## 121 Material and Fabrication

The material of choice for low-loss optical fibers is pure silica glass synthesized by fusing SiO2 molecules. The refractive-index difference between the core and the cladding is realized by the selective use of dopants during the fabrication process. Dopants such as GeO2 and P2O5 increase the refractive index of pure silica and are suitable for the core, while materials such as boron and fluorine are used for the cladding because they decrease the refractive index of silica. Additional dopants...

## 242 Finite Difference Methods

Although the split-step Fourier method is commonly used for analyzing nonlinear effects in optical fibers, its use becomes quite time-consuming when the NLS equation is solved for simulating the performance of wavelength-division-multiplexed (WDM) lightwave systems. In such systems, the temporal resolution should be a small fraction of the entire bandwidth of the WDM signal. For a 100-channel system, the bandwidth approaches 10 THz, requiring a temporal resolution of 10 fs. At the same time,...

## Self Phase Modulation

An interesting manifestation of the intensity dependence of the refractive index in nonlinear optical media occurs through self-phase modulation (SPM), a phenomenon that leads to spectral broadening of optical pulses 1 - 9 . SPM is the temporal analog of self-focusing. Indeed, it was first observed in 1967 in the context of transient self-focusing of optical pulses propagating in a CS> -filled cell 1 . By 1970, SPM had been observed in solids and glasses by using picosecond pulses. The...

## 132 Stimulated Inelastic Scattering

The nonlinear effects governed by the third-order susceptibility X3 are elastic in the sense that no energy is exchanged between the electromagnetic field and the dielectric medium. A second class of nonlinear effects results from stimulated inelastic scattering in which the optical field transfers part of its energy to the nonlinear medium. Two important nonlinear effects in optical fibers fall in this category both of them are related to vibrational excitation modes of silica. These...

## 7z m Uz mmU5z m dm

Performing the differentiation and limit operations indicated in Eq. (3.3.6), we obtain In the case of a chirped Gaussian pulse U7 z m can be obtained from Eqs. (3.2.15) and (3.3.2) and is given by If we differentiate Eq. (3.3.10) two times and substitute the result in Eq. (3.3.9), we find that the integration over m can be performed analytically. Both T and (T2) can be obtained by this procedure. Using the resulting expressions in Eq. (3.2.25), we obtain 9 where c0 is the initial RMS width of...

## Z5f goSKW4310

A similar relation holds for a sech pulse with only a slight change in the numerical coefficient (0.43 in place of 0.39). For picosecond pulses with T0 1 Figure 4.16 Self-steepening of a Gaussian pulse in the dispersionless case. Dashed curve shows the input pulse shape at z 0. Figure 4.17 Spectrum of a Gaussian pulse at a distance z 0.2LNL 5, where s 0.01 and Lnl is the nonlinear length. Self-steepening is responsible for the asymmetry in the SPM-broadened spectrum. The effects of GVD are...

## Nonlinear Fiber Optics

The Institute of Optics University of Rochester A Harcourt Science and Technology Company San Diego San Francisco New York Boston London Sydney Tokyo This book is printed on acid-free paper. Copyright 2001, 1995 by ACADEMIC PRESS Copyright 1989 by AT amp T Bell Laboratories All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system,...