Abstract

The scattering phenomenon from an arbitrary-shaped end of a asymmetrical slab waveguide for the cases of TE and TM guided modes is simulated by means of boundary integral equations that are called guided-mode extracted integral equations. The integral equations that we derive can be solved by the conventional boundary-element method. Numerical results are presented for problems of three-layer asymmetrical waveguides with tilted ends. The reflection coefficient, reflected and scattered powers, and radiation patterns are calculated numerically for the cases of incident TE and TM guided modes.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. Aoyama, K. Nakagawa, T. Itoh, “Optical time domain reflectometry in a single-mode fiber,” IEEE J. Quantum Electron. QE-17, 862–868 (1981).
    [CrossRef]
  2. E. Nishimura, N. Morita, N. Kumagai, “Scattering of guided-modes caused by an arbitrarily shaped broken end in a dielectric slab waveguide,” IEEE Trans. Microwave Theory Tech. MTT-31, 923–930 (1983).
    [CrossRef]
  3. D. Marcuse, “Radiation losses of tapered dielectric slab waveguides,” Bell Syst. Tech. J. 49, 273–290 (1970).
    [CrossRef]
  4. G. H. Brooke, M. M. Z. Kharadly, “Step discontinuities on dielectric waveguides,” Electron. Lett. 12, 473–475 (1976).
    [CrossRef]
  5. T. E. Rozzi, “Rigorous analysis of the step discontinuity in a planar dielectric waveguide,” IEEE Trans. Microwave Theory Tech. MTT-26, 738–746 (1978).
    [CrossRef]
  6. K. Morishita, S. Inagaki, N. Kumagai, “Analysis of discontinuities in dielectric waveguides by means of the least-squares boundary residual method,” IEEE Trans. Microwave Theory Tech. MTT-27, 310–315 (1979).
    [CrossRef]
  7. A. Ittipiboon, M. Hamid, “Scattering of surface waves at a slab waveguide discontinuity,” Proc. Inst. Electr. Eng. 126, 798–804 (1979).
    [CrossRef]
  8. H. Yajima, “Coupled mode analysis of dielectric planar branching waveguides,” IEEE J. Quantum Electron. QE-14, 749–755 (1978).
    [CrossRef]
  9. K. Uchida, K. Aoki, “Scattering of surface waves on transverse discontinuities in symmetrical three-layer dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-32, 11–19 (1984).
    [CrossRef]
  10. Y. P. Chiou, H. C. Chang, “Analysis of optical waveguide discontinuities using Pade approximants,” IEEE Photon. Technol. Lett. 9, 964–966 (1997).
    [CrossRef]
  11. A. B. Manenkov, “Propagation of a surface wave along a dielectric waveguide with an abrupt change of parameters. II: Solution by variational method,” Radiophys. Quantum Electron. 25, 1050–1055 (1982).
    [CrossRef]
  12. A. B. Manenkov, “Step discontinuities in dielectric waveguide (fibres),” Opt. Quantum Electron. 22, 65–76 (1990).
    [CrossRef]
  13. A. B. Manenkov, “Reflection of the surface mode from an abruptly ended W-fibre,” IEE Proc. J. 139, 101–104 (1992).
  14. T. J. M. Boyd, I. Moshkun, I. M. Stephenson, “Radiation losses due to discontinuities in asymmetric three-layer optical waveguides,” Opt. Quantum Electron. 12, 143–158 (1980).
    [CrossRef]
  15. I. G. Tigelis, A. B. Manenkov, “Scattering from an abruptly terminated asymmetrical slab waveguide,” J. Opt. Soc. Am. A 16, 523–532 (1999).
    [CrossRef]
  16. G. Latsas, A. B. Manenkov, I. G. Tigelis, E. Sarri, “Reflectivity properties of an abruptly ended asymmetrical slab waveguide for the case of transverse magnetic modes,” J. Opt. Soc. Am. A 17, 162–172 (2000).
    [CrossRef]
  17. Q. Liu, W. C. Chew, “Analysis of discontinuities in planar dielectric waveguides: an eigenmode propagation method,” IEEE Trans. Microwave Theory Tech. 39, 422–429 (1991).
    [CrossRef]
  18. K. Ogusu, “Transmission characteristics of single-mode asymmetric dielectric waveguide Y-junction,” Opt. Commun. 53, 169–172 (1985).
    [CrossRef]
  19. C. Vassallo, “Reflectivity of multi-dielectric coatings depos-ited on the end facet of a weakly guiding dielectric slab waveguide,” J. Opt. Soc. Am. A 5, 1918–1928 (1988).
    [CrossRef]
  20. J. Buus, “Analytic approximation for the reflectivity of DH lasers,” IEEE J. Quantum Electron. QE-17, 2256–2257 (1981).
    [CrossRef]
  21. M. Kosiba, K. Ooishi, T. Miki, M. Suzuki, “Finite-element analysis of the discontinuities in a dielectric slab waveguide bounded by parallel plates,” Electron. Lett. 18, 33–34 (1982).
    [CrossRef]
  22. M. Kosiba, M. Suzuki, “Boundary-element analysis of dielectric slab waveguide discontinuities,” Appl. Opt. 25, 828–829 (1986).
    [CrossRef]
  23. E. Nishimura, N. Morita, N. Kumagai, “An integral equation approach to electromagnetic scattering from arbitrary shaped junction between multilayered dielectric planer waveguides,” J. Lightwave Technol. LT-3, 887–894 (1985).
    [CrossRef]
  24. D. Marcuse, Theory of Dielectric Optical Waveguide, 2nd ed. (Academic, London, 1991), Chap. 1.
  25. K. Tanaka, M. Kojima, “New boundary integral equa-tions for computer-aided design of dielectric waveguide circuits,” J. Opt. Soc. Am. A 6, 667–674 (1989).
    [CrossRef]
  26. K. Tanaka, M. Tanaka, “Computer-aided design of dielectric optical waveguide by the boundary-element method based on guided-mode extracted integral equations,” J. Opt. Soc. Am. A 13, 1362–1368 (1996).
    [CrossRef]
  27. K. Tanaka, M. Tanaka, H. Tashima, H. Ootera, Y. Yoshino, “New integral equation method for CAD of open waveguide bends,” Radio Sci. 28, 1219–1227 (1993).
    [CrossRef]
  28. M. Tanaka, K. Tanaka, “Boundary integral equations for computer-aided design and simulations of near-field optics: two-dimensional optical manipulator,” J. Opt. Soc. Am. A 15, 101–108 (1997).
    [CrossRef]
  29. K. Tanaka, M. Tanaka, T. Omoya, “Boundary integral equations for a two-dimensional simulator of a photon scanning tunneling microscope,” J. Opt. Soc. Am. A 15, 1918–1931 (1998).
    [CrossRef]
  30. K. Tanaka, “New integral equations for designing dielectric waveguide bend circuits: guided-mode extracted integral equations,” Electron. Commun. Jpn. Part 2 76, 1–11 (1993).
    [CrossRef]

