OSA's Digital Library

Journal of Lightwave Technology

Journal of Lightwave Technology


  • Vol. 30, Iss. 15 — Aug. 1, 2012
  • pp: 2455–2471

Exact Solution of Facet Reflections for Guided Modes in High-Refractive-Index-Contrast Sub-Wavelength Waveguide Via a Fourier Analysis and Perturbative Series Summation: Derivation and Applications

Yijing Chen, Yicheng Lai, Tow Chong Chong, and Seng-Tiong Ho

Journal of Lightwave Technology, Vol. 30, Issue 15, pp. 2455-2471 (2012)

View Full Text Article

Acrobat PDF (3909 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

  • Export Citation/Save Click for help


Facet reflections at the waveguide-air interface for strongly-guiding waveguides with sub-wavelength scale dimensions do not follow the usual Snell's law. Significant amount of reflected power can be channeled into higher order modes as well as radiation modes. This paper shows for the first time how the exact analytical solution of the facet reflection can be obtained by using a new technique based on Fourier analysis and perturbative series summation without the need for approximation or iteration. The proposed analysis enables the distribution of power reflected into various guided and radiation modes to be readily computed. Through this technique, a spectral overlapping criterion and a coupling matrix are derived that analyze effectively the power distribution among all the strongly and weakly-coupled radiation modes in an end-facet reflection. Accurate pre-determination of the number of radiation modes for efficient computation without compromising resultant accuracy is achieved. More importantly, the anomalous wave reflection behaviors at the facet of a strongly-guiding waveguide are presented. These include anomalous high radiation modes coupling as a function of cladding refractive index not reported before. This paper further includes an exemplary illustration of the analysis based on a symmetric planar nano-waveguide with high refractive index contrast for both TE and TM polarization under fundamental incident mode.

© 2012 IEEE

Yijing Chen, Yicheng Lai, Tow Chong Chong, and Seng-Tiong Ho, "Exact Solution of Facet Reflections for Guided Modes in High-Refractive-Index-Contrast Sub-Wavelength Waveguide Via a Fourier Analysis and Perturbative Series Summation: Derivation and Applications," J. Lightwave Technol. 30, 2455-2471 (2012)

Sort:  Year  |  Journal  |  Reset


  1. G. L. Lewin, "A method for the calculation of the radiation-pattern and mode-conversion properties of a solid-state heterojunction laser," IEEE Trans. Microw. Theory Tech. MTT-23, 576-585 (1975).
  2. M. Öz, R. R. Krchnavek, "Power loss analysis at a step discontinuity of a multimode optical waveguide," J. Lightw. Technol. 16, 2451-2457 (1998).
  3. A. Yariv, "Coupled-mode theory for guided-wave optics," IEEE J. Quantum Electron. QE-9, 919-933 (1973).
  4. P. G. Suchoski, Jr.V. Ramaswamy, "Exact numerical technique for the analysis of step discontinuities and tapers in optical dielectric waveguides," J. Opt. Soc. Amer. A 3, 194-202 (1986).
  5. T. E. Rozzi, "Rigorous analysis of the step discontinuity in a planar dielectric waveguide," IEEE Trans. Microw. Theory Tech. MTT-26, 738-746 (1978).
  6. T.-L. Wu, H.-W. Chang, "Guiding mode expansion of a TE and TM transverse-integral equation for dielectric slab waveguides with an abrupt termination," J. Opt. Soc. Amer. A 18, 2823-2832 (2001).
  7. K. P. Fakhri, P. Benech, "A new technique for the analysis of planar optical discontinuities: An iterative modal method," Opt. Commun. 177, 233-243 (2000).
  8. I. G. Tigelis, A. B. Manenkov, "Analysis of mode scattering from an abruptly ended dielectric slab waveguide by an accelerated iteration technique," J. Opt. Soc. Amer. A 17, 2249-2259 (2000).
  9. B. M. A. Rahman, J. B. Davies, "Analysis of optical waveguide discontinuities," J. Lightw. Technol. 6, 52-57 (1988).
  10. J. Gerdes, B. Lunitz, D. Benish, R. Pregla, "Analysis of slab waveguide discontinuities including radiation and absorption effects," Electron. Lett. 28, 1013-1015 (1992).
  11. G. Sztefka, H. P. Nolting, "Bidirectional eigenmode propagation for large refractive index steps," IEEE Photon. Technol. Lett. 5, 554 (1993).
  12. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, 1972).
  13. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1991).
  14. F. Colombeau, "A multiplication of distributions," J. Math. Anal. Appl. 94, 96-115 (1983).
  15. L. Berg, "Multiplication of distributions," Math. Nachr. 195-202 (1977).

Cited By

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