Abstract

Part III of this series gave several theorems concerning lossless birefringent networks and their properties. This paper uses some of these results to develop two methods of synthesizing lossless birefringent networks containing only half the number of crystals normally required. The two methods are modifications of the synthesis procedure of Part I of this series, and require fewer crystals because the light makes two passes through the network. The two methods complement each other, for in one case the output and input coincide (i.e., are spatially degenerate) while in the second case, the output and input are spatially separated.

© 1966 Optical Society of America

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References

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  1. S. E. Harris, E. O. Ammann, and I. C. Chang, J. Opt. Soc. Am. 54, 1267 (1964).
    [Crossref]
  2. E. O. Ammann, J. Opt. Soc. Am. 56, 943 (1966).
    [Crossref]
  3. H. G. Jerrard, J. Opt. Soc. Am. 38, 35 (1948).
    [Crossref]
  4. The expressions differ only by a minus sign which is introduced by reflection at the mirror. As explained in Part III, this sign difference is of no practical importance and is neglected in what follows.
  5. I. Solc, J. Opt. Soc. Am. 55, 621 (1965).
    [Crossref]
  6. J. W. Evans, J. Opt. Soc. Am. 39, 229 (1949).
    [Crossref]

1966 (1)

1965 (1)

1964 (1)

1949 (1)

1948 (1)

J. Opt. Soc. Am. (5)

Other (1)

The expressions differ only by a minus sign which is introduced by reflection at the mirror. As explained in Part III, this sign difference is of no practical importance and is neglected in what follows.

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Figures (4)

F. 1
F. 1

General form of network and corresponding spatial relationship of output to input which results from (a) method A, and (b) method B.

F. 2
F. 2

Two equivalent birefringent networks: (a) single-pass network, and (b) corresponding double-pass network.

F. 3
F. 3

(a) Form of birefringent network which results when the desired amplitude transmittance C(ω) satisfies the restrictions C0 = −Cn, C1 = −Cn−1, C2 = −Cn−2, ⋯ etc. (b) Symmetrical birefringent network obtained from that in Fig. 3(a) by rotating the output polarizer by 90°. The amplitude transmittance of this network is D(ω). (c) Double-pass birefringent network which is equivalent to the network of Fig. 3(b).

F. 4
F. 4

Double-pass birefringent network which results from method B. The optic axis of the calcite polarizing beam-splitter is shown dotted. The x direction is out of the page.

Equations (1)

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C ( ω ) = C 0 + C 1 e i a ω + C 2 e i 2 a ω + + C n e ina ω