Using the principles of quantum electrodynamics, the theory of twohyphen;, threehyphen;, and fourhyphen;photon absorption in polyatomic gases and liquids is developed. Expressions are derived for the rates of singlehyphen;frequency absorption from plane polarized, circularly polarized, and unpolarized light. It is shown that fornhyphen;photon absorption withnquest;3, the rate for unpolarized radiation is in each case expressible as a linear combination of the rates for plane polarized and circularly polarized light; no such relationship exists for fourhyphen;photon absorption. For each multiphoton process, it is demonstrated how the fullest information about the symmetry properties of excited states can be derived by a simple linear processing of the results from experiments with different polarizations. A detailed examination of the selection rules is made, based on a reduction of the molecular transition tensor into irreducible components, and a new classification scheme is introduced to assist with the interpretation of experimental results. Finally, it is shown that the theory may also be applied to resonancehyphen;enhanced multiphoton ionization spectroscopy.
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