Abstract

Active phase matching of multiline HF laser beams by means of a phase-locked Mach-Zehnder interferometer was demonstrated by locking the interferometer to the central interference fringe at zero optical path length difference. The central fringe could be found by varying the spectral content of the input beam. Laser amplification in one leg of the interferometer decreased fringe visibility without adversely affecting locking. Single-line fringe patterns produced by an array spectrometer (while the interferometer was operated in its scanning mode) were analyzed to show that no significant dispersion occurred in the amplifier. The techniques developed have potential for measuring dispersion mismatch between larger parallel amplifiers. These experiments demonstrated in principle that a number of multiline HF amplified beams can be recombined and phase-matched to produce a high beam quality output beam.

© 1983 Optical Society of America

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References

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  1. R. W. F. Gross, J. G. Coffer, R. A. Chodzko, E. B. Turner, “Interference Patterns Produced by a Mach-Zehnder Interferometer and a Multiline HF Laser,” TR-0080(5764)-2, Aerospace Corp., El Segundo, Calif. 90245.
  2. W. R. Warren, “The Parallel Internal-Master-Oscillator Power Amplifier for Phase Matching the Output Beams of Multiline Lasers,” TR-0078(9990)-6, Aerospace Corp., El Segundo, Calif. 90245.
  3. A. A. Michelson, Light Waves and Their Uses (The University of Chicago Press, Chicago, 1907).
  4. T. R. O’Meara, J. Opt. Soc. Am. 67, 306 (1977).
    [CrossRef]
  5. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).
  6. R. W. F. Gross, R. Chodzko, E. B. Turner, J. G. Coffer, “Measurements of the Anomalous Dispersion of HF in Absorption,” TR-0079(4764)-2.
  7. D. J. Spencer, J. A. Beggs, H. Mirels, J. Appl. Phys. 48, 1206 (1977).
    [CrossRef]
  8. R. A. Chodzko, D. J. Spencer, H. Mirels, S. B. Mason, D. H. Ross, “Zero-Power-Gain Measurements in CW HF(DF) Laser by Means of Fast-Scan Technique,” IEEE J. Quantum Electron. QE-12, 660 (1976).
    [CrossRef]
  9. R. L. Varwig, C. P. Wang, The Aerospace Corp.; private communication.

1977 (2)

T. R. O’Meara, J. Opt. Soc. Am. 67, 306 (1977).
[CrossRef]

D. J. Spencer, J. A. Beggs, H. Mirels, J. Appl. Phys. 48, 1206 (1977).
[CrossRef]

1976 (1)

R. A. Chodzko, D. J. Spencer, H. Mirels, S. B. Mason, D. H. Ross, “Zero-Power-Gain Measurements in CW HF(DF) Laser by Means of Fast-Scan Technique,” IEEE J. Quantum Electron. QE-12, 660 (1976).
[CrossRef]

Beggs, J. A.

D. J. Spencer, J. A. Beggs, H. Mirels, J. Appl. Phys. 48, 1206 (1977).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

Chodzko, R.

R. W. F. Gross, R. Chodzko, E. B. Turner, J. G. Coffer, “Measurements of the Anomalous Dispersion of HF in Absorption,” TR-0079(4764)-2.

Chodzko, R. A.

R. A. Chodzko, D. J. Spencer, H. Mirels, S. B. Mason, D. H. Ross, “Zero-Power-Gain Measurements in CW HF(DF) Laser by Means of Fast-Scan Technique,” IEEE J. Quantum Electron. QE-12, 660 (1976).
[CrossRef]

R. W. F. Gross, J. G. Coffer, R. A. Chodzko, E. B. Turner, “Interference Patterns Produced by a Mach-Zehnder Interferometer and a Multiline HF Laser,” TR-0080(5764)-2, Aerospace Corp., El Segundo, Calif. 90245.

Coffer, J. G.