2000

1999

1998

1997

M. Tanaka, K. Tanaka, “Boundary integral equations for computer-aided design and simulations of near-field optics: two-dimensional optical manipulator,” J. Opt. Soc. Am. A 15, 101–108 (1997).
[CrossRef]

Y. P. Chiou, H. C. Chang, “Analysis of optical waveguide discontinuities using Pade approximants,” IEEE Photon. Technol. Lett. 9, 964–966 (1997).
[CrossRef]

1996

1993

K. Tanaka, M. Tanaka, H. Tashima, H. Ootera, Y. Yoshino, “New integral equation method for CAD of open waveguide bends,” Radio Sci. 28, 1219–1227 (1993).
[CrossRef]

K. Tanaka, “New integral equations for designing dielectric waveguide bend circuits: guided-mode extracted integral equations,” Electron. Commun. Jpn. Part 2 76, 1–11 (1993).
[CrossRef]

1992

A. B. Manenkov, “Reflection of the surface mode from an abruptly ended W-fibre,” IEE Proc. J. 139, 101–104 (1992).

1991

Q. Liu, W. C. Chew, “Analysis of discontinuities in planar dielectric waveguides: an eigenmode propagation method,” IEEE Trans. Microwave Theory Tech. 39, 422–429 (1991).
[CrossRef]

1990

A. B. Manenkov, “Step discontinuities in dielectric waveguide (fibres),” Opt. Quantum Electron. 22, 65–76 (1990).
[CrossRef]

