Analysis of Mode Coupling in Planar Optical Waveguides

Abstract

Coupling between the modes in a planar optical waveguide induced by a boundary step discontinuity, by a single groove and by a grating with arbitrary cross section, is investigated theoretically. Analytical expressions for the coupling mode coefficients are obtained by the mode-matching method, containing the angular dependence in explicit form for both TE and TM incidence. An analogy of Brewster's law for a planar waveguide with a single step boundary discontinuity is obtained. The results for gratings are compared with the coupled-mode theory and the total field analysis.

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“…One of the significant advantages of this approach is that it is immediately applicable to all types of waves, including bulk, guided, and surface optical and acoustic waves in oblique periodic Bragg arrays with sufficiently small grating amplitude, and thickness 8 that is much larger than the wavelength of the incident wave (or the grating period). For example, the derived couple wave equations describe DEAS of optical modes guided by a slab with a corrugated boundary if the coupling coefficients Γ 0j and Γ 1j are taken from the known coupled wave theories for the conventional Bragg scattering [15,21,22,23]. Therefore, all the graphs presented above are valid for slab modes if the wave numbers of the incident and scattered modes are equal: k 0 = k 1 (i.e.…”

“…1 is the plane of a guiding slab, and the incident and scattered waves are modes guided by this slab. The only difference between scattering of different types of waves are different values of coupling coefficients Γ 0j and Γ 1j that are already determined in the conventional theory of scattering [5,15,16,21,22,23]. For example, in the case of bulk TE electromagnetic waves in arrays described by Equation (1) we obtain [5,16]:…”

“…Detailed discussions of applicability conditions for this approximation in the cases of EAS and DEAS are presented below in Section 4. Similarly to how it was done in [3,5,7,8,14], the coupled wave equations in the separated arrays, describing DEAS, can be derived by means of separate analyses of the diffractional divergence of the scattered wave (by means of the parabolic equation of diffraction [3,7,8,14] or Fourier analysis [5,14]), and scattering (by means of the conventional theory of scattering [5,15,16,21,22,23]). In the steady-state DEAS the contribution to the scattered wave amplitude from scattering is exactly compensated by the contribution from the diffractional divergence.…”

“…1), Γ 0j and Γ 1j are the coupling coefficients in the wellknown coupled wave equations [5,15,16,21,22,23] …”

Extremely asymmetrical scattering in gratings with varying mean structural parameters

“…Using speculations similar to those in section 2, one comes to the conclusion that equations (4) also describe EAS of guided modes in gratings with varying mean thickness at the grating boundaries. However, the coupling coefficients Γ 0 and Γ 1 are obviously different from those for bulk TE waves and are determined in the approximate theories of conventional Bragg scattering in corrugation gratings with grooves parallel to the grating boundaries [22][23][24][25]. The wave numbers for the incident and scattered modes (e.g.…”