Abstract

A coupled-mode theory is derived from the scalar wave equation for the interaction between forward- and backward-traveling waves in a general slowly varying coupled waveguide array containing an arbitrary number of guides with a grating overlay. The equations include the effects of nonnegligible model overlap terms and changes in modal overlap but still demonstrate power conservation. Numerical results are presented for a contradirectional track-changing filter, which show that the modifications made to the equations are significant for practical devices.

© 1991 Optical Society of America

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  1. D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, “Grating filters for thin-film optical waveguides,” Appl. Phys. Lett. 24, 194–196 (1974).
    [CrossRef]
  2. R. C. Alferness, C. H. Joyner, M. D. Divino, L. L. Buhl, “InGaAsP/InP waveguide grating filters for λ= 1.5 μm,” Appl. Phys. Lett. 45, 1278–1280 (1984).
    [CrossRef]
  3. W. V. Sorin, H. J. Shaw, “A single-mode fiber evanescent grating reflector,” IEEE J. Lightwave Technol. LT-3, 1041–1043 (1985).
    [CrossRef]
  4. E. Brinkmeyer, W. Brennecke, M. Zurn, R. Ulrich, “Fibre Bragg reflector for mode selection and line-narrowing of injection lasers,” Electron. Lett. 22, 134–135 (1986).
    [CrossRef]
  5. I. Bennion, D. C. J. Reid, C. J. Rowe, W. J. Stewart, “High-reflectivity monomode-fibre grating reflectors,” Electron. Lett. 22, 341–343 (1986).
    [CrossRef]
  6. C. Vassilopoulos, J. R. Cozens, “Backward wave couplers and reflectors,” in Novel Optoelectronic Devices, M. J. Adams, ed., Proc. Soc. Photo-Opt. Instrum. Eng.800, 123–127 (1987).
    [CrossRef]
  7. M. S. Whalen, M. D. Divino, R. C. Alferness, “Demonstration of a narrowband Bragg-reflection filter in a single-mode fibre directional coupler,” Electron. Lett. 22, 681–682 (1986).
    [CrossRef]
  8. A. S. Svakhin, V. A. Sychugov, “Narrow-band Bragg reflecting filter based on a single-mode fiber,” Sov. Phys. Tech. Phys. 32, 701–702 (1987).
  9. P. Yeh, H. R. Taylor, “Contradirectional frequency-selective couplers for guided-wave optics,” Appl. Opt. 19, 2848–2855 (1980).
    [CrossRef] [PubMed]
  10. C. Elachi, C. Yeh, “Frequency-selective coupler for integrated optics systems,” Opt. Commun. 7, 201–204 (1973).
    [CrossRef]
  11. N. Tsukada, “Modification of the coupling coefficient by periodic modulation of the propagation constants,” Opt. Commun. 22, 113–115 (1977).
    [CrossRef]
  12. R. C. Alferness, L. L. Buhl, “Polarization independent optical filter using interwaveguide TE–TM conversion,” Appl. Phys. Lett. 39, 131–134 (1981).
    [CrossRef]
  13. J. S. Wilkinson, M. G. F. Wilson, “The experimental evaluation of a directional coupler wavelength filter having a periodic electrode,” in Proceedings of the Institution of Electrical Engineers Workshop on Integrated Optical and Related Technologies for Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1984).
  14. H.-P. Nolting, D. Hoffmann, M. Schlichting, “Integrated optical wavelength multiplexer/demultiplexer for optical communications,” in Proceedings of the European Conference on Integrated Optics ’85 (Springer-Verlag, Berlin, 1985), pp. 215–220.
  15. C. Vassilopoulos, J. R. C. Cozens, “Combined directional and contradirectional coupling in a three-waveguide configuration,” IEEE J. Quantum Electron. 25, 2113–2118 (1989).
    [CrossRef]
  16. R. R. A. Syms, “Multiple-waveguide distributed feedback lasers,” IEEE J. Quantum Electron. QE-22, 411–418 (1986).
    [CrossRef]
  17. A. Yariv, “Coupled-wave theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
    [CrossRef]
  18. H. F. Taylor, A. Yariv, “Guided-wave optics,” Proc. IEEE 62, 1044–1060 (1974).
    [CrossRef]
  19. H. Stoll, A. Yariv, “Coupled-mode analysis of periodic dielectric waveguides,” Opt. Commun. 8, 5–8 (1973).
    [CrossRef]
  20. A. Yariv, M. Nakamura, “Periodic structures for integrated optics,” IEEE J. Quantum Electron. QE-13, 233–253 (1977).
    [CrossRef]
  21. R. R. A. Syms, “Optical directional coupler with a grating overlay,” Appl. Opt. 24, 717–726 (1985).
    [CrossRef] [PubMed]
  22. R. Marz, H. P. Nolting, “Spectral properties of asymmetrical optical directional couplers with periodic structures,” Opt. Quantum Electron. 19, 273–287 (1987).
    [CrossRef]
  23. A. Hardy, W. Streifer, “Analysis of phased-array diode lasers,” Opt. Lett. 10, 335–337 (1985).
    [CrossRef] [PubMed]
  24. A. Hardy, W. Streifer, “Coupled mode theory of parallel waveguides,” IEEE J. Lightwave Technol. LT-3, 1135–1146 (1985).
    [CrossRef]
  25. A. Hardy, W. Streifer, “Coupled modes of multiwaveguide systems and phased arrays,” IEEE J. Lightwave Technol. LT-4, 90–99 (1986).
    [CrossRef]
  26. A. Hardy, W. Streifer, “Coupled mode solutions of multi-waveguide systems,” IEEE J. Quantum Electron. QE-22, 528–534 (1986).
    [CrossRef]
  27. W. Streifer, M. Osinski, A. Hardy, “A critical overview of coupled mode theory,” in Integrated Optical Circuit Engineering V, M. A. Menner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.835, 178–187 (1987).
    [CrossRef]
  28. C. Vassallo, “About coupled-mode theories for dielectric waveguides,” IEEE J. Lightwave Technol. LT-6, 294–303 (1988).
    [CrossRef]
  29. H. A. Haus, W. P. Huang, S. Kawakami, N. Whitaker, “Coupled-mode theory of optical waveguides,” IEEE J. Lightwave Technol. LT-5, 16–23 (1987).
    [CrossRef]
  30. S.-L. Chuang, “A coupled mode formulation by reciprocity and a variational principle,” IEEE J. Lightwave Technol. LT-5, 5–15 (1987).
    [CrossRef]
  31. S.-L. Chuang, “A coupled mode theory for multiwaveguide systems satisfying the reciprocity theorem and power conservation,” IEEE J. Lightwave Technol. LT-5, 174–183 (1987).
    [CrossRef]
  32. S.-L. Chuang, “Application of the strongly coupled-mode theory to integrated optical devices,” IEEE J. Quantum Electron. QE-23, 499–509 (1987).
    [CrossRef]
  33. W. Streifer, M. Osinski, A. Hardy, “Reformulation of the coupled-mode theory of multiwaveguide systems,” IEEE Lightwave Technol. LT-5, 1–4 (1987).
    [CrossRef]
  34. A. W. Synder, A. Ankiewicz, “Fibre couplers composed of unequal cores,” Electron. Lett. 22, 1237–1238 (1986).
    [CrossRef]
  35. W. Streifer, “Coupled mode theory,” Electron. Lett. 23, 315–316 (1987).
    [CrossRef]
  36. A. W. Snyder, A. Ankiewicz, A. Altintas, “Fundamental error of recent coupled mode formulations,” Electron. Lett. 23, 1097–1098 (1987).
    [CrossRef]
  37. W. Streifer, “Comment: fundamental error of recent coupled mode formulations,” Electron. Lett. 24, 718–719 (1988).
    [CrossRef]
  38. J.-R. Qian, “Generalised coupled-mode equations and their applications to fibre couplers,” Electron. Lett. 22, 304–306 (1986).
    [CrossRef]
  39. E. A. J. Marcatili, “Improved coupled-mode equations for dielectric guides,” IEEE J. Quantum. Electron. QE-22, 988–993 (1986).
    [CrossRef]
  40. R. G. Peall, R. R. A. Syms, “Scalar strong coupled mode theory for slowly varying waveguide arrays,” Opt. Commun. 67, 421–424 (1988).
    [CrossRef]
  41. R. R. A. Syms, R. G. Peall, “Explanation of asymmetric switch response of three-arm directional couplers in Ti:LiNbO3using strong coupling theory,” Opt. Commun. 66, 260–264 (1988).
    [CrossRef]
  42. R. G. Peall, R. R. A. Syms, “Comparison between strong coupling theory and experiment for three-arm directional couplers in Ti:LiNbO3,” IEEE J. Lightwave Technol. 7, 540–554 (1989).
    [CrossRef]
  43. R. G. Peall, R. R. A. Syms, “Further evidence of strong coupling effects in three-arm Ti:LiNbO3directional couplers,” IEEE J. Quantum Electron. 25, 729–735 (1989).
    [CrossRef]
  44. T. Findakly, C.-L. Chen, “Optical directional couplers with variable spacing,” Appl. Opt. 17, 769–773 (1978).
    [CrossRef] [PubMed]
  45. A. Hardy, M. Osinski, W. Streifer, “Application of coupled-mode theory to nearly parallel waveguide systems,” Electron. Lett. 22, 1249–1250 (1986).
    [CrossRef]
  46. H. A. Haus, W.-P. Huang, “Mode coupling in tapered structures,” IEEE J. Lightwave Technol. 7, 729–730 (1989).
    [CrossRef]
  47. D. Marcuse, Light Transmission Optics (Van Nostrand, New York, 1972).
  48. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).
  49. H. A. Haus, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Mass. 02139 (personal communication).
  50. R. C. Alferness, R. V. Schmidt, E. H. Turner, “Characteristics of Ti-diffused lithium niobate optical directional couplers,” Appl. Opt. 18, 4012–4016 (1979).
    [CrossRef] [PubMed]
  51. N. Noda, M. Fukama, O. Mikami, “Design calculations for directional couplers fabricated by Ti-diffused LiNbO3waveguides,” Appl. Opt. 20, 2284–2290 (1981).
    [CrossRef] [PubMed]
  52. M. D. Feit, J. A. Fleck, L. McCaughan, “Comparison of calculated and measured performance of diffused channel waveguide couplers,” J. Opt. Soc. Am. A 73, 1296–1304 (1983).
    [CrossRef]
  53. E. A. J. Marcatili, L. L. Buhl, R. C. Alferness, “Experimental verification of the improved coupled mode equations,” Appl. Phys. Lett. 49, 1692–1693 (1986).
    [CrossRef]
  54. R. R. A. Syms, R. G. Peall, “Mode confinement and modal overlap in electro-optic channel waveguide devices,” Opt. Commun. 74, 46–48 (1989).
    [CrossRef]
  55. L. A. Molter, H. A. Haus, “Optical two-guide coupler switches in GaAs: ideal and non-ideal operation,” in Integrated and Guided-Wave Optics, Vol. 5 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. 248–251.
  56. H. A. Haus, C. G. Fonstad, “Three-waveguide couplers for improved sampling and filtering,” IEEE J. Quantum Electron. QE-17, 2321–2325 (1981).
    [CrossRef]
  57. D. Marcuse, “Directional couplers made of nonidentical asymmetric slab guides. Part II: grating-assisted couplers,” IEEE J. Lightwave Technol. LT-5, 268–273 (1987).
    [CrossRef]
  58. W.-P. Huang, H. A. Haus, “Power exchange in grating-assisted couplers,” IEEE J. Lightwave Technol. 7, 920–924 (1989).
    [CrossRef]

