Abstract

We investigate a system of two waveguides with leaky modes sharing a common substrate (radiatively coupled waveguides). The main advantage of such a system is the possibility of remote coupling. A perturbation theory is developed for both TE and TM polarization. Numerical calculations of dispersion curves and of the coupling length allow us to determine the limitations of the perturbation theory. We study the influence of multimode interference on the process of beating by considering the propagation of a given initial field. Finally, we propose a new design for an effective, integrated optical TE–TM polarization splitter.

© 1997 Optical Society of America

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  1. H. F. Taylor, “Optical switching and modulation in parallel dielectric waveguides,” J. Appl. Phys. 44, 3257–3262 (1974).
    [Crossref]
  2. H. Kogelnik, R. V. Schmidt, “Switched directional couplers with alternating Δβ,” IEEE J. Quantum Electron. QE-12, 396–401 (1976).
    [Crossref]
  3. R. C. Alferness, R. V. Schmidt, “Tunable optical waveguide directional coupler filter,” Appl. Phys. Lett. 33, 161–163 (1978).
    [Crossref]
  4. R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer-Verlag, Berlin, 1982).
  5. M. A. Duguay, Y. Kokubun, T. L. Koch, L. Pfeiffer, “Antiresonant reflecting optical waveguide in SiO2 -Si multilayer structures,” Appl. Phys. Lett. 49, 13–15 (1986).
    [Crossref]
  6. T. Baba, Y. Kokubun, “Dispersion and radiation loss characteristics of antiresonant reflecting optical waveguides—numerical results and analytical expression,” IEEE J. Quantum Electron. 28, 1689–1700 (1992).
    [Crossref]
  7. M. Mann, U. Trutschel, C. Wächter, L. Leine, F. Lederer, “Directional coupler based on an antiresonant reflecting optical waveguide,” Opt. Lett. 16, 805–807 (1991).
    [Crossref] [PubMed]
  8. F. Lederer, L. Leine, M. Mann, T. Peschel, R. Muschall, U. Trutschel, C. Wächter, C. Carigan, M. A. Duguay, F. Ouelette, “Linear mode beating and nonlinear mode coupling in resonant optical waveguides,” in Integrated Optics and Micro-Optics with Polymers, G. Wegner, W. Karthe, W. Ehrfeld, eds., Vol. 27 of Teubner-Texte zur Physik Series (Teubner-Verlagsgesellschaft, Stuttgart, 1993), pp. 301–331.
  9. V. L. Maslennikov, V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, “Light generation in a system of two coupled waveguides,” Sov. J. Quantum Electron. 22, 1041–1044 (1992).
    [Crossref]
  10. S. M. Loktev, V. A. Sychugov, B. A. Usievich, “Propagation of light in a system of two radiatively coupled waveguides,” Sov. J. Quantum Electron. 24, 435–438 (1994).
    [Crossref]
  11. M. T. Wlodarczyk, S. R. Seshadri, “Analysis of grating couplers for planar dielectric waveguides,” J. Appl. Phys. 58, 69–87 (1985).
    [Crossref]
  12. This means that n* + Re (δnlk) is the effective mode index of a waveguide with leaky mode shown in Fig. 1(b), and α rad is its leakage parameter.
  13. G. J. M. Krijnen, “All-optical switching in nonlinear integrated optic devices, Ph.D. dissertation (University of Twente, Enschede, The Netherlands, 1992).
  14. J. Willems, J. Haes, R. Baets, “The bidirectional mode expansion method for two-dimensional waveguides: the TM case,” Opt. Quantum Electron. 27, 995–1007 (1995).
    [Crossref]
  15. Y. Chung, N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335–1339 (1990).
    [Crossref]
  16. W. Huang, C. Xu, S.-T. Chu, S. K. Chaudhuri, “The finite-difference vector beam propagation method: analysis and assessment,” J. Lightwave Technol. LT-10, 293–304 (1992).
  17. W. H. Weber, S. L. McCarthy, G. W. Ford, “Perturbation theory applied to gain or loss in an optical waveguide,” Appl. Opt. 13, 715–716 (1974).
    [Crossref]
  18. Y. Shani, C. H. Henry, R. C. Kistler, K. J. Orlowsky, “Four-port integrated optic polarization splitter,” Appl. Opt. 29, 337–339 (1990).
    [Crossref] [PubMed]
  19. M. Eisenmann, E. Weidel, “Single-mode fused biconical coupler optimized for polarization beamsplitting,” J. Lightwave Technol. 9, 853–858 (1991).
    [Crossref]
  20. K. Thyagarajan, S. D. Seshadri, A. K. Ghatak, “Waveguide polarizer based on resonant tunelling,” J. Lightwave Technol. 9, 315–317 (1991).
    [Crossref]
  21. K. Thyagarajan, S. Pilevar, “Resonant tunnelling three-waveguide polarization splitter,” J. Lightwave Technol. 10, 1334–1337 (1992).
    [Crossref]
  22. U. Trutschel, F. Ouelette, V. Delisle, M. A. Duguay, G. Fogarty, F. Lederer, “Polarization splitter based on antiresonant reflecting optical waveguides,” J. Lightwave Technol. LT-13, 239–243 (1995).
    [Crossref]
  23. X. Li, R. T. Deck, “Light polarizer based on antiresonant reflecting layers in a directional coupler,” Appl. Phys. Lett. 66, 130–132 (1995).
    [Crossref]
  24. M. Shamonin, A. Erdmann, P. Hertel, “Properties of TE/TM polarized-mode propagation in a system of two radiatively coupled waveguides,” in European Optical Society, Annual Meetings Digest Series, Vol. 2A, Photonics’95 (Czech and Slovak Society for Photonics, Prague, Czechoslovakia, 1995), pp. 170–173.

