Abstract

The effectiveness of a reverse wave suppressor (RWS) mirror in an unstable ring resonator has been investigated theoretically and experimentally for the case of an inhomogeneously broadened gain medium. The theory indicates that the RWS mirror is effective when (δνh)2 ≪ 1, where Δνh is the characteristic homogeneous linewidth of the gain medium and δ = Δu(ν0/c) is a measure of the separation between competing forward and reverse waves. Unstable linear ring resonator experiments were conducted using a continuous wave HF laser. Successful suppression of the reverse wave was achieved. In these tests the ratio of forward to reverse power had an average value of 41. An unstable annular ring resonator was investigated using a pulsed CO2 laser. Reverse wave suppression was achieved when the resonator and RWS mirror were in good alignment. Suppression effectiveness and beam quality were degraded when the RWS mirror was tilted.

© 1984 Optical Society of America

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References

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  1. F. Aronowitz, R. J. Collins, “Mode Coupling Due to Backscattering in a He–Ne Travelling Wave Ring Laser,” Appl. Phys. Lett. 9, 55 (1July1966).
    [Crossref]
  2. F. R. Faxvog, “Modes of a Unidirectional Ring Laser,” Opt. Lett. 5, 285 (1980).
    [Crossref] [PubMed]
  3. F. R. Faxvog, A. D. Gara, “Traveling-Wave Gas Laser,” Appl. Phys. Lett. 25, 306 (1974).
    [Crossref]
  4. A. H. Paxton, “A Preliminary Look at the Competition of Forward and Reverse Modes in a Ring Resonator,” AFWL-TR-81-137 (1981).
  5. H. Mirels, “Inhomogeneous Broadening Effects in cw Chemical Lasers,” AIAA J. 17, 478 (1979).
    [Crossref]
  6. W. D. Adams et al., “The RESALE Chemical Laser Computer Program,” TR-0075(5530)-5, The Aerospace Corp., El Segundo, Calif. (20Feb.1975).
  7. A. E. Siegman, “Unstable Optical Resonators for Laser Applications,” Proc. IEEE 53, 277 (1965).
    [Crossref]
  8. F. Aronowitz, R. J. Collins, “Lock-In and Intensity-Phase Interaction in The Ring Laser,” Appl. Phys. 41, 130 (Jan.1970).
  9. B. K. Garside, “Mode Spectra in Ring and Normal Lasers,” IEEE J. Quantum Electron. QE-4, 940 (1968).
    [Crossref]
  10. R. A. Chodzko et al., “Zero Power Gain Measurements in cw HF(DF) Laser by Means of Fast Scan Technique,” IEEE J. Quantum Electron. QE-12, 660 (1976).
    [Crossref]
  11. R. A. Chodzko, S. B. Mason, E. B. Turner, W. W. Plummer, “Annular (HSURIA) Resonator: Some Experimental Studies Including Polarization Effects,” Appl. Opt. 19, 778 (1980).
    [Crossref] [PubMed]
  12. D. L. Bullock, J. B. Kaelberer, J. Munch, A. Murthy, K. T. Yano, “New Resonators for High Power Chemical Lasers,” Report 33619–6002-RU-00, TRW, Redondo Beach, Calif. (15May1979).

1980 (2)

1979 (1)

H. Mirels, “Inhomogeneous Broadening Effects in cw Chemical Lasers,” AIAA J. 17, 478 (1979).
[Crossref]

1976 (1)

R. A. Chodzko et al., “Zero Power Gain Measurements in cw HF(DF) Laser by Means of Fast Scan Technique,” IEEE J. Quantum Electron. QE-12, 660 (1976).
[Crossref]

1974 (1)

F. R. Faxvog, A. D. Gara, “Traveling-Wave Gas Laser,” Appl. Phys. Lett. 25, 306 (1974).
[Crossref]

1970 (1)

F. Aronowitz, R. J. Collins, “Lock-In and Intensity-Phase Interaction in The Ring Laser,” Appl. Phys. 41, 130 (Jan.1970).

