Abstract

A new pair of second-order coupled-mode equations are derived, solved, and applied to the case of reflection and transmission by a spatially modulated slab medium. The derivation is compared with those that arrive at first-order coupled-mode equations. The solutions of the second-order coupled-mode equations are facilitated by reducing them to two uncoupled Helmholtz equations. The solutions of the boundary-value problem for a slab medium are analytical and expressed in closed form. They are confirmed by the rigorous modal theory in the limit of small modulation strength. At the Bragg angle of incidence, energy conservation is shown to be preserved for all modulation strengths.

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  1. H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909–2947 (1969).
  2. W. R. Klein and B. D. Cook, "Unified approach to ultrasonic light diffraction," IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).
  3. P. Phariseau, "On the diffraction of light by progressive supersonic waves," Proc. Ind. Acad. Sci. 44, 165–170 (1956).
  4. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).
  5. H. Kogelnik and C. V. Shank, "Simulated emission in a periodic structure," Appl. Phys. Lett. 18, 152–154 (1971).
  6. T. Tamir, editor, Integrated Optics, in Topics in Applied Physics, Vol. 7 (Springer-Verlag, New York, 1975).
  7. J. M. Hammer, D. J. Chaunin, M. T. Duffy, and C. C. Neil, "High-speed electrooptic waveguide grating modulator using epitaxial ZnO, "IEEE J. Quantum Electron QE-11, 138–147 (1975).
  8. L. Kuhn, M. L. Dakss, P. F. Heidrich, and B. A. Scott, "Deflection of an optical guided wave by a surface acoustic wave," Appl. Phys. Lett. 17, 265–267 (1970).
  9. R. S. Chu and T. Tamir, "Guided-wave theory of light diffraction by acoustic microwaves," IEEE Trans. Microwave Theory Tech. MTT-18, 486–504 (1970).
  10. R. S. Chu and J. A. Kong, "Modal theory of a spatially periodic medium," IEEE Trans. Microwave Theory Tech., MTT-25, 18–24 (1977).
  11. J. A. Kong, Theory of Electromagnetic Waves (Wiley, New York, 1975).

1977

R. S. Chu and J. A. Kong, "Modal theory of a spatially periodic medium," IEEE Trans. Microwave Theory Tech., MTT-25, 18–24 (1977).

1975

J. M. Hammer, D. J. Chaunin, M. T. Duffy, and C. C. Neil, "High-speed electrooptic waveguide grating modulator using epitaxial ZnO, "IEEE J. Quantum Electron QE-11, 138–147 (1975).

1971

H. Kogelnik and C. V. Shank, "Simulated emission in a periodic structure," Appl. Phys. Lett. 18, 152–154 (1971).

1970

L. Kuhn, M. L. Dakss, P. F. Heidrich, and B. A. Scott, "Deflection of an optical guided wave by a surface acoustic wave," Appl. Phys. Lett. 17, 265–267 (1970).

R. S. Chu and T. Tamir, "Guided-wave theory of light diffraction by acoustic microwaves," IEEE Trans. Microwave Theory Tech. MTT-18, 486–504 (1970).

1969

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909–2947 (1969).

1967

W. R. Klein and B. D. Cook, "Unified approach to ultrasonic light diffraction," IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).

1956

P. Phariseau, "On the diffraction of light by progressive supersonic waves," Proc. Ind. Acad. Sci. 44, 165–170 (1956).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

Chaunin, D. J.

J. M. Hammer, D. J. Chaunin, M. T. Duffy, and C. C. Neil, "High-speed electrooptic waveguide grating modulator using epitaxial ZnO, "IEEE J. Quantum Electron QE-11, 138–147 (1975).

Chu, R. S.

R. S. Chu and J. A. Kong, "Modal theory of a spatially periodic medium," IEEE Trans. Microwave Theory Tech., MTT-25, 18–24 (1977).

R. S. Chu and T. Tamir, "Guided-wave theory of light diffraction by acoustic microwaves," IEEE Trans. Microwave Theory Tech. MTT-18, 486–504 (1970).

Cook, B. D.

W. R. Klein and B. D. Cook, "Unified approach to ultrasonic light diffraction," IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).

Dakss, M. L.

L. Kuhn, M. L. Dakss, P. F. Heidrich, and B. A. Scott, "Deflection of an optical guided wave by a surface acoustic wave," Appl. Phys. Lett. 17, 265–267 (1970).

