Temperature determination of transient species by degenerate four wave mixing: Application of the independently determined power law of the transition dipole moment and geometric factors

Abstract

We investigated the dependence of the degenerate four wave mixing ͑DFWM͒ signal intensities on the electronic transition dipole moment of isolated lines in the A 1 ⌺ ϩ ←X 1 ⌺ ϩ transition band of NaH. We applied a new method to determine this dependence in transient species without previous knowledge of the sample temperature. By using different appropriate pairs of DFWM lines sharing common lower level, the relative population difference is eliminated. We found that this ratio is well described by a power law ( 1 / 2 ) x where i is the electronic one-photon transition dipole moment. As a result of saturation the exponent x depends on the total laser energy deposited in the medium. The observations are in good agreement with a modified two-level model, which includes the effects of polarization of the laser beams used in the experimental setup by introducing geometric factors. The exponent of the integrated signal intensities varies between 3 and 8 for high and low laser intensities with a rapid decrease to high intensities. This makes it possible to compare signal intensities at different DFWM laser intensities in order to obtain relative level populations, i.e., temperature, with high sensitivity.

Combustion flame diagnostics using degenerate four-wave mixing: the dipole moment power law and rotational temperature for nitric oxide

“…For weak laser intensities I I sat 0 the signal I int c becomes proportional to µ 8 , whereas for strong saturation I I sat 0 the signal is proportional to µ 3 . For intermediate cases the signal intensity may be described by a power law [12,18,19]…”

“…By using ratios of DFWM intensities from lines originating from the same lower level and therewith with the same population Klamminger et al [18] were able to determine the exponent x independently of the temperature. This method was extended to the use of geometric factors by Lehr et al [19]. The integrated signal intensity now reads…”

“…With x determined from a double logarithmic plot of equation ( 7) the rotational temperature can now be obtained from a Boltzmann plot of equation ( 8). This method developed by Klamminger et al [18] and Lehr et al [19] is derived from the cases I I 0 sat and I I 0 sat , for which x can be assumed to be constant. However, x is not constant generally, but may be assumed so for some very limited interval of transition dipole moments.…”

“…During recent years degenerate four-wave mixing (DFWM) has proven to be a powerful spectroscopic tool for the determination of major and minor species [1,2] in jets, cells, flames [3] and discharges [4,5] under a large variety of pressures. The investigated molecules and radicals were among others OH [6][7][8][9][10][11], NO [12][13][14][15], NO 2 [16], NaH [17][18][19], NH [6], C 2 [20,21], C 2 H 2 [22], HCO [23], CH 3 [24] and CH 4 [22]. The wavelengths used covered the range from the ultraviolet [12] to the mid infra-red [22,25].…”

“…The laser energies in their experiments were 200 µJ in each pump beam and 20 µJ in the probe beam. This procedure was extended by Lehr et al [19] to involve the geometrical factors of Williams et al [28,29]. This resulted in exponents that varied between x = 3 and x = 8 for high and low laser intensities, respectively.…”