Abstract

A simple technique based on a Fizeau interferometer to measure the absolute phase shift on reflection for a Fabry–Perot interferometer dielectric stack mirror is described. Excellent agreement between the measured and predicted phase shift on reflection was found. Also described are the salient features of low-order Fabry–Perot interferometers and the demonstration of a near ideal low-order (1–10) Fabry–Perot interferometer through minimizing the phase dispersion on reflection of the dielectric stack. This near ideal performance of a low-order Fabry–Perot interferometer should enable several applications such as compact spectral imagers for solid and gas detection. The large free spectral range of such systems combined with an active control system will also allow simple interactive tuning of wavelength agile laser sources such as CO2 lasers, external cavity diode lasers, and optical parametric oscillators.

© 1997 Optical Society of America

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References

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  1. H. J. Kramer, Observation of the Earth and its Environment, 3rd ed. (Springer-Verlag, Berlin, 1994).
    [CrossRef]
  2. J. T. Knudtson, D. S. Levy, K. C. Herr, “Electronically tunable, first-order Fabry–Perot infrared filter,” Opt. Eng. 35, 2313–2320 (1996).
    [CrossRef]
  3. G. Hernandez, Fabry–Perot Interferometers (Cambridge U. Press, Cambridge, U.K., 1988).
  4. J. M. Vaughn, The Fabry–Perot Interferometer (Hilger, Philadephia, 1989).
  5. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1986).
  6. P. D. Atherton, N. K. Reay, J. Ring, T. R. Hicks, “Tunable Fabry–Perot filters,” Opt. Eng. 20, 806–814 (1981).
    [CrossRef]
  7. Y. R. Shen, Nonlinear Infrared Generation, Vol. 16 of Topics in Applied Physics (Springer-Verlag, New York, 1977).
    [CrossRef]

1996 (1)

J. T. Knudtson, D. S. Levy, K. C. Herr, “Electronically tunable, first-order Fabry–Perot infrared filter,” Opt. Eng. 35, 2313–2320 (1996).
[CrossRef]

1981 (1)

P. D. Atherton, N. K. Reay, J. Ring, T. R. Hicks, “Tunable Fabry–Perot filters,” Opt. Eng. 20, 806–814 (1981).
[CrossRef]

Atherton, P. D.

P. D. Atherton, N. K. Reay, J. Ring, T. R. Hicks, “Tunable Fabry–Perot filters,” Opt. Eng. 20, 806–814 (1981).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1986).

Hernandez, G.

G. Hernandez, Fabry–Perot Interferometers (Cambridge U. Press, Cambridge, U.K., 1988).

Herr, K. C.

J. T. Knudtson, D. S. Levy, K. C. Herr, “Electronically tunable, first-order Fabry–Perot infrared filter,” Opt. Eng. 35, 2313–2320 (1996).
[CrossRef]

Hicks, T. R.

P. D. Atherton, N. K. Reay, J. Ring, T. R. Hicks, “Tunable Fabry–Perot filters,” Opt. Eng. 20, 806–814 (1981).
[CrossRef]

Knudtson, J. T.

J. T. Knudtson, D. S. Levy, K. C. Herr, “Electronically tunable, first-order Fabry–Perot infrared filter,” Opt. Eng. 35, 2313–2320 (1996).
[CrossRef]

Kramer, H. J.

H. J. Kramer, Observation of the Earth and its Environment, 3rd ed. (Springer-Verlag, Berlin, 1994).
[CrossRef]

Levy, D. S.

J. T. Knudtson, D. S. Levy, K. C. Herr, “Electronically tunable, first-order Fabry–Perot infrared filter,” Opt. Eng. 35, 2313–2320 (1996).
[CrossRef]

Reay, N. K.

P. D. Atherton, N. K. Reay, J. Ring, T. R. Hicks, “Tunable Fabry–Perot filters,” Opt. Eng. 20, 806–814 (1981).
[CrossRef]

Ring, J.

P. D. Atherton, N. K. Reay, J. Ring, T. R. Hicks, “Tunable Fabry–Perot filters,” Opt. Eng. 20, 806–814 (1981).
[CrossRef]

Shen, Y. R.

