By J. K. Shaw
ISBN-10: 0898715563
ISBN-13: 9780898715569
The synergism among the realm huge internet and fiber optics is a well-known tale to researchers of electronic communications. Fibers are the enablers of the premiums of knowledge movement that make the web attainable. at present transoceanic optical fiber cables transmit information at charges which could move the contents of a good collage library in a couple of minutes. No different medium is able to this cost of transmission at such distances.
With the maturing of cellular moveable telephony and the rising broadband entry industry, better fiber transmission skill should be crucial within the early twenty first century. because the call for for extra means drives the advance of latest optics-based applied sciences, fiber optics consequently continues to be a colourful quarter for examine. figuring out that the fundamental fiber optic know-how is mature signifies that open questions are extra sharply centred and allow deeper mathematic content material.
Mathematical ideas of Optical Fiber Communications is meant to help and advertise interdisciplinary learn in optical fiber communications by way of offering crucial heritage in either the actual and mathematical ideas of the self-discipline. bankruptcy themes comprise the fundamentals of fibers and their development, fiber modes and the criterion of unmarried mode operation, the nonlinear Schrödinger equation, the variational method of the research of pulse propagation, and, eventually, solitons and a few new effects on soliton formation power thresholds. those chapters are written to be as autonomous as attainable whereas taking the reader to the frontiers of study on fiber optics communications.
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Additional info for Mathematical Principles of Optical Fiber Communication (CBMS-NSF Regional Conference Series in Applied Mathematics)
Sample text
Important further simplification arise from the slowly varying envelope approximation (S VEA) [ Ag 1 ], which begins by postulating that the signal under consideration has a central 32 Chapter 3. Fiber Dispersion and Nonlinearity carrier frequency WQ and that the distributed frequency components are concentrated near (OQ. 10) are then postulated to have the form where cc stands for the complex conjugate. 12) the most rapid oscillations are accounted for by the exponentials; the complex-valued function T(x, y, z, t) is called the complex envelope of the carrier wQ.
4. 6) that |A(0,0)|2 = |M(0)|2 = PQ, where PQ is the peak power. 7) actually reduce to a single differential equation. 7) is differentiated to obtain azz = —2/82(0^ + azb), then a(z)bz can be replaced by 48 Chapter 4. 7). 8), and taking advantage of a fortuitous cancellation leads to the second-order nonlinear ordinary differential equation for the pulse width parameter a(z). 9), the initial width fl(0) will be specified; that is, «(0) = GO will be given. 6) one sees that «0 = T0 and also b(0) = -C/(2702) = -C/(2flj§).
U = A,v = A*. 2 Gaussian Ansatz and Width Parameter The variational method is used in fiber optics by combining the Lagrangian with the Ritz procedure [BPJ], in which a particular form, or class of shapes, for the envelope A(z, t) is assumed and the functional /(A) = f£ L(z, t, A, A*, A,, A*, A,, A*)dzdt is minimized over the restricted class. As mentioned, the most widely used envelope pattern is the Gaussian. 41) led Anderson [And] to the Gaussian pulse ansatz where M(z), a(z), and b(z) are functions of z only with M(z) complex valued.