Abstract

The use and analysis of solid Fabry–Perot etalons for interferometry and laser control are discussed and supported with experimental data. Low angle scattering is found to be an important factor influencing finesse and peak transmission. Thermal tuning sensitivity and wedge-angle control with thermal gradients are analyzed and illustrated. Control of laser oscillations using a solid-state etalon as a laser cavity end mirror is discussed. The use of the solid etalon as an optical cavity coupler is applied to the problem of sideband energy removal from an internally modulated laser.

© 1966 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principles of Optics (The Macmillan Company, New York, 1964), 2nd ed.
  2. C. Dufour, R. Picca, Rev. Opt. 24, 19 (1945).
  3. R. Chabbal, J. Phys. Radium 19, 295 (1958).
    [CrossRef]
  4. V. N. Del Piano, A. F. Quesada, Appl. Opt. 4, 1386 (1965).
    [CrossRef]
  5. H. W. Moos, G. F. Imbusch, L. F. Mollenauer, A. L. Schawlow, Appl. Opt. 2, 817 (1963).
    [CrossRef]
  6. Brochure, SiO2 (Engelhard Industries, Inc., Amersil Quartz Division, Hillsdale, N.J., 1963).
  7. A. Yariv, in Quantum Electronics III, P. Grivet, N. Bloembergen, Eds. (Columbia University Press, New York, 1964), Vol. 2, pp. 1055–1064.
  8. D. G. Peterson, A. Yariv, Appl. Phys. Letters 5, 184 (1964).
    [CrossRef]
  9. A. Yariv, J. Appl. Phys. 36, 388 (1965); A. Yariv, Trans. IEEE QE-2, 30 (1966).
    [CrossRef]
  10. D. G. Peterson, A. Yariv, Technical Brief for Research on Single Frequency Output Gas Lasers, Lockheed Missiles & Space Company, Palo Alto, Calif., 1965 (unpublished).
  11. S. E. Harris, B. J. McMurtry, Appl. Phys. Letters 7, 289 (1965).
    [CrossRef]

1965 (3)

A. Yariv, J. Appl. Phys. 36, 388 (1965); A. Yariv, Trans. IEEE QE-2, 30 (1966).
[CrossRef]

S. E. Harris, B. J. McMurtry, Appl. Phys. Letters 7, 289 (1965).
[CrossRef]

V. N. Del Piano, A. F. Quesada, Appl. Opt. 4, 1386 (1965).
[CrossRef]

1964 (1)

D. G. Peterson, A. Yariv, Appl. Phys. Letters 5, 184 (1964).
[CrossRef]

1963 (1)

1958 (1)

R. Chabbal, J. Phys. Radium 19, 295 (1958).
[CrossRef]

1945 (1)

C. Dufour, R. Picca, Rev. Opt. 24, 19 (1945).

Born, M.

M. Born, E. Wolf, Principles of Optics (The Macmillan Company, New York, 1964), 2nd ed.

Chabbal, R.

R. Chabbal, J. Phys. Radium 19, 295 (1958).
[CrossRef]

Del Piano, V. N.

Dufour, C.

C. Dufour, R. Picca, Rev. Opt. 24, 19 (1945).

Harris, S. E.

S. E. Harris, B. J. McMurtry, Appl. Phys. Letters 7, 289 (1965).
[CrossRef]

Imbusch, G. F.

McMurtry, B. J.

S. E. Harris, B. J. McMurtry, Appl. Phys. Letters 7, 289 (1965).
[CrossRef]

Mollenauer, L. F.

Moos, H. W.

Peterson, D. G.

D. G. Peterson, A. Yariv, Appl. Phys. Letters 5, 184 (1964).
[CrossRef]

D. G. Peterson, A. Yariv, Technical Brief for Research on Single Frequency Output Gas Lasers, Lockheed Missiles & Space Company, Palo Alto, Calif., 1965 (unpublished).

Picca, R.

C. Dufour, R. Picca, Rev. Opt. 24, 19 (1945).

Quesada, A. F.

Schawlow, A. L.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (The Macmillan Company, New York, 1964), 2nd ed.

Yariv, A.

A. Yariv, J. Appl. Phys. 36, 388 (1965); A. Yariv, Trans. IEEE QE-2, 30 (1966).
[CrossRef]

D. G. Peterson, A. Yariv, Appl. Phys. Letters 5, 184 (1964).
[CrossRef]

D. G. Peterson, A. Yariv, Technical Brief for Research on Single Frequency Output Gas Lasers, Lockheed Missiles & Space Company, Palo Alto, Calif., 1965 (unpublished).

A. Yariv, in Quantum Electronics III, P. Grivet, N. Bloembergen, Eds. (Columbia University Press, New York, 1964), Vol. 2, pp. 1055–1064.

Appl. Opt. (2)

Appl. Phys. Letters (2)

D. G. Peterson, A. Yariv, Appl. Phys. Letters 5, 184 (1964).
[CrossRef]

S. E. Harris, B. J. McMurtry, Appl. Phys. Letters 7, 289 (1965).
[CrossRef]

J. Appl. Phys. (1)

A. Yariv, J. Appl. Phys. 36, 388 (1965); A. Yariv, Trans. IEEE QE-2, 30 (1966).
[CrossRef]

J. Phys. Radium (1)

R. Chabbal, J. Phys. Radium 19, 295 (1958).
[CrossRef]

Rev. Opt. (1)

C. Dufour, R. Picca, Rev. Opt. 24, 19 (1945).

Other (4)

M. Born, E. Wolf, Principles of Optics (The Macmillan Company, New York, 1964), 2nd ed.

Brochure, SiO2 (Engelhard Industries, Inc., Amersil Quartz Division, Hillsdale, N.J., 1963).

