2015光通信原理与技术--12-20150520Joseph C Palais.pdfVIP

Optical Communications: Principles and Technologies 2015/05/20 Nonlinear Effects in Optical Fibers Four Wave Mixing (FWM) Consider the incidence of three waves at th f i d i tree requenc es 2, 3, an 4 n o an optical fiber. In the presence of the three waves, the third- order nonlinearity in the fiber leads to the generation of a nonlinear polarization at frequency 1 given by Four Wave Mixing (FWM) This nonlinear polarization can, under some circumstances, lead to the generation of electromagnetic waves at the new frequency 1. This phenomenon is referred to as four-wave mixing (FWM). In a dense wavelength division multiplexed (DWDM) system, FWM leads to cross talk among different wavelength channels of the system. Four Wave Mixing (FWM) The nonlinear polarization at frequency 1 due to the presence of other waves is given by 3 4 2 1where , and and i iA represent the an modal field profid di amplit d f udes les correspon ng to mo es at requency .i Four Wave Mixing (FWM) From the expression for the nonlinear polarization it can be seen that, in general, the velocity of the nonlinear polarization is not equal to the velocity of the electromagnetic waves that it is generating . Four Wave Mixing (FWM) For efficient generation of the electromagnetic wave at the frequency 1, there must be phase matching, i.e., the velocity of the nonlinear polarization (which acts as the source of the radiation at frequency 1) and the electromagnetic wave (at frequency 1) must be equal. Four Wave Mixing (FWM) For this to happen we must have 0. 1 2 3 2 4 2 Assuming the frequencies to be closely and equally spaced (i.e., , , ) and making a2 2Taylor series expansion of all s about a frequency 2 24 D where represents the frequency spacing =2 c between adjacent channels. Dispersion coefficient (fiber chromatic dispersion) D dd 22 dc d d c d d d d D g 2 2 2 c d 2 2 2 22 22 d d cd d c 2 2 2 2 d dc 332 afafafff ... !3!2!1 axaxaxax 2 3 2 2 3 32 2 . 4