1989 (6)

C. Vassilopoulos, J. R. C. Cozens, “Combined directional and contradirectional coupling in a three-waveguide configuration,” IEEE J. Quantum Electron. 25, 2113–2118 (1989).
[CrossRef]

R. G. Peall, R. R. A. Syms, “Comparison between strong coupling theory and experiment for three-arm directional couplers in Ti:LiNbO3,” IEEE J. Lightwave Technol. 7, 540–554 (1989).
[CrossRef]

R. G. Peall, R. R. A. Syms, “Further evidence of strong coupling effects in three-arm Ti:LiNbO3directional couplers,” IEEE J. Quantum Electron. 25, 729–735 (1989).
[CrossRef]

H. A. Haus, W.-P. Huang, “Mode coupling in tapered structures,” IEEE J. Lightwave Technol. 7, 729–730 (1989).
[CrossRef]

W.-P. Huang, H. A. Haus, “Power exchange in grating-assisted couplers,” IEEE J. Lightwave Technol. 7, 920–924 (1989).
[CrossRef]

R. R. A. Syms, R. G. Peall, “Mode confinement and modal overlap in electro-optic channel waveguide devices,” Opt. Commun. 74, 46–48 (1989).
[CrossRef]

1988 (4)

R. G. Peall, R. R. A. Syms, “Scalar strong coupled mode theory for slowly varying waveguide arrays,” Opt. Commun. 67, 421–424 (1988).
[CrossRef]

R. R. A. Syms, R. G. Peall, “Explanation of asymmetric switch response of three-arm directional couplers in Ti:LiNbO3using strong coupling theory,” Opt. Commun. 66, 260–264 (1988).
[CrossRef]

C. Vassallo, “About coupled-mode theories for dielectric waveguides,” IEEE J. Lightwave Technol. LT-6, 294–303 (1988).
[CrossRef]

W. Streifer, “Comment: fundamental error of recent coupled mode formulations,” Electron. Lett. 24, 718–719 (1988).
[CrossRef]

1987 (10)

W. Streifer, “Coupled mode theory,” Electron. Lett. 23, 315–316 (1987).
[CrossRef]

A. W. Snyder, A. Ankiewicz, A. Altintas, “Fundamental error of recent coupled mode formulations,” Electron. Lett. 23, 1097–1098 (1987).
[CrossRef]

H. A. Haus, W. P. Huang, S. Kawakami, N. Whitaker, “Coupled-mode theory of optical waveguides,” IEEE J. Lightwave Technol. LT-5, 16–23 (1987).
[CrossRef]

S.-L. Chuang, “A coupled mode formulation by reciprocity and a variational principle,” IEEE J. Lightwave Technol. LT-5, 5–15 (1987).
[CrossRef]

S.-L. Chuang, “A coupled mode theory for multiwaveguide systems satisfying the reciprocity theorem and power conservation,” IEEE J. Lightwave Technol. LT-5, 174–183 (1987).
[CrossRef]

S.-L. Chuang, “Application of the strongly coupled-mode theory to integrated optical devices,” IEEE J. Quantum Electron. QE-23, 499–509 (1987).
[CrossRef]

W. Streifer, M. Osinski, A. Hardy, “Reformulation of the coupled-mode theory of multiwaveguide systems,” IEEE Lightwave Technol. LT-5, 1–4 (1987).
[CrossRef]

A. S. Svakhin, V. A. Sychugov, “Narrow-band Bragg reflecting filter based on a single-mode fiber,” Sov. Phys. Tech. Phys. 32, 701–702 (1987).

