Abstract

The pseudospectral method, proposed in our previous work, has not yet been constructed for optical waveguides with leaky modes or anisotropic materials. Our present study focuses on antiresonant reflecting optical waveguides (ARROWS) made by anisotropic materials. In contrast to the fields in the outermost subdomain expanded by Laguerre-Gaussian functions for guided mode problems, the fields in the high-index outermost subdomain are expanded by the Chebyshev polynomials with Mur’s absorbing boundary condition (ABC). Accordingly, the traveling waves can leak freely out of the computational window, and the desirable properties of the pseudospectral scheme, i.e., provision of fast and accurate solutions, can be preserved. A number of numerical examples tested by the present approach are shown to be in good agreement with exact data and published results achieved by other numerical methods.

© 2006 Optical Society of America

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  1. M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, "Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures," Appl. Phys. Lett. 49, 13-15 (1986).
    [CrossRef]
  2. T. Baba, Y. Kokubun, T. Sakaki, and K. Iga, "Loss reduction of an ARROW waveguide in shorter wavelength and its stack configuration," J. Lightwave Technol. 6, 1440-1445 (1988).
    [CrossRef]
  3. M. Mann, U. Trutschel, C. Wachter, L. Leine, and F. Lederer, "Directional coupler based on antiresonant reflecting optical waveguide," Opt. Lett. 16, 805-807 (1991).
    [CrossRef] [PubMed]
  4. Z. M. Mao and W. P. Huang, "An ARROW optical wavelength filter: design and analysis," J. Lightwave Technol. 11, 1183-1188 (1992).
    [CrossRef]
  5. F. Prieto, A. Llobera, D. Jimenez, C. Domenguez, A. Calle, and L. M. Lechuga, "Design and analysis of silicon antiresonant reflecting optical waveguides for evanescent field sensor," J. Lightwave Technol. 18, 966-972 (2000).
    [CrossRef]
  6. T. Baba and Y. Kokubun, "Dispersion and radiation loss characteristics of antiresonant reflecting optical waveguides-numerical results and analytical expressions," IEEE J. Quantum Electron. 28, 1689-1700 (1992).
    [CrossRef]
  7. W. P. Huang, R. M. Shubair, A. Nathan, and Y. L. Chow, "The modal characteristics of ARROW structures," J. Lightwave Technol. 10, 1015-1022 (1992).
    [CrossRef]
  8. T. Baba and Y. Kokubun, "New polarization-insensitive antiresonant reflecting optical waveguide (ARROW-B)," IEEE Photon. Technol. Lett. 1, 232-234 (1989).
    [CrossRef]
  9. W. Jiang, J. Chrostowski, and M. Fontaine, "Analysis of ARROW waveguides," Opt. Commun. 72, 180-186 (1989).
    [CrossRef]
  10. J. Chilwell and I. Hodgkinson, "Thin-film field-transfer matrix theory for planar multilayer waveguides and reflection from prism-loaded waveguides," J. Opt. Soc. Am. A 1, 742-753 (1984).
    [CrossRef]
  11. J. Kubica, D. Uttamchandani, and B. Culshaw, "Modal propagation within ARROW waveguides," Opt. Commun. 78, 133-136 (1990).
    [CrossRef]
  12. J. M. Kubica, "Numerical analysis of InP/InGaAsP ARROW waveguides using transfer matrix approach," J. Lightwave Technol. 10, 767-771 (1992).
    [CrossRef]
  13. E. Anemogiannis and E. N. Glytsis, "Multilayer waveguides: efficient numerical analysis of general structures," J. Lightwave Technol. 10, 1344-1351 (1992).
    [CrossRef]
  14. C. K. Chen, P. Berini, D. Feng, S. Tanev, and V. P. Tzolov, "Efficient and accurate numerical analysis of multilayer planar waveguides in lossy anisotropic media," Opt. Express 7, 260-272 (2000).
    [CrossRef] [PubMed]
  15. W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, "The perfectly matched layer boundary conditions for modal analysis of optical waveguides: leaky mode calculations," IEEE Photon. Technol. Lett. 8, 652-654 (1996).
    [CrossRef]
  16. J. C. Grant, J. C. Beal, and N. J. P. Frenette, "Finite element analysis of the ARROW leaky optical waveguide," IEEE J. Quantum Electron. 30, 1250-1253 (1994).
    [CrossRef]
  17. H. P. Uranus, H. J. W. M. Hoekstra, and E. V. Groesen, "Simple high-order Galerkin finite scheme for the investigation of both guided and leaky modes in anisotropic planar waveguides," Opt. Quantum Electron. 36, 239-257 (2004).
    [CrossRef]
  18. Y. Tsuji and M. Koshiba, "Guided-mode and leaky-mode analysis by imaginary distance beam propagation method based on finite element scheme," J. Lightwave Technol. 18, 618-623 (2000).
    [CrossRef]
  19. J. P. Boyd, "Chebyshev and Fourier Spectral methods," in Lecture Notes in Engineering, 2nd ed. (Springer Verlag, 2001).
  20. C. C. Huang, C. C. Huang, and J. Y. Yang, "An efficient method for computing optical waveguides with discontinuous refractive index profiles using spectral collocation method with domain decomposition," J. Lightwave Technol. 21, 2284-2296 (2003).
    [CrossRef]
  21. C. C. Huang, C. C. Huang, and J. Y. Yang, "A full-vectorial pseudospectral modal analysis of dielectric optical waveguides with stepped refractive index profiles," IEEE J. Sel. Top. Quantum Electron. 11, 457-465 (2005).
    [CrossRef]
  22. C. C. Huang and C. C. Huang, "An efficient and accurate semivectorial spectral collocation method for analyzing polarized modes of rib waveguides," J. Lightwave Technol. 23, 2309-2317 (2005).
    [CrossRef]
  23. G. Mur, "Absorbing boundary conditions for the finite difference approximation of the time-domain electromagnetic field equations," IEEE Trans. Electromagn. Compat. 23, 377-382 (1981).
    [CrossRef]
  24. A. Hardy and W. Streifer, "Coupled mode theory of parallel waveguides," J. Lightwave Technol. 3, 1135-1146 (1985).
    [CrossRef]
  25. M. Mann, U. Trutschel, C. Wachter, L. Leine, and F. Lederer, "Directional coupler based on an antiresonant reflecting optical waveguide," Opt. Lett. 16, 805-807 (1991).
    [CrossRef] [PubMed]
  26. Y. H. Chen and Y. T. Huang, "Coupling-efficiency analysis and control of dual antiresonant reflecting optical waveguides," J. Lightwave Technol. 14, 1507-1513 (1996).
    [CrossRef]