1989

1988

1986

1985

E. Nishimura, N. Morita, N. Kumagai, “An integral equation approach to electromagnetic scattering from arbitrary shaped junction between multilayered dielectric planer waveguides,” J. Lightwave Technol. LT-3, 887–894 (1985).
[CrossRef]

K. Ogusu, “Transmission characteristics of single-mode asymmetric dielectric waveguide Y-junction,” Opt. Commun. 53, 169–172 (1985).
[CrossRef]

1984

K. Uchida, K. Aoki, “Scattering of surface waves on transverse discontinuities in symmetrical three-layer dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-32, 11–19 (1984).
[CrossRef]

1983

E. Nishimura, N. Morita, N. Kumagai, “Scattering of guided-modes caused by an arbitrarily shaped broken end in a dielectric slab waveguide,” IEEE Trans. Microwave Theory Tech. MTT-31, 923–930 (1983).
[CrossRef]

1982

A. B. Manenkov, “Propagation of a surface wave along a dielectric waveguide with an abrupt change of parameters. II: Solution by variational method,” Radiophys. Quantum Electron. 25, 1050–1055 (1982).
[CrossRef]

M. Kosiba, K. Ooishi, T. Miki, M. Suzuki, “Finite-element analysis of the discontinuities in a dielectric slab waveguide bounded by parallel plates,” Electron. Lett. 18, 33–34 (1982).
[CrossRef]

1981

J. Buus, “Analytic approximation for the reflectivity of DH lasers,” IEEE J. Quantum Electron. QE-17, 2256–2257 (1981).
[CrossRef]

K. Aoyama, K. Nakagawa, T. Itoh, “Optical time domain reflectometry in a single-mode fiber,” IEEE J. Quantum Electron. QE-17, 862–868 (1981).
[CrossRef]

1980

T. J. M. Boyd, I. Moshkun, I. M. Stephenson, “Radiation losses due to discontinuities in asymmetric three-layer optical waveguides,” Opt. Quantum Electron. 12, 143–158 (1980).
[CrossRef]

1979

K. Morishita, S. Inagaki, N. Kumagai, “Analysis of discontinuities in dielectric waveguides by means of the least-squares boundary residual method,” IEEE Trans. Microwave Theory Tech. MTT-27, 310–315 (1979).
[CrossRef]

A. Ittipiboon, M. Hamid, “Scattering of surface waves at a slab waveguide discontinuity,” Proc. Inst. Electr. Eng. 126, 798–804 (1979).
[CrossRef]

1978

H. Yajima, “Coupled mode analysis of dielectric planar branching waveguides,” IEEE J. Quantum Electron. QE-14, 749–755 (1978).
[CrossRef]

T. E. Rozzi, “Rigorous analysis of the step discontinuity in a planar dielectric waveguide,” IEEE Trans. Microwave Theory Tech. MTT-26, 738–746 (1978).
[CrossRef]

1976

G. H. Brooke, M. M. Z. Kharadly, “Step discontinuities on dielectric waveguides,” Electron. Lett. 12, 473–475 (1976).
[CrossRef]

1970

D. Marcuse, “Radiation losses of tapered dielectric slab waveguides,” Bell Syst. Tech. J. 49, 273–290 (1970).
[CrossRef]

Aoki, K.

K. Uchida, K. Aoki, “Scattering of surface waves on transverse discontinuities in symmetrical three-layer dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-32, 11–19 (1984).
[CrossRef]

Aoyama, K.

K. Aoyama, K. Nakagawa, T. Itoh, “Optical time domain reflectometry in a single-mode fiber,” IEEE J. Quantum Electron. QE-17, 862–868 (1981).
[CrossRef]

Boyd, T. J. M.

T. J. M. Boyd, I. Moshkun, I. M. Stephenson, “Radiation losses due to discontinuities in asymmetric three-layer optical waveguides,” Opt. Quantum Electron. 12, 143–158 (1980).
[CrossRef]

Brooke, G. H.

G. H. Brooke, M. M. Z. Kharadly, “Step discontinuities on dielectric waveguides,” Electron. Lett. 12, 473–475 (1976).
[CrossRef]

Buus, J.

J. Buus, “Analytic approximation for the reflectivity of DH lasers,” IEEE J. Quantum Electron. QE-17, 2256–2257 (1981).
[CrossRef]

Chang, H. C.

