Coherent Raman (CARS/SRS) Calculator

Coherent anti-Stokes Raman scattering (CARS) and stimulated Raman scattering (SRS): wavelengths, focal intensity, lineshapes and excitation bandwidth.

Model: Textbook approximation

Mode

Pump wavelength (nm)Raman shift (cm⁻¹)Pump power (mW)Stokes power (mW)Pulse width, FWHM (ps)Rep rate (MHz)NARaman linewidth Γ, HWHM (cm⁻¹)Non-resonant χ_NR (relative to peak Im χ_R)

Results

Stokes wavelength1036.3 nm

Anti-Stokes (CARS signal) wavelength651.5 nm

Frequency difference85.44 THz

Pulse energy (pump / Stokes)0.625 / 0.625 nJ

Peak power (pump / Stokes)293.6 / 293.6 W

Focal peak intensity, pump138.2 GW/cm²

Focal peak intensity, Stokes82.4 GW/cm²

CARS maximum (dispersive line)-4.2 cm⁻¹ from resonance

Excitation bandwidth (transform-limited pulses)10.4 cm⁻¹ vs line FWHM 30 cm⁻¹

ν̃_S = ν̃_P − Ω̃, ν̃_aS = ν̃_P + Ω̃ (energy conservation)

CARS ∝ |χ_NR + χ_R|² · I_p² · I_S; SRS ∝ Im χ_R · I_p · I_S, χ_R = −Γ/(Δ + iΓ)

CARS has a non-resonant background and a dispersive line; SRS is background-free and linear in concentration (Cheng & Xie, J. Phys. Chem. B 108, 827, 2004; Freudiger et al., Science 322, 1857, 2008).

Focal intensity P_peak/(2π ω_xy²), ω_xy from Zipfel et al. 2003 at each beam's wavelength; Gaussian pulses. Absolute signal levels need χ⁽³⁾ and the detection chain, so the charts are relative.

Excitation bandwidth √2·(2 ln 2/π)/(c·τ): the spectrum of the drive E_p·E_S* of two identical transform-limited Gaussian pulses, whose envelope I_p·I_S lasts τ/√2. The shift follows from the two wavelengths as 1/λ_p − 1/λ_S; the Raman shift page converts either way.

Active mode: CARS

CARS spectral shape

Power scaling illustration (both beams scaled together)

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

Wavelengths follow from energy conservation (exact); lineshapes are a single Lorentzian Raman line; the excitation bandwidth is that of identical transform-limited Gaussian pulses; focal intensity uses Zipfel's Gaussian fit. Signal levels are relative, as they need χ⁽³⁾ and the detection chain.

Cheng J.-X., Xie X. S. (2004). Coherent Anti-Stokes Raman Scattering Microscopy: Instrumentation, Theory, and Applications. J. Phys. Chem. B 108, 827–840. CARS and SRS signals and the Raman lineshape. doi:10.1021/jp035693v
Freudiger C. W. et al. (2008). Label-Free Biomedical Imaging with High Sensitivity by Stimulated Raman Scattering Microscopy. Science 322, 1857–1861. SRS; check case: a 816.8 nm pump and a 2845 cm⁻¹ shift give a 1064.07 nm Stokes beam. doi:10.1126/science.1165758
Zipfel W. R., Williams R. M., Webb W. W. (2003). Nonlinear magic: multiphoton microscopy in the biosciences. Nat. Biotechnol. 21, 1369–1377. Focal radius ω_xy at each beam's wavelength. doi:10.1038/nbt899

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