Applications of Nonlinear Fiber Optics by Govind Agrawal

By Govind Agrawal

This moment variation should be an account of nonlinear optical phenomena in fiber optics. It synthesizes examine fabric. specific realization is paid to the significance of nonlinear results within the layout of optical fiber communique platforms.

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9), where the soliton period becomes so long as v 1 that nothing much happens to the pulse over a few-cm-long grating. As δ is reduced, the pulse narrows down considerably. A reduction in pulse width by a factor of 3 occurs for δ 1053 m 1 in Fig. 16. This pulse narrowing is an indication that a Bragg soliton is beginning to form. However, the soliton period is still much longer than the grating length. In other words, the grating is not long enough to observe the final steady-state shape of the Bragg soliton.

6 Grating-induced GVD plotted as a function of δ for several values of the coupling coefficient κ . with the grating. If the pulse spectrum falls entirely within the stop band, the entire pulse is reflected by the grating. On the other hand, if a part of the pulse spectrum is outside the stop band, that part will be transmitted through the grating. The shape of the reflected and transmitted pulses will be quite different than that of the incident pulse because of the splitting of the spectrum and the dispersive properties of the fiber grating.

The analysis used to reduce the nonlinear coupled-mode equations to an effective NLS equation makes use of the Bloch formalism well known in solidstate physics. Even in the absence of nonlinear effects, the eigenfunctions associated with the photonic bands, corresponding to the dispersion relation q2 δ 2 κ 2 , are not A f and Ab but the Bloch waves formed by a linear combination of A f and Ab . If this basis is used for the nonlinear problem, Eqs. 4) reduce to an effective NLS equation provided two conditions are met.

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