Integrated Optics - download pdf or read online

By T. Tamir (auth.), Professor Theodor Tamir (eds.)

ISBN-10: 3662432080

ISBN-13: 9783662432082

ISBN-10: 3662432102

ISBN-13: 9783662432105

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27) 34 H. 4. Mode Properties Following from Symmetry Several phase relationships between the modal field components follow directly from the symmetry of both the waveguide and of Maxwell's equations. We shall use both time-reversal and z-reversal to construct new solutions E2 (r,t), H2 (r,t) from known solutions E1 (r,t), H1 (r,t). 28) In terms of the complex amplitudes, this can be written as E2 (r)=Ei(r); H 2 (r) = -Hf(r). 30) which is true for all isotropic dielectric waveguides. 32) where we have omitted to indicate the (x,y) dependence in order to emphasize the z-reversal operation.

The energy W stored per unit guide length is obtained by integrating w over the guide cross section +oo W= JJdxdyw(x,y). 79) -oo The group velocity v9 of the mode is the velocity at which signals carried by the mode propagate. It is determined from the dispersion relation w(f3) of the guide by v9 =dw/df3. 73) to cases where all variations are caused by perturbations in w alone, we deduce the simple relation P=(dwjd{J)W=v 9 W, which is known to hold for many other waveguide structures. 82) -co +co JS dxdyJ1Hz·H;.

35) We have constructed an evanescent mode with a real valued electric field and an imaginary magnetic field. In general, Ev and Hv of an evanescent mode are 90° out of phase. 5. 18, 19]. This important property holds for both the guided and the radiation modes; it is the basis for much of waveguide theory, including the theories of waveguide excitation, of waveguide discontinuities and waveguide perturbations. We will sketch here a derivation of the orthogonality relations which makes apparent their connection with power conservation and reciprocity.

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Integrated Optics by T. Tamir (auth.), Professor Theodor Tamir (eds.)

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