D. Marcuse, “Directional couplers made of nonidentical asymmetric slab guides. Part II: grating-assisted couplers,” IEEE J. Lightwave Technol. LT-5, 268–273 (1987).
[CrossRef]

R. Marz, H. P. Nolting, “Spectral properties of asymmetrical optical directional couplers with periodic structures,” Opt. Quantum Electron. 19, 273–287 (1987).
[CrossRef]

1986 (11)

E. Brinkmeyer, W. Brennecke, M. Zurn, R. Ulrich, “Fibre Bragg reflector for mode selection and line-narrowing of injection lasers,” Electron. Lett. 22, 134–135 (1986).
[CrossRef]

I. Bennion, D. C. J. Reid, C. J. Rowe, W. J. Stewart, “High-reflectivity monomode-fibre grating reflectors,” Electron. Lett. 22, 341–343 (1986).
[CrossRef]

M. S. Whalen, M. D. Divino, R. C. Alferness, “Demonstration of a narrowband Bragg-reflection filter in a single-mode fibre directional coupler,” Electron. Lett. 22, 681–682 (1986).
[CrossRef]

R. R. A. Syms, “Multiple-waveguide distributed feedback lasers,” IEEE J. Quantum Electron. QE-22, 411–418 (1986).
[CrossRef]

A. Hardy, W. Streifer, “Coupled modes of multiwaveguide systems and phased arrays,” IEEE J. Lightwave Technol. LT-4, 90–99 (1986).
[CrossRef]

A. Hardy, W. Streifer, “Coupled mode solutions of multi-waveguide systems,” IEEE J. Quantum Electron. QE-22, 528–534 (1986).
[CrossRef]

A. W. Synder, A. Ankiewicz, “Fibre couplers composed of unequal cores,” Electron. Lett. 22, 1237–1238 (1986).
[CrossRef]

J.-R. Qian, “Generalised coupled-mode equations and their applications to fibre couplers,” Electron. Lett. 22, 304–306 (1986).
[CrossRef]

E. A. J. Marcatili, “Improved coupled-mode equations for dielectric guides,” IEEE J. Quantum. Electron. QE-22, 988–993 (1986).
[CrossRef]

A. Hardy, M. Osinski, W. Streifer, “Application of coupled-mode theory to nearly parallel waveguide systems,” Electron. Lett. 22, 1249–1250 (1986).
[CrossRef]

E. A. J. Marcatili, L. L. Buhl, R. C. Alferness, “Experimental verification of the improved coupled mode equations,” Appl. Phys. Lett. 49, 1692–1693 (1986).
[CrossRef]

1985 (4)

A. Hardy, W. Streifer, “Coupled mode theory of parallel waveguides,” IEEE J. Lightwave Technol. LT-3, 1135–1146 (1985).
[CrossRef]

W. V. Sorin, H. J. Shaw, “A single-mode fiber evanescent grating reflector,” IEEE J. Lightwave Technol. LT-3, 1041–1043 (1985).
[CrossRef]

A. Hardy, W. Streifer, “Analysis of phased-array diode lasers,” Opt. Lett. 10, 335–337 (1985).
[CrossRef] [PubMed]

R. R. A. Syms, “Optical directional coupler with a grating overlay,” Appl. Opt. 24, 717–726 (1985).
[CrossRef] [PubMed]

1984 (1)

R. C. Alferness, C. H. Joyner, M. D. Divino, L. L. Buhl, “InGaAsP/InP waveguide grating filters for λ= 1.5 μm,” Appl. Phys. Lett. 45, 1278–1280 (1984).
[CrossRef]

1983 (1)

M. D. Feit, J. A. Fleck, L. McCaughan, “Comparison of calculated and measured performance of diffused channel waveguide couplers,” J. Opt. Soc. Am. A 73, 1296–1304 (1983).
[CrossRef]

1981 (3)

R. C. Alferness, L. L. Buhl, “Polarization independent optical filter using interwaveguide TE–TM conversion,” Appl. Phys. Lett. 39, 131–134 (1981).
[CrossRef]

N. Noda, M. Fukama, O. Mikami, “Design calculations for directional couplers fabricated by Ti-diffused LiNbO3waveguides,” Appl. Opt. 20, 2284–2290 (1981).
[CrossRef] [PubMed]

H. A. Haus, C. G. Fonstad, “Three-waveguide couplers for improved sampling and filtering,” IEEE J. Quantum Electron. QE-17, 2321–2325 (1981).
[CrossRef]

1980 (1)

1979 (1)

1978 (1)

1977 (2)

A. Yariv, M. Nakamura, “Periodic structures for integrated optics,” IEEE J. Quantum Electron. QE-13, 233–253 (1977).
[CrossRef]

N. Tsukada, “Modification of the coupling coefficient by periodic modulation of the propagation constants,” Opt. Commun. 22, 113–115 (1977).
[CrossRef]

1974 (2)

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, “Grating filters for thin-film optical waveguides,” Appl. Phys. Lett. 24, 194–196 (1974).
[CrossRef]

H. F. Taylor, A. Yariv, “Guided-wave optics,” Proc. IEEE 62, 1044–1060 (1974).
[CrossRef]

1973 (3)

H. Stoll, A. Yariv, “Coupled-mode analysis of periodic dielectric waveguides,” Opt. Commun. 8, 5–8 (1973).
[CrossRef]

A. Yariv, “Coupled-wave theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
[CrossRef]

C. Elachi, C. Yeh, “Frequency-selective coupler for integrated optics systems,” Opt. Commun. 7, 201–204 (1973).
[CrossRef]

Alferness, R. C.

M. S. Whalen, M. D. Divino, R. C. Alferness, “Demonstration of a narrowband Bragg-reflection filter in a single-mode fibre directional coupler,” Electron. Lett. 22, 681–682 (1986).
[CrossRef]

E. A. J. Marcatili, L. L. Buhl, R. C. Alferness, “Experimental verification of the improved coupled mode equations,” Appl. Phys. Lett. 49, 1692–1693 (1986).
[CrossRef]

R. C. Alferness, C. H. Joyner, M. D. Divino, L. L. Buhl, “InGaAsP/InP waveguide grating filters for λ= 1.5 μm,” Appl. Phys. Lett. 45, 1278–1280 (1984).
[CrossRef]

R. C. Alferness, L. L. Buhl, “Polarization independent optical filter using interwaveguide TE–TM conversion,” Appl. Phys. Lett. 39, 131–134 (1981).
[CrossRef]

R. C. Alferness, R. V. Schmidt, E. H. Turner, “Characteristics of Ti-diffused lithium niobate optical directional couplers,” Appl. Opt. 18, 4012–4016 (1979).
[CrossRef] [PubMed]

Altintas, A.

A. W. Snyder, A. Ankiewicz, A. Altintas, “Fundamental error of recent coupled mode formulations,” Electron. Lett. 23, 1097–1098 (1987).
[CrossRef]

Ankiewicz, A.

A. W. Snyder, A. Ankiewicz, A. Altintas, “Fundamental error of recent coupled mode formulations,” Electron. Lett. 23, 1097–1098 (1987).
[CrossRef]

A. W. Synder, A. Ankiewicz, “Fibre couplers composed of unequal cores,” Electron. Lett. 22, 1237–1238 (1986).
[CrossRef]

Bennion, I.

