Abstract

The conventional solutions to the problem of normally incident light transmission through homogeneous, birefringent, nonoptically active, nonabsorbing, crystalline plate are not exact. When it is treated as a boundary value problem in electromagnetic field theory, exact expressions are obtained for the retardation or phase difference and the electric field amplitude ratio. The two solutions differ in some interesting ways that become of substantial importance in the examination of laser light. The nature of the exact solutions is examined in detail and numerical comparisons with the conventional solutions are given for the cases of calcite and quartz, neglecting the optical activity of crystalline quartz. For quartz it is shown that one can obtain a quarter-wave plate by using any one of a number of different crystal thicknesses. The application of wave plates in the investigation of elliptically polarized light is briefly discussed. For small angles of incidence, the effects to be expected for light which is obliquely incident on the plate surface are investigated.

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  1. For an equivalent analysis see, for example, M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), p. 688.
  2. B. I. Stepanov and A. P. Khapalyuk, Opt. i Spectroskopiya 13, 714 (1962) [English transl.: Opt. Spectry. 13, 404 (1962)].
  3. F. Gabler and P. Sokob, Z. Physik 116, 47 (1940).
  4. Thornton C. Fry, J. Opt. Soc. Am. and Rev. Sci. Instr. 16, 1 (1928).
  5. H. Jacobs, D. A. Holmes, L. Hatkin, and F. A. Brand, J. Appl. Phys. 34, 2617 (1963).
  6. S. Ramo and J. R. Whinnery, Fields and Waves in Modern Radio (John Wiley & Sons, Inc., New York, 1960), p. 290.
  7. H. Jacobs, F. A. Brand, J. D. Meindl, S. Weitz, R. Benjamin, and D. A. Holmes, Proc. IEEE 51, 581 (1963).
  8. For the purposes of numerical computations, we have chosen optical constants for calcite and quartz which correspond to near infrared wavelengths because we are using GaAs injection laser sources (8400 Å) in some of our work. The general concepts advanced in this work, however, are valid for other wavelengths. The numerical values for the optical constants were taken from: Dwight E. Gray, Coordinating Editor, American Institute of Physics Handbook (McGraw-Hill Book Company, Inc., New York, 2nd edition, 1963), Calcite, p. 6–18; Crystal Quartz, p. 6–24; Rutile, p. 6–33.
  9. G. N. Ramachandran and S. Ramaseshan in Handbuck der Physik, edited by S. Fhügge (Springer-Verlag, Berlin, 1961), Vol. 25, Chap. 1, p. 76.
  10. Reference 1, p. 24.
  11. A. C. Hall, J. Opt. Soc. Am. 53, 801 (1963). We have observed a typographical error in Eq. (12) of Hall’s work. The corrected forms, in Hall’s notation, are cos2ψ=[+cosδ sinδ±cot2γ(k tanΔ-sin2δ)½]/k, sin2ψ=[-sinδcot2γ±cosδ(k tanΔ-sin2δ)½]/k. The geometry used by Hall is equivalent to that used in the present work.
  12. D. Bergman, J. Opt. Soc. Am. 52, 1080 (1962).
  13. H. Weinberger and J. Harris, J. Opt. Soc. Am. 54, 552 (1964).

Benjamin, R.

H. Jacobs, F. A. Brand, J. D. Meindl, S. Weitz, R. Benjamin, and D. A. Holmes, Proc. IEEE 51, 581 (1963).

Bergman, D.

D. Bergman, J. Opt. Soc. Am. 52, 1080 (1962).

Born, M.

For an equivalent analysis see, for example, M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), p. 688.

Brand, F. A.

H. Jacobs, D. A. Holmes, L. Hatkin, and F. A. Brand, J. Appl. Phys. 34, 2617 (1963).

H. Jacobs, F. A. Brand, J. D. Meindl, S. Weitz, R. Benjamin, and D. A. Holmes, Proc. IEEE 51, 581 (1963).

C. Fry, Thornton

Thornton C. Fry, J. Opt. Soc. Am. and Rev. Sci. Instr. 16, 1 (1928).

Gabler, F.

F. Gabler and P. Sokob, Z. Physik 116, 47 (1940).

Hall, A. C.

A. C. Hall, J. Opt. Soc. Am. 53, 801 (1963). We have observed a typographical error in Eq. (12) of Hall’s work. The corrected forms, in Hall’s notation, are cos2ψ=[+cosδ sinδ±cot2γ(k tanΔ-sin2δ)½]/k, sin2ψ=[-sinδcot2γ±cosδ(k tanΔ-sin2δ)½]/k. The geometry used by Hall is equivalent to that used in the present work.

Harris, J.

H. Weinberger and J. Harris, J. Opt. Soc. Am. 54, 552 (1964).

Hatkin, L.

H. Jacobs, D. A. Holmes, L. Hatkin, and F. A. Brand, J. Appl. Phys. 34, 2617 (1963).

Holmes, D. A.