Duffy, M. T.

J. M. Hammer, D. J. Chaunin, M. T. Duffy, and C. C. Neil, "High-speed electrooptic waveguide grating modulator using epitaxial ZnO, "IEEE J. Quantum Electron QE-11, 138–147 (1975).

Hammer, J. M.

J. M. Hammer, D. J. Chaunin, M. T. Duffy, and C. C. Neil, "High-speed electrooptic waveguide grating modulator using epitaxial ZnO, "IEEE J. Quantum Electron QE-11, 138–147 (1975).

Heidrich, P. F.

L. Kuhn, M. L. Dakss, P. F. Heidrich, and B. A. Scott, "Deflection of an optical guided wave by a surface acoustic wave," Appl. Phys. Lett. 17, 265–267 (1970).

Klein, W. R.

W. R. Klein and B. D. Cook, "Unified approach to ultrasonic light diffraction," IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).

Kogelnik, H.

H. Kogelnik and C. V. Shank, "Simulated emission in a periodic structure," Appl. Phys. Lett. 18, 152–154 (1971).

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909–2947 (1969).

Kong, J. A.

R. S. Chu and J. A. Kong, "Modal theory of a spatially periodic medium," IEEE Trans. Microwave Theory Tech., MTT-25, 18–24 (1977).

J. A. Kong, Theory of Electromagnetic Waves (Wiley, New York, 1975).

Kuhn, L.

L. Kuhn, M. L. Dakss, P. F. Heidrich, and B. A. Scott, "Deflection of an optical guided wave by a surface acoustic wave," Appl. Phys. Lett. 17, 265–267 (1970).

Neil, C. C.

J. M. Hammer, D. J. Chaunin, M. T. Duffy, and C. C. Neil, "High-speed electrooptic waveguide grating modulator using epitaxial ZnO, "IEEE J. Quantum Electron QE-11, 138–147 (1975).

Phariseau, P.

P. Phariseau, "On the diffraction of light by progressive supersonic waves," Proc. Ind. Acad. Sci. 44, 165–170 (1956).

Scott, B. A.

L. Kuhn, M. L. Dakss, P. F. Heidrich, and B. A. Scott, "Deflection of an optical guided wave by a surface acoustic wave," Appl. Phys. Lett. 17, 265–267 (1970).

Shank, C. V.

H. Kogelnik and C. V. Shank, "Simulated emission in a periodic structure," Appl. Phys. Lett. 18, 152–154 (1971).

Tamir, T.

R. S. Chu and T. Tamir, "Guided-wave theory of light diffraction by acoustic microwaves," IEEE Trans. Microwave Theory Tech. MTT-18, 486–504 (1970).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

Appl. Phys. Lett.

L. Kuhn, M. L. Dakss, P. F. Heidrich, and B. A. Scott, "Deflection of an optical guided wave by a surface acoustic wave," Appl. Phys. Lett. 17, 265–267 (1970).

H. Kogelnik and C. V. Shank, "Simulated emission in a periodic structure," Appl. Phys. Lett. 18, 152–154 (1971).

Bell Syst. Tech. J.

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909–2947 (1969).

IEEE J. Quantum Electron

J. M. Hammer, D. J. Chaunin, M. T. Duffy, and C. C. Neil, "High-speed electrooptic waveguide grating modulator using epitaxial ZnO, "IEEE J. Quantum Electron QE-11, 138–147 (1975).

IEEE Trans. Microwave Theory Tech.

R. S. Chu and T. Tamir, "Guided-wave theory of light diffraction by acoustic microwaves," IEEE Trans. Microwave Theory Tech. MTT-18, 486–504 (1970).

IEEE Trans. Sonics Ultrason.

W. R. Klein and B. D. Cook, "Unified approach to ultrasonic light diffraction," IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).

Proc. Ind. Acad. Sci.

P. Phariseau, "On the diffraction of light by progressive supersonic waves," Proc. Ind. Acad. Sci. 44, 165–170 (1956).

Other

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

R. S. Chu and J. A. Kong, "Modal theory of a spatially periodic medium," IEEE Trans. Microwave Theory Tech., MTT-25, 18–24 (1977).

J. A. Kong, Theory of Electromagnetic Waves (Wiley, New York, 1975).

T. Tamir, editor, Integrated Optics, in Topics in Applied Physics, Vol. 7 (Springer-Verlag, New York, 1975).

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