2005 (2)

C. C. Huang, C. C. Huang, and J. Y. Yang, "A full-vectorial pseudospectral modal analysis of dielectric optical waveguides with stepped refractive index profiles," IEEE J. Sel. Top. Quantum Electron. 11, 457-465 (2005).
[CrossRef]

C. C. Huang and C. C. Huang, "An efficient and accurate semivectorial spectral collocation method for analyzing polarized modes of rib waveguides," J. Lightwave Technol. 23, 2309-2317 (2005).
[CrossRef]

2004 (1)

H. P. Uranus, H. J. W. M. Hoekstra, and E. V. Groesen, "Simple high-order Galerkin finite scheme for the investigation of both guided and leaky modes in anisotropic planar waveguides," Opt. Quantum Electron. 36, 239-257 (2004).
[CrossRef]

2003 (1)

2000 (3)

1996 (2)

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, "The perfectly matched layer boundary conditions for modal analysis of optical waveguides: leaky mode calculations," IEEE Photon. Technol. Lett. 8, 652-654 (1996).
[CrossRef]

Y. H. Chen and Y. T. Huang, "Coupling-efficiency analysis and control of dual antiresonant reflecting optical waveguides," J. Lightwave Technol. 14, 1507-1513 (1996).
[CrossRef]

1994 (1)

J. C. Grant, J. C. Beal, and N. J. P. Frenette, "Finite element analysis of the ARROW leaky optical waveguide," IEEE J. Quantum Electron. 30, 1250-1253 (1994).
[CrossRef]

1992 (5)

Z. M. Mao and W. P. Huang, "An ARROW optical wavelength filter: design and analysis," J. Lightwave Technol. 11, 1183-1188 (1992).
[CrossRef]