I. Bennion, D. C. J. Reid, C. J. Rowe, W. J. Stewart, “High-reflectivity monomode-fibre grating reflectors,” Electron. Lett. 22, 341–343 (1986).
[CrossRef]

Brennecke, W.

E. Brinkmeyer, W. Brennecke, M. Zurn, R. Ulrich, “Fibre Bragg reflector for mode selection and line-narrowing of injection lasers,” Electron. Lett. 22, 134–135 (1986).
[CrossRef]

Brinkmeyer, E.

E. Brinkmeyer, W. Brennecke, M. Zurn, R. Ulrich, “Fibre Bragg reflector for mode selection and line-narrowing of injection lasers,” Electron. Lett. 22, 134–135 (1986).
[CrossRef]

Buhl, L. L.

E. A. J. Marcatili, L. L. Buhl, R. C. Alferness, “Experimental verification of the improved coupled mode equations,” Appl. Phys. Lett. 49, 1692–1693 (1986).
[CrossRef]

R. C. Alferness, C. H. Joyner, M. D. Divino, L. L. Buhl, “InGaAsP/InP waveguide grating filters for λ= 1.5 μm,” Appl. Phys. Lett. 45, 1278–1280 (1984).
[CrossRef]

R. C. Alferness, L. L. Buhl, “Polarization independent optical filter using interwaveguide TE–TM conversion,” Appl. Phys. Lett. 39, 131–134 (1981).
[CrossRef]

Chen, C.-L.

Chuang, S.-L.

S.-L. Chuang, “A coupled mode formulation by reciprocity and a variational principle,” IEEE J. Lightwave Technol. LT-5, 5–15 (1987).
[CrossRef]

S.-L. Chuang, “A coupled mode theory for multiwaveguide systems satisfying the reciprocity theorem and power conservation,” IEEE J. Lightwave Technol. LT-5, 174–183 (1987).
[CrossRef]

S.-L. Chuang, “Application of the strongly coupled-mode theory to integrated optical devices,” IEEE J. Quantum Electron. QE-23, 499–509 (1987).
[CrossRef]

Cozens, J. R.

C. Vassilopoulos, J. R. Cozens, “Backward wave couplers and reflectors,” in Novel Optoelectronic Devices, M. J. Adams, ed., Proc. Soc. Photo-Opt. Instrum. Eng.800, 123–127 (1987).
[CrossRef]

Cozens, J. R. C.

C. Vassilopoulos, J. R. C. Cozens, “Combined directional and contradirectional coupling in a three-waveguide configuration,” IEEE J. Quantum Electron. 25, 2113–2118 (1989).
[CrossRef]

Divino, M. D.

M. S. Whalen, M. D. Divino, R. C. Alferness, “Demonstration of a narrowband Bragg-reflection filter in a single-mode fibre directional coupler,” Electron. Lett. 22, 681–682 (1986).
[CrossRef]

R. C. Alferness, C. H. Joyner, M. D. Divino, L. L. Buhl, “InGaAsP/InP waveguide grating filters for λ= 1.5 μm,” Appl. Phys. Lett. 45, 1278–1280 (1984).
[CrossRef]

Elachi, C.

C. Elachi, C. Yeh, “Frequency-selective coupler for integrated optics systems,” Opt. Commun. 7, 201–204 (1973).
[CrossRef]

Feit, M. D.

M. D. Feit, J. A. Fleck, L. McCaughan, “Comparison of calculated and measured performance of diffused channel waveguide couplers,” J. Opt. Soc. Am. A 73, 1296–1304 (1983).
[CrossRef]

Findakly, T.

Flanders, D. C.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, “Grating filters for thin-film optical waveguides,” Appl. Phys. Lett. 24, 194–196 (1974).
[CrossRef]

Fleck, J. A.

M. D. Feit, J. A. Fleck, L. McCaughan, “Comparison of calculated and measured performance of diffused channel waveguide couplers,” J. Opt. Soc. Am. A 73, 1296–1304 (1983).
[CrossRef]

Fonstad, C. G.

H. A. Haus, C. G. Fonstad, “Three-waveguide couplers for improved sampling and filtering,” IEEE J. Quantum Electron. QE-17, 2321–2325 (1981).
[CrossRef]

Fukama, M.

Hardy, A.

W. Streifer, M. Osinski, A. Hardy, “Reformulation of the coupled-mode theory of multiwaveguide systems,” IEEE Lightwave Technol. LT-5, 1–4 (1987).
[CrossRef]

A. Hardy, W. Streifer, “Coupled modes of multiwaveguide systems and phased arrays,” IEEE J. Lightwave Technol. LT-4, 90–99 (1986).
[CrossRef]

A. Hardy, W. Streifer, “Coupled mode solutions of multi-waveguide systems,” IEEE J. Quantum Electron. QE-22, 528–534 (1986).
[CrossRef]

A. Hardy, M. Osinski, W. Streifer, “Application of coupled-mode theory to nearly parallel waveguide systems,” Electron. Lett. 22, 1249–1250 (1986).
[CrossRef]

A. Hardy, W. Streifer, “Analysis of phased-array diode lasers,” Opt. Lett. 10, 335–337 (1985).
[CrossRef] [PubMed]

A. Hardy, W. Streifer, “Coupled mode theory of parallel waveguides,” IEEE J. Lightwave Technol. LT-3, 1135–1146 (1985).
[CrossRef]

W. Streifer, M. Osinski, A. Hardy, “A critical overview of coupled mode theory,” in Integrated Optical Circuit Engineering V, M. A. Menner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.835, 178–187 (1987).
[CrossRef]

Haus, H. A.

W.-P. Huang, H. A. Haus, “Power exchange in grating-assisted couplers,” IEEE J. Lightwave Technol. 7, 920–924 (1989).
[CrossRef]

H. A. Haus, W.-P. Huang, “Mode coupling in tapered structures,” IEEE J. Lightwave Technol. 7, 729–730 (1989).
[CrossRef]

H. A. Haus, W. P. Huang, S. Kawakami, N. Whitaker, “Coupled-mode theory of optical waveguides,” IEEE J. Lightwave Technol. LT-5, 16–23 (1987).
[CrossRef]

H. A. Haus, C. G. Fonstad, “Three-waveguide couplers for improved sampling and filtering,” IEEE J. Quantum Electron. QE-17, 2321–2325 (1981).
[CrossRef]

L. A. Molter, H. A. Haus, “Optical two-guide coupler switches in GaAs: ideal and non-ideal operation,” in Integrated and Guided-Wave Optics, Vol. 5 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. 248–251.

H. A. Haus, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Mass. 02139 (personal communication).

Hoffmann, D.

H.-P. Nolting, D. Hoffmann, M. Schlichting, “Integrated optical wavelength multiplexer/demultiplexer for optical communications,” in Proceedings of the European Conference on Integrated Optics ’85 (Springer-Verlag, Berlin, 1985), pp. 215–220.

Huang, W. P.

H. A. Haus, W. P. Huang, S. Kawakami, N. Whitaker, “Coupled-mode theory of optical waveguides,” IEEE J. Lightwave Technol. LT-5, 16–23 (1987).
[CrossRef]

Huang, W.-P.

H. A. Haus, W.-P. Huang, “Mode coupling in tapered structures,” IEEE J. Lightwave Technol. 7, 729–730 (1989).
[CrossRef]

W.-P. Huang, H. A. Haus, “Power exchange in grating-assisted couplers,” IEEE J. Lightwave Technol. 7, 920–924 (1989).
[CrossRef]

Joyner, C. H.

