SCATTERING-THEORY OF OSCILLATOR DEFECTS IN AN OPTICAL-FIBER

We examine harmonic oscillator defects coupled to a photon field in th e environs of an optical fiber. Using techniques borrowed or extended from the theory of two-dimensional quantum fields with boundaries and defects, we are able to compute exactly a number of interesting quanti ties. We calculate the scattering S matrices (i.e., the reflection and transmission amplitudes) of photons off a single defect. We determine using techniques derived from thermodynamic Bethe ansatz the thermody namic potentials of the interacting photon-defect system, and we compu te several correlators of physical interest. We find the photon occupa ncy at finite temperature, the spontaneous emission spectrum from the decay of an excited state, and the correlation functions of the defect degrees of freedom. In an extension of the single defect theory, we f ind the photonic band structure that arises from a periodic array of h armonic oscillators. In another extension, we examine a continuous arr ay of defects and exactly derive its dispersion relation. With some di fferences, the spectrum is similar to that found for electromagnetic w ave propagation in covalent crystals. We then add to this continuum th eory isolated defects, so as to obtain a more realistic model of defec ts embedded in a frequency-dependent dielectric medium. We do this bot h with a single isolated defect and with an array of isolated defects, and so compute how the S matrices and the band structure change in a dynamic medium.