T. Baba and Y. Kokubun, "Dispersion and radiation loss characteristics of antiresonant reflecting optical waveguides-numerical results and analytical expressions," IEEE J. Quantum Electron. 28, 1689-1700 (1992).
[CrossRef]

W. P. Huang, R. M. Shubair, A. Nathan, and Y. L. Chow, "The modal characteristics of ARROW structures," J. Lightwave Technol. 10, 1015-1022 (1992).
[CrossRef]

J. M. Kubica, "Numerical analysis of InP/InGaAsP ARROW waveguides using transfer matrix approach," J. Lightwave Technol. 10, 767-771 (1992).
[CrossRef]

E. Anemogiannis and E. N. Glytsis, "Multilayer waveguides: efficient numerical analysis of general structures," J. Lightwave Technol. 10, 1344-1351 (1992).
[CrossRef]

1991 (2)

1990 (1)

J. Kubica, D. Uttamchandani, and B. Culshaw, "Modal propagation within ARROW waveguides," Opt. Commun. 78, 133-136 (1990).
[CrossRef]

1989 (2)

T. Baba and Y. Kokubun, "New polarization-insensitive antiresonant reflecting optical waveguide (ARROW-B)," IEEE Photon. Technol. Lett. 1, 232-234 (1989).
[CrossRef]

W. Jiang, J. Chrostowski, and M. Fontaine, "Analysis of ARROW waveguides," Opt. Commun. 72, 180-186 (1989).
[CrossRef]

1988 (1)

T. Baba, Y. Kokubun, T. Sakaki, and K. Iga, "Loss reduction of an ARROW waveguide in shorter wavelength and its stack configuration," J. Lightwave Technol. 6, 1440-1445 (1988).
[CrossRef]

1986 (1)

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, "Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

1985 (1)

A. Hardy and W. Streifer, "Coupled mode theory of parallel waveguides," J. Lightwave Technol. 3, 1135-1146 (1985).
[CrossRef]

1984 (1)

1981 (1)

G. Mur, "Absorbing boundary conditions for the finite difference approximation of the time-domain electromagnetic field equations," IEEE Trans. Electromagn. Compat. 23, 377-382 (1981).
[CrossRef]

Anemogiannis, E.

E. Anemogiannis and E. N. Glytsis, "Multilayer waveguides: efficient numerical analysis of general structures," J. Lightwave Technol. 10, 1344-1351 (1992).
[CrossRef]

Baba, T.

T. Baba and Y. Kokubun, "Dispersion and radiation loss characteristics of antiresonant reflecting optical waveguides-numerical results and analytical expressions," IEEE J. Quantum Electron. 28, 1689-1700 (1992).
[CrossRef]

T. Baba and Y. Kokubun, "New polarization-insensitive antiresonant reflecting optical waveguide (ARROW-B)," IEEE Photon. Technol. Lett. 1, 232-234 (1989).
[CrossRef]

T. Baba, Y. Kokubun, T. Sakaki, and K. Iga, "Loss reduction of an ARROW waveguide in shorter wavelength and its stack configuration," J. Lightwave Technol. 6, 1440-1445 (1988).
[CrossRef]

Beal, J. C.

J. C. Grant, J. C. Beal, and N. J. P. Frenette, "Finite element analysis of the ARROW leaky optical waveguide," IEEE J. Quantum Electron. 30, 1250-1253 (1994).
[CrossRef]

Berini, P.

Calle, A.

Chen, C. K.

Chen, Y. H.

Y. H. Chen and Y. T. Huang, "Coupling-efficiency analysis and control of dual antiresonant reflecting optical waveguides," J. Lightwave Technol. 14, 1507-1513 (1996).
[CrossRef]

Chilwell, J.

Chow, Y. L.

W. P. Huang, R. M. Shubair, A. Nathan, and Y. L. Chow, "The modal characteristics of ARROW structures," J. Lightwave Technol. 10, 1015-1022 (1992).
[CrossRef]

Chrostowski, J.

W. Jiang, J. Chrostowski, and M. Fontaine, "Analysis of ARROW waveguides," Opt. Commun. 72, 180-186 (1989).
[CrossRef]

Culshaw, B.

J. Kubica, D. Uttamchandani, and B. Culshaw, "Modal propagation within ARROW waveguides," Opt. Commun. 78, 133-136 (1990).
[CrossRef]

Domenguez, C.

