We propose a scheme of multiplex nonresonant pump four-wave mixing (NRP-FWM) process which is highly immune to saturation problems. The process is accomplished with two high-intensity pump beams detuned far from the resonance of the sample under investigation and a resonant probe beam as weak as possible not to give rise to nonlinear absorption. Only a single-broadband probe beam is used for the multiplex experiment to detect the electronic swan band spectrum of C 2 molecules in a premixed

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... lene-oxygen flame. Comparing the signal of the degenerate four-wave mixing (DFWM) experiment on the same sample, we found that the signal level at which the NRP-FWM starts to show saturation is about 250 times higher than in the case of the DFWM. Nonlinear optical four-wave mixing (FWM) processes have been widely studied for many applications including phase conjugation, spectroscopy, and microscopy. 1-3 Among them, coherent anti-Stokes Raman scattering (CARS) has been demonstrated as useful a diagnostic tool to measure the temperature and concentrations of major molecular species in a hostile environment like internal combustion engines. Degenerate FWM (DFWM) has received much attention because it compensates for the poor aspects of CARS. The resonant DFWM has very high signal-to-noise ratio due to its large resonance enhancement effect so that it can be used for probing the electronic states of minor species in combustion and plasma environments. 4,5 Even though it is a promising technique, the strong saturation behavior of the DFWM signal even at a low input laser power prevents it from being a practical method in many spectroscopic applications. 6-8 As has been generally understood, the generation of a DFWM signal is a scattering of one laser beam off grating created by the other two laser beams. The modulation contrast of grating depends on two input laser powers, and the scattered intensity of the remaining laser beam off the grating is proportional to the contrast. Therefore, a DFWM signal generated in weak field necessarily shows cubic dependence on incident laser power. 9,10 As the incident power increases, however, the signal intensity deviates from the cubic dependence and gets saturated. It is due to the fact that the molecules in the sample undergo real electronic transition from the lower to upper state and stay there quite a long time. The real electronic transition in a molecular system with a long relaxation time consequently shows a slow response to an input laser field. According to the theory of a saturable absorber, the input saturation intensity of a system is inversely proportional to the product of system relaxation time and cross section of transition from the lower state to excited state. 11,12 Therefore, the resonant DFWM process which has a long response time and a resonantly enhanced transition rate is easily saturated at a very low input laser power. As one simple way of avoiding such an easy saturation, we pro-pose a scheme in the present study that two pump laser beams be far detuned from molecular resonance frequency making the response time fast by virtual transition-i.e., utilizing nonresonant electronic nonlinearity, 11 while a probe laser beam is kept in resonance with the sample under investigation and as weak as possible not to give rise to a saturation. In Fig. 1(a) , the energy diagram of the nonresonant pump FWM (NRP-FWM) process is illustrated. And the third-order nonlinear susceptibility of the process can be readily found starting from a general lengthy expression obtained by the density matrix formalism of the perturbation theory. 11 Taking advantage of equal frequencies of two pump beams and dominance of the resonance terms involving ͑ 3 − mn ͒ as denominator, we get much simplified expression as follows: where is the transition dipole moment and the indices k, j, i, h represent the polarizations of light. Assuming no initial population on upper states and using the expression of Rayleigh scattering cross section leads us to the final result, 13 a) Electronic mail: jaewhahn@yonsei.ac.kr FIG. 1. (a) Energy level diagram of NRP-FWM. (b) Forward box-type phase matching configuration. APPLIED PHYSICS LETTERS