Abstract

A rigorous solution is presented for plane-wave scattering by an asymmetric diffraction grating, which consists of a corrugated structure with three different groove depths per period. After establishing that asymmetry effects in the scattered amplitudes may be observed only if at least three spectral orders are present, we find that maximum asymmetry occurs when the angle of incidence closely satisfies a Bragg condition. For normal incidence, the peak asymmetry coincides with blazing, the degree of which may be quite significant. By employing simple phasing considerations, we derive a scheme for optimizing the grating design, and present examples illustrating that very high blazing efficiencies are easily attainable.

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  1. G. W. Stroke, in Handbuch der Physik, 29, edited by S. Flügge (Springer, Berlin, 1967), pp. 426–754. Refer also to the extensive bibliography therein.
  2. J. F. Carlson and A. E. Heins, Q. Appl. Math. 5, 82 (1947).
  3. A. Hessel and H. Hochstadt, Radio Sci. 3, 1019 (1968).
  4. D. Tseng, Ph.D. dissertation, Polytechnic Institute of Brooklyn, Brooklyn, N. Y. (1967) (University Microfilms, Ann Arbor, Mich., order No. 67-13425).
  5. R. J. Ikola, Ph.D. dissertation, Polytechnic Institute of Brooklyn, Brooklyn, N. Y. (1972) (University Microfilms, Ann Arbor, Mich., order No. 72-28243).
  6. R. E. Collin, Field Theory of Guided Waves (McGraw—Hill, New York, 1960), Sec. 5.7, pp. 209–214.
  7. Reference 6, Sec. 10.2, pp. 430–438.
  8. A. Wirgin and R. Deleuil, J. Opt. Soc. Am. 59, 1348 (1969).
  9. J. Shmoys and A. Hessel, J. Opt. Soc. Am. 62, 742 (1972).

1972

R. J. Ikola, Ph.D. dissertation, Polytechnic Institute of Brooklyn, Brooklyn, N. Y. (1972) (University Microfilms, Ann Arbor, Mich., order No. 72-28243).

J. Shmoys and A. Hessel, J. Opt. Soc. Am. 62, 742 (1972).

1969

A. Wirgin and R. Deleuil, J. Opt. Soc. Am. 59, 1348 (1969).

1968

A. Hessel and H. Hochstadt, Radio Sci. 3, 1019 (1968).

1967

D. Tseng, Ph.D. dissertation, Polytechnic Institute of Brooklyn, Brooklyn, N. Y. (1967) (University Microfilms, Ann Arbor, Mich., order No. 67-13425).

1947

J. F. Carlson and A. E. Heins, Q. Appl. Math. 5, 82 (1947).

Carlson, J. F.

J. F. Carlson and A. E. Heins, Q. Appl. Math. 5, 82 (1947).

Collin, R. E.

R. E. Collin, Field Theory of Guided Waves (McGraw—Hill, New York, 1960), Sec. 5.7, pp. 209–214.

Deleuil, R.

A. Wirgin and R. Deleuil, J. Opt. Soc. Am. 59, 1348 (1969).

Heins, A. E.

J. F. Carlson and A. E. Heins, Q. Appl. Math. 5, 82 (1947).

Hessel, A.

J. Shmoys and A. Hessel, J. Opt. Soc. Am. 62, 742 (1972).

A. Hessel and H. Hochstadt, Radio Sci. 3, 1019 (1968).

Hochstadt, H.

A. Hessel and H. Hochstadt, Radio Sci. 3, 1019 (1968).

Ikola, R. J.

R. J. Ikola, Ph.D. dissertation, Polytechnic Institute of Brooklyn, Brooklyn, N. Y. (1972) (University Microfilms, Ann Arbor, Mich., order No. 72-28243).

Shmoys, J.

J. Shmoys and A. Hessel, J. Opt. Soc. Am. 62, 742 (1972).

Stroke, G. W.

G. W. Stroke, in Handbuch der Physik, 29, edited by S. Flügge (Springer, Berlin, 1967), pp. 426–754. Refer also to the extensive bibliography therein.

Tseng, D.

D. Tseng, Ph.D. dissertation, Polytechnic Institute of Brooklyn, Brooklyn, N. Y. (1967) (University Microfilms, Ann Arbor, Mich., order No. 67-13425).

Wirgin, A.

A. Wirgin and R. Deleuil, J. Opt. Soc. Am. 59, 1348 (1969).

Other

G. W. Stroke, in Handbuch der Physik, 29, edited by S. Flügge (Springer, Berlin, 1967), pp. 426–754. Refer also to the extensive bibliography therein.

J. F. Carlson and A. E. Heins, Q. Appl. Math. 5, 82 (1947).

A. Hessel and H. Hochstadt, Radio Sci. 3, 1019 (1968).

D. Tseng, Ph.D. dissertation, Polytechnic Institute of Brooklyn, Brooklyn, N. Y. (1967) (University Microfilms, Ann Arbor, Mich., order No. 67-13425).

R. J. Ikola, Ph.D. dissertation, Polytechnic Institute of Brooklyn, Brooklyn, N. Y. (1972) (University Microfilms, Ann Arbor, Mich., order No. 72-28243).

R. E. Collin, Field Theory of Guided Waves (McGraw—Hill, New York, 1960), Sec. 5.7, pp. 209–214.

Reference 6, Sec. 10.2, pp. 430–438.

A. Wirgin and R. Deleuil, J. Opt. Soc. Am. 59, 1348 (1969).

J. Shmoys and A. Hessel, J. Opt. Soc. Am. 62, 742 (1972).

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