OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 1, Iss. 7 — Jul. 1, 1984
  • pp: 742–753

Thin-films field-transfer matrix theory of planar multilayer waveguides and reflection from prism-loaded waveguides

John Chilwell and Ian Hodgkinson  »View Author Affiliations

JOSA A, Vol. 1, Issue 7, pp. 742-753 (1984)

View Full Text Article

Enhanced HTML    Acrobat PDF (1503 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A standard 2 × 2 matrix method-used in thin-film optics is applied to planar multilayer optical waveguides. All modes are required to satisfy substrate-to-cover field-transfer equations that reduce to the equation γcm11 + γcγsm12 + m21 + γsm22 = 0 for bound modes and leaky waves. Expressions are derived for the field profiles and the power in each medium. A first-order perturbation theory is developed and applied to absorbing multilayer guides and to the reflection of plane waves from the prism-loaded lossy multilayer guide. The latter leads to experimental arrangements for measuring losses in which the gap thickness and propagation constant are accessible parameters.

© 1984 Optical Society of America

Original Manuscript: October 27, 1983
Manuscript Accepted: February 17, 1984
Published: July 1, 1984

John Chilwell and Ian 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)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. G. Al-Jumaily, S. D. Browning, A. F. Turner, “Polarization-insensitive refracting system for integrated optics,” J. Opt. Soc. Am. 72, 1822 (A) (1982).
  2. H. Ito, H. Inaba, “Efficient phase matched second-harmonic generation method in four-layered optical-waveguide structure,” Opt. Lett. 2, 139–141 (1978). [CrossRef] [PubMed]
  3. P. K. Tien, “Light waves in thin films and integrated optics,” Appl. Opt. 10, 2395–2413 (1971). [CrossRef] [PubMed]
  4. P. K. Tien, R. Ulrich, “Theory of prism-film coupler and thin-film light guides,” J. Opt. Soc. Am. 60, 1325–1337 (1970). [CrossRef]
  5. N. S. Kapany, J. J. Burke, Optical Waveguides (Academic, New York, 1972).
  6. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).
  7. P. Yeh, A. Yariv, C. Hong, “Electromagnetic propagation in stratified media. 1. General theory,” J. Opt. Soc. Am. periodic 67, 423–438 (1977). [CrossRef]
  8. J. F. Revelli, D. Sarid, “Prism coupling into clad uniform optical waveguides,” J. Appl. Phys. 51, 3566–3575 (1980). [CrossRef]
  9. J. F. Revelli, “Enhancement of prism coupling efficiency in uniform optical waveguides: a correction,” J. Appl. Phys. 52, 3185–3189 (1981). [CrossRef]
  10. J. F. Revelli, “Mode analysis and prism coupling for multilayered optical waveguides,” Appl. Opt. 20, 3158–3167 (1981). [CrossRef] [PubMed]
  11. J. T. Chilwell, “Optical waveguiding in multilayer thin film stacks and the prism coupler: a matrix method,” Doctoral thesis (University of Otago, Dunedin, New Zealand, 1982).
  12. J. T. Chilwell, I. J. Hodgkinson, “Thin-film-matrix description of optical multilayer planar waveguides,” J. Opt. Soc. Am. 72, 1821 (A) (1982).
  13. I. J. Hodgkinson, J. T. Chilwell, “Reflection of plane waves from a prism-loaded lossy multilayer waveguide,” J. Opt. Soc. Am. 72, 1744–1745 (1982).
  14. S. A. Shakir, A. F. Turner, “Method of poles for multilayer thin-film waveguides,” Appl. Phys. A 29, 151–155 (1982). [CrossRef]
  15. M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975).
  16. R. Jacobsson, “Light reflection from films of continuously varying refractive index,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1966), Vol. 5. [CrossRef]
  17. R. Jacobsson, “Inhomogeneous and coevaporated homogeneous films for optical applications,” in Physics of Thin Films, G. Hass, M. H. Francombe, R. W. Hoffman, eds. (Academic, New York, 1975), Vol. 8.