Y. P. Chiou, H. C. Chang, “Analysis of optical waveguide discontinuities using Pade approximants,” IEEE Photon. Technol. Lett. 9, 964–966 (1997).
[CrossRef]

Chew, W. C.

Q. Liu, W. C. Chew, “Analysis of discontinuities in planar dielectric waveguides: an eigenmode propagation method,” IEEE Trans. Microwave Theory Tech. 39, 422–429 (1991).
[CrossRef]

Chiou, Y. P.

Y. P. Chiou, H. C. Chang, “Analysis of optical waveguide discontinuities using Pade approximants,” IEEE Photon. Technol. Lett. 9, 964–966 (1997).
[CrossRef]

Hamid, M.

A. Ittipiboon, M. Hamid, “Scattering of surface waves at a slab waveguide discontinuity,” Proc. Inst. Electr. Eng. 126, 798–804 (1979).
[CrossRef]

Inagaki, S.

K. Morishita, S. Inagaki, N. Kumagai, “Analysis of discontinuities in dielectric waveguides by means of the least-squares boundary residual method,” IEEE Trans. Microwave Theory Tech. MTT-27, 310–315 (1979).
[CrossRef]

Itoh, T.

K. Aoyama, K. Nakagawa, T. Itoh, “Optical time domain reflectometry in a single-mode fiber,” IEEE J. Quantum Electron. QE-17, 862–868 (1981).
[CrossRef]

Ittipiboon, A.

A. Ittipiboon, M. Hamid, “Scattering of surface waves at a slab waveguide discontinuity,” Proc. Inst. Electr. Eng. 126, 798–804 (1979).
[CrossRef]

Kharadly, M. M. Z.

G. H. Brooke, M. M. Z. Kharadly, “Step discontinuities on dielectric waveguides,” Electron. Lett. 12, 473–475 (1976).
[CrossRef]

Kojima, M.

Kosiba, M.

M. Kosiba, M. Suzuki, “Boundary-element analysis of dielectric slab waveguide discontinuities,” Appl. Opt. 25, 828–829 (1986).
[CrossRef]

M. Kosiba, K. Ooishi, T. Miki, M. Suzuki, “Finite-element analysis of the discontinuities in a dielectric slab waveguide bounded by parallel plates,” Electron. Lett. 18, 33–34 (1982).
[CrossRef]

Kumagai, N.

E. Nishimura, N. Morita, N. Kumagai, “An integral equation approach to electromagnetic scattering from arbitrary shaped junction between multilayered dielectric planer waveguides,” J. Lightwave Technol. LT-3, 887–894 (1985).
[CrossRef]

E. Nishimura, N. Morita, N. Kumagai, “Scattering of guided-modes caused by an arbitrarily shaped broken end in a dielectric slab waveguide,” IEEE Trans. Microwave Theory Tech. MTT-31, 923–930 (1983).
[CrossRef]

K. Morishita, S. Inagaki, N. Kumagai, “Analysis of discontinuities in dielectric waveguides by means of the least-squares boundary residual method,” IEEE Trans. Microwave Theory Tech. MTT-27, 310–315 (1979).
[CrossRef]

Latsas, G.

Liu, Q.

Q. Liu, W. C. Chew, “Analysis of discontinuities in planar dielectric waveguides: an eigenmode propagation method,” IEEE Trans. Microwave Theory Tech. 39, 422–429 (1991).
[CrossRef]

Manenkov, A. B.

G. Latsas, A. B. Manenkov, I. G. Tigelis, E. Sarri, “Reflectivity properties of an abruptly ended asymmetrical slab waveguide for the case of transverse magnetic modes,” J. Opt. Soc. Am. A 17, 162–172 (2000).
[CrossRef]

I. G. Tigelis, A. B. Manenkov, “Scattering from an abruptly terminated asymmetrical slab waveguide,” J. Opt. Soc. Am. A 16, 523–532 (1999).
[CrossRef]

A. B. Manenkov, “Reflection of the surface mode from an abruptly ended W-fibre,” IEE Proc. J. 139, 101–104 (1992).

A. B. Manenkov, “Step discontinuities in dielectric waveguide (fibres),” Opt. Quantum Electron. 22, 65–76 (1990).
[CrossRef]

A. B. Manenkov, “Propagation of a surface wave along a dielectric waveguide with an abrupt change of parameters. II: Solution by variational method,” Radiophys. Quantum Electron. 25, 1050–1055 (1982).
[CrossRef]

Marcuse, D.

