Abstract

Diffraction by a dielectric surface-relief grating is analyzed using rigorous coupled-wave theory. The analysis applies to arbitrary grating profiles, groove depths, angles of incidence, and wavelengths. Example results for a wide range of groove depths are presented for sinusoidal, square-wave triangular, and sawtooth gratings. Diffraction efficiencies obtained from the present method of analysis are compared with previously published numerical results. To obtain large diffraction efficiencies (greater than 85%) for gratings with typical substrate perinittivities, it is shown that the grating profile should possess even symmetry.

© 1982 Optical Society of America

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  1. R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
  2. M. Neviere, R. Petit, and M. Cadilhac, "About the theory of optical grating coupler-waveguide systems," Opt. Commun. 8, 113–117 (1973).
  3. S. T. Peng, H. L. Bertoni, and T. Tamir, "Analysis of periodic thin-film structures with rectangular profiles," Opt. Commun. 10, 91–94 (1974).
  4. S. T. Peng and T. Tamir, "Directional blazing of waves guided by asymmetrical dielectric gratings," Opt. Commun. 11, 405–409 (1974).
  5. S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).
  6. D. Marcuse, "Exact theory of TE-wave scattering from blazed dielectric gratings," Bell Syst. Tech. J. 55, 1295–1317 (1976).
  7. K. Knop, "Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves," J. Opt. Soc. Am. 68, 1206–1210 (1978).
  8. K. C. Chang and T. Tamir, "Simplified approach to surface-wave scattering by blazed dielectric gratings," Appl. Opt. 19, 282–288 (1980).
  9. 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, 422–428 (1976).
  10. T. Tamir and S. T. Peng, "Analysis and design of grating couplers," Appl. Phys. 14, 235–254 (1977).
  11. A. R. Neureuther and K. Zaki, "Numerical methods for the analysis of scattering from nonplanar and periodic structures," Alta Freq. 38, 282–285 (1969).
  12. K. Zaki, "Numerical methods for the analysis of scattering from nonplanar periodic structures," Ph.D. thesis (University of California, Berkeley, Calif., 1969) (unpublished).
  13. P. M. van den Berg, "Rigorous diffraction theory of optical reflection and transmission gratings," Ph.D. thesis (Delft University of Technology, Delft, The Netherlands, 1971), rep. no. 1971–16 (unpublished).
  14. D. E. Tremain and K. K. Mei, "Application of the unimoment method to scattering from periodic dielectric structures," J. Opt. Soc. Am. 68, 775–783 (1978).
  15. K. C. Chang, "Surface-wave scattering by dielectric gratings with arbitrary profiles," Ph.D. thesis (Polytechnic Institute of New York, New York, 1979) (unpublished).
  16. K. C. Chang, V. Shah, and T. Tamir, "Scattering and guiding of waves by dielectric gratings with arbitrary profiles," J. Opt. Soc. Am. 70, 804–813 (1980).
  17. M. G. Moharam and T. K. Gaylord, "Rigorous coupled-wave analysis of planar grating diffraction," J. Opt. Soc. Am. 71, 811–818 (1981).
  18. L. R. Lewis and A. Hessel, "Propagation characteristics of periodic arrays of dielectric slabs," IEEE Trans. Microwave Theory Tech. MTT-19, 276–286 (1971).
  19. E.g., C. L. Liu and J. W. S. Liu, Linear Systems Analysis (McGraw-Hill, New York, 1975).
  20. E.g., program EIGRF from the International Mathematics and Statistics Library (IMSL), Houston, Texas.
  21. E.g., B. Carnahan, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969).

1981 (1)

1980 (2)

1978 (2)

1977 (1)

T. Tamir and S. T. Peng, "Analysis and design of grating couplers," Appl. Phys. 14, 235–254 (1977).

1976 (2)

D. Marcuse, "Exact theory of TE-wave scattering from blazed dielectric gratings," Bell Syst. Tech. J. 55, 1295–1317 (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, 422–428 (1976).

1975 (1)

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).

1974 (2)

S. T. Peng, H. L. Bertoni, and T. Tamir, "Analysis of periodic thin-film structures with rectangular profiles," Opt. Commun. 10, 91–94 (1974).

S. T. Peng and T. Tamir, "Directional blazing of waves guided by asymmetrical dielectric gratings," Opt. Commun. 11, 405–409 (1974).

1973 (1)

M. Neviere, R. Petit, and M. Cadilhac, "About the theory of optical grating coupler-waveguide systems," Opt. Commun. 8, 113–117 (1973).

1971 (1)

L. R. Lewis and A. Hessel, "Propagation characteristics of periodic arrays of dielectric slabs," IEEE Trans. Microwave Theory Tech. MTT-19, 276–286 (1971).

1969 (1)

A. R. Neureuther and K. Zaki, "Numerical methods for the analysis of scattering from nonplanar and periodic structures," Alta Freq. 38, 282–285 (1969).

Carnahan, B.

E.g., B. Carnahan, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969).

Liu, C. L.

E.g., C. L. Liu and J. W. S. Liu, Linear Systems Analysis (McGraw-Hill, New York, 1975).

Liu, J. W. S.

E.g., C. L. Liu and J. W. S. Liu, Linear Systems Analysis (McGraw-Hill, New York, 1975).

Luther, H. A.

E.g., B. Carnahan, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969).

van den Berg, P. M.

P. M. van den Berg, "Rigorous diffraction theory of optical reflection and transmission gratings," Ph.D. thesis (Delft University of Technology, Delft, The Netherlands, 1971), rep. no. 1971–16 (unpublished).

Wilkes, J. O.

E.g., B. Carnahan, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969).

Bertoni, H. L.

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).