1968 (1)

B. K. Garside, “Mode Spectra in Ring and Normal Lasers,” IEEE J. Quantum Electron. QE-4, 940 (1968).
[Crossref]

1966 (1)

F. Aronowitz, R. J. Collins, “Mode Coupling Due to Backscattering in a He–Ne Travelling Wave Ring Laser,” Appl. Phys. Lett. 9, 55 (1July1966).
[Crossref]

1965 (1)

A. E. Siegman, “Unstable Optical Resonators for Laser Applications,” Proc. IEEE 53, 277 (1965).
[Crossref]

Adams, W. D.

W. D. Adams et al., “The RESALE Chemical Laser Computer Program,” TR-0075(5530)-5, The Aerospace Corp., El Segundo, Calif. (20Feb.1975).

Aronowitz, F.

F. Aronowitz, R. J. Collins, “Lock-In and Intensity-Phase Interaction in The Ring Laser,” Appl. Phys. 41, 130 (Jan.1970).

F. Aronowitz, R. J. Collins, “Mode Coupling Due to Backscattering in a He–Ne Travelling Wave Ring Laser,” Appl. Phys. Lett. 9, 55 (1July1966).
[Crossref]

Bullock, D. L.

D. L. Bullock, J. B. Kaelberer, J. Munch, A. Murthy, K. T. Yano, “New Resonators for High Power Chemical Lasers,” Report 33619–6002-RU-00, TRW, Redondo Beach, Calif. (15May1979).

Chodzko, R. A.

R. A. Chodzko, S. B. Mason, E. B. Turner, W. W. Plummer, “Annular (HSURIA) Resonator: Some Experimental Studies Including Polarization Effects,” Appl. Opt. 19, 778 (1980).
[Crossref] [PubMed]

R. A. Chodzko et al., “Zero Power Gain Measurements in cw HF(DF) Laser by Means of Fast Scan Technique,” IEEE J. Quantum Electron. QE-12, 660 (1976).
[Crossref]

Collins, R. J.

F. Aronowitz, R. J. Collins, “Lock-In and Intensity-Phase Interaction in The Ring Laser,” Appl. Phys. 41, 130 (Jan.1970).

F. Aronowitz, R. J. Collins, “Mode Coupling Due to Backscattering in a He–Ne Travelling Wave Ring Laser,” Appl. Phys. Lett. 9, 55 (1July1966).
[Crossref]

Faxvog, F. R.

F. R. Faxvog, “Modes of a Unidirectional Ring Laser,” Opt. Lett. 5, 285 (1980).
[Crossref] [PubMed]

F. R. Faxvog, A. D. Gara, “Traveling-Wave Gas Laser,” Appl. Phys. Lett. 25, 306 (1974).
[Crossref]

Gara, A. D.

F. R. Faxvog, A. D. Gara, “Traveling-Wave Gas Laser,” Appl. Phys. Lett. 25, 306 (1974).
[Crossref]

Garside, B. K.

B. K. Garside, “Mode Spectra in Ring and Normal Lasers,” IEEE J. Quantum Electron. QE-4, 940 (1968).
[Crossref]

Kaelberer, J. B.

D. L. Bullock, J. B. Kaelberer, J. Munch, A. Murthy, K. T. Yano, “New Resonators for High Power Chemical Lasers,” Report 33619–6002-RU-00, TRW, Redondo Beach, Calif. (15May1979).

Mason, S. B.

Mirels, H.

H. Mirels, “Inhomogeneous Broadening Effects in cw Chemical Lasers,” AIAA J. 17, 478 (1979).
[Crossref]

Munch, J.

D. L. Bullock, J. B. Kaelberer, J. Munch, A. Murthy, K. T. Yano, “New Resonators for High Power Chemical Lasers,” Report 33619–6002-RU-00, TRW, Redondo Beach, Calif. (15May1979).

Murthy, A.

D. L. Bullock, J. B. Kaelberer, J. Munch, A. Murthy, K. T. Yano, “New Resonators for High Power Chemical Lasers,” Report 33619–6002-RU-00, TRW, Redondo Beach, Calif. (15May1979).

Paxton, A. H.

