Abstract

A theoretical analysis of graded-index optical channel waveguides and directional couplers fabricated by the beam-writing technique is presented. The analysis is based on a combination of the effective-index-of-refraction method and the WKB method, which is shown to apply for directional couplers as well as for channel waveguides, when special care is taken in connecting the field at the gap region. The mode dispersion characteristics and the field profile of a channel waveguide were derived. The conversion length of a directional coupler was also determined as a function of the coupler parameters and the mode order. The guided mode field has long evanescent tails outside the guide, and the positions of the turning points are located further away from the guide center for higher-order modes. Accordingly, the conversion length of a coupler increases slowly with the waveguide spacing and exhibits a strong dependence on the transverse mode order. The results are summarized in a few practically useful design charts by employing the normalizations of the device parameters. Some design examples are given and the fabrication tolerances are discussed.

© 1979 Optical Society of America

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  1. E. A. Marcatili, "Dielectric rectangular waveguide and directional coupler for integrated optics," Bell Syst. Tech. J. 48, 2071–2102 (1969).
  2. J. E. Goell, "A circular-harmonic computer analysis of rectangular dielectric waveguides," Bell Syst. Tech. J. 48, 2133–2160 (1969).
  3. J. E. Goell, "Electron-resist fabrication of bends and couplers for integrated optical circuits," Appl. Opt. 12, 729–736 (1973).
  4. H. Furuta, H. Noda, and A. Ihaya, "Novel optical waveguides for integrated optics," Appl. Opt. 13, 322–326 (1974).
  5. M. Sasaki, A. Okamoto, H. Furuta, and T. Kudo, "Directional couplers consisting of modified optical striplines," Technical Digest of International Conference on Integrated Optics and Optical Fiber Communication (IOOC ′77), B5-3, Tokyo (1977) (unpublished).
  6. G. B. Hocker and W. K. Burns, "Mode dispersion in diffused channel waveguides by the effective index method," Appl. Opt. 16, 113–118 (1977).
  7. H. F. Taylor, "Dispersion characteristics of diffused channel waveguides," IEEE J. Quantum Electron QE-12, 748–752 (1976).
  8. T. Taniuchi, M. Kudo, and Y. Mushiake, "Coupling characteristics between optical slab waveguides with gradual distribution of refractive index," Trans. IECE of Jpn. J61-C, 256–263 (1978).
  9. T. Suhara, H. Nishihara, and J. Koyama, "Electron-beam-induced refractive-index change of amorphous semiconductors," Jpn. J. Appl. Phys. 14, 1079–1080 (1975).
  10. H. Nishihara, "Direct writing technique using a scanning electron microscope: fabrication of optical gratings in amorphous chalcogenide films," Technical Digest of International Conference on Integrated Optics and Optical Fiber Communication (IOOC ′77) 02-4, Osaka (1977) (unpublished).
  11. H. Nishihara, Y. Handa, T. Suhara, and J. Koyama, "Direct writing of optical gratings using a scanning electron microscope," Appl. Opt. 17, 2342–2345 (1978).
  12. Y. Handa, T. Suhara, H. Nishihara, and J. Koyama, "Scanningelectron-microscope-written gratings in chalcogenide films for optical integrated circuits," Appl. Opt. 18, 248–252 (1979).
  13. W. J. Tomlinson, I. P. Kaminow, E. A. Chandross, R. L. Fork, and W. T. Silfvast, "Photoinduced refractive index increase in poly (methylmethacrylate) and its applications," Appl. Phys. Lett. 16, 486–489 (1970).
  14. W. J. Tomlinson, H. P. Weber, C. A. Pryde, and E. A. Chandross, "Optical directional couplers and grating couplers using a new high-resolution photolocking material," Appl. Phys. Lett. 26, 303–306 (1975).
  15. Integrated optics, edited by T. Tamir (Springer Verlag, Berlin, 1975), p. 40.
  16. L. I. Schiff, Quantum mechanics, (McGraw Hill, New York, 1968), p. 268.
  17. R. Courant and D. Hilbert, Method of mathematical physics (Springer Verlag, Berlin, 1937), chap. 7.
  18. A. Yariv, "Coupled-mode theory for guided-wave optics," IEEE J. Quantum Electron. QE-9, 919–933 (1973).

1979 (1)

1978 (2)

H. Nishihara, Y. Handa, T. Suhara, and J. Koyama, "Direct writing of optical gratings using a scanning electron microscope," Appl. Opt. 17, 2342–2345 (1978).

T. Taniuchi, M. Kudo, and Y. Mushiake, "Coupling characteristics between optical slab waveguides with gradual distribution of refractive index," Trans. IECE of Jpn. J61-C, 256–263 (1978).

1977 (1)

1976 (1)

H. F. Taylor, "Dispersion characteristics of diffused channel waveguides," IEEE J. Quantum Electron QE-12, 748–752 (1976).

1975 (2)

T. Suhara, H. Nishihara, and J. Koyama, "Electron-beam-induced refractive-index change of amorphous semiconductors," Jpn. J. Appl. Phys. 14, 1079–1080 (1975).

