Quantum theory of a one-dimensional optical cavity with output coupling. III. Cavity quasimodes as the field eigenvalue

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Abstract
The quantum theory is developed for an arbitrarily stratified one-dimensional optical cavity which transmits light at one of its end The field is expanded in terms of the modes of the universe and each universal mode is quantized separately by means of the usual method. A class of coherent states which yields oscillation wave shapes of the cavity quasimodes as the field eigenvalue is studied. A state of this class gives an eigenvalue for the annihilation operator of a universal mode which is an analytic function of the mode frequency except for a mode-dependent phase factor. The mathematical meaning of the phase factor is studied. A new scheme of field quantization is developed which absorbs the above phase factor and yields simpler forms of the eigenvalue equations for the above class of states. For a state of the class, the local intensity, its fluctuation, and the various correlations of the field decay with time. For the local field inside or outside of an optical structure which is coupled to the free space, the almost definite phase relationship among the universal modes plays a decisive role.