1995 (3)

J. Willems, J. Haes, R. Baets, “The bidirectional mode expansion method for two-dimensional waveguides: the TM case,” Opt. Quantum Electron. 27, 995–1007 (1995).
[Crossref]

U. Trutschel, F. Ouelette, V. Delisle, M. A. Duguay, G. Fogarty, F. Lederer, “Polarization splitter based on antiresonant reflecting optical waveguides,” J. Lightwave Technol. LT-13, 239–243 (1995).
[Crossref]

X. Li, R. T. Deck, “Light polarizer based on antiresonant reflecting layers in a directional coupler,” Appl. Phys. Lett. 66, 130–132 (1995).
[Crossref]

1994 (1)

S. M. Loktev, V. A. Sychugov, B. A. Usievich, “Propagation of light in a system of two radiatively coupled waveguides,” Sov. J. Quantum Electron. 24, 435–438 (1994).
[Crossref]

1992 (4)

T. Baba, Y. Kokubun, “Dispersion and radiation loss characteristics of antiresonant reflecting optical waveguides—numerical results and analytical expression,” IEEE J. Quantum Electron. 28, 1689–1700 (1992).
[Crossref]

W. Huang, C. Xu, S.-T. Chu, S. K. Chaudhuri, “The finite-difference vector beam propagation method: analysis and assessment,” J. Lightwave Technol. LT-10, 293–304 (1992).

V. L. Maslennikov, V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, “Light generation in a system of two coupled waveguides,” Sov. J. Quantum Electron. 22, 1041–1044 (1992).
[Crossref]

K. Thyagarajan, S. Pilevar, “Resonant tunnelling three-waveguide polarization splitter,” J. Lightwave Technol. 10, 1334–1337 (1992).
[Crossref]

1991 (3)

M. Eisenmann, E. Weidel, “Single-mode fused biconical coupler optimized for polarization beamsplitting,” J. Lightwave Technol. 9, 853–858 (1991).
[Crossref]

K. Thyagarajan, S. D. Seshadri, A. K. Ghatak, “Waveguide polarizer based on resonant tunelling,” J. Lightwave Technol. 9, 315–317 (1991).
[Crossref]

M. Mann, U. Trutschel, C. Wächter, L. Leine, F. Lederer, “Directional coupler based on an antiresonant reflecting optical waveguide,” Opt. Lett. 16, 805–807 (1991).
[Crossref] [PubMed]

1990 (2)

Y. Shani, C. H. Henry, R. C. Kistler, K. J. Orlowsky, “Four-port integrated optic polarization splitter,” Appl. Opt. 29, 337–339 (1990).
[Crossref] [PubMed]