H. Jacobs, D. A. Holmes, L. Hatkin, and F. A. Brand, J. Appl. Phys. 34, 2617 (1963).

H. Jacobs, F. A. Brand, J. D. Meindl, S. Weitz, R. Benjamin, and D. A. Holmes, Proc. IEEE 51, 581 (1963).

Jacobs, H.

H. Jacobs, D. A. Holmes, L. Hatkin, and F. A. Brand, J. Appl. Phys. 34, 2617 (1963).

H. Jacobs, F. A. Brand, J. D. Meindl, S. Weitz, R. Benjamin, and D. A. Holmes, Proc. IEEE 51, 581 (1963).

Khapalyuk, A. P.

B. I. Stepanov and A. P. Khapalyuk, Opt. i Spectroskopiya 13, 714 (1962) [English transl.: Opt. Spectry. 13, 404 (1962)].

Meindl, J. D.

H. Jacobs, F. A. Brand, J. D. Meindl, S. Weitz, R. Benjamin, and D. A. Holmes, Proc. IEEE 51, 581 (1963).

Ramachandran, G. N.

G. N. Ramachandran and S. Ramaseshan in Handbuck der Physik, edited by S. Fhügge (Springer-Verlag, Berlin, 1961), Vol. 25, Chap. 1, p. 76.

Ramaseshan, S.

G. N. Ramachandran and S. Ramaseshan in Handbuck der Physik, edited by S. Fhügge (Springer-Verlag, Berlin, 1961), Vol. 25, Chap. 1, p. 76.

Ramo, S.

S. Ramo and J. R. Whinnery, Fields and Waves in Modern Radio (John Wiley & Sons, Inc., New York, 1960), p. 290.

Sokob, P.

F. Gabler and P. Sokob, Z. Physik 116, 47 (1940).

Stepanov, B. I.

B. I. Stepanov and A. P. Khapalyuk, Opt. i Spectroskopiya 13, 714 (1962) [English transl.: Opt. Spectry. 13, 404 (1962)].

Weinberger, H.

H. Weinberger and J. Harris, J. Opt. Soc. Am. 54, 552 (1964).

Weitz, S.

H. Jacobs, F. A. Brand, J. D. Meindl, S. Weitz, R. Benjamin, and D. A. Holmes, Proc. IEEE 51, 581 (1963).

Whinnery, J. R.

S. Ramo and J. R. Whinnery, Fields and Waves in Modern Radio (John Wiley & Sons, Inc., New York, 1960), p. 290.

Wolf, E.

For an equivalent analysis see, for example, M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), p. 688.

Other (13)

For an equivalent analysis see, for example, M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), p. 688.

B. I. Stepanov and A. P. Khapalyuk, Opt. i Spectroskopiya 13, 714 (1962) [English transl.: Opt. Spectry. 13, 404 (1962)].

F. Gabler and P. Sokob, Z. Physik 116, 47 (1940).

Thornton C. Fry, J. Opt. Soc. Am. and Rev. Sci. Instr. 16, 1 (1928).

H. Jacobs, D. A. Holmes, L. Hatkin, and F. A. Brand, J. Appl. Phys. 34, 2617 (1963).

S. Ramo and J. R. Whinnery, Fields and Waves in Modern Radio (John Wiley & Sons, Inc., New York, 1960), p. 290.

H. Jacobs, F. A. Brand, J. D. Meindl, S. Weitz, R. Benjamin, and D. A. Holmes, Proc. IEEE 51, 581 (1963).

For the purposes of numerical computations, we have chosen optical constants for calcite and quartz which correspond to near infrared wavelengths because we are using GaAs injection laser sources (8400 Å) in some of our work. The general concepts advanced in this work, however, are valid for other wavelengths. The numerical values for the optical constants were taken from: Dwight E. Gray, Coordinating Editor, American Institute of Physics Handbook (McGraw-Hill Book Company, Inc., New York, 2nd edition, 1963), Calcite, p. 6–18; Crystal Quartz, p. 6–24; Rutile, p. 6–33.

G. N. Ramachandran and S. Ramaseshan in Handbuck der Physik, edited by S. Fhügge (Springer-Verlag, Berlin, 1961), Vol. 25, Chap. 1, p. 76.

Reference 1, p. 24.

A. C. Hall, J. Opt. Soc. Am. 53, 801 (1963). We have observed a typographical error in Eq. (12) of Hall’s work. The corrected forms, in Hall’s notation, are cos2ψ=[+cosδ sinδ±cot2γ(k tanΔ-sin2δ)½]/k, sin2ψ=[-sinδcot2γ±cosδ(k tanΔ-sin2δ)½]/k. The geometry used by Hall is equivalent to that used in the present work.

D. Bergman, J. Opt. Soc. Am. 52, 1080 (1962).

H. Weinberger and J. Harris, J. Opt. Soc. Am. 54, 552 (1964).

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