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Quantum mechanical treatment of the third order nonlinear term in NLS equation and the supercontinuum generation

Making use of the canonical quantization theory and defining proper creation and annihilation operators, the total Hamiltonian for the pulse propagation through the optical fiber is quantized. An operator form of the nonlinear Schrodinger equation is obtained implementing the resulted Hamiltonian. We, then, use the results of the positive P-representation and obtain a coupled stochastic nonlinear Schrodinger equation. Finally, we simulate these equations and argue about supercontinuum generation process in optical fiber (especially in photonic crystal fiber).