A. Yariv, in Quantum Electronics III, P. Grivet, N. Bloembergen, Eds. (Columbia University Press, New York, 1964), Vol. 2, pp. 1055–1064.

D. G. Peterson, A. Yariv, Technical Brief for Research on Single Frequency Output Gas Lasers, Lockheed Missiles & Space Company, Palo Alto, Calif., 1965 (unpublished).

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Figures (12)

Fig. 1
Fig. 1

Photograph of the transmitted light pattern at the output surface of a solid-state etalon when illuminated with a well-collimated laser beam (6328 Å) at near normal incidence. The single fringe indicates a wedge angle of approximately 3 sec of arc.

Fig. 2
Fig. 2

Diagram of the experimental set up for studying thermal transients in solid state etalons.

Fig. 3
Fig. 3

Transient transmission fringe patterns caused by a thermal step applied to cylindrical surface of a solid-state etalon. (a) The residual wedge angle fringe before application of thermal step. (b) The wedge angle begins to curve shortly after application of step. (c) The wedge angle fringe has been almost completely overcome by the transient. The concentric fringes of several orders are centered very near the center of the SSE. (d) and (e) The transient fringes decay. (f) All fringes disappear. (g) A new steady state at a higher temperature has been reached, and a single straight fringe due to the residual wedge angle is again seen.

Fig. 4
Fig. 4

The transmission characteristics (τ vs ν) of a solid state etalon. The full vertical scale corresponds to 100% transmission. The intermode spacing on the horizontal scale is approximately 18 Gc/sec.

Fig. 5
Fig. 5

Distribution of intensity in the far field of a solid state etalon obtained by masking the central spot and focusing the scattered energy at the output on the film plane. The first ten rings correspond to scattering into a half one-angle of approximately 1°.

Fig. 6
Fig. 6

Photograph of double chamber heat-exchanging mount used to apply thermal gradients to solid state etalons for wedge angle control.

Fig. 7
Fig. 7

Cutaway view of the double chamber heat-exchanging mount used in wedge angle control experiment.

Fig. 8
Fig. 8

Transmission pattern of solid-state etalon with thermal-gradient wedge-angle control. (a) Residual single fringe with no wedge angle correction applied. (b) Increased wedge angle caused by approximately 12°C temperature gradient. (c) Same fringe pattern as in (b) taken 1 min later shows a slight shift downward indicating a small average temperature change. (d) Decreased wedge angle caused by approximately 2°C gradient opposite in direction to that applied in (b) and (c). (e) Same single fringe as in (d) taken 1 min later shows a slight shift upward.

Fig. 9
Fig. 9

Relative power output from the two ends of a He–Ne laser controlled with a solid state etalon used as a variable reflectivity end mirror. (a) Power output from solid state etalon mirror. (b) Power output from high reflectivity mirror on the same time scale indicates what happens to the internal cavity energy.

Fig. 10
Fig. 10

(a) Diagram of the experimental set up for performing frequency translation within a laser and frequency selective output coupling. (b) The relative positions of the laser oscillation frequency f0, the modulation sideband frequencies f0 ± fm, and the solid state etalon passbands.

Fig. 11
Fig. 11

Output of internally modulated laser analyzed by a Fabry–Perot interferometer with intermode spacing of 18 Gc sec (a) Fringe system corresponding to nonmodulated oscillation at 6328 Å. (b) Fringe system with internal modulation at 8.9 Gc sec The new intermediate fringes indicate the presence of laser output power shifted by 8.9 Gc sec from the laser oscillation frequency.

Fig. 12
Fig. 12

The off-axis transmission characteristics of a solid-state etalon when illuminated by beams of finite size. Full vertical scale is 100% transmission. The off-axis angle is zero at the midpoint between the maxima and increases symmetrically by approximately 1° per major horizontal division. The etalon length is 6 mm. (a) Incident beam diameter D = 3.2 mm. (b) Incident beam diameter D = 1.4 mm.

Equations (10)

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2 L = m λ 0 / n ,
τ = I trans . I incid . = 1 1 + [ 4 R / ( 1 - R ) 2 ] sin 2 ( 2 π n L cos θ / λ 0 ) ,
( Δ ν ) 1 2 = c 0 ( 1 - R ) / 2 π n L R 1 2 ,
f = π R 1 2 / ( 1 - R ) .
I trans I incid = ( 1 - R - γ 1 - R e - σ ) 2 1 1 - [ 4 R e - σ / ( 1 - R e - σ ) 2 ] sin 2 ( δ / 2 ) ,
τ max = 1 - { ( γ + R σ ) / [ ( 1 - R ) + ( γ + R σ ) ] } ,
f = π [ R - ( γ + R σ ) ] 1 2 / [ ( 1 - R ) + ( γ + R σ ) ] ,
d ( m ) = 2 n L λ 0 ( 1 L d L d T + 1 d n n d T ) d T .
1 L d L d T = 0.6 × 10 - 6 ° C , 1 d n n d T = 7 × 10 - 6 ° C .
d m / d T = 0.41 fringe / ° C ,

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