R. C. Alferness, C. H. Joyner, M. D. Divino, L. L. Buhl, “InGaAsP/InP waveguide grating filters for λ= 1.5 μm,” Appl. Phys. Lett. 45, 1278–1280 (1984).
[CrossRef]

Kawakami, S.

H. A. Haus, W. P. Huang, S. Kawakami, N. Whitaker, “Coupled-mode theory of optical waveguides,” IEEE J. Lightwave Technol. LT-5, 16–23 (1987).
[CrossRef]

Kogelnik, H.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, “Grating filters for thin-film optical waveguides,” Appl. Phys. Lett. 24, 194–196 (1974).
[CrossRef]

Marcatili, E. A. J.

E. A. J. Marcatili, “Improved coupled-mode equations for dielectric guides,” IEEE J. Quantum. Electron. QE-22, 988–993 (1986).
[CrossRef]

E. A. J. Marcatili, L. L. Buhl, R. C. Alferness, “Experimental verification of the improved coupled mode equations,” Appl. Phys. Lett. 49, 1692–1693 (1986).
[CrossRef]

Marcuse, D.

D. Marcuse, “Directional couplers made of nonidentical asymmetric slab guides. Part II: grating-assisted couplers,” IEEE J. Lightwave Technol. LT-5, 268–273 (1987).
[CrossRef]

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

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

Marz, R.

R. Marz, H. P. Nolting, “Spectral properties of asymmetrical optical directional couplers with periodic structures,” Opt. Quantum Electron. 19, 273–287 (1987).
[CrossRef]

McCaughan, L.

M. D. Feit, J. A. Fleck, L. McCaughan, “Comparison of calculated and measured performance of diffused channel waveguide couplers,” J. Opt. Soc. Am. A 73, 1296–1304 (1983).
[CrossRef]

Mikami, O.

Molter, L. A.

L. A. Molter, H. A. Haus, “Optical two-guide coupler switches in GaAs: ideal and non-ideal operation,” in Integrated and Guided-Wave Optics, Vol. 5 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. 248–251.

Nakamura, M.

A. Yariv, M. Nakamura, “Periodic structures for integrated optics,” IEEE J. Quantum Electron. QE-13, 233–253 (1977).
[CrossRef]

Noda, N.

Nolting, H. P.

R. Marz, H. P. Nolting, “Spectral properties of asymmetrical optical directional couplers with periodic structures,” Opt. Quantum Electron. 19, 273–287 (1987).
[CrossRef]

Nolting, H.-P.

H.-P. Nolting, D. Hoffmann, M. Schlichting, “Integrated optical wavelength multiplexer/demultiplexer for optical communications,” in Proceedings of the European Conference on Integrated Optics ’85 (Springer-Verlag, Berlin, 1985), pp. 215–220.

Osinski, M.

W. Streifer, M. Osinski, A. Hardy, “Reformulation of the coupled-mode theory of multiwaveguide systems,” IEEE Lightwave Technol. LT-5, 1–4 (1987).
[CrossRef]

A. Hardy, M. Osinski, W. Streifer, “Application of coupled-mode theory to nearly parallel waveguide systems,” Electron. Lett. 22, 1249–1250 (1986).
[CrossRef]

W. Streifer, M. Osinski, A. Hardy, “A critical overview of coupled mode theory,” in Integrated Optical Circuit Engineering V, M. A. Menner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.835, 178–187 (1987).
[CrossRef]

Peall, R. G.

R. R. A. Syms, R. G. Peall, “Mode confinement and modal overlap in electro-optic channel waveguide devices,” Opt. Commun. 74, 46–48 (1989).
[CrossRef]

R. G. Peall, R. R. A. Syms, “Comparison between strong coupling theory and experiment for three-arm directional couplers in Ti:LiNbO3,” IEEE J. Lightwave Technol. 7, 540–554 (1989).
[CrossRef]

R. G. Peall, R. R. A. Syms, “Further evidence of strong coupling effects in three-arm Ti:LiNbO3directional couplers,” IEEE J. Quantum Electron. 25, 729–735 (1989).
[CrossRef]

R. G. Peall, R. R. A. Syms, “Scalar strong coupled mode theory for slowly varying waveguide arrays,” Opt. Commun. 67, 421–424 (1988).
[CrossRef]

R. R. A. Syms, R. G. Peall, “Explanation of asymmetric switch response of three-arm directional couplers in Ti:LiNbO3using strong coupling theory,” Opt. Commun. 66, 260–264 (1988).
[CrossRef]

Qian, J.-R.

J.-R. Qian, “Generalised coupled-mode equations and their applications to fibre couplers,” Electron. Lett. 22, 304–306 (1986).
[CrossRef]

Reid, D. C. J.

I. Bennion, D. C. J. Reid, C. J. Rowe, W. J. Stewart, “High-reflectivity monomode-fibre grating reflectors,” Electron. Lett. 22, 341–343 (1986).
[CrossRef]

Rowe, C. J.

I. Bennion, D. C. J. Reid, C. J. Rowe, W. J. Stewart, “High-reflectivity monomode-fibre grating reflectors,” Electron. Lett. 22, 341–343 (1986).
[CrossRef]

Schlichting, M.

H.-P. Nolting, D. Hoffmann, M. Schlichting, “Integrated optical wavelength multiplexer/demultiplexer for optical communications,” in Proceedings of the European Conference on Integrated Optics ’85 (Springer-Verlag, Berlin, 1985), pp. 215–220.

Schmidt, R. V.

R. C. Alferness, R. V. Schmidt, E. H. Turner, “Characteristics of Ti-diffused lithium niobate optical directional couplers,” Appl. Opt. 18, 4012–4016 (1979).
[CrossRef] [PubMed]

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, “Grating filters for thin-film optical waveguides,” Appl. Phys. Lett. 24, 194–196 (1974).
[CrossRef]

Shank, C. V.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, “Grating filters for thin-film optical waveguides,” Appl. Phys. Lett. 24, 194–196 (1974).
[CrossRef]

Shaw, H. J.

W. V. Sorin, H. J. Shaw, “A single-mode fiber evanescent grating reflector,” IEEE J. Lightwave Technol. LT-3, 1041–1043 (1985).
[CrossRef]

Snyder, A. W.

A. W. Snyder, A. Ankiewicz, A. Altintas, “Fundamental error of recent coupled mode formulations,” Electron. Lett. 23, 1097–1098 (1987).
[CrossRef]

Sorin, W. V.

W. V. Sorin, H. J. Shaw, “A single-mode fiber evanescent grating reflector,” IEEE J. Lightwave Technol. LT-3, 1041–1043 (1985).
[CrossRef]

Stewart, W. J.

I. Bennion, D. C. J. Reid, C. J. Rowe, W. J. Stewart, “High-reflectivity monomode-fibre grating reflectors,” Electron. Lett. 22, 341–343 (1986).
[CrossRef]

Stoll, H.

H. Stoll, A. Yariv, “Coupled-mode analysis of periodic dielectric waveguides,” Opt. Commun. 8, 5–8 (1973).
[CrossRef]

Streifer, W.

