Excitation of polyatomic molecules by the simultaneous absorption of three photons provides a method for observing and unambiguously assigning molecular electronic and vibronic transitions which may be inaccessible to onehyphen; or twohyphen;photon spectroscopy. Such threehyphen;photon allowed states may be forbidden to onehyphen;photon processes by reason of symmetry, even though the states may be parity (grarr;u) allowed. Also, the states may be onehyphen;photon allowed but lie at inaccessibly high energies, such as in the vacuum ultraviolet. Calculation of the polarization dependence of the threehyphen;photon absorption intensity requires a knowledge of the third rank tensor pattern for the threehyphen;photon transition. These patterns are presented here for the symmetry species of several molecular point groups, and their applications are discussed. Tensor patterns for the special case of threehyphen;photon excitation by a single laser are also presented. In several symmetry species the polarization ratio (circular/linear) for excitation of fluid media becomes 5/2. The intensities vanish for a few species possessing antisymmetric tensors. This phenomenon of rsquo;rsquo;identity forbiddennessrsquo;rsquo; is discussed.
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