Duguay, M. A.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, "Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

Feng, D.

Fontaine, M.

W. Jiang, J. Chrostowski, and M. Fontaine, "Analysis of ARROW waveguides," Opt. Commun. 72, 180-186 (1989).
[CrossRef]

Frenette, N. J. P.

J. C. Grant, J. C. Beal, and N. J. P. Frenette, "Finite element analysis of the ARROW leaky optical waveguide," IEEE J. Quantum Electron. 30, 1250-1253 (1994).
[CrossRef]

Glytsis, E. N.

E. Anemogiannis and E. N. Glytsis, "Multilayer waveguides: efficient numerical analysis of general structures," J. Lightwave Technol. 10, 1344-1351 (1992).
[CrossRef]

Grant, J. C.

J. C. Grant, J. C. Beal, and N. J. P. Frenette, "Finite element analysis of the ARROW leaky optical waveguide," IEEE J. Quantum Electron. 30, 1250-1253 (1994).
[CrossRef]

Groesen, E. V.

H. P. Uranus, H. J. W. M. Hoekstra, and E. V. Groesen, "Simple high-order Galerkin finite scheme for the investigation of both guided and leaky modes in anisotropic planar waveguides," Opt. Quantum Electron. 36, 239-257 (2004).
[CrossRef]

Hardy, A.

A. Hardy and W. Streifer, "Coupled mode theory of parallel waveguides," J. Lightwave Technol. 3, 1135-1146 (1985).
[CrossRef]

Hodgkinson, I.

Hoekstra, H. J. W. M.

H. P. Uranus, H. J. W. M. Hoekstra, and E. V. Groesen, "Simple high-order Galerkin finite scheme for the investigation of both guided and leaky modes in anisotropic planar waveguides," Opt. Quantum Electron. 36, 239-257 (2004).
[CrossRef]

Huang, C. C.

Huang, W. P.

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, "The perfectly matched layer boundary conditions for modal analysis of optical waveguides: leaky mode calculations," IEEE Photon. Technol. Lett. 8, 652-654 (1996).
[CrossRef]

W. P. Huang, R. M. Shubair, A. Nathan, and Y. L. Chow, "The modal characteristics of ARROW structures," J. Lightwave Technol. 10, 1015-1022 (1992).
[CrossRef]

Z. M. Mao and W. P. Huang, "An ARROW optical wavelength filter: design and analysis," J. Lightwave Technol. 11, 1183-1188 (1992).
[CrossRef]

Huang, Y. T.

Y. H. Chen and Y. T. Huang, "Coupling-efficiency analysis and control of dual antiresonant reflecting optical waveguides," J. Lightwave Technol. 14, 1507-1513 (1996).
[CrossRef]

Iga, K.

T. Baba, Y. Kokubun, T. Sakaki, and K. Iga, "Loss reduction of an ARROW waveguide in shorter wavelength and its stack configuration," J. Lightwave Technol. 6, 1440-1445 (1988).
[CrossRef]

Jiang, W.

W. Jiang, J. Chrostowski, and M. Fontaine, "Analysis of ARROW waveguides," Opt. Commun. 72, 180-186 (1989).
[CrossRef]

Jimenez, D.

Koch, T. L.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, "Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

Kokubun, Y.

T. Baba and Y. Kokubun, "Dispersion and radiation loss characteristics of antiresonant reflecting optical waveguides-numerical results and analytical expressions," IEEE J. Quantum Electron. 28, 1689-1700 (1992).
[CrossRef]

T. Baba and Y. Kokubun, "New polarization-insensitive antiresonant reflecting optical waveguide (ARROW-B)," IEEE Photon. Technol. Lett. 1, 232-234 (1989).
[CrossRef]

T. Baba, Y. Kokubun, T. Sakaki, and K. Iga, "Loss reduction of an ARROW waveguide in shorter wavelength and its stack configuration," J. Lightwave Technol. 6, 1440-1445 (1988).
[CrossRef]

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, "Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

Koshiba, M.

Kubica, J.

J. Kubica, D. Uttamchandani, and B. Culshaw, "Modal propagation within ARROW waveguides," Opt. Commun. 78, 133-136 (1990).
[CrossRef]

Kubica, J. M.

