Abstract

The continuous spectrum of radiation modes along open-boundary dielectric waveguides of arbitrary cross-section shape is considered. Orthogonality of the spectral components of these radiation modes is established in a general manner. This development is based on the Lorentz reciprocity theorem, and it is demonstrated that orthogonality is a direct consequence of (1) satisfaction of Maxwell’s equations by spectral-component fields and (2) satisfaction of the radiation condition by total radiation-mode fields. The amplitude spectrum of continuous radiation modes, maintained by impressed excitatory electric currents immersed in either the waveguide core or cladding regions, is determined. These results are of general use in the study of discontinuities along open-boundary dielectric waveguides.

© 1981 Optical Society of America

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  1. R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, New York, 1960), pp. 470–485.
  2. V. V. Shevchenko, Continuous Transitions in Open Waveguides (Golem, Boulder, Colo., 1971), pp. 21–29, 93–101, 138–142.
  3. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, Princeton, N.J., 1972), Chap. 8.
  4. G. Goubau, "On the excitation of surface waves," Proc. IRE 40, 865–868 (1952).
  5. K. Morishita, S. I. Inagaki, and K. Kumagai, "Analysis of discontinuities in dielectric waveguides by means of the least squares boundary residual method," IEEE Trans. Microwave Theory Tech. MTT-27, 310–315 (1979).
  6. L. Lewin, "A method for the calculation of the radiation pattern and mode-conversion properties of a solid-state heterojunction laser," IEEE Trans. Microwave Theory Tech. MTT-23, 576–585 (1975).
  7. R. W. Davies and J. N. Walpole, "Output coupling for closely confined Pb1-xSnx Te double-heterostructure lasers," IEEE J. Quantum Electron. QE-12, 291–303 (1976).
  8. C. C. Ghizoni, J. M. Ballantyne, and C. L. Tang, "Theory of optical-waveguide distributed feedback lasers: a Green’s function approach," IEEE J. Quantum Electron.IEEE J. Quantum Electron, 843–848 (1977).
  9. S. V. Hsu and D. P. Nyquist, "Integral equation formulation for scattering from obstacles in dielectric optical waveguides," in Digest of National Radio Science Meeting (National Academy of Sciences, Washington, D.C., 1979), p. 90.
  10. T. E. Rozzi, "Rigorous analysis of the step discontinuity in a planar dielectric waveguide," IEEE Trans. Microwave Theory Tech. MTT-26, 738–746 (1978).
  11. A. W. Snyder, "Continuous mode spectrum of a dielectric rod," IEEE Trans. Microwave Theory Tech. MTT-19, 720–727 (1971).
  12. C. T. Tai, Dyadic Green’s Functions in Electromagnetic Theory (Intext Educational, Scranton, Pa., 1971), p. 27.
  13. R. E. Collin, Foundations for Microwave Engineering (McGraw-Hill, New York, 1966), pp. 56–59.
  14. R. F. Harrington, Time-Harmonic Electromagnetic Fields (McGraw-Hill, New York, 1961), pp. 116–120.
  15. S. W. Lee, C. L. Law, and G. A. Deschamps, "Singularity in Green’s function and its numerical evaluation," in Digest of National Radio Science Meeting (National Academy of Sciences, Washington, D.C., 1979), p. 67.
  16. Y. Rahmat-Samii, "On the question of computation of the dyadic Green’s function at the source region in waveguides and cavities," IEEE Trans. Microwave Theory Tech. MTT-23, 762–765 (1975).

1979 (1)

K. Morishita, S. I. Inagaki, and K. Kumagai, "Analysis of discontinuities in dielectric waveguides by means of the least squares boundary residual method," IEEE Trans. Microwave Theory Tech. MTT-27, 310–315 (1979).

1978 (1)

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

1977 (1)

C. C. Ghizoni, J. M. Ballantyne, and C. L. Tang, "Theory of optical-waveguide distributed feedback lasers: a Green’s function approach," IEEE J. Quantum Electron.IEEE J. Quantum Electron, 843–848 (1977).

1976 (1)

R. W. Davies and J. N. Walpole, "Output coupling for closely confined Pb1-xSnx Te double-heterostructure lasers," IEEE J. Quantum Electron. QE-12, 291–303 (1976).