Y. Chung, N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335–1339 (1990).
[Crossref]

1986 (1)

M. A. Duguay, Y. Kokubun, T. L. Koch, L. Pfeiffer, “Antiresonant reflecting optical waveguide in SiO2 -Si multilayer structures,” Appl. Phys. Lett. 49, 13–15 (1986).
[Crossref]

1985 (1)

M. T. Wlodarczyk, S. R. Seshadri, “Analysis of grating couplers for planar dielectric waveguides,” J. Appl. Phys. 58, 69–87 (1985).
[Crossref]

1978 (1)

R. C. Alferness, R. V. Schmidt, “Tunable optical waveguide directional coupler filter,” Appl. Phys. Lett. 33, 161–163 (1978).
[Crossref]

1976 (1)

H. Kogelnik, R. V. Schmidt, “Switched directional couplers with alternating Δβ,” IEEE J. Quantum Electron. QE-12, 396–401 (1976).
[Crossref]

1974 (2)

H. F. Taylor, “Optical switching and modulation in parallel dielectric waveguides,” J. Appl. Phys. 44, 3257–3262 (1974).
[Crossref]

W. H. Weber, S. L. McCarthy, G. W. Ford, “Perturbation theory applied to gain or loss in an optical waveguide,” Appl. Opt. 13, 715–716 (1974).
[Crossref]

Alferness, R. C.

R. C. Alferness, R. V. Schmidt, “Tunable optical waveguide directional coupler filter,” Appl. Phys. Lett. 33, 161–163 (1978).
[Crossref]

Baba, T.

T. Baba, Y. Kokubun, “Dispersion and radiation loss characteristics of antiresonant reflecting optical waveguides—numerical results and analytical expression,” IEEE J. Quantum Electron. 28, 1689–1700 (1992).
[Crossref]

Baets, R.

J. Willems, J. Haes, R. Baets, “The bidirectional mode expansion method for two-dimensional waveguides: the TM case,” Opt. Quantum Electron. 27, 995–1007 (1995).
[Crossref]

Carigan, C.

F. Lederer, L. Leine, M. Mann, T. Peschel, R. Muschall, U. Trutschel, C. Wächter, C. Carigan, M. A. Duguay, F. Ouelette, “Linear mode beating and nonlinear mode coupling in resonant optical waveguides,” in Integrated Optics and Micro-Optics with Polymers, G. Wegner, W. Karthe, W. Ehrfeld, eds., Vol. 27 of Teubner-Texte zur Physik Series (Teubner-Verlagsgesellschaft, Stuttgart, 1993), pp. 301–331.

Chaudhuri, S. K.

W. Huang, C. Xu, S.-T. Chu, S. K. Chaudhuri, “The finite-difference vector beam propagation method: analysis and assessment,” J. Lightwave Technol. LT-10, 293–304 (1992).

Chu, S.-T.

W. Huang, C. Xu, S.-T. Chu, S. K. Chaudhuri, “The finite-difference vector beam propagation method: analysis and assessment,” J. Lightwave Technol. LT-10, 293–304 (1992).

Chung, Y.

Y. Chung, N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335–1339 (1990).
[Crossref]

Dagli, N.

Y. Chung, N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335–1339 (1990).
[Crossref]

Deck, R. T.

X. Li, R. T. Deck, “Light polarizer based on antiresonant reflecting layers in a directional coupler,” Appl. Phys. Lett. 66, 130–132 (1995).
[Crossref]

Delisle, V.

U. Trutschel, F. Ouelette, V. Delisle, M. A. Duguay, G. Fogarty, F. Lederer, “Polarization splitter based on antiresonant reflecting optical waveguides,” J. Lightwave Technol. LT-13, 239–243 (1995).
[Crossref]

Duguay, M. A.