Y. R. Shen, Nonlinear Infrared Generation, Vol. 16 of Topics in Applied Physics (Springer-Verlag, New York, 1977).
[CrossRef]

Vaughn, J. M.

J. M. Vaughn, The Fabry–Perot Interferometer (Hilger, Philadephia, 1989).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1986).

Opt. Eng. (2)

J. T. Knudtson, D. S. Levy, K. C. Herr, “Electronically tunable, first-order Fabry–Perot infrared filter,” Opt. Eng. 35, 2313–2320 (1996).
[CrossRef]

P. D. Atherton, N. K. Reay, J. Ring, T. R. Hicks, “Tunable Fabry–Perot filters,” Opt. Eng. 20, 806–814 (1981).
[CrossRef]

Other (5)

Y. R. Shen, Nonlinear Infrared Generation, Vol. 16 of Topics in Applied Physics (Springer-Verlag, New York, 1977).
[CrossRef]

H. J. Kramer, Observation of the Earth and its Environment, 3rd ed. (Springer-Verlag, Berlin, 1994).
[CrossRef]

G. Hernandez, Fabry–Perot Interferometers (Cambridge U. Press, Cambridge, U.K., 1988).

J. M. Vaughn, The Fabry–Perot Interferometer (Hilger, Philadephia, 1989).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1986).

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Figures (6)

Fig. 1
Fig. 1

Phase shift upon reflection for various coatings. The dashed line is an ideal dielectric mirror. The dotted line is a conventional mirror. The solid line is the Northrop Grumman mirror designed for low phase dispersion.

Fig. 2
Fig. 2

Theoretical transmission spectra for a Fabry–Perot interferometer constructed of mirrors with phase-shift properties from Fig. 1. The effective gap spacing is 6.80 µm. The dotted line is the spectrum obtained with a conventional mirror with no phase control. The dashed line is the spectrum obtained with mirrors with ideal phase-shift characteristics. The solid line is the spectrum obtained with our mirrors. Note that the FSR with the ideal mirrors and the Northrop Grumman mirrors are very similar, whereas the conventional mirror FSR is smaller.

Fig. 3
Fig. 3

Schematic of symmetric/asymmetric Fizeau interferometer.

Fig. 4
Fig. 4

Transmitted spectrum of the ZnSe–dielectric stack portion of the Fizeau interferometer, d = 19.5 ± 0.1 µm. The variation in peak heights is a systematic effect in the apparatus.

Fig. 5
Fig. 5

Phase shift on reflection as a function of frequency for four ZnSe–dielectric stack spectra. The four spectra were taken at different locations on the Fizeau interferometer. The phase-shift calculations were made with distances extrapolated from the measurements on the ZnSe–ZnSe portion of the interferometer. The solid line is the theoretical prediction of the phase variation of the dielectric stack based on the specified stack layers. Our measurements agree with the theoretical prediction to within our systematic uncertainty of the exact dielectric stack thickness.

Fig. 6
Fig. 6

Transmitted spectrum through a Fabry–Perot interferometer constructed of our phase-shift controlled mirrors. A spectrum taken through the edge of the Fabry–Perot interferometer was used to determine the spacing between the mirrors, d = 10.3 ± 0.2 µm. The solid curve is an Airy function incorporating the theoretical phase shift of our mirrors as well as nonideal transmission. The exact distance used for the Airy function is d = 10.242 µm.

Equations (8)

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Aσ=T1T21-R1 R2211+4R1 R21-R1 R22 sin22πμdσ cos θ-ϕ1σ2-ϕ2σ2,
δ=2πμdσ cos θ-ϕ1σ2-ϕ2σ2,
ϕσ=ϕ0+dϕdσσ=σ0σ+,
δ=2πμd cos θ-12dϕ1dσ-12dϕ2dσσ-ϕ102-ϕ202,
FSR=12d-12πdϕ1dσ-12πdϕ2dσ,
Δσ=FSRF,
F=πR1R241-R1R2.
δ=2πμdσ cos θ-ϕσFP2-π2,

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