R. W. F. Gross, J. G. Coffer, R. A. Chodzko, E. B. Turner, “Interference Patterns Produced by a Mach-Zehnder Interferometer and a Multiline HF Laser,” TR-0080(5764)-2, Aerospace Corp., El Segundo, Calif. 90245.

R. W. F. Gross, R. Chodzko, E. B. Turner, J. G. Coffer, “Measurements of the Anomalous Dispersion of HF in Absorption,” TR-0079(4764)-2.

Gross, R. W. F.

R. W. F. Gross, J. G. Coffer, R. A. Chodzko, E. B. Turner, “Interference Patterns Produced by a Mach-Zehnder Interferometer and a Multiline HF Laser,” TR-0080(5764)-2, Aerospace Corp., El Segundo, Calif. 90245.

R. W. F. Gross, R. Chodzko, E. B. Turner, J. G. Coffer, “Measurements of the Anomalous Dispersion of HF in Absorption,” TR-0079(4764)-2.

Mason, S. B.

R. A. Chodzko, D. J. Spencer, H. Mirels, S. B. Mason, D. H. Ross, “Zero-Power-Gain Measurements in CW HF(DF) Laser by Means of Fast-Scan Technique,” IEEE J. Quantum Electron. QE-12, 660 (1976).
[CrossRef]

Michelson, A. A.

A. A. Michelson, Light Waves and Their Uses (The University of Chicago Press, Chicago, 1907).

Mirels, H.

D. J. Spencer, J. A. Beggs, H. Mirels, J. Appl. Phys. 48, 1206 (1977).
[CrossRef]

R. A. Chodzko, D. J. Spencer, H. Mirels, S. B. Mason, D. H. Ross, “Zero-Power-Gain Measurements in CW HF(DF) Laser by Means of Fast-Scan Technique,” IEEE J. Quantum Electron. QE-12, 660 (1976).
[CrossRef]

O’Meara, T. R.

Ross, D. H.

R. A. Chodzko, D. J. Spencer, H. Mirels, S. B. Mason, D. H. Ross, “Zero-Power-Gain Measurements in CW HF(DF) Laser by Means of Fast-Scan Technique,” IEEE J. Quantum Electron. QE-12, 660 (1976).
[CrossRef]

Spencer, D. J.

D. J. Spencer, J. A. Beggs, H. Mirels, J. Appl. Phys. 48, 1206 (1977).
[CrossRef]

R. A. Chodzko, D. J. Spencer, H. Mirels, S. B. Mason, D. H. Ross, “Zero-Power-Gain Measurements in CW HF(DF) Laser by Means of Fast-Scan Technique,” IEEE J. Quantum Electron. QE-12, 660 (1976).
[CrossRef]

Turner, E. B.

R. W. F. Gross, R. Chodzko, E. B. Turner, J. G. Coffer, “Measurements of the Anomalous Dispersion of HF in Absorption,” TR-0079(4764)-2.

R. W. F. Gross, J. G. Coffer, R. A. Chodzko, E. B. Turner, “Interference Patterns Produced by a Mach-Zehnder Interferometer and a Multiline HF Laser,” TR-0080(5764)-2, Aerospace Corp., El Segundo, Calif. 90245.

Varwig, R. L.

R. L. Varwig, C. P. Wang, The Aerospace Corp.; private communication.

Wang, C. P.

R. L. Varwig, C. P. Wang, The Aerospace Corp.; private communication.

Warren, W. R.

