Elements of Photonics, Volume II : For Fiber and Integrated by Keigo Iizuka; John Wiley & Sons, Inc

By Keigo Iizuka; John Wiley & Sons, Inc

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Extra info for Elements of Photonics, Volume II : For Fiber and Integrated Optics

Example text

3, the characteristic equation was derived by the method of wave optics. In this section, a few other available methods are presented. Since the methods will be explained using the simplest geometry, there is little basis for preferring one method over the other; but for more complicated multilayer guides, the choice of the method makes a marked difference in complexity of the treatment. For the sake of comparison, the same geometry and the familiar TM wave are used for all cases. The three methods described in this section for obtaining the characteristic equation are (1) the coefficient matrix method, (2) the transmission matrix method, and (3) the modified ray model method.

This section deals with guides whose boundary fields are evanescent waves. Now let us deal with the case of a guide for which the fields in the bottom layer as well as in the top layer are unbounded waves. The unbounded field in the bottom layer is the evanescent wave Hy0 x , which is expressed by the bottom equation of Eq. 11). The bottom equation of Eq. 11) is inserted into Eq. 83 The unbounded field Hy2 x in the top layer is also an evanescent wave and is expressed by the top equation of Eq.

All other parameters are the same as before. 81 Ez 2d Ez 0 cos 2Kd Z sin 2Kd 1 The geometry of the layers alone can never determine the field inside the medium. It is only after the fields on the boundary are specified that the field inside the medium is determined. The specification of the field can be the field Hy or Ez itself, as in the case of a given incident field to the boundary; or the field specification can be an unbounded traveling wave, a ratio of reflected to incident waves (standing wave), or an evanescent wave.

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