Abstract

An efficient, simple numerical method is employed in, conjuntion with an optimum perturbation scheme to solve for the radiating and guided waves of a periodic corrugated dielectric waveguide. Results for sinusoidal, triangular, and rectangular grating profiles on waveguides and waveguidelasers are obtained and compared with approximate analytic expressions.

© 1979 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Kogelnik and C. V. Shank, "Coupled mode theory of distributed feedback lasers," J. Appl. Phys., 43, 2327 (1972).
  2. D. R. Scifres, R. D. Burnham, and W. Streifer, "Output coupling and distributed feedback utilizing substrate corrugations in doubleheterostructure GaAs lasers," Appl. Phys. Lett, 27, 295 (1975).
  3. R. D. Burnham, D. R. Scifres, and W. Streifer "Low divergence beam from grating coupled composite guide heterostructure GaAlAs diode lasers," Appl. Phys. Lett, 26, 644 (1975).
  4. W. Ng and A. Yariv, "Highly collimated broadside emission from room-temperature GaAs distributed Bragg reflector lasers," Appl. Phys. Lett., 31, 613 (1977).
  5. V. A. Kiselev, "Diffraction coupling of radiation into a thin-film waveguide," Sov. J. Quantum Electron., 4, 872 (1975).
  6. A. A. Zlenko, V. A. Kiselev, A. M. Prokhorov, A. A. Spikhal’skii, and V. A. Sychugov, "Emission of surface light wave from a corrugated part of a thin film waveguide," Sov. J. Quantum Electron., 4, 839 (1975).
  7. A. A. Zlenko, A. M. Prokhorov, A. A. Spikhal’skii, and V. A. Sychugov, "Emission of E waves from a corrugated section of a waveguide," Sov. J. Quantum Electron., 6, 565 (1976).
  8. W. W. Rigrod and D. Marcuse, "Radiation loss coefficients of asymmetric dielectric waveguides with shallow sinusoidal corrugations," IEEE J. of Quantum Electron. QE-12, 673 (1976).
  9. S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. MTT-23, 123 (1975).
  10. K. Handa, S. T. Peng, and T. Tamir, "Improved perturbation analysis of dielectric grating," Appl. Phys. 5, 325 (1975).
  11. S. T. Peng and T. Tamir, "TM-Mode perturbation analysis of dielectric gratings," Appl. Phys. 7, 35 (1975).
  12. W. Streifer, D. R. Scifres, and R. D. Burnham "Analysis of grating coupled radiation in GaAs:GaAlAs lasers and waveguides," IEEE J. Quantum Electron., QE-12, 422 (1976).
  13. W. Streifer, R. D. Burnham, and D. R. Scifres, "Analysis of grating coupled radiation in GaAs:GaAlAs lasers and waveguides," IEEE J. Quant. Electron, QE-12, 494 (1976).
  14. C. Lanczos, "Trigonometric interpolation of empirical and analytical Functions," J. Math. Phys., 17, 123 (1938).
  15. C. Lanczos, Applied Analysis (Prentice Hall, Englewood Cliffs, N.J., 1956), Chap 7.
  16. Y. L. Luke, Mathematical Functions and their Approximations (Academic, New York, 1975), p. 495.

1977 (1)

W. Ng and A. Yariv, "Highly collimated broadside emission from room-temperature GaAs distributed Bragg reflector lasers," Appl. Phys. Lett., 31, 613 (1977).

1976 (4)

A. A. Zlenko, A. M. Prokhorov, A. A. Spikhal’skii, and V. A. Sychugov, "Emission of E waves from a corrugated section of a waveguide," Sov. J. Quantum Electron., 6, 565 (1976).

W. W. Rigrod and D. Marcuse, "Radiation loss coefficients of asymmetric dielectric waveguides with shallow sinusoidal corrugations," IEEE J. of Quantum Electron. QE-12, 673 (1976).

W. Streifer, D. R. Scifres, and R. D. Burnham "Analysis of grating coupled radiation in GaAs:GaAlAs lasers and waveguides," IEEE J. Quantum Electron., QE-12, 422 (1976).

W. Streifer, R. D. Burnham, and D. R. Scifres, "Analysis of grating coupled radiation in GaAs:GaAlAs lasers and waveguides," IEEE J. Quant. Electron, QE-12, 494 (1976).

