media and at the same time as Raman converters.

Diamond

Synthetic diamond crystals have quite intriguing qualities as Raman crystals: a high Raman gain combined with a large Stokes shift (peak at 1333 cm⁻¹) and substantial bandwidth. It is also extremely robust and has a very high thermal conductivity. Unfortunately, diamond is rather expensive to produce, and thus rarely used.

Glasses

Various optical glasses can in principle be used as Raman gain media. Probably most common is the use of glasses of optical fibers, where a large Raman gain can be achieved despite the small Raman gain coefficient because one can realize a long interaction length with a small effective mode area.

Bulk glasses are less common due to their typically weak Raman gain. However, some glass types such as chalcogenide and tellurite glasses have been developed which offer substantially improved Raman gain. They are typically transparent in the infrared spectral region, not much in the visible.

Gases as Raman Gain Media

Some molecular gases such as hydrogen (H₂) and methane (CH₄) are occasionally used as Raman gain media. Due to their low density, they provide relatively small Raman gain. However, they can be used in large volumes (compared with single crystals, for example) and are rather robust. They are thus suitable for some very high power applications, where large beam diameters are required.

Liquids as Raman Gain Media

Some liquids such as carbon disulfide (CS₂) and benzene may also serve as Raman gain media. Compared with gases, they can deliver far higher Raman gain, and they can still be used in large volumes.

More to Learn

Encyclopedia articles:

• laser gain media
• Raman gain
• Raman scattering
• Raman lasers
• Raman amplifiers