By Govind Agrawal
This moment version might be an account of nonlinear optical phenomena in fiber optics. It synthesizes learn fabric. specific recognition is paid to the significance of nonlinear results within the layout of optical fiber conversation structures.
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29) The transmission coefficient tg can be obtained in a similar manner. The frequency dependence of rg and tg shows the filter characteristics associated with a fiber grating. 7 shows the reflectivity rg 2 and the phase of rg as a function of detuning δ for two values of κ L. The grating reflectivity within the stop band approaches 100% for κ L 3 or larger. Maximum reflectivity occurs at the center of the stop band and, by setting δ 0 in Eq. 3 µ m. (After Ref. 93. The condition κ L 2 with κ 2πδ n1 λ can be used to estimate the grating length required for high reflectivity inside the stop band.
These nonlinear effects can be included by solving the nonlinear coupled-mode equations, Eqs. 12). 23 CW Nonlinear Effects In this section, these equations are used to study the nonlinear effects for CW beams. The time-dependent effects are discussed in later sections. 1 Nonlinear Dispersion Curves In almost all cases of practical interest, the β 2 term can be neglected in Eqs. 12). For typical grating lengths ( 1 m), the loss term can also be neglected by setting α 0. 2) where vg is the group velocity far from the stop band associated with the grating.
8), the GVD parameter β2g can be shown to be the same as in Eq. 26). Several features of Eq. 9) are noteworthy when this equation is compared with the standard NLS equations. First, the variable U represents the amplitude of the envelope associated with the Bloch wave formed by a superposition of A f and Ab . Second, the parameters β2g and γg are not constants but 32 Fiber Gratings depend on the speed-reduction factor v. Both increase as v decreases and become infinite at the edges of the stop band where v 0.