U. Trutschel, F. Ouelette, V. Delisle, M. A. Duguay, G. Fogarty, F. Lederer, “Polarization splitter based on antiresonant reflecting optical waveguides,” J. Lightwave Technol. LT-13, 239–243 (1995).
[Crossref]

M. A. Duguay, Y. Kokubun, T. L. Koch, L. Pfeiffer, “Antiresonant reflecting optical waveguide in SiO2 -Si multilayer structures,” Appl. Phys. Lett. 49, 13–15 (1986).
[Crossref]

F. Lederer, L. Leine, M. Mann, T. Peschel, R. Muschall, U. Trutschel, C. Wächter, C. Carigan, M. A. Duguay, F. Ouelette, “Linear mode beating and nonlinear mode coupling in resonant optical waveguides,” in Integrated Optics and Micro-Optics with Polymers, G. Wegner, W. Karthe, W. Ehrfeld, eds., Vol. 27 of Teubner-Texte zur Physik Series (Teubner-Verlagsgesellschaft, Stuttgart, 1993), pp. 301–331.

Eisenmann, M.

M. Eisenmann, E. Weidel, “Single-mode fused biconical coupler optimized for polarization beamsplitting,” J. Lightwave Technol. 9, 853–858 (1991).
[Crossref]

Erdmann, A.

M. Shamonin, A. Erdmann, P. Hertel, “Properties of TE/TM polarized-mode propagation in a system of two radiatively coupled waveguides,” in European Optical Society, Annual Meetings Digest Series, Vol. 2A, Photonics’95 (Czech and Slovak Society for Photonics, Prague, Czechoslovakia, 1995), pp. 170–173.

Fogarty, G.

U. Trutschel, F. Ouelette, V. Delisle, M. A. Duguay, G. Fogarty, F. Lederer, “Polarization splitter based on antiresonant reflecting optical waveguides,” J. Lightwave Technol. LT-13, 239–243 (1995).
[Crossref]

Ford, G. W.

Ghatak, A. K.

K. Thyagarajan, S. D. Seshadri, A. K. Ghatak, “Waveguide polarizer based on resonant tunelling,” J. Lightwave Technol. 9, 315–317 (1991).
[Crossref]

Haes, J.

J. Willems, J. Haes, R. Baets, “The bidirectional mode expansion method for two-dimensional waveguides: the TM case,” Opt. Quantum Electron. 27, 995–1007 (1995).
[Crossref]

Henry, C. H.

Hertel, P.

M. Shamonin, A. Erdmann, P. Hertel, “Properties of TE/TM polarized-mode propagation in a system of two radiatively coupled waveguides,” in European Optical Society, Annual Meetings Digest Series, Vol. 2A, Photonics’95 (Czech and Slovak Society for Photonics, Prague, Czechoslovakia, 1995), pp. 170–173.

Huang, W.

W. Huang, C. Xu, S.-T. Chu, S. K. Chaudhuri, “The finite-difference vector beam propagation method: analysis and assessment,” J. Lightwave Technol. LT-10, 293–304 (1992).

Hunsperger, R. G.

R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer-Verlag, Berlin, 1982).

Kistler, R. C.

Koch, T. L.

M. A. Duguay, Y. Kokubun, T. L. Koch, L. Pfeiffer, “Antiresonant reflecting optical waveguide in SiO2 -Si multilayer structures,” Appl. Phys. Lett. 49, 13–15 (1986).
[Crossref]

Kogelnik, H.

H. Kogelnik, R. V. Schmidt, “Switched directional couplers with alternating Δβ,” IEEE J. Quantum Electron. QE-12, 396–401 (1976).
[Crossref]

Kokubun, Y.

T. Baba, Y. Kokubun, “Dispersion and radiation loss characteristics of antiresonant reflecting optical waveguides—numerical results and analytical expression,” IEEE J. Quantum Electron. 28, 1689–1700 (1992).
[Crossref]

M. A. Duguay, Y. Kokubun, T. L. Koch, L. Pfeiffer, “Antiresonant reflecting optical waveguide in SiO2 -Si multilayer structures,” Appl. Phys. Lett. 49, 13–15 (1986).
[Crossref]

Krijnen, G. J. M.

G. J. M. Krijnen, “All-optical switching in nonlinear integrated optic devices, Ph.D. dissertation (University of Twente, Enschede, The Netherlands, 1992).

Lederer, F.