J. M. Kubica, "Numerical analysis of InP/InGaAsP ARROW waveguides using transfer matrix approach," J. Lightwave Technol. 10, 767-771 (1992).
[CrossRef]

Lechuga, L. M.

Lederer, F.

Leine, L.

Llobera, A.

Lui, W.

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, "The perfectly matched layer boundary conditions for modal analysis of optical waveguides: leaky mode calculations," IEEE Photon. Technol. Lett. 8, 652-654 (1996).
[CrossRef]

Mann, M.

Mao, Z. M.

Z. M. Mao and W. P. Huang, "An ARROW optical wavelength filter: design and analysis," J. Lightwave Technol. 11, 1183-1188 (1992).
[CrossRef]

Mur, G.

G. Mur, "Absorbing boundary conditions for the finite difference approximation of the time-domain electromagnetic field equations," IEEE Trans. Electromagn. Compat. 23, 377-382 (1981).
[CrossRef]

Nathan, A.

W. P. Huang, R. M. Shubair, A. Nathan, and Y. L. Chow, "The modal characteristics of ARROW structures," J. Lightwave Technol. 10, 1015-1022 (1992).
[CrossRef]

Pfeiffer, L.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, "Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

Prieto, F.

Sakaki, T.

T. Baba, Y. Kokubun, T. Sakaki, and K. Iga, "Loss reduction of an ARROW waveguide in shorter wavelength and its stack configuration," J. Lightwave Technol. 6, 1440-1445 (1988).
[CrossRef]

Shubair, R. M.

W. P. Huang, R. M. Shubair, A. Nathan, and Y. L. Chow, "The modal characteristics of ARROW structures," J. Lightwave Technol. 10, 1015-1022 (1992).
[CrossRef]

Streifer, W.

A. Hardy and W. Streifer, "Coupled mode theory of parallel waveguides," J. Lightwave Technol. 3, 1135-1146 (1985).
[CrossRef]

Tanev, S.

Trutschel, U.

Tsuji, Y.

Tzolov, V. P.

Uranus, H. P.

H. P. Uranus, H. J. W. M. Hoekstra, and E. V. Groesen, "Simple high-order Galerkin finite scheme for the investigation of both guided and leaky modes in anisotropic planar waveguides," Opt. Quantum Electron. 36, 239-257 (2004).
[CrossRef]

Uttamchandani, D.

J. Kubica, D. Uttamchandani, and B. Culshaw, "Modal propagation within ARROW waveguides," Opt. Commun. 78, 133-136 (1990).
[CrossRef]

Wachter, C.

Xu, C. L.

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, "The perfectly matched layer boundary conditions for modal analysis of optical waveguides: leaky mode calculations," IEEE Photon. Technol. Lett. 8, 652-654 (1996).
[CrossRef]

Yang, J. Y.

C. C. Huang, C. C. Huang, and J. Y. Yang, "A full-vectorial pseudospectral modal analysis of dielectric optical waveguides with stepped refractive index profiles," IEEE J. Sel. Top. Quantum Electron. 11, 457-465 (2005).
[CrossRef]

C. C. Huang, C. C. Huang, and J. Y. Yang, "An efficient method for computing optical waveguides with discontinuous refractive index profiles using spectral collocation method with domain decomposition," J. Lightwave Technol. 21, 2284-2296 (2003).
[CrossRef]

Yokoyama, K.

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, "The perfectly matched layer boundary conditions for modal analysis of optical waveguides: leaky mode calculations," IEEE Photon. Technol. Lett. 8, 652-654 (1996).
[CrossRef]

Appl. Phys. Lett. (1)

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, "Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

IEEE J. Quantum Electron. (2)

T. Baba and Y. Kokubun, "Dispersion and radiation loss characteristics of antiresonant reflecting optical waveguides-numerical results and analytical expressions," IEEE J. Quantum Electron. 28, 1689-1700 (1992).
[CrossRef]

J. C. Grant, J. C. Beal, and N. J. P. Frenette, "Finite element analysis of the ARROW leaky optical waveguide," IEEE J. Quantum Electron. 30, 1250-1253 (1994).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

