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Quantum Theory of Amplified Total Internal Reflection by Evanescent Wave

The amplification method using evanescent wave coupling has a long history and has been widely used as a new lasing method, especially, in the waveguide optics$^{(1)}$ . In particular, it has been observed experimentally that when the light wave propagating in a dielectric medium is totally reflected at the planar interface between the dielectric and a pumped active medium, the reflectance may be greater than unity, i.e., amplification is possible$^{(2)}$ . There were several attempts by other authors to explain this enhanced internal reflection (EIR) classically$^{(3)}$ . They commonly introduced a complex refractive index for the active medium with its imaginary part being negative, and this scheme was also used to describe an amplification process in a waveguide having active-cladding region$^{(4)}$ . However these theories are phenomenological, using macroscopic constants, and therefore a microscopic theory is needed to understand EIR in a fundamental level. (omitted)