A. H. Paxton, “A Preliminary Look at the Competition of Forward and Reverse Modes in a Ring Resonator,” AFWL-TR-81-137 (1981).

Plummer, W. W.

Siegman, A. E.

A. E. Siegman, “Unstable Optical Resonators for Laser Applications,” Proc. IEEE 53, 277 (1965).
[Crossref]

Turner, E. B.

Yano, K. T.

D. L. Bullock, J. B. Kaelberer, J. Munch, A. Murthy, K. T. Yano, “New Resonators for High Power Chemical Lasers,” Report 33619–6002-RU-00, TRW, Redondo Beach, Calif. (15May1979).

AIAA J. (1)

H. Mirels, “Inhomogeneous Broadening Effects in cw Chemical Lasers,” AIAA J. 17, 478 (1979).
[Crossref]

Appl. Opt. (1)

Appl. Phys. (1)

F. Aronowitz, R. J. Collins, “Lock-In and Intensity-Phase Interaction in The Ring Laser,” Appl. Phys. 41, 130 (Jan.1970).

Appl. Phys. Lett. (2)

F. Aronowitz, R. J. Collins, “Mode Coupling Due to Backscattering in a He–Ne Travelling Wave Ring Laser,” Appl. Phys. Lett. 9, 55 (1July1966).
[Crossref]

F. R. Faxvog, A. D. Gara, “Traveling-Wave Gas Laser,” Appl. Phys. Lett. 25, 306 (1974).
[Crossref]

IEEE J. Quantum Electron. (2)

B. K. Garside, “Mode Spectra in Ring and Normal Lasers,” IEEE J. Quantum Electron. QE-4, 940 (1968).
[Crossref]

R. A. Chodzko et al., “Zero Power Gain Measurements in cw HF(DF) Laser by Means of Fast Scan Technique,” IEEE J. Quantum Electron. QE-12, 660 (1976).
[Crossref]

Opt. Lett. (1)

Proc. IEEE (1)

A. E. Siegman, “Unstable Optical Resonators for Laser Applications,” Proc. IEEE 53, 277 (1965).
[Crossref]

Other (3)

D. L. Bullock, J. B. Kaelberer, J. Munch, A. Murthy, K. T. Yano, “New Resonators for High Power Chemical Lasers,” Report 33619–6002-RU-00, TRW, Redondo Beach, Calif. (15May1979).

A. H. Paxton, “A Preliminary Look at the Competition of Forward and Reverse Modes in a Ring Resonator,” AFWL-TR-81-137 (1981).

W. D. Adams et al., “The RESALE Chemical Laser Computer Program,” TR-0075(5530)-5, The Aerospace Corp., El Segundo, Calif. (20Feb.1975).

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Figures (12)

Fig. 1
Fig. 1

Longitudinal mode structure in ring resonator.

Fig. 2
Fig. 2

Simple ring resonator with reverse wave suppressor mirror.

Fig. 3
Fig. 3

Two regimes that characterize forward and reverse mode competition.

Fig. 4
Fig. 4

Unstable linear ring resonator used with cw HF laser. Mirror configuration.

Fig. 5
Fig. 5

Unstable linear ring resonator used with cw HF laser. Mode envelope.

Fig. 6
Fig. 6

Unstable annular ring (BRIA) resonator used with pulsed CO2 laser.

Fig. 7
Fig. 7

Forward and reverse waveforms for the case of the BRIA resonator without the RWS mirror.

Fig. 8
Fig. 8

Effect of RWS mirror on the forward to reverse wave energy ratio and on beam quality of the BRIA resonator. Well aligned resonator.

Fig. 9
Fig. 9

Effect of RWS mirror on the forward to reverse wave energy ratio and on beam quality of the BRIA resonator. Misaligned suppressor mirror.

Fig. 10
Fig. 10

Waveforms in a modified BRIA resonator without suppressor mirror. Pulse duration is ~1 msec.

Fig. 11
Fig. 11

Effect of resonator length variation on the spectral output from the modified BRIA resonator without the RWS mirror.

Fig. 12
Fig. 12

Effect of RWS mirror tilt on reverse wave suppression and beam quality of a modified BRIA resonator.