1975 (2)

L. Lewin, "A method for the calculation of the radiation pattern and mode-conversion properties of a solid-state heterojunction laser," IEEE Trans. Microwave Theory Tech. MTT-23, 576–585 (1975).

Y. Rahmat-Samii, "On the question of computation of the dyadic Green’s function at the source region in waveguides and cavities," IEEE Trans. Microwave Theory Tech. MTT-23, 762–765 (1975).

1971 (1)

A. W. Snyder, "Continuous mode spectrum of a dielectric rod," IEEE Trans. Microwave Theory Tech. MTT-19, 720–727 (1971).

1952 (1)

G. Goubau, "On the excitation of surface waves," Proc. IRE 40, 865–868 (1952).

Ballantyne, J. M.

C. C. Ghizoni, J. M. Ballantyne, and C. L. Tang, "Theory of optical-waveguide distributed feedback lasers: a Green’s function approach," IEEE J. Quantum Electron.IEEE J. Quantum Electron, 843–848 (1977).

Collin, R. E.

R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, New York, 1960), pp. 470–485.

R. E. Collin, Foundations for Microwave Engineering (McGraw-Hill, New York, 1966), pp. 56–59.

Davies, R. W.

R. W. Davies and J. N. Walpole, "Output coupling for closely confined Pb1-xSnx Te double-heterostructure lasers," IEEE J. Quantum Electron. QE-12, 291–303 (1976).

Deschamps, G. A.

S. W. Lee, C. L. Law, and G. A. Deschamps, "Singularity in Green’s function and its numerical evaluation," in Digest of National Radio Science Meeting (National Academy of Sciences, Washington, D.C., 1979), p. 67.

Ghizoni, C. C.

C. C. Ghizoni, J. M. Ballantyne, and C. L. Tang, "Theory of optical-waveguide distributed feedback lasers: a Green’s function approach," IEEE J. Quantum Electron.IEEE J. Quantum Electron, 843–848 (1977).

Goubau, G.

G. Goubau, "On the excitation of surface waves," Proc. IRE 40, 865–868 (1952).

Harrington, R. F.

R. F. Harrington, Time-Harmonic Electromagnetic Fields (McGraw-Hill, New York, 1961), pp. 116–120.

Hsu, S. V.

S. V. Hsu and D. P. Nyquist, "Integral equation formulation for scattering from obstacles in dielectric optical waveguides," in Digest of National Radio Science Meeting (National Academy of Sciences, Washington, D.C., 1979), p. 90.

Inagaki, S. I.

K. Morishita, S. I. Inagaki, and K. Kumagai, "Analysis of discontinuities in dielectric waveguides by means of the least squares boundary residual method," IEEE Trans. Microwave Theory Tech. MTT-27, 310–315 (1979).

Kumagai, K.

K. Morishita, S. I. Inagaki, and K. Kumagai, "Analysis of discontinuities in dielectric waveguides by means of the least squares boundary residual method," IEEE Trans. Microwave Theory Tech. MTT-27, 310–315 (1979).

Law, C. L.

S. W. Lee, C. L. Law, and G. A. Deschamps, "Singularity in Green’s function and its numerical evaluation," in Digest of National Radio Science Meeting (National Academy of Sciences, Washington, D.C., 1979), p. 67.

Lee, S. W.

S. W. Lee, C. L. Law, and G. A. Deschamps, "Singularity in Green’s function and its numerical evaluation," in Digest of National Radio Science Meeting (National Academy of Sciences, Washington, D.C., 1979), p. 67.

Lewin, L.

L. Lewin, "A method for the calculation of the radiation pattern and mode-conversion properties of a solid-state heterojunction laser," IEEE Trans. Microwave Theory Tech. MTT-23, 576–585 (1975).

Marcuse, D.

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, Princeton, N.J., 1972), Chap. 8.

Morishita, K.

K. Morishita, S. I. Inagaki, and K. Kumagai, "Analysis of discontinuities in dielectric waveguides by means of the least squares boundary residual method," IEEE Trans. Microwave Theory Tech. MTT-27, 310–315 (1979).

Nyquist, D. P.