S. T. Peng, H. L. Bertoni, and T. Tamir, "Analysis of periodic thin-film structures with rectangular profiles," Opt. Commun. 10, 91–94 (1974).

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, 422–428 (1976).

Cadilhac, M.

M. Neviere, R. Petit, and M. Cadilhac, "About the theory of optical grating coupler-waveguide systems," Opt. Commun. 8, 113–117 (1973).

Chang, K. C.

Gaylord, T. K.

Hessel, A.

L. R. Lewis and A. Hessel, "Propagation characteristics of periodic arrays of dielectric slabs," IEEE Trans. Microwave Theory Tech. MTT-19, 276–286 (1971).

Knop, K.

Lewis, L. R.

L. R. Lewis and A. Hessel, "Propagation characteristics of periodic arrays of dielectric slabs," IEEE Trans. Microwave Theory Tech. MTT-19, 276–286 (1971).

Marcuse, D.

D. Marcuse, "Exact theory of TE-wave scattering from blazed dielectric gratings," Bell Syst. Tech. J. 55, 1295–1317 (1976).

Mei, K. K.

Moharam, M. G.

Neureuther, A. R.

A. R. Neureuther and K. Zaki, "Numerical methods for the analysis of scattering from nonplanar and periodic structures," Alta Freq. 38, 282–285 (1969).

Neviere, M.

M. Neviere, R. Petit, and M. Cadilhac, "About the theory of optical grating coupler-waveguide systems," Opt. Commun. 8, 113–117 (1973).

Peng, S. T.

T. Tamir and S. T. Peng, "Analysis and design of grating couplers," Appl. Phys. 14, 235–254 (1977).

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).

S. T. Peng, H. L. Bertoni, and T. Tamir, "Analysis of periodic thin-film structures with rectangular profiles," Opt. Commun. 10, 91–94 (1974).

S. T. Peng and T. Tamir, "Directional blazing of waves guided by asymmetrical dielectric gratings," Opt. Commun. 11, 405–409 (1974).

Petit, R.

M. Neviere, R. Petit, and M. Cadilhac, "About the theory of optical grating coupler-waveguide systems," Opt. Commun. 8, 113–117 (1973).

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, 422–428 (1976).

Shah, V.

Streifer, W.

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, 422–428 (1976).

Tamir, T.

K. C. Chang and T. Tamir, "Simplified approach to surface-wave scattering by blazed dielectric gratings," Appl. Opt. 19, 282–288 (1980).

K. C. Chang, V. Shah, and T. Tamir, "Scattering and guiding of waves by dielectric gratings with arbitrary profiles," J. Opt. Soc. Am. 70, 804–813 (1980).

T. Tamir and S. T. Peng, "Analysis and design of grating couplers," Appl. Phys. 14, 235–254 (1977).

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).

S. T. Peng and T. Tamir, "Directional blazing of waves guided by asymmetrical dielectric gratings," Opt. Commun. 11, 405–409 (1974).

S. T. Peng, H. L. Bertoni, and T. Tamir, "Analysis of periodic thin-film structures with rectangular profiles," Opt. Commun. 10, 91–94 (1974).

Tremain, D. E.

Zaki, K.

A. R. Neureuther and K. Zaki, "Numerical methods for the analysis of scattering from nonplanar and periodic structures," Alta Freq. 38, 282–285 (1969).

K. Zaki, "Numerical methods for the analysis of scattering from nonplanar periodic structures," Ph.D. thesis (University of California, Berkeley, Calif., 1969) (unpublished).

Alta Freq. (1)

A. R. Neureuther and K. Zaki, "Numerical methods for the analysis of scattering from nonplanar and periodic structures," Alta Freq. 38, 282–285 (1969).

Appl. Opt. (1)

Appl. Phys. (1)

T. Tamir and S. T. Peng, "Analysis and design of grating couplers," Appl. Phys. 14, 235–254 (1977).

Bell Syst. Tech. J. (1)

D. Marcuse, "Exact theory of TE-wave scattering from blazed dielectric gratings," Bell Syst. Tech. J. 55, 1295–1317 (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, 422–428 (1976).

IEEE Trans. Microwave Theory Tech. (2)

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).

L. R. Lewis and A. Hessel, "Propagation characteristics of periodic arrays of dielectric slabs," IEEE Trans. Microwave Theory Tech. MTT-19, 276–286 (1971).

J. Opt. Soc. Am. (4)

Opt. Commun. (3)

M. Neviere, R. Petit, and M. Cadilhac, "About the theory of optical grating coupler-waveguide systems," Opt. Commun. 8, 113–117 (1973).

S. T. Peng, H. L. Bertoni, and T. Tamir, "Analysis of periodic thin-film structures with rectangular profiles," Opt. Commun. 10, 91–94 (1974).

S. T. Peng and T. Tamir, "Directional blazing of waves guided by asymmetrical dielectric gratings," Opt. Commun. 11, 405–409 (1974).

Other (7)

R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).

K. C. Chang, "Surface-wave scattering by dielectric gratings with arbitrary profiles," Ph.D. thesis (Polytechnic Institute of New York, New York, 1979) (unpublished).

K. Zaki, "Numerical methods for the analysis of scattering from nonplanar periodic structures," Ph.D. thesis (University of California, Berkeley, Calif., 1969) (unpublished).

P. M. van den Berg, "Rigorous diffraction theory of optical reflection and transmission gratings," Ph.D. thesis (Delft University of Technology, Delft, The Netherlands, 1971), rep. no. 1971–16 (unpublished).

E.g., C. L. Liu and J. W. S. Liu, Linear Systems Analysis (McGraw-Hill, New York, 1975).

E.g., program EIGRF from the International Mathematics and Statistics Library (IMSL), Houston, Texas.

E.g., B. Carnahan, H. A. Luther, and J. O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969).

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