Method of integral equations and an extinction theorem in bulk and surface phenomena in nonlinear optics

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Abstract
This work is a response to a problem which was most clearly formulated by Wolf [Coherence and Quantum Optics, edited by L. Mandel and E. Wolf (Plenum, New York, 1973), p. 339] in this way: ‘‘Attempts to generalize [the extinction theorem] within the framework of molecular optics encounters formidable difficulties.’’ Here the method of integral equations is applied to an arbitrary nonlinear and anisotropic medium, taking into account quadrupole and magnetic-dipole radiation. Using the fundamental equations of molecular optics, we prove the extinction theorem in a general case, and its physical interpretation is elucidated. The question about structure of a surface layer that produces the reflected wave is clarified. A connection between the microscopic and macroscopic characteristics of nonlinear media is obtained. This advance was achieved by the implementation of the straightforward idea of variable substitution in the original integral equation. This substitution turns out to yield insight into the transition from a local to a Maxwellian field.

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