W. J. Tomlinson, H. P. Weber, C. A. Pryde, and E. A. Chandross, "Optical directional couplers and grating couplers using a new high-resolution photolocking material," Appl. Phys. Lett. 26, 303–306 (1975).

1974 (1)

1973 (2)

J. E. Goell, "Electron-resist fabrication of bends and couplers for integrated optical circuits," Appl. Opt. 12, 729–736 (1973).

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

1970 (1)

W. J. Tomlinson, I. P. Kaminow, E. A. Chandross, R. L. Fork, and W. T. Silfvast, "Photoinduced refractive index increase in poly (methylmethacrylate) and its applications," Appl. Phys. Lett. 16, 486–489 (1970).

1969 (2)

E. A. Marcatili, "Dielectric rectangular waveguide and directional coupler for integrated optics," Bell Syst. Tech. J. 48, 2071–2102 (1969).

J. E. Goell, "A circular-harmonic computer analysis of rectangular dielectric waveguides," Bell Syst. Tech. J. 48, 2133–2160 (1969).

Burns, W. K.

Chandross, E. A.

W. J. Tomlinson, H. P. Weber, C. A. Pryde, and E. A. Chandross, "Optical directional couplers and grating couplers using a new high-resolution photolocking material," Appl. Phys. Lett. 26, 303–306 (1975).

W. J. Tomlinson, I. P. Kaminow, E. A. Chandross, R. L. Fork, and W. T. Silfvast, "Photoinduced refractive index increase in poly (methylmethacrylate) and its applications," Appl. Phys. Lett. 16, 486–489 (1970).

Courant, R.

R. Courant and D. Hilbert, Method of mathematical physics (Springer Verlag, Berlin, 1937), chap. 7.

Fork, R. L.

W. J. Tomlinson, I. P. Kaminow, E. A. Chandross, R. L. Fork, and W. T. Silfvast, "Photoinduced refractive index increase in poly (methylmethacrylate) and its applications," Appl. Phys. Lett. 16, 486–489 (1970).

Furuta, H.

H. Furuta, H. Noda, and A. Ihaya, "Novel optical waveguides for integrated optics," Appl. Opt. 13, 322–326 (1974).

M. Sasaki, A. Okamoto, H. Furuta, and T. Kudo, "Directional couplers consisting of modified optical striplines," Technical Digest of International Conference on Integrated Optics and Optical Fiber Communication (IOOC ′77), B5-3, Tokyo (1977) (unpublished).

Goell, J. E.

J. E. Goell, "Electron-resist fabrication of bends and couplers for integrated optical circuits," Appl. Opt. 12, 729–736 (1973).

J. E. Goell, "A circular-harmonic computer analysis of rectangular dielectric waveguides," Bell Syst. Tech. J. 48, 2133–2160 (1969).

Handa, Y.

Hilbert, D.

R. Courant and D. Hilbert, Method of mathematical physics (Springer Verlag, Berlin, 1937), chap. 7.

Hocker, G. B.

Ihaya, A.

Kaminow, I. P.

W. J. Tomlinson, I. P. Kaminow, E. A. Chandross, R. L. Fork, and W. T. Silfvast, "Photoinduced refractive index increase in poly (methylmethacrylate) and its applications," Appl. Phys. Lett. 16, 486–489 (1970).

Koyama, J.

Kudo, M.

T. Taniuchi, M. Kudo, and Y. Mushiake, "Coupling characteristics between optical slab waveguides with gradual distribution of refractive index," Trans. IECE of Jpn. J61-C, 256–263 (1978).

Kudo, T.

M. Sasaki, A. Okamoto, H. Furuta, and T. Kudo, "Directional couplers consisting of modified optical striplines," Technical Digest of International Conference on Integrated Optics and Optical Fiber Communication (IOOC ′77), B5-3, Tokyo (1977) (unpublished).

Marcatili, E. A.

E. A. Marcatili, "Dielectric rectangular waveguide and directional coupler for integrated optics," Bell Syst. Tech. J. 48, 2071–2102 (1969).

Mushiake, Y.

T. Taniuchi, M. Kudo, and Y. Mushiake, "Coupling characteristics between optical slab waveguides with gradual distribution of refractive index," Trans. IECE of Jpn. J61-C, 256–263 (1978).

Nishihara, H.

Y. Handa, T. Suhara, H. Nishihara, and J. Koyama, "Scanningelectron-microscope-written gratings in chalcogenide films for optical integrated circuits," Appl. Opt. 18, 248–252 (1979).

H. Nishihara, Y. Handa, T. Suhara, and J. Koyama, "Direct writing of optical gratings using a scanning electron microscope," Appl. Opt. 17, 2342–2345 (1978).

T. Suhara, H. Nishihara, and J. Koyama, "Electron-beam-induced refractive-index change of amorphous semiconductors," Jpn. J. Appl. Phys. 14, 1079–1080 (1975).

H. Nishihara, "Direct writing technique using a scanning electron microscope: fabrication of optical gratings in amorphous chalcogenide films," Technical Digest of International Conference on Integrated Optics and Optical Fiber Communication (IOOC ′77) 02-4, Osaka (1977) (unpublished).

