Anal. Chem. 1991, 63,1449-1451
1449
Enhanced Selectivity for Spectrochemical Measurement by Mode Selection in Fully Resonant Nonlinear Mixing Roger J. Carlson’ and John C. Wright* Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, Wisconsin 53706
I n this paper, we demonstrate the feaslMHty of a new family of mode-seiective spectroscopies based on multiresonant nonlinear mixing. Three tunable iaclen are used for fully resonant fow-wave mbhg so the output signal depends on the dmultanwus contrlbutlon from three resonances. Mode selection is accomplished by tunlng the lasers to a particular Vibrational resonance. Vlbratlonal spectra are obtalned by rcannlng the second resonance. The resulting spectrum shows sekctlve enhancements of ail the modes that are related to the mode selected by the first resonance. I n this paper, we demonstrate the capabilities of this approach for enhancing features that are very weak in conventional spectroscopies and for separating features that are spectrally overlapped.
INTRODUCTION Multiresonant nonlinear mixing represents a new frontier for spectroscopy with the promise of high spectral selectivity ( I ) . In conventional spectroscopies that are controlled by single optical resonances, a single spectrum must represent a given sample. The spectra for multiresonant mixing spectroscopy can be very different from each other because they depend on a multiplicity of resonances. This multiplicity potentially can provide the experimentalist with great control and selectivity over the measurement. Multiwave mixing is performed by focusing several lasers into a sample and measuring the output light that occurs at frequency combinations of the input lasers. The light is generated because the electric fields of the lasers induce polarizations in the electron clouds of the sample that are oscillating at the laser frequencies. If the fields are large, there are distortions in the oscillating polarization that have Fourier components at combinationsof input frequencies. The light launched by these Fourier components is the signal frequency measured in the experimnt. The efficiency of generating the new light is enhanced if there are resonances with energy states of the sample material. The resonances used for the four-wave mixing experiments reported in this paper are shown in Figure 1. They are identical with a coherent anti-Stokes Raman scattering (CARS) experiment, but the resonances are used for specific purposes. One resonance is used to choose a vibrational mode while a second resonance is established with an excited electronic state. This second resonance can select particular components from a mixture or narrow an inhomogeneous profie. The third resonance is scanned to provide a spectrum. The spectrum contains enhancements for those transitions associated with the mode selected by the first resonance. For molecular samples, the v level is a vibrational state of the ground electronic state, the 0’ level is an excited electronic state, and the v‘ level is a vibrational state of the excited electronic state. If states v and v’ correspond to the same !Present address: The James Franck Institute, 5640 Ellis Ave, Chicago, IL 60637.
vibrational mode or if there is mixing of the two modes, there is an enhancement in the signal that can be quite large. This effect has been used to identify the different vibrational and vibronic features of pentacene-doped benzoic acid (2). In this paper, we show how this effect can be used to enhance weak transitions and to resolve peaks that are overlapped. THEORY The efficiency of the four-wave mixing process is controlled by the third-order susceptibility, x ( ~(3). ) In the third-order perturbation theory, x@) is x(3)
where
-( Ty(
= N n2+2 h3
c
~
d,W,v,O
~
V
W
~VO6&0
L
v
)
.
0
(1)
avo = ww0 - R,, - irw0 ,6 = W~ - Quo + - irm ado = wdo - nw0+ no, - nv.v- ir,
0, 0’, v, and v‘ represent the vibrationless ground and excited electronic states and their vibrational and vibronic states, respectively, N is the concentration of chromophores, n is the index of refraction, Qij is the laser frequency for the ij resonance, and pU, q,and rijare the dipole transition moment, the transition frquency, and the dephasing rate for the i j transition. The summation occurs over all possible states of the molecule. The intensity of the four-wave mixing is proportional to ( x ( ~and ) ( ~it can become quite large if several terms in the denominator become simultaneously resonant. The multiple resonances for the four-wave mixing are controlled by the bii in the denominator. In the scans reported in this paper, avo and ,6 are held at constant values while,6 is changed by the scanning. Peaks appear when 6$o becomes resonant. This spectrum is related to the absorption spectrum since the linear absorption intensity depends on l b 1 2 / 6 t ~One can show that the relative intensity of lines in the four-wave mixing spectrum scales as the square of the absorption spectrum if there are no specific enhancements from the other resonances (4). In this paper, we will be concerned specifically with such enhancements as a means of improving detectability and selectivity. The key idea is to use one of the resonances to select a specific mode that will be labeled v, for the mode selected. In order to clarify the discussion, we assume that only the states in resonance are important in the summation of 0, v, and 0’ in eq 1and that v, is the mode selected for resonance. We further assume that there are only two excited vibrational states that are important for v‘. The first mode will be labeled v l and is the same as the mode selected by the ground vibrational state resonance. The second mode is labeled by vd’ and represents all the modes that are different from the selected mode. With this approximation x(3) =
-
-(d( N n2 + 2 h3
)
~cYo~CCVV,&,V~~CV~O + (2) ~vo~v,o~v;o ~vo~vso~vd~o
~VO~VV,&,V,+V;O
The first term in x ( ~has ) two resonance enhancements that
0003-2700/91/0363-1449$02.5OlO 0 lB9l Amerlcan Chemical Society
1450
ANALYTICAL
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