Raman Scattering
Stimulated Raman gain of diamond, Ba(NO₃)₂, KGW, As₂S₃ glass and fused silica: Stokes wavelength, peak gain at your pump wavelength, Lorentzian gain line, dephasing time and single-pass gain e^(gIL).
Diamond: Ω̃ = 1332.9 cm⁻¹, Δν̃ = 2.7 cm⁻¹; gain measured at 355 nm, 532 nm, 670 nm, 800 nm, 1064 nm, 1280 nm; Ω̃, Δν̃ Basiev 1999; g Savitski 2013 Table 1. g_R at 1064 nm is measured.
Stokes wavelength 1/λ_s = 1/λ_p − Ω̃
1239.83 nm
shift 39.96 THz
Peak Raman gain g_R
17 cm/GW
= 1.70e-10 m/W
Dephasing time T₂ = 1/(πcΔν̃)
3.93 ps
steady state needs pulses ≫ 3.9 ps
Single-pass gain exponent G = g_R I L
1.7
Stokes grows by e^G = 7.383 dB
Diamond gain line at 1064 nm pump
Raman media at 1064 nm pump
| Medium | Ω̃ (cm⁻¹) | Δν̃ (cm⁻¹) | g_R (cm/GW) | Stokes λ (nm) | Source |
|---|---|---|---|---|---|
| Diamond | 1332.9 | 2.7 | 17 | 1239.83 | Ω̃, Δν̃ Basiev 1999; g Savitski 2013 Table 1 |
| Ba(NO₃)₂ | 1048.6 | 0.4 | 11 | 1197.62 | Ω̃, Δν̃ Basiev 1999; g Markevich & Chulkov 2016 (532 nm), EKSMA (1064 nm) |
| KGW 901 cm⁻¹ (E ∥ N_m) | 901 | 5.4 | 3.3 | 1176.82 | Ω̃, Δν̃ Basiev 1999; g Markevich & Chulkov 2016 (532 nm), EKSMA (1064 nm) |
| KGW 768 cm⁻¹ (E ∥ N_g) | 768 | 6.4 | 4.4 | 1158.68 | Ω̃, Δν̃ Basiev 1999; g Markevich & Chulkov 2016 (532 nm), EKSMA (1064 nm) |
| As₂S₃ glass | 333.56 | broad | 0.74 | 1103.15 | Stegeman et al. 2006, Table 1 |
| Fused silica | 440.3 | broad | 0.0094* | 1116.3 | Agrawal, Nonlinear Fiber Optics |
Click a row to select the medium. * scaled as 1/λ_p outside the measured pump range.
Model
1/λ_s = 1/λ_p − Ω̃, g(Ω̃) = g_R / (1 + [2(Ω̃ − Ω̃₀)/Δν̃]²), I_s(L) = I_s(0)·e^(g_R I_p L)
Steady-state stimulated Raman scattering of a plane-wave pump that is not depleted. The gain holds for pulses much longer than T₂; shorter pulses are in the transient regime, where the gain is set by the integrated cross-section and is lower. Gains are for the pump polarization of the measurement (diamond along <111>).
The diamond gain falls with pump wavelength faster than 1/λ_p (Savitski 2013: 17 cm/GW at 1064 nm, 7.6 at 1280 nm); between measured points it is interpolated in pump wavenumber. The KGW and Ba(NO₃)₂ gains at 532 nm (Markevich & Chulkov 2016) and 1064 nm (EKSMA) come from different measurements and disagree by about 2× with the expected ω_s scaling; Basiev et al.'s spontaneous cross-sections relative to diamond side with the 1064 nm values, so treat gains between the two as ±50 %. Silica fibre gains and thresholds are on the fibre SRS pages.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Steady-state SRS (pulses much longer than T₂) of an undepleted plane-wave pump, with a homogeneous Lorentzian line. Gains are interpolated in pump wavenumber between measured points (diamond: six Savitski 2013 points; KGW and Ba(NO₃)₂: 532 nm measured, 1064 nm vendor; the two do not follow one 1/λ_p law, so between them the gain is good to about ±40 %); outside the measured pump range a gain is scaled as 1/λ_p and flagged as an estimate. The silica and As₂S₃ glass lines are broad and not Lorentzian; As₂S₃ absorbs visible pumps; no UV absorption edge is applied for KGW and Ba(NO₃)₂.
- Savitski V. G., Reilly S., Kemp A. J. (2013). Steady-state Raman gain in diamond as a function of pump wavelength. IEEE J. Quantum Electron. 49, 218–223. Table 1. doi:10.1109/JQE.2012.2237505
- Basiev T. T., Sobol A. A., Zverev P. G., Osiko V. V., Powell R. C. (1999). Comparative spontaneous Raman spectroscopy of crystals for Raman lasers. Appl. Opt. 38, 594–598. Raman shifts and linewidths. doi:10.1364/AO.38.000594
- EKSMA Optics. KGW / Ba(NO₃)₂ crystals for stimulated Raman scattering, data sheet. Raman gain at 1064 nm (vendor values; KGW 901 cm⁻¹ p[mm]p, 768 cm⁻¹ p[gg]p). eksmaoptics.com
- Markevich V. U., Chulkov R. V. (2016). Determination of the steady-state Raman gain coefficients of potassium-gadolinium tungstate at 532 nm. Vestsi NAN Belarusi, Ser. Fiz.-Mat. Navuk, no. 1, 102–106. KGW 14 ± 3 (901 cm⁻¹, E ∥ N_m) and 11 ± 3 cm/GW (767 cm⁻¹, E ∥ N_g); Ba(NO₃)₂ 43 ± 5 cm/GW. vestifm.belnauka.by
- Stegeman R., Stegeman G., Delfyett P., et al. (2006). Raman gain measurements and photo-induced transmission effects of germanium- and arsenic-based chalcogenide glasses. Opt. Express 14, 11702–11708. Table 1: As₂S₃ 74 ± 15e-13 m/W at 10 THz, 1064 nm pump. doi:10.1364/OE.14.011702
- Stolen R. H., Ippen E. P. (1973). Raman gain in glass optical waveguides. Appl. Phys. Lett. 22, 276–278. doi:10.1063/1.1654637
- Agrawal G. P. (2019). Nonlinear Fiber Optics, 6th ed. Academic Press. Silica Raman gain ≈ 1e-13 m/W at 1 µm, peak near 13.2 THz, scaling as 1/λ_p. doi:10.1016/C2018-0-01168-8