By Arthur Cox

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24 H. - II 'j_jl /, 'II II IVI I V I 1/ I. ,...... ::~ ~ h ~ II VI 'I/. 0 P" 'I. ~ ~-~ r---ijf-1/e_ I;,// 2 J v)) 4 6 /1/Y 8 110 V= kh(nf2-n,2)2 12 14 16 Fig. 8. 20), we determine the cutoff frequency V0 of the fundamental mode as V0 =tan- 1 Va. 24) For the TM-mode, we get cut-off conditions of the same form as for the TE-mode and w-[3 diagrams that are very similar. In fact, when the index differences (nr- n5 ) are small, we can apply the diagram of Fig. 8 to the TM modes. 2 under aM. 3. The Goos-Hiinchen Shift So far, we have described the light in the waveguide in terms of plane waves and their wave normals and phases.

82) -co +co JS dxdyJ1Hz·H;. 83) -co Here we have also distinguished between the energy portions stored by the transverse (t) and longitudinal (z) field components, and have left out the mode label v to simplify the notation. 5, that the first terms vanish. 86) f3P = 2w(W~- W~). 88) stating the equality of the stored electric energy W' and the stored magnetic energy W~'. The same relation also follows from the complex Poynting theorem. 90) 44 H. 21]. 91) which ties the difference between dinal field components.

3. The Goos-Hiinchen Shift So far, we have described the light in the waveguide in terms of plane waves and their wave normals and phases. In this subsection and in the next, we consider also the energy of the light and its flow through the guide. To prepare for this, we have to be more precise about what we mean by a light ray. A light ray is defined here as the direction of the Poynting vector or the energy flow of light. Consistent with this is the view of a ray as the axis of a narrow beam of light or wave packet.

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A system of optical design by Arthur Cox

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