U. Trutschel, F. Ouelette, V. Delisle, M. A. Duguay, G. Fogarty, F. Lederer, “Polarization splitter based on antiresonant reflecting optical waveguides,” J. Lightwave Technol. LT-13, 239–243 (1995).
[Crossref]

M. Mann, U. Trutschel, C. Wächter, L. Leine, F. Lederer, “Directional coupler based on an antiresonant reflecting optical waveguide,” Opt. Lett. 16, 805–807 (1991).
[Crossref] [PubMed]

F. Lederer, L. Leine, M. Mann, T. Peschel, R. Muschall, U. Trutschel, C. Wächter, C. Carigan, M. A. Duguay, F. Ouelette, “Linear mode beating and nonlinear mode coupling in resonant optical waveguides,” in Integrated Optics and Micro-Optics with Polymers, G. Wegner, W. Karthe, W. Ehrfeld, eds., Vol. 27 of Teubner-Texte zur Physik Series (Teubner-Verlagsgesellschaft, Stuttgart, 1993), pp. 301–331.

Leine, L.

M. Mann, U. Trutschel, C. Wächter, L. Leine, F. Lederer, “Directional coupler based on an antiresonant reflecting optical waveguide,” Opt. Lett. 16, 805–807 (1991).
[Crossref] [PubMed]

F. Lederer, L. Leine, M. Mann, T. Peschel, R. Muschall, U. Trutschel, C. Wächter, C. Carigan, M. A. Duguay, F. Ouelette, “Linear mode beating and nonlinear mode coupling in resonant optical waveguides,” in Integrated Optics and Micro-Optics with Polymers, G. Wegner, W. Karthe, W. Ehrfeld, eds., Vol. 27 of Teubner-Texte zur Physik Series (Teubner-Verlagsgesellschaft, Stuttgart, 1993), pp. 301–331.

Li, X.

X. Li, R. T. Deck, “Light polarizer based on antiresonant reflecting layers in a directional coupler,” Appl. Phys. Lett. 66, 130–132 (1995).
[Crossref]

Loktev, S. M.

S. M. Loktev, V. A. Sychugov, B. A. Usievich, “Propagation of light in a system of two radiatively coupled waveguides,” Sov. J. Quantum Electron. 24, 435–438 (1994).
[Crossref]

Mann, M.

M. Mann, U. Trutschel, C. Wächter, L. Leine, F. Lederer, “Directional coupler based on an antiresonant reflecting optical waveguide,” Opt. Lett. 16, 805–807 (1991).
[Crossref] [PubMed]

F. Lederer, L. Leine, M. Mann, T. Peschel, R. Muschall, U. Trutschel, C. Wächter, C. Carigan, M. A. Duguay, F. Ouelette, “Linear mode beating and nonlinear mode coupling in resonant optical waveguides,” in Integrated Optics and Micro-Optics with Polymers, G. Wegner, W. Karthe, W. Ehrfeld, eds., Vol. 27 of Teubner-Texte zur Physik Series (Teubner-Verlagsgesellschaft, Stuttgart, 1993), pp. 301–331.

Maslennikov, V. L.

V. L. Maslennikov, V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, “Light generation in a system of two coupled waveguides,” Sov. J. Quantum Electron. 22, 1041–1044 (1992).
[Crossref]

McCarthy, S. L.

Muschall, R.

F. Lederer, L. Leine, M. Mann, T. Peschel, R. Muschall, U. Trutschel, C. Wächter, C. Carigan, M. A. Duguay, F. Ouelette, “Linear mode beating and nonlinear mode coupling in resonant optical waveguides,” in Integrated Optics and Micro-Optics with Polymers, G. Wegner, W. Karthe, W. Ehrfeld, eds., Vol. 27 of Teubner-Texte zur Physik Series (Teubner-Verlagsgesellschaft, Stuttgart, 1993), pp. 301–331.

Orlowsky, K. J.

Ouelette, F.

U. Trutschel, F. Ouelette, V. Delisle, M. A. Duguay, G. Fogarty, F. Lederer, “Polarization splitter based on antiresonant reflecting optical waveguides,” J. Lightwave Technol. LT-13, 239–243 (1995).
[Crossref]

F. Lederer, L. Leine, M. Mann, T. Peschel, R. Muschall, U. Trutschel, C. Wächter, C. Carigan, M. A. Duguay, F. Ouelette, “Linear mode beating and nonlinear mode coupling in resonant optical waveguides,” in Integrated Optics and Micro-Optics with Polymers, G. Wegner, W. Karthe, W. Ehrfeld, eds., Vol. 27 of Teubner-Texte zur Physik Series (Teubner-Verlagsgesellschaft, Stuttgart, 1993), pp. 301–331.