W. Streifer, “Comment: fundamental error of recent coupled mode formulations,” Electron. Lett. 24, 718–719 (1988).
[CrossRef]

W. Streifer, “Coupled mode theory,” Electron. Lett. 23, 315–316 (1987).
[CrossRef]

W. Streifer, M. Osinski, A. Hardy, “Reformulation of the coupled-mode theory of multiwaveguide systems,” IEEE Lightwave Technol. LT-5, 1–4 (1987).
[CrossRef]

A. Hardy, W. Streifer, “Coupled mode solutions of multi-waveguide systems,” IEEE J. Quantum Electron. QE-22, 528–534 (1986).
[CrossRef]

A. Hardy, W. Streifer, “Coupled modes of multiwaveguide systems and phased arrays,” IEEE J. Lightwave Technol. LT-4, 90–99 (1986).
[CrossRef]

A. Hardy, M. Osinski, W. Streifer, “Application of coupled-mode theory to nearly parallel waveguide systems,” Electron. Lett. 22, 1249–1250 (1986).
[CrossRef]

A. Hardy, W. Streifer, “Analysis of phased-array diode lasers,” Opt. Lett. 10, 335–337 (1985).
[CrossRef] [PubMed]

A. Hardy, W. Streifer, “Coupled mode theory of parallel waveguides,” IEEE J. Lightwave Technol. LT-3, 1135–1146 (1985).
[CrossRef]

W. Streifer, M. Osinski, A. Hardy, “A critical overview of coupled mode theory,” in Integrated Optical Circuit Engineering V, M. A. Menner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.835, 178–187 (1987).
[CrossRef]

Svakhin, A. S.

A. S. Svakhin, V. A. Sychugov, “Narrow-band Bragg reflecting filter based on a single-mode fiber,” Sov. Phys. Tech. Phys. 32, 701–702 (1987).

Sychugov, V. A.

A. S. Svakhin, V. A. Sychugov, “Narrow-band Bragg reflecting filter based on a single-mode fiber,” Sov. Phys. Tech. Phys. 32, 701–702 (1987).

Syms, R. R. A.

R. R. A. Syms, R. G. Peall, “Mode confinement and modal overlap in electro-optic channel waveguide devices,” Opt. Commun. 74, 46–48 (1989).
[CrossRef]

R. G. Peall, R. R. A. Syms, “Further evidence of strong coupling effects in three-arm Ti:LiNbO3directional couplers,” IEEE J. Quantum Electron. 25, 729–735 (1989).
[CrossRef]

R. G. Peall, R. R. A. Syms, “Comparison between strong coupling theory and experiment for three-arm directional couplers in Ti:LiNbO3,” IEEE J. Lightwave Technol. 7, 540–554 (1989).
[CrossRef]

R. G. Peall, R. R. A. Syms, “Scalar strong coupled mode theory for slowly varying waveguide arrays,” Opt. Commun. 67, 421–424 (1988).
[CrossRef]

R. R. A. Syms, R. G. Peall, “Explanation of asymmetric switch response of three-arm directional couplers in Ti:LiNbO3using strong coupling theory,” Opt. Commun. 66, 260–264 (1988).
[CrossRef]

R. R. A. Syms, “Multiple-waveguide distributed feedback lasers,” IEEE J. Quantum Electron. QE-22, 411–418 (1986).
[CrossRef]

R. R. A. Syms, “Optical directional coupler with a grating overlay,” Appl. Opt. 24, 717–726 (1985).
[CrossRef] [PubMed]

Synder, A. W.

A. W. Synder, A. Ankiewicz, “Fibre couplers composed of unequal cores,” Electron. Lett. 22, 1237–1238 (1986).
[CrossRef]

Taylor, H. F.

H. F. Taylor, A. Yariv, “Guided-wave optics,” Proc. IEEE 62, 1044–1060 (1974).
[CrossRef]

Taylor, H. R.

Tsukada, N.

N. Tsukada, “Modification of the coupling coefficient by periodic modulation of the propagation constants,” Opt. Commun. 22, 113–115 (1977).
[CrossRef]

Turner, E. H.

Ulrich, R.

E. Brinkmeyer, W. Brennecke, M. Zurn, R. Ulrich, “Fibre Bragg reflector for mode selection and line-narrowing of injection lasers,” Electron. Lett. 22, 134–135 (1986).
[CrossRef]

Vassallo, C.

C. Vassallo, “About coupled-mode theories for dielectric waveguides,” IEEE J. Lightwave Technol. LT-6, 294–303 (1988).
[CrossRef]

Vassilopoulos, C.

C. Vassilopoulos, J. R. C. Cozens, “Combined directional and contradirectional coupling in a three-waveguide configuration,” IEEE J. Quantum Electron. 25, 2113–2118 (1989).
[CrossRef]

C. Vassilopoulos, J. R. Cozens, “Backward wave couplers and reflectors,” in Novel Optoelectronic Devices, M. J. Adams, ed., Proc. Soc. Photo-Opt. Instrum. Eng.800, 123–127 (1987).
[CrossRef]

Whalen, M. S.

M. S. Whalen, M. D. Divino, R. C. Alferness, “Demonstration of a narrowband Bragg-reflection filter in a single-mode fibre directional coupler,” Electron. Lett. 22, 681–682 (1986).
[CrossRef]

Whitaker, N.

H. A. Haus, W. P. Huang, S. Kawakami, N. Whitaker, “Coupled-mode theory of optical waveguides,” IEEE J. Lightwave Technol. LT-5, 16–23 (1987).
[CrossRef]

Wilkinson, J. S.

J. S. Wilkinson, M. G. F. Wilson, “The experimental evaluation of a directional coupler wavelength filter having a periodic electrode,” in Proceedings of the Institution of Electrical Engineers Workshop on Integrated Optical and Related Technologies for Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1984).

Wilson, M. G. F.

J. S. Wilkinson, M. G. F. Wilson, “The experimental evaluation of a directional coupler wavelength filter having a periodic electrode,” in Proceedings of the Institution of Electrical Engineers Workshop on Integrated Optical and Related Technologies for Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1984).

Yariv, A.

A. Yariv, M. Nakamura, “Periodic structures for integrated optics,” IEEE J. Quantum Electron. QE-13, 233–253 (1977).
[CrossRef]

H. F. Taylor, A. Yariv, “Guided-wave optics,” Proc. IEEE 62, 1044–1060 (1974).
[CrossRef]

A. Yariv, “Coupled-wave theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
[CrossRef]

H. Stoll, A. Yariv, “Coupled-mode analysis of periodic dielectric waveguides,” Opt. Commun. 8, 5–8 (1973).
[CrossRef]

Yeh, C.

C. Elachi, C. Yeh, “Frequency-selective coupler for integrated optics systems,” Opt. Commun. 7, 201–204 (1973).
[CrossRef]

Yeh, P.

Zurn, M.

