Quantum Theory of Fiber-Optics and Solitons
The complete equations of motion for an electromagnetic field propagating in a dielectric fiber must include a quantum description of the radiation field, if gain, absorption, and the electronic nonlinear response of the medium are all taken into account. In addition, the effects of thermal vibrational states of the fiber cause fluctuations on both the macroscopic and molecular scales. This leads to an extra nonlinear response with a delay time of the order of 100 femtoseconds or longer, due to Brillouin and Raman processes. The resulting equation for the quantum field has the form of a vector nonlinear Schrödinger equation, with a modified nonlinear term to account for the delayed response. Additional quantum noise terms arising from the vibrational coupling are also present. Besides offering a quantum-mechanical formulation for the problem of soliton propagation in fibers1, the classical behavior of ultra-short pulses predicted by the theory supports earlier heuristic models of Raman scattering.
KeywordsPhoton Number Quantum Noise Polarization Field Nonlinear Schrodinger Equation Vibrational Coupling
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