Abstract

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

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  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).

2001 (1)

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).

2000 (2)

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).

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).

1998 (1)

M. Öz, R. R. Krchnavek, "Power loss analysis at a step discontinuity of a multimode optical waveguide," J. Lightw. Technol. 16, 2451-2457 (1998).

1993 (1)

G. Sztefka, H. P. Nolting, "Bidirectional eigenmode propagation for large refractive index steps," IEEE Photon. Technol. Lett. 5, 554 (1993).

1992 (1)

J. Gerdes, B. Lunitz, D. Benish, R. Pregla, "Analysis of slab waveguide discontinuities including radiation and absorption effects," Electron. Lett. 28, 1013-1015 (1992).

1988 (1)

B. M. A. Rahman, J. B. Davies, "Analysis of optical waveguide discontinuities," J. Lightw. Technol. 6, 52-57 (1988).

1986 (1)

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).

1983 (1)

F. Colombeau, "A multiplication of distributions," J. Math. Anal. Appl. 94, 96-115 (1983).

1978 (1)

T. E. Rozzi, "Rigorous analysis of the step discontinuity in a planar dielectric waveguide," IEEE Trans. Microw. Theory Tech. MTT-26, 738-746 (1978).

1977 (1)

L. Berg, "Multiplication of distributions," Math. Nachr. 195-202 (1977).

1975 (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).

1973 (1)

A. Yariv, "Coupled-mode theory for guided-wave optics," IEEE J. Quantum Electron. QE-9, 919-933 (1973).

Electron. Lett. (1)

J. Gerdes, B. Lunitz, D. Benish, R. Pregla, "Analysis of slab waveguide discontinuities including radiation and absorption effects," Electron. Lett. 28, 1013-1015 (1992).

IEEE Trans. Microw. Theory Tech. (1)

T. E. Rozzi, "Rigorous analysis of the step discontinuity in a planar dielectric waveguide," IEEE Trans. Microw. Theory Tech. MTT-26, 738-746 (1978).

IEEE J. Quantum Electron. (1)

A. Yariv, "Coupled-mode theory for guided-wave optics," IEEE J. Quantum Electron. QE-9, 919-933 (1973).

IEEE Photon. Technol. Lett. (1)

G. Sztefka, H. P. Nolting, "Bidirectional eigenmode propagation for large refractive index steps," IEEE Photon. Technol. Lett. 5, 554 (1993).

IEEE Trans. Microw. Theory Tech. (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).

J. Lightw. Technol. (1)

M. Öz, R. R. Krchnavek, "Power loss analysis at a step discontinuity of a multimode optical waveguide," J. Lightw. Technol. 16, 2451-2457 (1998).

J. Lightw. Technol. (1)

B. M. A. Rahman, J. B. Davies, "Analysis of optical waveguide discontinuities," J. Lightw. Technol. 6, 52-57 (1988).

J. Math. Anal. Appl. (1)

F. Colombeau, "A multiplication of distributions," J. Math. Anal. Appl. 94, 96-115 (1983).

J. Opt. Soc. Amer. A (3)

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).

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).

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).

Math. Nachr. (1)

L. Berg, "Multiplication of distributions," Math. Nachr. 195-202 (1977).

Opt. Commun. (1)

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).

Other (2)

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, 1972).

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1991).

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