Peschel, T.

F. Lederer, L. Leine, M. Mann, T. Peschel, R. Muschall, U. Trutschel, C. Wächter, C. Carigan, M. A. Duguay, F. Ouelette, “Linear mode beating and nonlinear mode coupling in resonant optical waveguides,” in Integrated Optics and Micro-Optics with Polymers, G. Wegner, W. Karthe, W. Ehrfeld, eds., Vol. 27 of Teubner-Texte zur Physik Series (Teubner-Verlagsgesellschaft, Stuttgart, 1993), pp. 301–331.

Pfeiffer, L.

M. A. Duguay, Y. Kokubun, T. L. Koch, L. Pfeiffer, “Antiresonant reflecting optical waveguide in SiO2 -Si multilayer structures,” Appl. Phys. Lett. 49, 13–15 (1986).
[Crossref]

Pilevar, S.

K. Thyagarajan, S. Pilevar, “Resonant tunnelling three-waveguide polarization splitter,” J. Lightwave Technol. 10, 1334–1337 (1992).
[Crossref]

Schmidt, R. V.

R. C. Alferness, R. V. Schmidt, “Tunable optical waveguide directional coupler filter,” Appl. Phys. Lett. 33, 161–163 (1978).
[Crossref]

H. Kogelnik, R. V. Schmidt, “Switched directional couplers with alternating Δβ,” IEEE J. Quantum Electron. QE-12, 396–401 (1976).
[Crossref]

Seshadri, S. D.

K. Thyagarajan, S. D. Seshadri, A. K. Ghatak, “Waveguide polarizer based on resonant tunelling,” J. Lightwave Technol. 9, 315–317 (1991).
[Crossref]

Seshadri, S. R.

M. T. Wlodarczyk, S. R. Seshadri, “Analysis of grating couplers for planar dielectric waveguides,” J. Appl. Phys. 58, 69–87 (1985).
[Crossref]

Shamonin, M.

M. Shamonin, A. Erdmann, P. Hertel, “Properties of TE/TM polarized-mode propagation in a system of two radiatively coupled waveguides,” in European Optical Society, Annual Meetings Digest Series, Vol. 2A, Photonics’95 (Czech and Slovak Society for Photonics, Prague, Czechoslovakia, 1995), pp. 170–173.

Shani, Y.

Sychugov, V. A.

S. M. Loktev, V. A. Sychugov, B. A. Usievich, “Propagation of light in a system of two radiatively coupled waveguides,” Sov. J. Quantum Electron. 24, 435–438 (1994).
[Crossref]

V. L. Maslennikov, V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, “Light generation in a system of two coupled waveguides,” Sov. J. Quantum Electron. 22, 1041–1044 (1992).
[Crossref]

Taylor, H. F.

H. F. Taylor, “Optical switching and modulation in parallel dielectric waveguides,” J. Appl. Phys. 44, 3257–3262 (1974).
[Crossref]

Thyagarajan, K.

K. Thyagarajan, S. Pilevar, “Resonant tunnelling three-waveguide polarization splitter,” J. Lightwave Technol. 10, 1334–1337 (1992).
[Crossref]

K. Thyagarajan, S. D. Seshadri, A. K. Ghatak, “Waveguide polarizer based on resonant tunelling,” J. Lightwave Technol. 9, 315–317 (1991).
[Crossref]

Tishchenko, A. V.

V. L. Maslennikov, V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, “Light generation in a system of two coupled waveguides,” Sov. J. Quantum Electron. 22, 1041–1044 (1992).
[Crossref]

Trutschel, U.

