Quantum treatment of field propagation in a fiber near the zero dispersion wavelength

Abstract

In this report, we present a quantum theory describing the propagation of the electromagnetic radiation in a fiber in the presence of the third order dispersion coefficient. We obtained the quantum photonpolariton field, hence, we provide herein a coupled set of operator forms for the corresponding nonlinear Schrodinger equations when the third order dispersion coefficient is included. Coupled stochastic nonlinear Schrodinger equations were obtained by applying a positive P-representation that governs the propagation and interaction of quantum solitons in the presence of the third-order dispersion term.Finally, to reduce the fluctuations near solitons in the first approximation, we developed coupled stochastic linear equations.

A Quantum Theory for Propagation of Electromagnetic Waves through Lossy Dielectrics in Presence of Third Order Dispersion

“…This enabled us to include the third order dispersion and the attenuation into field propagation in dielectrics. This theory can be applied to the propagation of quantum solitons and their interactions in the presence of the third order dispersion and the attenuation terms by using the method presented in [42]. Additionally, in resemblance to other physical phenomena, there are noises present in nonlinear optical phenomena including quantum noise.…”

“…Additionally, in resemblance to other physical phenomena, there are noises present in nonlinear optical phenomena including quantum noise. This work could be applied to reduce these fluctuations and quantum noise in the vicinity of the solitons formed in the presence of the third order dispersion and the attenuation coefficients in dielectrics such as fibers [42]. Furthermore, the supercontinuum generation as well as soliton self-frequency shift phenomena could be studied quantum mechanically, if the retarded nonlinear response of the medium is considered.…”

“…where γ ν n = (ω ν n ) and α ν n = (ω ν n ). Applying the method introduced in [42], one can obtain a coupled stochastic nonlinear Schrödinger equations describing pulse propagation through a one dimensional slab quantum mechanically in the presence of the attenuation term (loss). A Gaussian pulse of peak power 10W and the width of 1ps is assumed to be launched into a slab waveguide and the evolution of the pulse along the slab is simulated in the mean case [53] as shown in fig.…”

“…Also, to achieve more reasonable and accurate results, the attenuation of medium must be considered in a theory for quantization of the pulse propagation through a dielectric. Similar to some other phenomena in physics [38][39][40], field propagation in dielectrics, such as optical fibers, experiences noise of different sources [41][42][43][44]. For example supercontinuum generation [45,46] suffers up to 50% fluctuation in its temporal intensity profile, affecting its usage in many applications [47][48][49][50][51].…”

Quantum model for supercontinuum generation process

“…Previously, we have presented a preliminary report 36 on the quantum treatment of radiation near the zero dispersion wavelengths of the fiber. The quantum theories used to date for the propagation of electromagnetic wave omit the higher order dispersion terms and the dispersive nature of the nonlinear response 9 , 19 , 36 – 40 . We have developed a theory for canonical quantization of the radiation in the presence of the third order dispersion term 41 .…”