D. Marcuse, “Radiation losses of tapered dielectric slab waveguides,” Bell Syst. Tech. J. 49, 273–290 (1970).
[CrossRef]

D. Marcuse, Theory of Dielectric Optical Waveguide, 2nd ed. (Academic, London, 1991), Chap. 1.

Miki, T.

M. Kosiba, K. Ooishi, T. Miki, M. Suzuki, “Finite-element analysis of the discontinuities in a dielectric slab waveguide bounded by parallel plates,” Electron. Lett. 18, 33–34 (1982).
[CrossRef]

Morishita, K.

K. Morishita, S. Inagaki, N. Kumagai, “Analysis of discontinuities in dielectric waveguides by means of the least-squares boundary residual method,” IEEE Trans. Microwave Theory Tech. MTT-27, 310–315 (1979).
[CrossRef]

Morita, N.

E. Nishimura, N. Morita, N. Kumagai, “An integral equation approach to electromagnetic scattering from arbitrary shaped junction between multilayered dielectric planer waveguides,” J. Lightwave Technol. LT-3, 887–894 (1985).
[CrossRef]

E. Nishimura, N. Morita, N. Kumagai, “Scattering of guided-modes caused by an arbitrarily shaped broken end in a dielectric slab waveguide,” IEEE Trans. Microwave Theory Tech. MTT-31, 923–930 (1983).
[CrossRef]

Moshkun, I.

T. J. M. Boyd, I. Moshkun, I. M. Stephenson, “Radiation losses due to discontinuities in asymmetric three-layer optical waveguides,” Opt. Quantum Electron. 12, 143–158 (1980).
[CrossRef]

Nakagawa, K.

K. Aoyama, K. Nakagawa, T. Itoh, “Optical time domain reflectometry in a single-mode fiber,” IEEE J. Quantum Electron. QE-17, 862–868 (1981).
[CrossRef]

Nishimura, E.

E. Nishimura, N. Morita, N. Kumagai, “An integral equation approach to electromagnetic scattering from arbitrary shaped junction between multilayered dielectric planer waveguides,” J. Lightwave Technol. LT-3, 887–894 (1985).
[CrossRef]

E. Nishimura, N. Morita, N. Kumagai, “Scattering of guided-modes caused by an arbitrarily shaped broken end in a dielectric slab waveguide,” IEEE Trans. Microwave Theory Tech. MTT-31, 923–930 (1983).
[CrossRef]

Ogusu, K.

K. Ogusu, “Transmission characteristics of single-mode asymmetric dielectric waveguide Y-junction,” Opt. Commun. 53, 169–172 (1985).
[CrossRef]

Omoya, T.

Ooishi, K.

M. Kosiba, K. Ooishi, T. Miki, M. Suzuki, “Finite-element analysis of the discontinuities in a dielectric slab waveguide bounded by parallel plates,” Electron. Lett. 18, 33–34 (1982).
[CrossRef]

Ootera, H.

K. Tanaka, M. Tanaka, H. Tashima, H. Ootera, Y. Yoshino, “New integral equation method for CAD of open waveguide bends,” Radio Sci. 28, 1219–1227 (1993).
[CrossRef]

Rozzi, T. E.

T. E. Rozzi, “Rigorous analysis of the step discontinuity in a planar dielectric waveguide,” IEEE Trans. Microwave Theory Tech. MTT-26, 738–746 (1978).
[CrossRef]

Sarri, E.

Stephenson, I. M.

T. J. M. Boyd, I. Moshkun, I. M. Stephenson, “Radiation losses due to discontinuities in asymmetric three-layer optical waveguides,” Opt. Quantum Electron. 12, 143–158 (1980).
[CrossRef]

Suzuki, M.

M. Kosiba, M. Suzuki, “Boundary-element analysis of dielectric slab waveguide discontinuities,” Appl. Opt. 25, 828–829 (1986).
[CrossRef]

M. Kosiba, K. Ooishi, T. Miki, M. Suzuki, “Finite-element analysis of the discontinuities in a dielectric slab waveguide bounded by parallel plates,” Electron. Lett. 18, 33–34 (1982).
[CrossRef]

Tanaka, K.

Tanaka, M.

Tashima, H.