U. Trutschel, F. Ouelette, V. Delisle, M. A. Duguay, G. Fogarty, F. Lederer, “Polarization splitter based on antiresonant reflecting optical waveguides,” J. Lightwave Technol. LT-13, 239–243 (1995).
[Crossref]

M. Mann, U. Trutschel, C. Wächter, L. Leine, F. Lederer, “Directional coupler based on an antiresonant reflecting optical waveguide,” Opt. Lett. 16, 805–807 (1991).
[Crossref] [PubMed]

F. Lederer, L. Leine, M. Mann, T. Peschel, R. Muschall, U. Trutschel, C. Wächter, C. Carigan, M. A. Duguay, F. Ouelette, “Linear mode beating and nonlinear mode coupling in resonant optical waveguides,” in Integrated Optics and Micro-Optics with Polymers, G. Wegner, W. Karthe, W. Ehrfeld, eds., Vol. 27 of Teubner-Texte zur Physik Series (Teubner-Verlagsgesellschaft, Stuttgart, 1993), pp. 301–331.

Usievich, B. A.

S. M. Loktev, V. A. Sychugov, B. A. Usievich, “Propagation of light in a system of two radiatively coupled waveguides,” Sov. J. Quantum Electron. 24, 435–438 (1994).
[Crossref]

V. L. Maslennikov, V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, “Light generation in a system of two coupled waveguides,” Sov. J. Quantum Electron. 22, 1041–1044 (1992).
[Crossref]

Wächter, C.

M. Mann, U. Trutschel, C. Wächter, L. Leine, F. Lederer, “Directional coupler based on an antiresonant reflecting optical waveguide,” Opt. Lett. 16, 805–807 (1991).
[Crossref] [PubMed]

F. Lederer, L. Leine, M. Mann, T. Peschel, R. Muschall, U. Trutschel, C. Wächter, C. Carigan, M. A. Duguay, F. Ouelette, “Linear mode beating and nonlinear mode coupling in resonant optical waveguides,” in Integrated Optics and Micro-Optics with Polymers, G. Wegner, W. Karthe, W. Ehrfeld, eds., Vol. 27 of Teubner-Texte zur Physik Series (Teubner-Verlagsgesellschaft, Stuttgart, 1993), pp. 301–331.

Weber, W. H.

Weidel, E.

M. Eisenmann, E. Weidel, “Single-mode fused biconical coupler optimized for polarization beamsplitting,” J. Lightwave Technol. 9, 853–858 (1991).
[Crossref]

Willems, J.

J. Willems, J. Haes, R. Baets, “The bidirectional mode expansion method for two-dimensional waveguides: the TM case,” Opt. Quantum Electron. 27, 995–1007 (1995).
[Crossref]

Wlodarczyk, M. T.

M. T. Wlodarczyk, S. R. Seshadri, “Analysis of grating couplers for planar dielectric waveguides,” J. Appl. Phys. 58, 69–87 (1985).
[Crossref]

Xu, C.

W. Huang, C. Xu, S.-T. Chu, S. K. Chaudhuri, “The finite-difference vector beam propagation method: analysis and assessment,” J. Lightwave Technol. LT-10, 293–304 (1992).

Appl. Opt. (2)

Appl. Phys. Lett. (3)

R. C. Alferness, R. V. Schmidt, “Tunable optical waveguide directional coupler filter,” Appl. Phys. Lett. 33, 161–163 (1978).
[Crossref]

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Other (5)

This means that n* + Re (δnlk) is the effective mode index of a waveguide with leaky mode shown in Fig. 1(b), and α rad is its leakage parameter.

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Figures (10)

Fig. 1
Fig. 1

(a) Basic slab waveguide (WG) and (b) a slab waveguide with leaky modes are shown. (c) If two waveguides with leaky modes share a substrate, they form radiatively coupled waveguides. Note that the refractive index n 3 of the central layer is larger than the effective index of the waveguide mode n *. Arrows illustrate the power flow. H = 0 corresponds to conventionally coupled waveguides.

Fig. 2
Fig. 2

Field profiles of some TM modes for two radiatively coupled waveguides. The fields are normalized as ∫ ∊-1|Hy|2dx = 1. Parameters n 0 = 1, n 1 = 1.49, n 2 = 1.46, n 3 = 1.52,h = 1.35 µm, t = 0.8 µm, and λ = 0.6328 µm are taken from Ref. 10. The thickness H of the central layer is 12.5 µm. The entire structure supports 61 TM modes.

