Accurate convolutions of coherent anti-Stokes Raman spectra

Abstract

The standard approach for including laser line-shape effects in calculated coherent anti-Stokes Raman spectra is shown to be incorrect. The correct approach involves extra terms that become important if the laser linewidth is larger than the Raman linewidths. The standard approach can lead to errors in measurements of concentration or nonresonant susceptibility. A closed-form solution for the special case of Lorentzian laser line shapes is presented. Measurements using broadband and narrow-band lasers support the modified theory but are inconsistent with the standard theory.

CARS Temperature Measurements in Sooting, Laminar Diffusion Flames

“…The spectra were analysed using the standard convolution given by Yuratich (1979). Teets (1984) has pointed out that when nonresonant background effects are present and the pump laser linewidth is much larger than the Raman linep.…”

Comparative analysis of Herman‐Wallis factors for uses in coherent anti‐Stokes Raman spectra of light molecules

“…The solution for degenerate pump laser beams contains the well-known dependence on the laser intensities of the degenerate pump L 1 and the Stokes laser L S , that is I CARS ∝ |χ (3) | 2 L 2 1 L S . [3] Although this dependence is oversimplified (degeneracy of the pump lasers, no influence of finite laser linewidths) in comparison with the more complete understanding of CARS measurements, [17,18] it is still indicative of the fact that the spectral details of the signal I CARS emerge from the squared modulus of the third-order optical susceptibility χ (3) . Neglecting background contributions, this is written as…”

High-speed N2-CARS thermometry

“…For Gaussian [12] and Lorentzian [13] pump laser lineshapes, analytical expressions for Z (3) including cross-coherence have been derived. Cross-coherence is particularly important when large nonresonant signal contributions are detected.…”