E. Brinkmeyer, W. Brennecke, M. Zurn, R. Ulrich, “Fibre Bragg reflector for mode selection and line-narrowing of injection lasers,” Electron. Lett. 22, 134–135 (1986).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. Lett. (4)

E. A. J. Marcatili, L. L. Buhl, R. C. Alferness, “Experimental verification of the improved coupled mode equations,” Appl. Phys. Lett. 49, 1692–1693 (1986).
[CrossRef]

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, “Grating filters for thin-film optical waveguides,” Appl. Phys. Lett. 24, 194–196 (1974).
[CrossRef]

R. C. Alferness, C. H. Joyner, M. D. Divino, L. L. Buhl, “InGaAsP/InP waveguide grating filters for λ= 1.5 μm,” Appl. Phys. Lett. 45, 1278–1280 (1984).
[CrossRef]

R. C. Alferness, L. L. Buhl, “Polarization independent optical filter using interwaveguide TE–TM conversion,” Appl. Phys. Lett. 39, 131–134 (1981).
[CrossRef]

Electron. Lett. (9)

E. Brinkmeyer, W. Brennecke, M. Zurn, R. Ulrich, “Fibre Bragg reflector for mode selection and line-narrowing of injection lasers,” Electron. Lett. 22, 134–135 (1986).
[CrossRef]

I. Bennion, D. C. J. Reid, C. J. Rowe, W. J. Stewart, “High-reflectivity monomode-fibre grating reflectors,” Electron. Lett. 22, 341–343 (1986).
[CrossRef]

M. S. Whalen, M. D. Divino, R. C. Alferness, “Demonstration of a narrowband Bragg-reflection filter in a single-mode fibre directional coupler,” Electron. Lett. 22, 681–682 (1986).
[CrossRef]

A. W. Synder, A. Ankiewicz, “Fibre couplers composed of unequal cores,” Electron. Lett. 22, 1237–1238 (1986).
[CrossRef]

W. Streifer, “Coupled mode theory,” Electron. Lett. 23, 315–316 (1987).
[CrossRef]

A. W. Snyder, A. Ankiewicz, A. Altintas, “Fundamental error of recent coupled mode formulations,” Electron. Lett. 23, 1097–1098 (1987).
[CrossRef]

W. Streifer, “Comment: fundamental error of recent coupled mode formulations,” Electron. Lett. 24, 718–719 (1988).
[CrossRef]

J.-R. Qian, “Generalised coupled-mode equations and their applications to fibre couplers,” Electron. Lett. 22, 304–306 (1986).
[CrossRef]

A. Hardy, M. Osinski, W. Streifer, “Application of coupled-mode theory to nearly parallel waveguide systems,” Electron. Lett. 22, 1249–1250 (1986).
[CrossRef]

IEEE J. Lightwave Technol. (11)

H. A. Haus, W.-P. Huang, “Mode coupling in tapered structures,” IEEE J. Lightwave Technol. 7, 729–730 (1989).
[CrossRef]

R. G. Peall, R. R. A. Syms, “Comparison between strong coupling theory and experiment for three-arm directional couplers in Ti:LiNbO3,” IEEE J. Lightwave Technol. 7, 540–554 (1989).
[CrossRef]

D. Marcuse, “Directional couplers made of nonidentical asymmetric slab guides. Part II: grating-assisted couplers,” IEEE J. Lightwave Technol. LT-5, 268–273 (1987).
[CrossRef]

W.-P. Huang, H. A. Haus, “Power exchange in grating-assisted couplers,” IEEE J. Lightwave Technol. 7, 920–924 (1989).
[CrossRef]

A. Hardy, W. Streifer, “Coupled mode theory of parallel waveguides,” IEEE J. Lightwave Technol. LT-3, 1135–1146 (1985).
[CrossRef]

A. Hardy, W. Streifer, “Coupled modes of multiwaveguide systems and phased arrays,” IEEE J. Lightwave Technol. LT-4, 90–99 (1986).
[CrossRef]

C. Vassallo, “About coupled-mode theories for dielectric waveguides,” IEEE J. Lightwave Technol. LT-6, 294–303 (1988).
[CrossRef]

H. A. Haus, W. P. Huang, S. Kawakami, N. Whitaker, “Coupled-mode theory of optical waveguides,” IEEE J. Lightwave Technol. LT-5, 16–23 (1987).
[CrossRef]

S.-L. Chuang, “A coupled mode formulation by reciprocity and a variational principle,” IEEE J. Lightwave Technol. LT-5, 5–15 (1987).
[CrossRef]

S.-L. Chuang, “A coupled mode theory for multiwaveguide systems satisfying the reciprocity theorem and power conservation,” IEEE J. Lightwave Technol. LT-5, 174–183 (1987).
[CrossRef]

W. V. Sorin, H. J. Shaw, “A single-mode fiber evanescent grating reflector,” IEEE J. Lightwave Technol. LT-3, 1041–1043 (1985).
[CrossRef]

IEEE J. Quantum Electron. (8)

A. Yariv, M. Nakamura, “Periodic structures for integrated optics,” IEEE J. Quantum Electron. QE-13, 233–253 (1977).
[CrossRef]

C. Vassilopoulos, J. R. C. Cozens, “Combined directional and contradirectional coupling in a three-waveguide configuration,” IEEE J. Quantum Electron. 25, 2113–2118 (1989).
[CrossRef]

R. R. A. Syms, “Multiple-waveguide distributed feedback lasers,” IEEE J. Quantum Electron. QE-22, 411–418 (1986).
[CrossRef]

A. Yariv, “Coupled-wave theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
[CrossRef]

S.-L. Chuang, “Application of the strongly coupled-mode theory to integrated optical devices,” IEEE J. Quantum Electron. QE-23, 499–509 (1987).
[CrossRef]

A. Hardy, W. Streifer, “Coupled mode solutions of multi-waveguide systems,” IEEE J. Quantum Electron. QE-22, 528–534 (1986).
[CrossRef]

H. A. Haus, C. G. Fonstad, “Three-waveguide couplers for improved sampling and filtering,” IEEE J. Quantum Electron. QE-17, 2321–2325 (1981).
[CrossRef]

R. G. Peall, R. R. A. Syms, “Further evidence of strong coupling effects in three-arm Ti:LiNbO3directional couplers,” IEEE J. Quantum Electron. 25, 729–735 (1989).
[CrossRef]

IEEE J. Quantum. Electron. (1)

E. A. J. Marcatili, “Improved coupled-mode equations for dielectric guides,” IEEE J. Quantum. Electron. QE-22, 988–993 (1986).
[CrossRef]

IEEE Lightwave Technol. (1)

W. Streifer, M. Osinski, A. Hardy, “Reformulation of the coupled-mode theory of multiwaveguide systems,” IEEE Lightwave Technol. LT-5, 1–4 (1987).
[CrossRef]

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

M. D. Feit, J. A. Fleck, L. McCaughan, “Comparison of calculated and measured performance of diffused channel waveguide couplers,” J. Opt. Soc. Am. A 73, 1296–1304 (1983).
[CrossRef]

Opt. Commun. (6)

R. R. A. Syms, R. G. Peall, “Mode confinement and modal overlap in electro-optic channel waveguide devices,” Opt. Commun. 74, 46–48 (1989).
[CrossRef]

R. G. Peall, R. R. A. Syms, “Scalar strong coupled mode theory for slowly varying waveguide arrays,” Opt. Commun. 67, 421–424 (1988).
[CrossRef]

R. R. A. Syms, R. G. Peall, “Explanation of asymmetric switch response of three-arm directional couplers in Ti:LiNbO3using strong coupling theory,” Opt. Commun. 66, 260–264 (1988).
[CrossRef]

H. Stoll, A. Yariv, “Coupled-mode analysis of periodic dielectric waveguides,” Opt. Commun. 8, 5–8 (1973).
[CrossRef]

C. Elachi, C. Yeh, “Frequency-selective coupler for integrated optics systems,” Opt. Commun. 7, 201–204 (1973).
[CrossRef]

N. Tsukada, “Modification of the coupling coefficient by periodic modulation of the propagation constants,” Opt. Commun. 22, 113–115 (1977).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

R. Marz, H. P. Nolting, “Spectral properties of asymmetrical optical directional couplers with periodic structures,” Opt. Quantum Electron. 19, 273–287 (1987).
[CrossRef]

Proc. IEEE (1)

H. F. Taylor, A. Yariv, “Guided-wave optics,” Proc. IEEE 62, 1044–1060 (1974).
[CrossRef]

Sov. Phys. Tech. Phys. (1)

A. S. Svakhin, V. A. Sychugov, “Narrow-band Bragg reflecting filter based on a single-mode fiber,” Sov. Phys. Tech. Phys. 32, 701–702 (1987).