C. C. Huang, C. C. Huang, and J. Y. Yang, "A full-vectorial pseudospectral modal analysis of dielectric optical waveguides with stepped refractive index profiles," IEEE J. Sel. Top. Quantum Electron. 11, 457-465 (2005).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, "The perfectly matched layer boundary conditions for modal analysis of optical waveguides: leaky mode calculations," IEEE Photon. Technol. Lett. 8, 652-654 (1996).
[CrossRef]

T. Baba and Y. Kokubun, "New polarization-insensitive antiresonant reflecting optical waveguide (ARROW-B)," IEEE Photon. Technol. Lett. 1, 232-234 (1989).
[CrossRef]

IEEE Trans. Electromagn. Compat. (1)

G. Mur, "Absorbing boundary conditions for the finite difference approximation of the time-domain electromagnetic field equations," IEEE Trans. Electromagn. Compat. 23, 377-382 (1981).
[CrossRef]

J. Lightwave Technol. (11)

A. Hardy and W. Streifer, "Coupled mode theory of parallel waveguides," J. Lightwave Technol. 3, 1135-1146 (1985).
[CrossRef]

Y. H. Chen and Y. T. Huang, "Coupling-efficiency analysis and control of dual antiresonant reflecting optical waveguides," J. Lightwave Technol. 14, 1507-1513 (1996).
[CrossRef]

J. M. Kubica, "Numerical analysis of InP/InGaAsP ARROW waveguides using transfer matrix approach," J. Lightwave Technol. 10, 767-771 (1992).
[CrossRef]

E. Anemogiannis and E. N. Glytsis, "Multilayer waveguides: efficient numerical analysis of general structures," J. Lightwave Technol. 10, 1344-1351 (1992).
[CrossRef]

W. P. Huang, R. M. Shubair, A. Nathan, and Y. L. Chow, "The modal characteristics of ARROW structures," J. Lightwave Technol. 10, 1015-1022 (1992).
[CrossRef]

T. Baba, Y. Kokubun, T. Sakaki, and K. Iga, "Loss reduction of an ARROW waveguide in shorter wavelength and its stack configuration," J. Lightwave Technol. 6, 1440-1445 (1988).
[CrossRef]

Z. M. Mao and W. P. Huang, "An ARROW optical wavelength filter: design and analysis," J. Lightwave Technol. 11, 1183-1188 (1992).
[CrossRef]

Y. Tsuji and M. Koshiba, "Guided-mode and leaky-mode analysis by imaginary distance beam propagation method based on finite element scheme," J. Lightwave Technol. 18, 618-623 (2000).
[CrossRef]

F. Prieto, A. Llobera, D. Jimenez, C. Domenguez, A. Calle, and L. M. Lechuga, "Design and analysis of silicon antiresonant reflecting optical waveguides for evanescent field sensor," J. Lightwave Technol. 18, 966-972 (2000).
[CrossRef]

C. C. Huang, C. C. Huang, and J. Y. Yang, "An efficient method for computing optical waveguides with discontinuous refractive index profiles using spectral collocation method with domain decomposition," J. Lightwave Technol. 21, 2284-2296 (2003).
[CrossRef]

C. C. Huang and C. C. Huang, "An efficient and accurate semivectorial spectral collocation method for analyzing polarized modes of rib waveguides," J. Lightwave Technol. 23, 2309-2317 (2005).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

W. Jiang, J. Chrostowski, and M. Fontaine, "Analysis of ARROW waveguides," Opt. Commun. 72, 180-186 (1989).
[CrossRef]

J. Kubica, D. Uttamchandani, and B. Culshaw, "Modal propagation within ARROW waveguides," Opt. Commun. 78, 133-136 (1990).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

H. P. Uranus, H. J. W. M. Hoekstra, and E. V. Groesen, "Simple high-order Galerkin finite scheme for the investigation of both guided and leaky modes in anisotropic planar waveguides," Opt. Quantum Electron. 36, 239-257 (2004).
[CrossRef]

Other (1)

J. P. Boyd, "Chebyshev and Fourier Spectral methods," in Lecture Notes in Engineering, 2nd ed. (Springer Verlag, 2001).

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Figures (9)

Fig. 1.
Fig. 1.

Schematic diagrams of geometry and refractive index profile of the ARROW structure.

Fig. 2.
Fig. 2.