W. R. Warren, “The Parallel Internal-Master-Oscillator Power Amplifier for Phase Matching the Output Beams of Multiline Lasers,” TR-0078(9990)-6, Aerospace Corp., El Segundo, Calif. 90245.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

IEEE J. Quantum Electron. (1)

R. A. Chodzko, D. J. Spencer, H. Mirels, S. B. Mason, D. H. Ross, “Zero-Power-Gain Measurements in CW HF(DF) Laser by Means of Fast-Scan Technique,” IEEE J. Quantum Electron. QE-12, 660 (1976).
[CrossRef]

J. Appl. Phys. (1)

D. J. Spencer, J. A. Beggs, H. Mirels, J. Appl. Phys. 48, 1206 (1977).
[CrossRef]

J. Opt. Soc. Am. (1)

Other (6)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

R. W. F. Gross, R. Chodzko, E. B. Turner, J. G. Coffer, “Measurements of the Anomalous Dispersion of HF in Absorption,” TR-0079(4764)-2.

R. W. F. Gross, J. G. Coffer, R. A. Chodzko, E. B. Turner, “Interference Patterns Produced by a Mach-Zehnder Interferometer and a Multiline HF Laser,” TR-0080(5764)-2, Aerospace Corp., El Segundo, Calif. 90245.

W. R. Warren, “The Parallel Internal-Master-Oscillator Power Amplifier for Phase Matching the Output Beams of Multiline Lasers,” TR-0078(9990)-6, Aerospace Corp., El Segundo, Calif. 90245.

A. A. Michelson, Light Waves and Their Uses (The University of Chicago Press, Chicago, 1907).

R. L. Varwig, C. P. Wang, The Aerospace Corp.; private communication.

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Figures (8)

Fig. 1
Fig. 1

Experimental equipment.

Fig. 2
Fig. 2

(a) Multiline fringe intensities I+(g = 0) and I(g = 0) locking without gain. Relative intensity is measured upward from base lines (I = 0). (b) Multiline fringe intensities I+(g) and I(g) locking with gain (amplifier on). Base lines are the same as in (a).

Fig. 3
Fig. 3

(a) Chopping of control loop and attainment of locking; (b) locking on two different fringes.

Fig. 4
Fig. 4

(a) Induced line switching analyzed; (b) effect of ILS at zero OPD; (c) effect of ILS off zero OPD.

Fig. 5
Fig. 5

Comparison of rotating grating with array spectrometer.

Fig. 6
Fig. 6

Scan of multiline interference fringes through zero OPD.

Fig. 7
Fig. 7

Scan of multiline interference fringes through zero OPD.

Fig. 8
Fig. 8

Scan of multiline interference fringes.

Tables (1)

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Table I Calibration Coefficients CI

Equations (17)

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I + = I 1 + I 2 + 2 I 1 I 2 cos δ + .
δ + = ( 2 π Z ) / λ ,
I + = 1 2 I ( 1 + cos 2 π Z λ ) .
δ = δ + + π .
I = 1 2 I ( 1 cos 2 π Z λ ) .
I ± = 1 2 I ( 1 ± cos 2 π Z λ ) .
I 1 ( g ) = I 1 ( 0 ) exp ( g L ) = 1 4 I exp ( g L ) .
I ± ( g ) = 1 4 I [ 1 + exp ( g L ) ± 2 exp ( g L / 2 ) cos 2 π Z λ ] .
I ± ( g ) max = 1 4 I [ 1 + exp ( g L / 2 ) ] 2 .
I ( g ) min = 1 4 I [ 1 exp ( g L / 2 ) ] 2 .
g = 2 L ln I max + I min I max I min ,
V = I max I min I max + I min .
I ± = i 1 2 I i ( 1 ± cos 2 π Z i λ i ) .
I ± ( g i , n i ) = 1 4 i I i { 1 + exp ( g i L ) ± 2 exp ( g i L / 2 ) cos 2 π λ i [ X + ( n i 1 ) L ] } .
I ± ( g i ) = 1 4 i I i [ 1 + exp ( g i L ) ± 2 exp ( g i L / 2 ) cos 2 π Z λ i ] .
I ± ( g i ) max = 1 4 i I i [ 1 + exp ( g i L ) ± 2 exp ( g i L / 2 ) ] .
V ( Z = 0 ) = Σ I max Σ I min Σ I max + Σ I min ,

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