Tables (3)

Tables Icon

Table I Resonator and Gain Medium Properties

Tables Icon

Table II Reverse Wave Suppression Data for Unstable Linear HF Ring Resonator. Individual Runs (12 Mar. 1983)

Tables Icon

Table III Reverse Wave Suppression Data for Unstable Linear HF Ring Resonator. Average Values

Equations (41)

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ν ± = ν 0 [ 1 ± ( u / c ) ] ,
g g 0 = exp [ - 4 ln 2 ( ν ± - ν 0 Δ ν d ) 2 ] ,
Δ ν m = c / L .
ν n ± - ν 0 = ( ν 1 + - ν 0 ) + ( n - 1 ) Δ ν m             for n 1 ,
= ( ν 1 + - ν 0 ) + n Δ ν m             for n - 1 ,
δ = 2 ( ν 1 + - ν 0 ) .
δ = Δ ν m - 2 ( ν 1 + - ν 0 ) .
( Δ u c ν 0 Δ ν h ) max ( δ Δ ν h ) max = 1 2 Δ ν m Δ ν h .
g t = ( 1 / l ) ln ( M 2 / R m j ) ,
N max = Δ ν d Δ ν m [ ln ( g 0 / g t ) ln 2 ] 1 / 2 + 1 ,
L / c E + d E + d t = ( g + - g t ) l 2 + [ - ρ - cos ( ψ + - ) ] ,
L / c E - d E - d t = ( g - - g t ) l 2 + [ - ρ + cos ( ψ - + ) ] ,
L c d ψ d t = ρ - sin ( ψ + - ) + ρ + sin ( ψ - + ) ,
ρ ± = E ± r s ± / E = ( I ± R s ± / I ) 1 / 2 .
2 L / c E + d E + d t = ( g + - g l ) l + 2 ρ - cos ( ϕ + ) ,
2 L / c E - d E - d t = ( g - - g t ) l + 2 ρ + cos ( ϕ - ) ,
( - 1 ) L c d ϕ d t = ρ - sin ( ϕ + ) + ρ + sin ( ϕ - ) ,
ϕ = ψ - π - ( + - - ) / 2 ,
= ( + + - ) / 2.
g ± = g 0 ( 1 + I ± + θ I ) - 1 / 2 ,
θ = [ 1 + ( δ / Δ ν h ) 2 ] - 1 .
ρ + ρ - = cos ( ϕ + ) cos ( ϕ - ) ,
ρ + ρ - = - sin ( ϕ + ) sin ( ϕ - ) ,
= arbitrary ,
ϕ = 0 ,
ρ + ρ - = r s + r s - ( E + E - ) 2 = ( R s + R s - ) 1 / 2 I + I - = 1.
d z d τ = cos ( ϕ + ) { 1 - [ cos ( ϕ - ) cos ( ϕ +     ) ] z 2 } ,
z = ( r s + / r s - ) 1 / 2 E + / E - ,
τ = ( r s - r s + ) 1 / 2 c t / L .
ϕ = = 0
ϕ = ± = ± π / 2.
z = ( 1 + z 0 ) - ( 1 - z 0 ) exp ( - 2 τ ) ( 1 + z 0 ) + ( 1 - z 0 ) exp ( - 2 τ ) = 1 ( τ ) ·
z = tan τ ,
I - = I + = ( g 0 / g t ) 2 - 1.
n 2 = ( P th / P exp ) r A ,
p HF : p He : p H 2 : p 0 2 = 0.12 : 0.39 : 0.47 : 0.02 ,
5 p ( Torr ) ( T 300 ) 1 / 2 Δ ν h = 15 × 10 6 sec - 1 ,
( 300 T ) 1 / 2 Δ ν d = 300 × 10 6 sec - 1 .
p CO 2 : p N 2 : p He = 0.13 : 0.19 : 0.68 ,
5 p ( Torr ) ( T 300 ) 1 / 2 Δ ν h = 24 × 10 6 sec - 1 ,
( 300 T ) 1 / 2 Δ ν d = 53 × 10 6 sec - 1 .

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