Fig. 3
Fig. 3

(a) Effective mode index β/ k of the TM modes versus the thickness H of the central layer. Parameters are the same as in Fig. 2. (b) Part of the dispersion curves from (a). The modes are designated. Solid curves denote symmetric modes, dashed curves denote antisymmetric modes.

Fig. 4
Fig. 4

Effective mode index β/ k of the TM modes as calculated by the perturbation theory (solid curves) and numerically (dashed curves) versus the thickness H of the central layer for different regions of the variation of H: (a) 0 ≤ H ≤ 5 µm, and (b) 15 ≤ H ≤ 20 µm. Only the effective mode indices close to n * = 1.4789 are shown. Parameters are the same as in Fig. 2.

Fig. 5
Fig. 5

Coupling length L c of TM and TE modes as calculated by the perturbation theory (solid curves) and numerically (dashed curves) versus the thickness H of the central layer for different regions of the variation of H: (a) 0 ≤ H ≤ 5 µm, and (b) 15 ≤ H ≤ 20 µm. The maximal coupling length L c max according to the perturbation theory is shown. Parameters are the same as in Fig. 2.

Fig. 6
Fig. 6

Power P 1 (solid curves), P 2 (dashed curves) of TM waves in WG1 and WG2, respectively, and the total power P 1 + P 2 (dotted curves) versus the propagation distance z for different values of the central layer thickness H. Note that the given values of H correspond to the same value of L c TM = 1 mm accordingly to the perturbation theory. The total number of modes supported by the entire structure increases with H. The structure supports 15, 32, and 87 TM modes, respectively. Parameters are the same as in Fig. 2.

Fig. 7
Fig. 7

Power P 1 (solid curves), P 2 (dashed curves) of TM waves in WG1 and WG2, respectively, and the total power P 1 + P 2 (dotted curves) versus the propagation distance z if a different number of propagating modes is taken into account. H = 19.855 µm; remaining parameters are the same as in Fig. 2.

Fig. 8
Fig. 8

Propagation of the (a) TE-polarized wave in comparison with the propagation of the (b) TM-polarized wave. The properly polarized mode of a basic slab waveguide was launched into WG1 at z = 0. According to the theoretical prediction, light with different polarization states is directed toward different output channels. Parameters are n 0 = 1.51065, n 1 = 1.52,n 2 = 1.512, n 3 = 1.70, h = 1.50 µm, t = 0.77 µm, λ = 0.6328 µm, and H = 10.108 µm. The total length of the device is L ps = 4548 µm.

Fig. 9
Fig. 9

Extinction ratios ER1 and ER2 versus the propagation distance z for the structure of Fig. 8.

Fig. 10
Fig. 10

Extinction ratios ER 1, ER 2 versus the thickness of the central layer H (a), the film thickness h (b), and the thickness t of the buffer layer (c). In each figure the remaining parameters are as in Fig. 8.

Tables (1)

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Table 1 Tolerances for Three Typical Values of H

Equations (13)

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Lc=λ2ns-na
ns,a=n*+Reδnlk+δns,a,
δnlk=2η1η2N12N2Aη12N12+η22N22η32N32+η22N22n*kheff×η22N22-η32N32+2iη2η3N3N2,
δns,a=4Aη1η22η3N12N22N3η32N32+η22N22η12N12+η22N22n*kheff×tanθs,a2+Ψ,
heff=h+η0kη1N0N12+N02N12+η0N0/η12+η2kη1N2N12+N22N12+η2N2/η12, Ψ=tan-1η3N3/η2N2, θs=kN3H, θa=kN3H+π, Ni=ni2-n*21/2i=0,,3, ηi=ni-2 i=0,,3.
αrad=k Imδnlk.
Fx, z=m cm mxexpiβmz,
P1z=Fx, z, ϕ1x2,P2z=Fx, z, ϕ2x2,
ER1=10 log10P1TMP1TEand ER2=10 log10P2TEP2TM.
Hy=al-exp-ikNlx-xl+Rl expikNlx-xlexpikn*z,
Rl=ηlNl1+Rl+1-ηl+1Nl+11-Rl+1ηlNl1+Rl+1+ηl+1Rl+11-Rl+1exp2ikNlhl,
D=η0N01+R1+η1N11-R1=0.
δn*=N12in*kheffη1N1-η0N0η1N1+η0N0δR1.

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