Abstract

Procedures have recently been given by Harris et al. and by Ammann for synthesizing single-pass and double-pass birefringent networks having arbitrary transmittance-vs-frequency characteristics. This paper describes the results of experiments which were performed on these two types of optical networks. A three-stage network was tested in the single-pass experiments, while three-, five-, and seven-stage networks were used in the double-pass experiments. Each stage of these networks consisted of a calcite crystal 2 cm in length followed by a quartz compensator. The transmittance characteristics of the networks were obtained by measuring network transmittance (at a fixed optical frequency) as a function of network temperature. Since the phase difference between fast- and slow-axis light components passing through a calcite crystal has the same functional dependence upon temperature as upon optical frequency, the transmittance-vs-temperature characteristic of a birefringent network will be the same as the transmittance-vs-frequency characteristic. This gives a very convenient, high-resolution method of measuring the transmittance of birefringent networks. The measured transmittances are shown together with values predicted by theory. The excellent agreement obtained serves both as a verification of the synthesis procedures and as a demonstration of the utility of the measurement technique.

© 1968 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 and I. C. Chang, J. Opt. Soc. Am. 55, 835 (1965).
    [Crossref]
  3. E. O. Ammann, J. Opt. Soc. Am. 56, 943 (1966).
    [Crossref]
  4. E. O. Ammann, J. Opt. Soc. Am. 56, 952 (1966).
    [Crossref]
  5. E. O. Ammann and J. M. Yarborough, J. Opt. Soc. Am. 56, 1746 (1966).
    [Crossref]
  6. E. O. Ammann and J. M. Yarborough, J. Opt. Soc. Am. 57, 349 (1967).
    [Crossref]
  7. J. W. Evans, J. Opt. Soc. Am. 39, 229 (1949).
    [Crossref]
  8. J. W. Evans, J. Opt. Soc. Am. 48, 142 (1958).
    [Crossref]
  9. J. W. Evans, Appl. Opt. 2, 193 (1963).
    [Crossref]
  10. I. Solc, Czech. J. Phys. 9, 237 (1959).
    [Crossref]
  11. R. Targ, L. M. Osterink, and J. M. French, Proc. IEEE 55, 1185 (1967).
    [Crossref]

1967 (2)

E. O. Ammann and J. M. Yarborough, J. Opt. Soc. Am. 57, 349 (1967).
[Crossref]

R. Targ, L. M. Osterink, and J. M. French, Proc. IEEE 55, 1185 (1967).
[Crossref]

1966 (3)

1965 (1)

1964 (1)

1963 (1)

1959 (1)

I. Solc, Czech. J. Phys. 9, 237 (1959).
[Crossref]

1958 (1)

1949 (1)

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Figures (13)

Fig. 1
Fig. 1

Basic configuration of the single-pass birefringent network (4 stages) obtained from the synthesis procedure of Ref. 1. F and S denote the fast and slow axes of the birefringent crystals.

Fig. 2
Fig. 2

Basic configuration of the double-pass birefringent network obtained from the synthesis procedure of Ref. 4.

Fig. 3
Fig. 3

(a) End view of calcite crystal holder. (b) Holders in which the crystals are mounted.

Fig. 4
Fig. 4

Schematic of the experimental setup used for the single-pass birefringent-network experiments.

Fig. 5
Fig. 5

Schematic of the experimental setup used for the double-pass birefringent-network experiments.

Fig. 6
Fig. 6

Experimental setup used for the single-pass-network experiments.

Fig. 7
Fig. 7

Ideal amplitude transmittances (solid curves) and corresponding power transmittances (dotted curves) used for the birefringent-network experiments: (a) triangular wave, (b) rectangular wave, and (c) parabolic wave. The amplitude-transmittance and power-transmittance curves for (b) are identical.

Fig. 8
Fig. 8

Measured and calculated results for a single-pass birefringent network with n = 3. The figure shows transmitted optical power-vs-network temperature: top, triangular wave; middle, rectangular wave; bottom, parabolic wave.

Fig. 9
Fig. 9

Measured and calculated results for a double-pass birefringent network with n = 3. The figure shows transmitted optical power-vs-network temperature: top, triangular wave; middle, rectangular wave; bottom, parabolic wave.

Fig. 10
Fig. 10

Measured and calculated results for a double-pass birefringent network with n = 5. The figure shows transmitted optical power-vs-network temperature: top, triangular wave; middle, rectangular wave; bottom, parabolic wave.

Fig. 11
Fig. 11

Measured and calculated results for a double-pass birefringent network with n = 7. The figure shows transmitted optical power vs network temperature: top, triangular wave; middle, rectangular wave; bottom, parabolic wave.

Fig. 12
Fig. 12

Ideal characteristic used for n = 7 double-pass bandpass filter.

Fig. 13
Fig. 13

Measured and calculated results for the n = 7 double-pass network designed to approximate the ideal characteristic of Fig. 12.

Tables (1)

Tables Icon

Table I Rotation angles used in single-pass and double-pass birefringent-network experiments.

Equations (2)

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C ( ω ) = C 0 + C 1 e i a ω + C 2 e i 2 a ω + + C n e i n a ω .
Δ φ = ω L ( η F η S ) / c = ω L Δ η / c ,