Homogeneous and inhomogeneous broadenings and the Voigt line shapes in the phase-resolved and intensity sum-frequency generation vibrational spectroscopy

In this report, we show that the ability to measure the sub-1 cm⁻¹ resolution phase-resolved and intensity high-resolution broadband sum frequency generation vibrational spectra of the –CN stretch vibration of the Langmuir-Blodgett (LB) monolayer of the 4-n-octyl-4′-cyanobiphenyl (8CB) on the z-cut α-quartz surface allows the direct comparison and understanding of the homogeneous and inhomogeneous broadenings in the imaginary and intensity SFG vibrational spectral line shapes in detail. The difference of the full width at half maximum (FWHM) of the imaginary and intensity sum-frequency generation vibrational spectroscopy spectra of the same vibrational mode is the signature of the Voigt line shape and it measures the relative contribution to the overall line shape from the homogeneous and inhomogeneous broadenings in SFG vibrational spectra. From the phase-resolved and intensity spectra, we found that the FWHM of the 2238.00 ± 0.02 cm⁻¹ peak in the phase-resolved imaginary and intensity spectra is 19.2 ± 0.2 cm⁻¹ and 21.6 ± 0.4 cm⁻¹, respectively, for the –CN group of the 8CB LB monolayer on the z-cut α-quartz crystal surface. The FWHM width difference of 2.4 cm⁻¹ agrees quantitatively with a Voigt line shape with a homogeneous broadening half width of Γ = 5.29 ± 0.08 cm⁻¹ and an inhomogeneous standard derivation width Δω = 5.42 ± 0.07 cm⁻¹. These results shed new lights on the understanding and interpretation of the line shapes of both the phase-resolved and the intensity SFG vibrational spectra, as well as other incoherent and coherent spectroscopic techniques in general.