1975 (7)

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. MTT-23, 123 (1975).

K. Handa, S. T. Peng, and T. Tamir, "Improved perturbation analysis of dielectric grating," Appl. Phys. 5, 325 (1975).

S. T. Peng and T. Tamir, "TM-Mode perturbation analysis of dielectric gratings," Appl. Phys. 7, 35 (1975).

V. A. Kiselev, "Diffraction coupling of radiation into a thin-film waveguide," Sov. J. Quantum Electron., 4, 872 (1975).

A. A. Zlenko, V. A. Kiselev, A. M. Prokhorov, A. A. Spikhal’skii, and V. A. Sychugov, "Emission of surface light wave from a corrugated part of a thin film waveguide," Sov. J. Quantum Electron., 4, 839 (1975).

D. R. Scifres, R. D. Burnham, and W. Streifer, "Output coupling and distributed feedback utilizing substrate corrugations in doubleheterostructure GaAs lasers," Appl. Phys. Lett, 27, 295 (1975).

R. D. Burnham, D. R. Scifres, and W. Streifer "Low divergence beam from grating coupled composite guide heterostructure GaAlAs diode lasers," Appl. Phys. Lett, 26, 644 (1975).

1972 (1)

H. Kogelnik and C. V. Shank, "Coupled mode theory of distributed feedback lasers," J. Appl. Phys., 43, 2327 (1972).

1938 (1)

C. Lanczos, "Trigonometric interpolation of empirical and analytical Functions," J. Math. Phys., 17, 123 (1938).

Bertoni, H. L.

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. MTT-23, 123 (1975).

Burnham, R. D.

W. Streifer, D. R. Scifres, and R. D. Burnham "Analysis of grating coupled radiation in GaAs:GaAlAs lasers and waveguides," IEEE J. Quantum Electron., QE-12, 422 (1976).

W. Streifer, R. D. Burnham, and D. R. Scifres, "Analysis of grating coupled radiation in GaAs:GaAlAs lasers and waveguides," IEEE J. Quant. Electron, QE-12, 494 (1976).

D. R. Scifres, R. D. Burnham, and W. Streifer, "Output coupling and distributed feedback utilizing substrate corrugations in doubleheterostructure GaAs lasers," Appl. Phys. Lett, 27, 295 (1975).

R. D. Burnham, D. R. Scifres, and W. Streifer "Low divergence beam from grating coupled composite guide heterostructure GaAlAs diode lasers," Appl. Phys. Lett, 26, 644 (1975).

Handa, K.

K. Handa, S. T. Peng, and T. Tamir, "Improved perturbation analysis of dielectric grating," Appl. Phys. 5, 325 (1975).

Kiselev, V. A.

A. A. Zlenko, V. A. Kiselev, A. M. Prokhorov, A. A. Spikhal’skii, and V. A. Sychugov, "Emission of surface light wave from a corrugated part of a thin film waveguide," Sov. J. Quantum Electron., 4, 839 (1975).

V. A. Kiselev, "Diffraction coupling of radiation into a thin-film waveguide," Sov. J. Quantum Electron., 4, 872 (1975).

Kogelnik, H.

H. Kogelnik and C. V. Shank, "Coupled mode theory of distributed feedback lasers," J. Appl. Phys., 43, 2327 (1972).

Lanczos, C.

C. Lanczos, "Trigonometric interpolation of empirical and analytical Functions," J. Math. Phys., 17, 123 (1938).

C. Lanczos, Applied Analysis (Prentice Hall, Englewood Cliffs, N.J., 1956), Chap 7.

Luke, Y. L.

Y. L. Luke, Mathematical Functions and their Approximations (Academic, New York, 1975), p. 495.

Marcuse, D.

W. W. Rigrod and D. Marcuse, "Radiation loss coefficients of asymmetric dielectric waveguides with shallow sinusoidal corrugations," IEEE J. of Quantum Electron. QE-12, 673 (1976).

Ng, W.

W. Ng and A. Yariv, "Highly collimated broadside emission from room-temperature GaAs distributed Bragg reflector lasers," Appl. Phys. Lett., 31, 613 (1977).

Peng, S. T.

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. MTT-23, 123 (1975).

K. Handa, S. T. Peng, and T. Tamir, "Improved perturbation analysis of dielectric grating," Appl. Phys. 5, 325 (1975).

S. T. Peng and T. Tamir, "TM-Mode perturbation analysis of dielectric gratings," Appl. Phys. 7, 35 (1975).

Prokhorov, A. M.

A. A. Zlenko, A. M. Prokhorov, A. A. Spikhal’skii, and V. A. Sychugov, "Emission of E waves from a corrugated section of a waveguide," Sov. J. Quantum Electron., 6, 565 (1976).

A. A. Zlenko, V. A. Kiselev, A. M. Prokhorov, A. A. Spikhal’skii, and V. A. Sychugov, "Emission of surface light wave from a corrugated part of a thin film waveguide," Sov. J. Quantum Electron., 4, 839 (1975).

Rigrod, W. W.

W. W. Rigrod and D. Marcuse, "Radiation loss coefficients of asymmetric dielectric waveguides with shallow sinusoidal corrugations," IEEE J. of Quantum Electron. QE-12, 673 (1976).

Scifres, D. R.

W. Streifer, D. R. Scifres, and R. D. Burnham "Analysis of grating coupled radiation in GaAs:GaAlAs lasers and waveguides," IEEE J. Quantum Electron., QE-12, 422 (1976).

W. Streifer, R. D. Burnham, and D. R. Scifres, "Analysis of grating coupled radiation in GaAs:GaAlAs lasers and waveguides," IEEE J. Quant. Electron, QE-12, 494 (1976).

D. R. Scifres, R. D. Burnham, and W. Streifer, "Output coupling and distributed feedback utilizing substrate corrugations in doubleheterostructure GaAs lasers," Appl. Phys. Lett, 27, 295 (1975).

R. D. Burnham, D. R. Scifres, and W. Streifer "Low divergence beam from grating coupled composite guide heterostructure GaAlAs diode lasers," Appl. Phys. Lett, 26, 644 (1975).

Shank, C. V.

H. Kogelnik and C. V. Shank, "Coupled mode theory of distributed feedback lasers," J. Appl. Phys., 43, 2327 (1972).

Spikhal’skii, A. A.

A. A. Zlenko, A. M. Prokhorov, A. A. Spikhal’skii, and V. A. Sychugov, "Emission of E waves from a corrugated section of a waveguide," Sov. J. Quantum Electron., 6, 565 (1976).

A. A. Zlenko, V. A. Kiselev, A. M. Prokhorov, A. A. Spikhal’skii, and V. A. Sychugov, "Emission of surface light wave from a corrugated part of a thin film waveguide," Sov. J. Quantum Electron., 4, 839 (1975).

Streifer, W.

W. Streifer, R. D. Burnham, and D. R. Scifres, "Analysis of grating coupled radiation in GaAs:GaAlAs lasers and waveguides," IEEE J. Quant. Electron, QE-12, 494 (1976).

W. Streifer, D. R. Scifres, and R. D. Burnham "Analysis of grating coupled radiation in GaAs:GaAlAs lasers and waveguides," IEEE J. Quantum Electron., QE-12, 422 (1976).

D. R. Scifres, R. D. Burnham, and W. Streifer, "Output coupling and distributed feedback utilizing substrate corrugations in doubleheterostructure GaAs lasers," Appl. Phys. Lett, 27, 295 (1975).

R. D. Burnham, D. R. Scifres, and W. Streifer "Low divergence beam from grating coupled composite guide heterostructure GaAlAs diode lasers," Appl. Phys. Lett, 26, 644 (1975).

Sychugov, V. A.

A. A. Zlenko, A. M. Prokhorov, A. A. Spikhal’skii, and V. A. Sychugov, "Emission of E waves from a corrugated section of a waveguide," Sov. J. Quantum Electron., 6, 565 (1976).

A. A. Zlenko, V. A. Kiselev, A. M. Prokhorov, A. A. Spikhal’skii, and V. A. Sychugov, "Emission of surface light wave from a corrugated part of a thin film waveguide," Sov. J. Quantum Electron., 4, 839 (1975).

Tamir, T.

