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Applied Optics

Applied Optics


  • Vol. 28, Iss. 17 — Sep. 1, 1989
  • pp: 3567–3576

Multilayered slab waveguide design using a hybrid field vector

J. de Jong  »View Author Affiliations

Applied Optics, Vol. 28, Issue 17, pp. 3567-3576 (1989)

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A model is introduced that facilitates an easy scheme to design planar multilayered waveguides. The basis of this model is a field related vector that follows simply shaped trajectories as a function of the depth coordinate in the waveguide. Its diagram provides qualitative insight into the effects upon guided modes of a change in the number of layers, in their phase thicknesses and in the state of polarization. In addition, the method offers the possibility of studying the corresponding effects upon field components inside the waveguide.

© 1989 Optical Society of America

Original Manuscript: January 11, 1989
Published: September 1, 1989

J. de Jong, "Multilayered slab waveguide design using a hybrid field vector," Appl. Opt. 28, 3567-3576 (1989)

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  1. J. Chilwell, I. Hodgkinson, “Thin-Films Field-Transfer Matrix Theory of Planar Multilayer Waveguides and Reflection from Prism-Loaded Waveguides,” J. Opt. Soc. Am. A, 1, 742–753 (1984). [CrossRef]
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  9. For guided modes other authors call this kind of condition dispersion relation, characteristic equation, eigen value equation, eigen mode equation, or (characteristic) mode equation.
  10. The formulas obtained in this way are comparable with Eq. (7) of Y.-F. Li and J. W. Y. Lit [6]; ϕj equals their hjdj in layers where nj > β; ψj,+ equals their −ϕj+1, but their ϕj+1 is limited to the interval [0,π) while our |ψj,+| may amount to many times 2π.
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  14. χj−1,+ as defined here, is comparable with ψj in Eqs. (9b) and (14b) of Y.-F. Li and J. W. Y. Lit (2), and in Eq. 3(c) of Y.-F. Li and J. W. Y. Lit (6), if our ψj−1,+ is in Region I. If our ψj−1,+ is in Region II, their ψj equals our χj−1,+ + 1/2 πi.
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