By M. S. Sodha, A. K. Ghatak (auth.)

The propagation of electromagnetic waves in "square-law" media, i.e., media characterised by means of a quadratic spatial edition of the dielectric consistent, has been a favourite topic of research in electromagnetic concept. even though, with the new fabrication of glass fibers with a quadratic radial version of the dielectric consistent and the appliance of such fibers to optical imaging and communications, this topic has additionally assumed functional significance. comparability of experimental effects on propagation, resolu tion, and pulse distortion in such inhomogeneous waveguides with idea has positioned the sphere on a valid base and spurred extra paintings. the current e-book goals at featuring a unified view of vital features of our wisdom of inhomogeneous optical waveguides. a short dialogue of homogeneous dielectric waveguides is unavoidable, in view that itforms a foundation for the appreciation of inhomogeneous waveguides. a brief direction according to a few chapters of this publication used to be provided to graduate scholars at IIT Delhi and used to be good obtained. We ponder that regardless of the unavoidable mathemati cal nature of the current e-book, the comparability of experimental effects with conception all through and the outline of fabrication expertise (Appen dixes A and B) may still make its allure common. The authors are thankful to Dr. okay. Thyagarajan for writing so much of bankruptcy nine and to their colleagues Dr. I. C. Goyal, Dr. B. P. friend, and Dr. A.

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19) +OO -00 K(x, x', z)cf>{x', z = 0) dx' where K(x, x', z) = L I{I~(x')I{In(x) exp(-if3nz) n *8mn = 0 if n ". m; 8mn = 1 if n = m. 20) CHAPTER 3 38 represents the kernel. 19) is of the same form as those encountered in diffraction theory [see, for example, Born and Wolf (1970)]. The summation appearing in Eq. 20) can be carried out provided we neglect terms of O[(c/ w ) (Ki/2 / Ko)] in the binomial expansion of the RHS ofEq. 21) Substituting the expressions for o/n from Eq. 16) and for f3n from Eq.

Therefore, in all subsequent analysis we will assume the cladding thickness to be infinite. , n2 = 1). However, it is always preferred to have a cladding because of the following reasons. (i) Since the fiber has to be supported, imperfections will arise at the boundary of the core. Such imperfections will lead to losses of the propagating beams. 55 CHAPTER 4 56 Fig. 1. The optical fiber; i denotes the angle of incidence of a ray incident on the fiber. (ii) The number of guided modes is determined (as will be shown later) by nh n2, and the core radius.

32) where C= exp(-2KZ) A(z) = (a 2+ 1)2+ C 2(a 2-1)2+2C(a4 -1) cos 25z ( X x, z )1/2_1<,) ) = (~(K C Or 2 Z U 1 +2 tan -1 [ eC(a 4 -1) sin 25z A(z) C(a 2-1) sin 25z ] a 2+ 1 + C(a 2-1) cos 25z 42 CHAPTER 3 and we have assumed that KOi « K or. 33) This equation reduces to Eq. 31) in the absence of absorption, namely as C -71. It is evident from Eq. 33) that in the limit z -7 00, C -70 and the beamwidth tends to a value equal to the fundamental beamwidth of the medium. 3. The Parabolic Equation Approach When Ko and K2 are dependent on z, the modal analysis approach (for finding the intensity distribution as the beam propagates through the medium) becomes very cumbersome.