Noda, H.

Okamoto, A.

M. Sasaki, A. Okamoto, H. Furuta, and T. Kudo, "Directional couplers consisting of modified optical striplines," Technical Digest of International Conference on Integrated Optics and Optical Fiber Communication (IOOC ′77), B5-3, Tokyo (1977) (unpublished).

Pryde, C. A.

W. J. Tomlinson, H. P. Weber, C. A. Pryde, and E. A. Chandross, "Optical directional couplers and grating couplers using a new high-resolution photolocking material," Appl. Phys. Lett. 26, 303–306 (1975).

Sasaki, M.

M. Sasaki, A. Okamoto, H. Furuta, and T. Kudo, "Directional couplers consisting of modified optical striplines," Technical Digest of International Conference on Integrated Optics and Optical Fiber Communication (IOOC ′77), B5-3, Tokyo (1977) (unpublished).

Schiff, L. I.

L. I. Schiff, Quantum mechanics, (McGraw Hill, New York, 1968), p. 268.

Silfvast, W. T.

W. J. Tomlinson, I. P. Kaminow, E. A. Chandross, R. L. Fork, and W. T. Silfvast, "Photoinduced refractive index increase in poly (methylmethacrylate) and its applications," Appl. Phys. Lett. 16, 486–489 (1970).

Suhara, T.

Taniuchi, T.

T. Taniuchi, M. Kudo, and Y. Mushiake, "Coupling characteristics between optical slab waveguides with gradual distribution of refractive index," Trans. IECE of Jpn. J61-C, 256–263 (1978).

Taylor, H. F.

H. F. Taylor, "Dispersion characteristics of diffused channel waveguides," IEEE J. Quantum Electron QE-12, 748–752 (1976).

Tomlinson, W. J.

W. J. Tomlinson, H. P. Weber, C. A. Pryde, and E. A. Chandross, "Optical directional couplers and grating couplers using a new high-resolution photolocking material," Appl. Phys. Lett. 26, 303–306 (1975).

W. J. Tomlinson, I. P. Kaminow, E. A. Chandross, R. L. Fork, and W. T. Silfvast, "Photoinduced refractive index increase in poly (methylmethacrylate) and its applications," Appl. Phys. Lett. 16, 486–489 (1970).

Weber, H. P.

W. J. Tomlinson, H. P. Weber, C. A. Pryde, and E. A. Chandross, "Optical directional couplers and grating couplers using a new high-resolution photolocking material," Appl. Phys. Lett. 26, 303–306 (1975).

Yariv, A.

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

Appl. Opt. (5)

Appl. Phys. Lett. (2)

W. J. Tomlinson, I. P. Kaminow, E. A. Chandross, R. L. Fork, and W. T. Silfvast, "Photoinduced refractive index increase in poly (methylmethacrylate) and its applications," Appl. Phys. Lett. 16, 486–489 (1970).

W. J. Tomlinson, H. P. Weber, C. A. Pryde, and E. A. Chandross, "Optical directional couplers and grating couplers using a new high-resolution photolocking material," Appl. Phys. Lett. 26, 303–306 (1975).

Bell Syst. Tech. J. (2)

E. A. Marcatili, "Dielectric rectangular waveguide and directional coupler for integrated optics," Bell Syst. Tech. J. 48, 2071–2102 (1969).

J. E. Goell, "A circular-harmonic computer analysis of rectangular dielectric waveguides," Bell Syst. Tech. J. 48, 2133–2160 (1969).

IEEE J. Quantum Electron (1)

H. F. Taylor, "Dispersion characteristics of diffused channel waveguides," IEEE J. Quantum Electron QE-12, 748–752 (1976).

IEEE J. Quantum Electron. (1)

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

Jpn. J. Appl. Phys. (1)

T. Suhara, H. Nishihara, and J. Koyama, "Electron-beam-induced refractive-index change of amorphous semiconductors," Jpn. J. Appl. Phys. 14, 1079–1080 (1975).

Trans. IECE of Jpn. (1)

T. Taniuchi, M. Kudo, and Y. Mushiake, "Coupling characteristics between optical slab waveguides with gradual distribution of refractive index," Trans. IECE of Jpn. J61-C, 256–263 (1978).

Other (5)

H. Nishihara, "Direct writing technique using a scanning electron microscope: fabrication of optical gratings in amorphous chalcogenide films," Technical Digest of International Conference on Integrated Optics and Optical Fiber Communication (IOOC ′77) 02-4, Osaka (1977) (unpublished).

M. Sasaki, A. Okamoto, H. Furuta, and T. Kudo, "Directional couplers consisting of modified optical striplines," Technical Digest of International Conference on Integrated Optics and Optical Fiber Communication (IOOC ′77), B5-3, Tokyo (1977) (unpublished).

Integrated optics, edited by T. Tamir (Springer Verlag, Berlin, 1975), p. 40.

L. I. Schiff, Quantum mechanics, (McGraw Hill, New York, 1968), p. 268.

R. Courant and D. Hilbert, Method of mathematical physics (Springer Verlag, Berlin, 1937), chap. 7.

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