(a). Dispersion characteristics; (b).Radiation loss characteristics of various modes of an isotropic ARROW versus the thickness of the first cladding.

Fig. 3.
Fig. 3.

(a). Dispersion characteristics; (b). Radiation loss characteristics of various modes of an isotropic ARROW versus the thickness of the second cladding.

Fig. 4.
Fig. 4.

(a). Dispersion characteristics; (b). Radiation loss characteristics of various modes of an isotropic ARROW versus the thickness of the core.

Fig. 5.
Fig. 5.

Relative field profiles of TE and TM modes of isotropic ARROW on the first antiresonant condition on (d1=0.142λ,d2=3.15λ, and dc=6.3λ): (a) TE0 and TM0 (the first cladding mode); (b) TE1 and TM1; (c)TE2 and TM2; (d) TE3 and TM3; (e) TE4 and TM4; (f) TE5 and TM5.

Fig. 6.
Fig. 6.

Schematic diagrams of the coupling structure and refractive index profile of the ARROW-based directional coupler with Si substrate, where dg1, dg1, and dsep are the thicknesses of core 1, core 2, and waveguide separation, respectively. Others layers, excluding the half space of air and substrate layers, d11, dh1, dh2 dh3, dh4, and d12 are the interference cladding layers.

Fig. 7.
Fig. 7.

Dispersion characteristics versus the upper cladding layer d11 for the lowest symmetric (even) and asymmetric (odd) modes.

Fig. 8.
Fig. 8.

Relative field profiles of the lowest symmetric (even) and asymmetric (odd) modes at different order of coupling: (a) maximum coupling, (b) half coupling, (c) decoupling.

Fig. 9.
Fig. 9.

The coupling lengths of TE and TM modes versus waveguide separation dsep.

Tables (3)

Tables Icon

Table 1. Complex Effective Indices of the TE and TM Modes of an Isotropic ARROW Structure by the Present Method for the First Three Iterations

Tables Icon

Table 2. Calculated Results of the Present Method and TMM Using APM [14]

Tables Icon

Table 3. Calculated Results of an Anisotropic ARROW Structure by the Present Method, Six-Order Accuracy FEM [17], and TMM Using APM [14]

Equations (17)

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ε = = ε 0 [ n xx 2 0 0 0 n yy 2 0 0 0 n zz 2 ] ,
x ( E y ( x ) x ) + k 0 2 ( n yy 2 ( x ) n ff 2 ) E y ( x ) = 0 ,
n xx 2 ( x ) x ( 1 n zz 2 ( x ) H y ( x ) x ) + k 0 2 ( n xx 2 ( x ) n eff 2 ) H y ( x ) = 0
φ ( x ) = k = 0 n C k ( x ) φ k ,
C k ( x ) = ψ n + 1 ( x ) ψ n + 1 ( x ) ( x x k ) , 0 k n .
C k ( x ) = ( 1 ) k + 1 ( 1 x 2 ) T n ( x ) c k n 2 ( x x k ) , x x k
C k ( α x ) = e α x 2 e α x k 2 ( α x ) L n ( α x ) ( α x L n ) ( α x k ) ( α x α x k ) , x x k .
A Φ = ( k 0 n eff ) 2 I Φ ,
A lk e = C k ( 2 ) ( x l ) + k 0 2 n yy 2 ( x l ) δ lk , ( l , k = 0 , 1 , 2 , . . . n )
A lk e = n xx 2 ( x l ) n zz 2 ( x l ) [ C k ( 2 ) ( x l ) 2 n zz ( x l ) C k ( 1 ) ( x l ) ] + k 0 2 n xx 2 ( x l ) δ lk , ( l , k = 0 , 1 , 2 , . . . n )
E y ( x r + ) = E y ( x r ) , E y ( x r + ) x = E y ( x r ) x
H y ( x l + ) = H y ( x l ) , n zz 2 ( x r ) H y ( x r + ) x = n zz 2 ( x r + ) H y ( x r ) x
( r + i k r ) 2 φ = 0 ,
( 2 x 2 + 2 i k x x k x 2 ) φ x = x b p = 0 ,
k x = k 0 n yy 2 n eff 2
k x = k 0 n zz n xx n xx 2 n eff 2 ,
( 2 i k x x 2 k x 2 ) φ x = x b p = 0

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