Other (8)

C. Vassilopoulos, J. R. Cozens, “Backward wave couplers and reflectors,” in Novel Optoelectronic Devices, M. J. Adams, ed., Proc. Soc. Photo-Opt. Instrum. Eng.800, 123–127 (1987).
[CrossRef]

J. S. Wilkinson, M. G. F. Wilson, “The experimental evaluation of a directional coupler wavelength filter having a periodic electrode,” in Proceedings of the Institution of Electrical Engineers Workshop on Integrated Optical and Related Technologies for Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1984).

H.-P. Nolting, D. Hoffmann, M. Schlichting, “Integrated optical wavelength multiplexer/demultiplexer for optical communications,” in Proceedings of the European Conference on Integrated Optics ’85 (Springer-Verlag, Berlin, 1985), pp. 215–220.

W. Streifer, M. Osinski, A. Hardy, “A critical overview of coupled mode theory,” in Integrated Optical Circuit Engineering V, M. A. Menner, ed., Proc. Soc. Photo-Opt. Instrum. Eng.835, 178–187 (1987).
[CrossRef]

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

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

H. A. Haus, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Mass. 02139 (personal communication).

L. A. Molter, H. A. Haus, “Optical two-guide coupler switches in GaAs: ideal and non-ideal operation,” in Integrated and Guided-Wave Optics, Vol. 5 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. 248–251.

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Figures (8)

Fig. 1
Fig. 1

Contradirectional fiber coupler: (a) schematic of component fabrication, (b) assembly.

Fig. 2
Fig. 2

Geometry of general grating-coupled waveguide array.

Fig. 3
Fig. 3

Geometry assumed for numerical calculations.

Fig. 4
Fig. 4

Variation of the codirectional coupling coefficients K11, K12, K21, and K22 with distance along the device. The device center is at z = 0.

Fig. 5
Fig. 5

Variation of the contradirectional coupling coefficients Γ11, Γ12, and Γ22 with distance along the device.

Fig. 6
Fig. 6

Variation of the modal-overlap term C12 and the power-redistribution term N12 with distance.

Fig. 7
Fig. 7

Variation with wavelength of the output powers from the device, as predicted by the new coupled-mode theory.

Fig. 8
Fig. 8

Variation with wavelength of the output powers from the device, assuming that CI and NO.

Equations (24)

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

2 E ( x , y , z ) + n i 2 ( x , y , z ) k 2 E ( x , y , z ) = 0 ( i = 1 , 2 , , N ) ,
E ( x , y , z ) = E i ( x , y , z ) exp [ - j 0 z β i ( z ) d z ] ,
T 2 E i + ( n i 2 k 2 - β i 2 ) E i = 0 ,
2 E ( x , y , z ) + n 2 ( x , y , z ) k 2 E = 0 ,
n ( x , y , z ) = n a ( x , y , z ) + Δ n ( x , y ) cos ( K z ) .
E ( x , y , z ) = i = 1 N E i ( x , y , z ) { A F i ( z ) exp [ - j 0 z β i ( z ) d z ] + A B i ( z ) exp [ + j 0 z β i ( z ) d z ] } .
i = 1 N { - 2 j β i E i / z [ A F i exp ( - j 0 z β i d z ) - A B i exp ( + j 0 z β i d z ) ] - 2 j β i E i [ d A F i / d z exp ( - j 0 z β i d z ) - d A B i / d z exp ( + j 0 z β i d z ) ] + k 2 ( n a 2 - n i 2 ) E i [ A F i exp ( - j 0 z β i d z ) + A B i exp ( + j 0 z β i d z ) ] } + 2 k 2 n a Δ n cos ( K z ) i = 1 N E i [ A F i exp ( - j 0 z β i d z ) + A B i exp ( + j 0 z β i d z ) ] = 0.
i = 1 N [ - 2 j β o E i d A F i / d z - 2 j β o E i / z A F i + k 2 ( n a 2 - n i 2 ) E i A F i ] exp ( - j 0 z Δ β i d z ) + k 2 n a Δ n E i A B i exp ( + j 0 z Δ β i d z ) = 0. i = 1 N [ + 2 j β o E i d A B i / d z + 2 j β o E i / z A B i + k 2 ( n a 2 - n i 2 ) E i A B i ] exp ( + j 0 z Δ β i d z ) + k 2 n a Δ n E i A F i exp ( - j 0 z Δ β i d z ) = 0.
F i ( z ) = A F i ( z ) exp [ - j 0 z Δ β i ( z ) d z ] , B i ( z ) = A B i ( z ) exp [ + j 0 z Δ β i ( z ) d z ] ,
i = 1 N { E i d F i / d z + j Δ β i E i F i + j [ k 2 ( n a 2 - n i 2 ) / 2 β o ] × E i F i + E i / z F i + j ( k 2 n a 2 Δ n / 2 β o ) E i B i } = 0 , i = 1 N { E i d B i / d z - j Δ β i E i B i - j [ k 2 ( n a 2 - n i 2 ) / 2 β o ] × E i B i + E i / z F i - j ( k 2 n a 2 Δ n / 2 β 0 ) E i F i } = 0.
d F / d z = [ - j ( Δ β + C - 1 K T ) - C - 1 N ] F - j C - 1 Γ B , d B / d z = [ + j ( Δ β + C - 1 K T ) - C - 1 N ] B + j C - 1 Γ F ,
Δ β i j = Δ β i δ i j , C i j = E i , E i , K i j T = ( k 2 / β o ) E i , ( n a 2 - n j 2 ) E j , N i j = E i , E j / z , Γ i j = ( k 2 / 2 β o ) E i , n a Δ n E i ,
d F / d z = - j ( Δ β + K T ) F - j Γ B , d B / d z = + j ( Δ β + K T ) B + j Γ F .
d F / d z = [ - j ( Δ β + C - 1 K T ) - C - 1 N ] F , d B / d z = [ + j ( Δ β + C - 1 K T ) - C - 1 N ] B .
P z = 1 / 2 Re [ all space ( E × H * ) · k ^ d x d y ] ,
P z = ( β o / 2 ω μ o ) Re ( F T CF * - B T CB * ) ,
( d F T / d z CF * + F T d C / d z F * + F T C d F * / d z ) - ( d B T / d z CB * + B T d C / d z B * + B T C d B * / d z ) = 0.
d F / d z = M C F + M G B , d B / d z = M C * B + M G * F ,
M C = - j ( Δ β + C - 1 K T ) - C - 1 N ,             M G = - j C - 1 Γ ,
F T ( M C T C + CM C * + d C / d z ) F * - B T ( M C * T C + CM C + d C / d z ) B * + F T ( CM G * - M G * T C ) B * - B T ( CM G - M G T C ) F * = 0.
M C T C + CM C * + d C / d z = 0.
C Δ β + K T = Δ β C + K .
d F / d z = [ - j C - 1 ( Δ β C + K ) - C - 1 N ] F - j C - 1 Γ B , d B / d z = [ + j C - 1 ( Δ β C + K ) - C - 1 N ] B + j C - 1 Γ F .
CM G * - M G * T C = 0 .

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