  18. A. Thelen, “Design of multilayer interference filters,” in Physics of Thin Films, G. Hass, R. E. Thun, eds. (Academic, New York, 1969), Vol. 5.
  19. In standard notation, we have k= 2πλ−1= ωc-1, where λ is the vacuum wavelength and c the vacuum speed of light. Also, μ is the magnetic permeability and ɛ is the electric permittivity of the medium. The refractive index is given by n= (μɛ)1/2(μ0ɛ0)−1/2.
  20. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  21. R. Ulrich, “Theory of the prism-film coupler by plane-wave analysis,” J. Opt. Soc. Am. 60, 1337–1350 (1970). [CrossRef]
  22. J. E. Sipe, J. Becher, “Surface energy transfer enhanced by optical cavity excitation: a pole analysis,” J. Opt. Soc. Am. 72, 288–295 (1982). [CrossRef]
  23. Lotspeich has presented an approximate explicit solution of the propagation constant for the modal-dispersion function of a symmetric single-film waveguide [J. F. Lotspeich, “Explicit general eigenvalue solutions for dielectric slab waveguides,” Appl. Opt. 14, 327–335 (1975)]. [CrossRef] [PubMed]
  24. To this end, Hardey et al. have derived expressions for the number of TE modes in periodic multilayer waveguides [A. Hardy, E. Kapon, A. Katzir, “Expression for the number of guided TE modes in periodic multilayer waveguides,” J. Opt. Soc. Am. 71, 1283–1285 (1981)]. [CrossRef]
  25. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972).
  26. The propagation constant is real or complex depending on the type of solution taken for Eq. (24) and whether or not the waveguide is perfect with real refractive indexes or dissipative. To summarize: (1) for bound modes (ns< β> nc), β is real in the nondissipative case and complex in the dissipative case; (2) for radiation modes (β< nc and/or ns), β is always real (or imaginary when evanescent radiation modes are considered; see Ref. 6, p. 27); (3) for leaky waves (β< nc and/or ns), β is always complex.
  27. Z. Knittl, Optics of Thin Films (Wiley, London, 1976), pp. 229–233.
  28. R. Ulrich, W. Prettl, “Planar leaky lightguides and couplers,” Appl. Phys. 1, 55–68 (1973). [CrossRef]
  29. R. Th. Kersten, “The prism–film coupler as a precision instrument. Part II. Measurements of refractive index and thickness of leaky wave guides,” Opt. Acta 22, 515–521 (1975). [CrossRef]
  30. R. Ulrich, W. Prettl [“Planar leaky lightguides and couplers,” Appl. Phys. 1, 55–68 (1973)] have classified leaky waves into two groups according to the properties of the stack. Lummer–Gehrcke waves occur when the waveguide can support bound modes. However, if the maximum refractive index of the waveguide is found to be the cover or substrate index, only leaky waves can be supported; these are referred to as low-index waves. [CrossRef]
  31. J. Kane, H. Osterberg, “Optical characteristics of planar guided modes,” J. Opt. Soc. Am. 54, 347–352 (1964). [CrossRef]
  32. The incident plane waves in the prism have real β, and β is a constant throughout the system. Note that this situation can be thought of as radiation modes of a particular class of waveguide.
  33. J. T. Chilwell, “Prism coupler jig: interference fringes enable observation of the coupling gap,” Appl. Opt. 21, 1310–1319 (1982). [CrossRef] [PubMed]
  34. O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).
  35. J. M. Eastman, “Scattering by all-dielectric multilayer bandpass filters and mirrors for lasers,” in Physics of Thin Films, G. Hass, M. H. Francombe, eds. (Academic, New York, 1978), Vol. 10.
  36. J. Ebert, H. Pannhorst, H. Küster, H. Welling, “Scatter losses of broadband interference coatings,” Appl. Opt. 18, 818–822 (1979). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited