Abstract

The propagation of electromagnetic radiation in periodically stratified media is considered. Media of finite, semi-infinite, and infinite extent are treated. A diagonalization of the unit cell translation operator is used to obtain exact solutions for the Bloch waves, the dispersion relations, and the band structure of the medium. Some new phenomena with applications to integrated optics and laser technology are presented.

© 1977 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. Abeles, Ann. Phys. (Paris) 5, 596 (1950); 5, 706 (1950).
  2. A. Ashkin and A. Yariv, Bell Labs. Tech. Memo MM-61-124-46 (13 November 1961) (unpublished).
  3. N. Bloembergen and A. J. Sievers, Appl. Phys. Lett. 17, 483 (1970).
  4. C. L. Tang and P. P. Bey, IEEE J. Quantum Electron. QE-9, 9 (1973).
  5. S. M. Rytov, Zh. Eksp. Teor. Fiz. 29, 605 (1955) [Sov. Phys. -JETP 2, 466 (1956)].
  6. J. P. van der Ziel, M. Illegems, and R. M. Mikulyak, Appl. Phys. Lett. 28, 735 (1976).
  7. A. Y. Cho and J. R. Arthur, Progress in Solid State Chemistry, Vol. 10 (Pergamon, New York, 1975), Part 3, pp. 157 157–191.
  8. A. Yariv, Appl. Phys. Lett. 25, 105 (1974).
  9. F. Bloch, Z. Phys. 52, 555 (1928).
  10. K. Aiki, M. Nakamura, J. Umeda, A. Yariv, A. Katzir, and H. W. Yen, Appl. Phys. Lett. 27, 145 (1975).
  11. H. C. Casey, Jr., S. Somekh, and M. Ilegems, Appl. Phys. Lett. 27, 142 (1975).
  12. F. K. Reinhart, R. A. Logan, and C. V. Shank, Appl. Phys. Lett. 27, 45 (1975).
  13. A. Yariv, IEEE J. Quant. Electron. QE-9, 919 (1973).
  14. M. Born and E. Wolf, Principles of Optics (Macmillan, New York, 1964), p. 67.
  15. H. Yajima, Proceedings of the Symposium on Optical and Acoustical Micro-Electronics, New York, April 1974) (unpublished).
  16. L. B. Stotts, Opt. Commun. 17, 133 (1976).
  17. s. Somekh, E. Garmire, A. Yariv, H. Garvin, and R. Hunsperger, Appl. Phys. Lett. 22, 46 (1973).
  18. A. B. Buckman, J. Opt. Soc. Am. 66, 30 (1976).
  19. E. A. Ash, "Grating Surface Waveguides," presented at International Microwave Symposium, Newport Beach, Calif., May 1970 (unpublished).
  20. A. Yariv, Quantum Electronics (Wiley, New York, 1975).
  21. P. K. Tien, Appl. Opt. 10, 2395 (1971).
  22. D. Kossel, "Analogies between Thin-Film Optics and Electron- Band Theory of Solids," J. Opt. Soc. Am. 56, 1434 (1966).
  23. J. A. Arnaud and A. A. M. Saleh, Appl. Opt. 13, 2343 (1974).
  24. W. Shockley, Phys. Rev. 56, 317 (1939).
  25. J. P. van der Ziel and M. Ilegems, Appl. Phys. Lett. 28, 437 (1976).

1966

D. Kossel, "Analogies between Thin-Film Optics and Electron- Band Theory of Solids," J. Opt. Soc. Am. 56, 1434 (1966).

van derZiel, J. P.

J. P. van der Ziel and M. Ilegems, Appl. Phys. Lett. 28, 437 (1976).

J. P. van der Ziel, M. Illegems, and R. M. Mikulyak, Appl. Phys. Lett. 28, 735 (1976).

Abeles, F.

F. Abeles, Ann. Phys. (Paris) 5, 596 (1950); 5, 706 (1950).

Aiki, K.

K. Aiki, M. Nakamura, J. Umeda, A. Yariv, A. Katzir, and H. W. Yen, Appl. Phys. Lett. 27, 145 (1975).

Arnaud, J. A.

J. A. Arnaud and A. A. M. Saleh, Appl. Opt. 13, 2343 (1974).

Arthur, J. R.

A. Y. Cho and J. R. Arthur, Progress in Solid State Chemistry, Vol. 10 (Pergamon, New York, 1975), Part 3, pp. 157 157–191.

Ash, E. A.

E. A. Ash, "Grating Surface Waveguides," presented at International Microwave Symposium, Newport Beach, Calif., May 1970 (unpublished).

Ashkin, A.

A. Ashkin and A. Yariv, Bell Labs. Tech. Memo MM-61-124-46 (13 November 1961) (unpublished).

Bey, P. P.

C. L. Tang and P. P. Bey, IEEE J. Quantum Electron. QE-9, 9 (1973).

Bloch, F.

F. Bloch, Z. Phys. 52, 555 (1928).

Bloembergen, N.

N. Bloembergen and A. J. Sievers, Appl. Phys. Lett. 17, 483 (1970).

Born, M.

M. Born and E. Wolf, Principles of Optics (Macmillan, New York, 1964), p. 67.

Buckman, A. B.

A. B. Buckman, J. Opt. Soc. Am. 66, 30 (1976).

Casey, Jr., H. C.

H. C. Casey, Jr., S. Somekh, and M. Ilegems, Appl. Phys. Lett. 27, 142 (1975).

Cho, A. Y.

A. Y. Cho and J. R. Arthur, Progress in Solid State Chemistry, Vol. 10 (Pergamon, New York, 1975), Part 3, pp. 157 157–191.

Garmire, E.

s. Somekh, E. Garmire, A. Yariv, H. Garvin, and R. Hunsperger, Appl. Phys. Lett. 22, 46 (1973).

Garvin, H.

s. Somekh, E. Garmire, A. Yariv, H. Garvin, and R. Hunsperger, Appl. Phys. Lett. 22, 46 (1973).

Hunsperger, R.

s. Somekh, E. Garmire, A. Yariv, H. Garvin, and R. Hunsperger, Appl. Phys. Lett. 22, 46 (1973).

Ilegems, M.

J. P. van der Ziel and M. Ilegems, Appl. Phys. Lett. 28, 437 (1976).

H. C. Casey, Jr., S. Somekh, and M. Ilegems, Appl. Phys. Lett. 27, 142 (1975).

Illegems, M.

J. P. van der Ziel, M. Illegems, and R. M. Mikulyak, Appl. Phys. Lett. 28, 735 (1976).

Katzir, A.

K. Aiki, M. Nakamura, J. Umeda, A. Yariv, A. Katzir, and H. W. Yen, Appl. Phys. Lett. 27, 145 (1975).

Kossel, D.

D. Kossel, "Analogies between Thin-Film Optics and Electron- Band Theory of Solids," J. Opt. Soc. Am. 56, 1434 (1966).

Logan, R. A.

F. K. Reinhart, R. A. Logan, and C. V. Shank, Appl. Phys. Lett. 27, 45 (1975).

Mikulyak, R. M.

J. P. van der Ziel, M. Illegems, and R. M. Mikulyak, Appl. Phys. Lett. 28, 735 (1976).

Nakamura, M.

K. Aiki, M. Nakamura, J. Umeda, A. Yariv, A. Katzir, and H. W. Yen, Appl. Phys. Lett. 27, 145 (1975).

Reinhart, F. K.

F. K. Reinhart, R. A. Logan, and C. V. Shank, Appl. Phys. Lett. 27, 45 (1975).

Rytov, S. M.

S. M. Rytov, Zh. Eksp. Teor. Fiz. 29, 605 (1955) [Sov. Phys. -JETP 2, 466 (1956)].

Saleh, A. A. M.

J. A. Arnaud and A. A. M. Saleh, Appl. Opt. 13, 2343 (1974).

Shank, C. V.

F. K. Reinhart, R. A. Logan, and C. V. Shank, Appl. Phys. Lett. 27, 45 (1975).

Shockley, W.

W. Shockley, Phys. Rev. 56, 317 (1939).

Sievers, A. J.

N. Bloembergen and A. J. Sievers, Appl. Phys. Lett. 17, 483 (1970).

Somekh, S.

H. C. Casey, Jr., S. Somekh, and M. Ilegems, Appl. Phys. Lett. 27, 142 (1975).

s. Somekh, E. Garmire, A. Yariv, H. Garvin, and R. Hunsperger, Appl. Phys. Lett. 22, 46 (1973).

Stotts, L. B.

L. B. Stotts, Opt. Commun. 17, 133 (1976).

Tang, C. L.

C. L. Tang and P. P. Bey, IEEE J. Quantum Electron. QE-9, 9 (1973).

Tien, P. K.

P. K. Tien, Appl. Opt. 10, 2395 (1971).

Umeda, J.

K. Aiki, M. Nakamura, J. Umeda, A. Yariv, A. Katzir, and H. W. Yen, Appl. Phys. Lett. 27, 145 (1975).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Macmillan, New York, 1964), p. 67.

Yajima, H.

H. Yajima, Proceedings of the Symposium on Optical and Acoustical Micro-Electronics, New York, April 1974) (unpublished).

Yariv, A.

A. Yariv, IEEE J. Quant. Electron. QE-9, 919 (1973).

s. Somekh, E. Garmire, A. Yariv, H. Garvin, and R. Hunsperger, Appl. Phys. Lett. 22, 46 (1973).

K. Aiki, M. Nakamura, J. Umeda, A. Yariv, A. Katzir, and H. W. Yen, Appl. Phys. Lett. 27, 145 (1975).

A. Yariv, Appl. Phys. Lett. 25, 105 (1974).

A. Ashkin and A. Yariv, Bell Labs. Tech. Memo MM-61-124-46 (13 November 1961) (unpublished).

A. Yariv, Quantum Electronics (Wiley, New York, 1975).

Yen, H. W.

K. Aiki, M. Nakamura, J. Umeda, A. Yariv, A. Katzir, and H. W. Yen, Appl. Phys. Lett. 27, 145 (1975).

J. Opt. Soc. Am.

D. Kossel, "Analogies between Thin-Film Optics and Electron- Band Theory of Solids," J. Opt. Soc. Am. 56, 1434 (1966).

Other

J. A. Arnaud and A. A. M. Saleh, Appl. Opt. 13, 2343 (1974).

W. Shockley, Phys. Rev. 56, 317 (1939).

J. P. van der Ziel and M. Ilegems, Appl. Phys. Lett. 28, 437 (1976).

F. Abeles, Ann. Phys. (Paris) 5, 596 (1950); 5, 706 (1950).

A. Ashkin and A. Yariv, Bell Labs. Tech. Memo MM-61-124-46 (13 November 1961) (unpublished).

N. Bloembergen and A. J. Sievers, Appl. Phys. Lett. 17, 483 (1970).

C. L. Tang and P. P. Bey, IEEE J. Quantum Electron. QE-9, 9 (1973).

S. M. Rytov, Zh. Eksp. Teor. Fiz. 29, 605 (1955) [Sov. Phys. -JETP 2, 466 (1956)].

J. P. van der Ziel, M. Illegems, and R. M. Mikulyak, Appl. Phys. Lett. 28, 735 (1976).

A. Y. Cho and J. R. Arthur, Progress in Solid State Chemistry, Vol. 10 (Pergamon, New York, 1975), Part 3, pp. 157 157–191.

A. Yariv, Appl. Phys. Lett. 25, 105 (1974).

F. Bloch, Z. Phys. 52, 555 (1928).

K. Aiki, M. Nakamura, J. Umeda, A. Yariv, A. Katzir, and H. W. Yen, Appl. Phys. Lett. 27, 145 (1975).

H. C. Casey, Jr., S. Somekh, and M. Ilegems, Appl. Phys. Lett. 27, 142 (1975).

F. K. Reinhart, R. A. Logan, and C. V. Shank, Appl. Phys. Lett. 27, 45 (1975).

A. Yariv, IEEE J. Quant. Electron. QE-9, 919 (1973).

M. Born and E. Wolf, Principles of Optics (Macmillan, New York, 1964), p. 67.

H. Yajima, Proceedings of the Symposium on Optical and Acoustical Micro-Electronics, New York, April 1974) (unpublished).

L. B. Stotts, Opt. Commun. 17, 133 (1976).

s. Somekh, E. Garmire, A. Yariv, H. Garvin, and R. Hunsperger, Appl. Phys. Lett. 22, 46 (1973).

A. B. Buckman, J. Opt. Soc. Am. 66, 30 (1976).

E. A. Ash, "Grating Surface Waveguides," presented at International Microwave Symposium, Newport Beach, Calif., May 1970 (unpublished).

A. Yariv, Quantum Electronics (Wiley, New York, 1975).

P. K. Tien, Appl. Opt. 10, 2395 (1971).

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.