S. T. Peng and T. Tamir, "TM-Mode perturbation analysis of dielectric gratings," Appl. Phys. 7, 35 (1975).

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. MTT-23, 123 (1975).

K. Handa, S. T. Peng, and T. Tamir, "Improved perturbation analysis of dielectric grating," Appl. Phys. 5, 325 (1975).

Yariv, A.

W. Ng and A. Yariv, "Highly collimated broadside emission from room-temperature GaAs distributed Bragg reflector lasers," Appl. Phys. Lett., 31, 613 (1977).

Zlenko, A. A.

A. A. Zlenko, A. M. Prokhorov, A. A. Spikhal’skii, and V. A. Sychugov, "Emission of E waves from a corrugated section of a waveguide," Sov. J. Quantum Electron., 6, 565 (1976).

A. A. Zlenko, V. A. Kiselev, A. M. Prokhorov, A. A. Spikhal’skii, and V. A. Sychugov, "Emission of surface light wave from a corrugated part of a thin film waveguide," Sov. J. Quantum Electron., 4, 839 (1975).

Appl. Phys. (2)

K. Handa, S. T. Peng, and T. Tamir, "Improved perturbation analysis of dielectric grating," Appl. Phys. 5, 325 (1975).

S. T. Peng and T. Tamir, "TM-Mode perturbation analysis of dielectric gratings," Appl. Phys. 7, 35 (1975).

Appl. Phys. Lett (1)

D. R. Scifres, R. D. Burnham, and W. Streifer, "Output coupling and distributed feedback utilizing substrate corrugations in doubleheterostructure GaAs lasers," Appl. Phys. Lett, 27, 295 (1975).

Appl. Phys. Lett. (2)

R. D. Burnham, D. R. Scifres, and W. Streifer "Low divergence beam from grating coupled composite guide heterostructure GaAlAs diode lasers," Appl. Phys. Lett, 26, 644 (1975).

W. Ng and A. Yariv, "Highly collimated broadside emission from room-temperature GaAs distributed Bragg reflector lasers," Appl. Phys. Lett., 31, 613 (1977).

IEEE J. of Quantum Electron. (1)

W. W. Rigrod and D. Marcuse, "Radiation loss coefficients of asymmetric dielectric waveguides with shallow sinusoidal corrugations," IEEE J. of Quantum Electron. QE-12, 673 (1976).

IEEE J. Quant. Electron (1)

W. Streifer, R. D. Burnham, and D. R. Scifres, "Analysis of grating coupled radiation in GaAs:GaAlAs lasers and waveguides," IEEE J. Quant. Electron, QE-12, 494 (1976).

IEEE J. Quantum Electron. (1)

W. Streifer, D. R. Scifres, and R. D. Burnham "Analysis of grating coupled radiation in GaAs:GaAlAs lasers and waveguides," IEEE J. Quantum Electron., QE-12, 422 (1976).

IEEE Trans. (1)

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. MTT-23, 123 (1975).

J. Appl. Phys. (1)

H. Kogelnik and C. V. Shank, "Coupled mode theory of distributed feedback lasers," J. Appl. Phys., 43, 2327 (1972).

J. Math. Phys. (1)

C. Lanczos, "Trigonometric interpolation of empirical and analytical Functions," J. Math. Phys., 17, 123 (1938).

Sov. J. Quantum Electron. (3)

V. A. Kiselev, "Diffraction coupling of radiation into a thin-film waveguide," Sov. J. Quantum Electron., 4, 872 (1975).

A. A. Zlenko, V. A. Kiselev, A. M. Prokhorov, A. A. Spikhal’skii, and V. A. Sychugov, "Emission of surface light wave from a corrugated part of a thin film waveguide," Sov. J. Quantum Electron., 4, 839 (1975).

A. A. Zlenko, A. M. Prokhorov, A. A. Spikhal’skii, and V. A. Sychugov, "Emission of E waves from a corrugated section of a waveguide," Sov. J. Quantum Electron., 6, 565 (1976).

Other (2)

C. Lanczos, Applied Analysis (Prentice Hall, Englewood Cliffs, N.J., 1956), Chap 7.

Y. L. Luke, Mathematical Functions and their Approximations (Academic, New York, 1975), p. 495.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.