Abstract

Part IV of this series gave two procedures (termed double-pass procedures) for synthesizing birefringent networks containing only half the number of crystals normally required. These techniques were applicable when the desired amplitude transmittance of the network satisfied certain restrictions. This paper describes additional double-pass procedures which apply to a substantially larger class of amplitude transmittances.

© 1967 Optical Society of America

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References

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  1. E. O. Ammann, J. Opt. Soc. Am. 56, 952 (1966).
    [Crossref]
  2. S. E. Harris, E. O. Ammann, and I. C. Chang, J. Opt. Soc. Am. 54, 1267 (1964).
    [Crossref]
  3. E. O. Ammann and J. M. Yarborough, J. Opt. Soc. Am. 56, 1746 (1966).
    [Crossref]
  4. R. C. Jones, J. Opt. Soc. Am. 31, 488 (1941).
    [Crossref]
  5. E. O. Ammann, J. Opt. Soc. Am. 56, 943 (1966).
    [Crossref]

1966 (3)

1964 (1)

1941 (1)

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Figures (4)

Fig. 1
Fig. 1

Basic configuration of birefringent network (4 stages) obtained from the synthesis procedure of Part I. F and S denote the “fast” and “slow” axes of the birefringent crystals.

Fig. 2
Fig. 2

Basic configuration of birefringent network (4 stages) obtained from the synthesis procedure of Part V.

Fig. 3
Fig. 3

Single stage of the network of Fig. 2. Components are a birefringent crystal and an optical compensator.

Fig. 4
Fig. 4

Network symmetry which is required in order for methods A and B (of Part IV of this series) to be applicable. (a) Lossless network without compensators, and (b) lossless network with compensators.

Tables (4)

Tables Icon

Table I Network symmetry which results for n = 9 when the (real) Ci are chosen to satisfy C0 = C9, C1 = C8, C2 = C7, C3 = C6, and C4 = C5.

Tables Icon

Table II Network which is equivalent to that listed in Table I.

Tables Icon

Table III Network symmetry which results for n = 9 when the (complex) Ci are chosen to satisfy C0 = C9*, C1 = C8*, C2 = C7*, C3 = C6*, and C4 = C5*.

Tables Icon

Table IV Network equivalent to that listed in Table III.

Equations (9)

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θ 1 = ϕ 1 , θ 2 = ϕ 2 - ϕ 1 , θ 3 = ϕ 3 - ϕ 2 ,                     θ n = ϕ n - ϕ n - 1 ,             and θ p = ϕ p - ϕ n .
E = M S ( - θ j ) E ,
( E u E v ) = ( exp ( - i b j ) exp ( - i a ω ) 0 0 1 ) ( cos θ j sin θ j - sin θ j cos θ j ) ( E u E v ) = ( exp ( - i b j ) exp ( - i a ω ) cos θ j exp ( - i b j ) exp ( - i a ω ) sin θ j - sin θ j cos θ j ) ( E u E v ) .
( A j B j C j D j ) .
( - A j B j - C j D j ) .
( - A j - 1 - B j - 1 C j - 1 D j - 1 ) .
( - A j B j - C j D j ) ( - A j - 1 - B j - 1 C j - 1 D j - 1 ) = ( A j A j - 1 + B j C j - 1 A j B j - 1 + B j D j - 1 C j A j - 1 + D j C j - 1 C j B j - 1 + D j D j - 1 ) .
C ( ω ) = C 0 + C 1 exp ( - i a ω ) + C 2 exp ( - i 2 a ω ) + + C n exp ( - i n a ω ) .
K ( ω ) = C 0 exp ( i ( n / 2 ) a ω ) + C 1 exp ( i [ ( n / 2 ) - 1 ] a ω ) + + C n - 1 exp ( - i [ ( n / 2 ) - 1 ] a ω ) + C n exp [ - i ( n / 2 ) a ω ] .