K. Tanaka, M. Tanaka, H. Tashima, H. Ootera, Y. Yoshino, “New integral equation method for CAD of open waveguide bends,” Radio Sci. 28, 1219–1227 (1993).
[CrossRef]

Tigelis, I. G.

Uchida, K.

K. Uchida, K. Aoki, “Scattering of surface waves on transverse discontinuities in symmetrical three-layer dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-32, 11–19 (1984).
[CrossRef]

Vassallo, C.

Yajima, H.

H. Yajima, “Coupled mode analysis of dielectric planar branching waveguides,” IEEE J. Quantum Electron. QE-14, 749–755 (1978).
[CrossRef]

Yoshino, Y.

K. Tanaka, M. Tanaka, H. Tashima, H. Ootera, Y. Yoshino, “New integral equation method for CAD of open waveguide bends,” Radio Sci. 28, 1219–1227 (1993).
[CrossRef]

Appl. Opt.

Bell Syst. Tech. J.

D. Marcuse, “Radiation losses of tapered dielectric slab waveguides,” Bell Syst. Tech. J. 49, 273–290 (1970).
[CrossRef]

Electron. Commun. Jpn. Part 2

K. Tanaka, “New integral equations for designing dielectric waveguide bend circuits: guided-mode extracted integral equations,” Electron. Commun. Jpn. Part 2 76, 1–11 (1993).
[CrossRef]

Electron. Lett.

M. Kosiba, K. Ooishi, T. Miki, M. Suzuki, “Finite-element analysis of the discontinuities in a dielectric slab waveguide bounded by parallel plates,” Electron. Lett. 18, 33–34 (1982).
[CrossRef]

G. H. Brooke, M. M. Z. Kharadly, “Step discontinuities on dielectric waveguides,” Electron. Lett. 12, 473–475 (1976).
[CrossRef]

IEE Proc. J.

A. B. Manenkov, “Reflection of the surface mode from an abruptly ended W-fibre,” IEE Proc. J. 139, 101–104 (1992).

IEEE J. Quantum Electron.

K. Aoyama, K. Nakagawa, T. Itoh, “Optical time domain reflectometry in a single-mode fiber,” IEEE J. Quantum Electron. QE-17, 862–868 (1981).
[CrossRef]

H. Yajima, “Coupled mode analysis of dielectric planar branching waveguides,” IEEE J. Quantum Electron. QE-14, 749–755 (1978).
[CrossRef]

J. Buus, “Analytic approximation for the reflectivity of DH lasers,” IEEE J. Quantum Electron. QE-17, 2256–2257 (1981).
[CrossRef]

IEEE Photon. Technol. Lett.

Y. P. Chiou, H. C. Chang, “Analysis of optical waveguide discontinuities using Pade approximants,” IEEE Photon. Technol. Lett. 9, 964–966 (1997).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

Q. Liu, W. C. Chew, “Analysis of discontinuities in planar dielectric waveguides: an eigenmode propagation method,” IEEE Trans. Microwave Theory Tech. 39, 422–429 (1991).
[CrossRef]

K. Uchida, K. Aoki, “Scattering of surface waves on transverse discontinuities in symmetrical three-layer dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-32, 11–19 (1984).
[CrossRef]

E. Nishimura, N. Morita, N. Kumagai, “Scattering of guided-modes caused by an arbitrarily shaped broken end in a dielectric slab waveguide,” IEEE Trans. Microwave Theory Tech. MTT-31, 923–930 (1983).
[CrossRef]

T. E. Rozzi, “Rigorous analysis of the step discontinuity in a planar dielectric waveguide,” IEEE Trans. Microwave Theory Tech. MTT-26, 738–746 (1978).
[CrossRef]

K. Morishita, S. Inagaki, N. Kumagai, “Analysis of discontinuities in dielectric waveguides by means of the least-squares boundary residual method,” IEEE Trans. Microwave Theory Tech. MTT-27, 310–315 (1979).
[CrossRef]

J. Lightwave Technol.

E. Nishimura, N. Morita, N. Kumagai, “An integral equation approach to electromagnetic scattering from arbitrary shaped junction between multilayered dielectric planer waveguides,” J. Lightwave Technol. LT-3, 887–894 (1985).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

K. Ogusu, “Transmission characteristics of single-mode asymmetric dielectric waveguide Y-junction,” Opt. Commun. 53, 169–172 (1985).
[CrossRef]

Opt. Quantum Electron.

