Degenerate four wave mixing of C₂ in forward geometry: Spectral lineshape analysis and temperature determination

Forward phase-matched degenerate four-wave mixing (DFWM) spectrum of C₂ molecules is studied to determine the temperature of a premixed oxyacetylene flame. Both theoretical calculation and experimental measurement of the d³Π_g ↔ d₃Π_u swan band of C₂ are performed at weak field intensity. The measured spectra excited with a narrow band optical parametric oscillator (OPO) showed good matches with the results of calculations. When a DFWM spectrum corresponding to the molecular transitions of both high (J = 36-42) and low (J = 8-15) rotational levels is used for a Boltzmann plot, we can determine the flame temperature of 3143 K with a very small temperature uncertainty of 1.6%. In addition, the uncertainty in temperature measurement caused by the line interference of the DFWM spectrum in the forward geometry is estimated to be only 0.5%, which is negligible for practical applications.