S. V. Hsu and D. P. Nyquist, "Integral equation formulation for scattering from obstacles in dielectric optical waveguides," in Digest of National Radio Science Meeting (National Academy of Sciences, Washington, D.C., 1979), p. 90.

Rahmat-Samii, Y.

Y. Rahmat-Samii, "On the question of computation of the dyadic Green’s function at the source region in waveguides and cavities," IEEE Trans. Microwave Theory Tech. MTT-23, 762–765 (1975).

Rozzi, T. E.

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

Shevchenk, V. V.

V. V. Shevchenko, Continuous Transitions in Open Waveguides (Golem, Boulder, Colo., 1971), pp. 21–29, 93–101, 138–142.

Snyder, A. W.

A. W. Snyder, "Continuous mode spectrum of a dielectric rod," IEEE Trans. Microwave Theory Tech. MTT-19, 720–727 (1971).

Tai, C. T.

C. T. Tai, Dyadic Green’s Functions in Electromagnetic Theory (Intext Educational, Scranton, Pa., 1971), p. 27.

Tang, C. L.

C. C. Ghizoni, J. M. Ballantyne, and C. L. Tang, "Theory of optical-waveguide distributed feedback lasers: a Green’s function approach," IEEE J. Quantum Electron.IEEE J. Quantum Electron, 843–848 (1977).

Walpole, J. N.

R. W. Davies and J. N. Walpole, "Output coupling for closely confined Pb1-xSnx Te double-heterostructure lasers," IEEE J. Quantum Electron. QE-12, 291–303 (1976).

IEEE J. Quantum Electron (2)

R. W. Davies and J. N. Walpole, "Output coupling for closely confined Pb1-xSnx Te double-heterostructure lasers," IEEE J. Quantum Electron. QE-12, 291–303 (1976).

C. C. Ghizoni, J. M. Ballantyne, and C. L. Tang, "Theory of optical-waveguide distributed feedback lasers: a Green’s function approach," IEEE J. Quantum Electron.IEEE J. Quantum Electron, 843–848 (1977).

IEEE Trans. Microwave Theory Tech (4)

L. Lewin, "A method for the calculation of the radiation pattern and mode-conversion properties of a solid-state heterojunction laser," IEEE Trans. Microwave Theory Tech. MTT-23, 576–585 (1975).

Y. Rahmat-Samii, "On the question of computation of the dyadic Green’s function at the source region in waveguides and cavities," IEEE Trans. Microwave Theory Tech. MTT-23, 762–765 (1975).

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

A. W. Snyder, "Continuous mode spectrum of a dielectric rod," IEEE Trans. Microwave Theory Tech. MTT-19, 720–727 (1971).

IEEE Trans. Microwave Theory Tech. (1)

K. Morishita, S. I. Inagaki, and K. Kumagai, "Analysis of discontinuities in dielectric waveguides by means of the least squares boundary residual method," IEEE Trans. Microwave Theory Tech. MTT-27, 310–315 (1979).

Proc. IRE (1)

G. Goubau, "On the excitation of surface waves," Proc. IRE 40, 865–868 (1952).

Other (8)

R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, New York, 1960), pp. 470–485.

V. V. Shevchenko, Continuous Transitions in Open Waveguides (Golem, Boulder, Colo., 1971), pp. 21–29, 93–101, 138–142.

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, Princeton, N.J., 1972), Chap. 8.

C. T. Tai, Dyadic Green’s Functions in Electromagnetic Theory (Intext Educational, Scranton, Pa., 1971), p. 27.

R. E. Collin, Foundations for Microwave Engineering (McGraw-Hill, New York, 1966), pp. 56–59.

R. F. Harrington, Time-Harmonic Electromagnetic Fields (McGraw-Hill, New York, 1961), pp. 116–120.

S. W. Lee, C. L. Law, and G. A. Deschamps, "Singularity in Green’s function and its numerical evaluation," in Digest of National Radio Science Meeting (National Academy of Sciences, Washington, D.C., 1979), p. 67.

S. V. Hsu and D. P. Nyquist, "Integral equation formulation for scattering from obstacles in dielectric optical waveguides," in Digest of National Radio Science Meeting (National Academy of Sciences, Washington, D.C., 1979), p. 90.

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