T. J. M. Boyd, I. Moshkun, I. M. Stephenson, “Radiation losses due to discontinuities in asymmetric three-layer optical waveguides,” Opt. Quantum Electron. 12, 143–158 (1980).
[CrossRef]

A. B. Manenkov, “Step discontinuities in dielectric waveguide (fibres),” Opt. Quantum Electron. 22, 65–76 (1990).
[CrossRef]

Proc. Inst. Electr. Eng.

A. Ittipiboon, M. Hamid, “Scattering of surface waves at a slab waveguide discontinuity,” Proc. Inst. Electr. Eng. 126, 798–804 (1979).
[CrossRef]

Radio Sci.

K. Tanaka, M. Tanaka, H. Tashima, H. Ootera, Y. Yoshino, “New integral equation method for CAD of open waveguide bends,” Radio Sci. 28, 1219–1227 (1993).
[CrossRef]

Radiophys. Quantum Electron.

A. B. Manenkov, “Propagation of a surface wave along a dielectric waveguide with an abrupt change of parameters. II: Solution by variational method,” Radiophys. Quantum Electron. 25, 1050–1055 (1982).
[CrossRef]

Other

D. Marcuse, Theory of Dielectric Optical Waveguide, 2nd ed. (Academic, London, 1991), Chap. 1.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

Geometry of a tilted-end asymmetrical slab waveguide.

Fig. 2
Fig. 2

Numerical examples of the disturbed fields of the TE and TM modes along the boundary C21 of the slab waveguide. The abscissa k0l is the normalized distance from point O in Fig. 1.

Fig. 3
Fig. 3

Numerical examples of the derivatives normal to the boundary of the disturbed fields of the TE and TM modes along the boundary C21 of the slab waveguide. The abscissa k0l is the normalized distance from point O in Fig. 1.

Fig. 4
Fig. 4

Normalized radiation pattern for an abruptly vertical-ended slab waveguide, with k0d=1, n2=3.6, Δ21=Δ23=10% (solid curve), Δ23=10%, and Δ21=50% (dotted curve) (TE mode).

Fig. 5
Fig. 5

Normalized radiation pattern for an abruptly vertical-ended slab waveguide, with k0d=1, n2=3.6, Δ21=Δ23=10% (solid curve), Δ23=10%, and Δ21=50% (dotted curve) (TM mode).

Fig. 6
Fig. 6

Dependence of the power-reflection coefficient (ΓR) and normalized scattering power (ΓS) on the tilted angle for the case of the TE mode, where k0d=1 (0.159λ), n2=1.458, n3=1.312, and n1=1.020 (i.e., Δ23=10% and Δ21=30%).

Fig. 7
Fig. 7

Dependence of the power-reflection coefficient (ΓR) and normalized scattering power (ΓS) on the tilted angle for the case of the TM mode, where k0d=1 (0.159λ), n2=1.458, n3=1.312, and n1=1.020 (i.e., Δ23=10% and Δ21=30%).

Fig. 8
Fig. 8

Normalized far-field pattern for a tilted-end slab waveguide, with k0d=1, n2=1.458, Δ23=10%, Δ21=30%, φ=0° (solid curve), and φ=25° (dotted curve) (TE mode).

Fig. 9
Fig. 9

Normalized far-field pattern for a tilted-ended slab waveguide, with k0d=1, n2=1.458, Δ23=10%, Δ21=30%, φ=0° (solid curve), and φ=25° (dotted curve) (TM mode).

Fig. 10
Fig. 10

Field intensity distribution |E|2 of the TE mode, with k0d=1, n2=1.458, n3=1.312, n1=1.020, and φ=10°. The field intensity is normalized by the amplitude of the incident guided mode.

Fig. 11
Fig. 11

Field intensity distribution |E|2 of the TM mode, with k0d=1, n2=1.458, n3=1.312, n1=1.020, and φ=10°. The field intensity is normalized by the amplitude of the incident guided mode.

