In. this note a general orthogonal property of optical resonator eigenmodes is analyzed. The orthogonality in the (u*, U) sense of the eigonmodes U and their adjoint modes u is obtained.
The phase-conjugation operator is investigated in the context of the canonical operator theory of first-order optics, which was introduced in a previous series of articles. The matrix representation of this operator and its action on the generalized modes are derived, elucidating the relation between forward and reversed propagation in this new context. The resulting formalism makes possible the derivation of the eigenmodes of conventional and phase-conjugated resonators with loss or gain. Various resonator properties—confinement, stability, mode biorthogonality, and real or complex character of the spot-size parameter—simply follow from the guiding-ray-label representation.
These lectures form a general introduction to the domain of Quantum Optics, with a special emphasis on the notion of field eigenmodes that are necessary to describe the quantum effects in light and define the photons: possibility of changing the basis of field eigenmodes and choosing the most appropriate one, definition of intrinsic properties, independent of the choice of basis. Are successively studied the single mode quantum effects, the quantum correlations existing in bimodal systems, and some interesting features of highly multimode systems such as the optical images.