Tables (3)

Tables Icon

Table 1 Comparison between the Various Methods Used To Calculate the Reflectivity from an Abruptly Ended Symmetrical Slab Waveguidea

Tables Icon

Table 2 Power-Reflection Coefficient ΓR, Normalized Radiation Power ΓS, and Their Total ΓTOTAL for the Incident TE Mode, with φ=10°

Tables Icon

Table 3 Power-Reflection Coefficient ΓR, Normalized Radiation Power ΓS, and Their Total ΓTOTAL for the Incident TM Mode, with φ=10°

Equations (37)

Equations on this page are rendered with MathJax. Learn more.

E(x)=E(z, x)=E(r, θ)
12E(x)=CG2(x|x)E(x)n-E(x)G2(x|x)ndl,
G2(x|x)=-j4H0(2)(n2k0|x-x|),
E(x)=E-(x)+RE+(x)+Ec(x),x on C21+C23,
E(x)=Ec(x),x onC20+(C21-C21)+(C31-C31),
12Ec(x)=CG2(x|x)Ec(x)n-Ec(x)G2(x|x)ndl-RU2+(x)-U2-(x),
U2(x)=C02G2(x|x)E(x)n-E(x)G2(x|x)ndl.
G2(x|x)=A2(r)g2(θ|x),
A2(r)=-j42jπn2k0r1/2 exp(-jn2k0r),
g2(θ|x)=exp[jn2k0(z cos θ+x sin θ)].
12Ec(r, θ)A2(r)=Cg2(θ|x)Ec(x)n-Ec(x)g2(θ|x)ndl-Ru2+(θ)-u2-(θ),
u2(θ)=C02g2(θ|x)E(x)n-E(x)g2(θ|x)ndl.
Ec(r, θ)A2(r)=0(r).
R=Cg2(θ|x)Ec(x)n-Ec(x)g2(θ|x)ndl-u2-(θ)u2+(θ).
12Ec(x)=CP2(x|x)Ec(x)n-Ec(x)P2(x|x)ndl-S2(x),
P2(x|x)=G2(x|x)-g2(θ|x)U2+(x)u2+(θ),
S2(x)=U2-(x)-u2-(θ)U2+(x)u2+(θ).
12Ec(x)=-C21P1(x|x)Ec(x)n-Ec(x)P1(x|x)ndl+C10G1(x|x)Ec(x)n-Ec(x)G1(x|x)ndl-U1+(x)u2+(θ)C20+C23×g2(θ|x)Ec(x)n-Ec(x)g2(θ|x)ndl-S1(x),
12Ec(x)=-C23P3(x|x)Ec(x)n-Ec(x)P3(x|x)ndl+C30G3(x|x)Ec(x)n-Ec(x)G3(x|x)ndl-U3+(x)u2+(θ)C20+C21×g2(θ|x)Ec(x)n-Ec(x)g2(θ|x)ndl-S3(x),
Pi(x|x)=Gi(x|x)+g2(θ|x)Ui+(x)u2+(θ),
Si(x)=Ui-(x)-u2-(θ)Ui+(x)u2+(θ),
Gi(x|x)=-j4H0(2)(nik0|x-x|),
g2(θ|x)=exp[jn2k0(z cos θ+x sin θ)],
Ui(x)=C0iGi(x|x)E(x)n-E(x)Gi(x|x)ndl,
u2(θ)=C02g2(θ|x)E(x)n-E(x)g2(θ|x)ndl,
12Ec(x)=-CG0(x|x)Ec(x)n-Ec(x)G0(x|x)ndl.
E0s(r, θ)=-j42jπn0k0r1/2 exp(-jn0k0r)B0(θ),
B0(θ)=-Cg0(x|x)Ec(x)n-Ec(x)g0(x|x)ndl,
E1s(r, θ)=-j42jπn1k0r1/2 exp(-jn1k0r)B1(θ),
E3s(r, θ)=-j42jπn3k0r1/2 exp(-jn3k0r)B3(θ),
B1(θ)=C21+C10g1(θ|x)Ec(x)n-Ec(x)g1(θ|x)ndl-Ru1+(θ)-u1-(θ),
B3(θ)=C31+C30g3(θ|x)Ec(x)n-Ec(x)g3(θ|x)ndl-Ru3+(θ)-u3-(θ),
ΓR+ΓS=Γtotal=1,
[Ec(x)]xC+=[Ec(x)]xC-,
Ec(x)nxC+=Ec(x)nxC-.
[Hc(x)]xC+=[Hc(x)]xC-,
n2(x)Hc(x)nxC+=n2(x)Hc(x)nxC-,

Metrics