Abstract

A numerical model of a three-mirror resonator for a TE CO2 laser was developed. This model was used to determine if a three-mirror resonator with an etalon could be used to ensure tunable single-mode action on the lower gain lines of CO2. Single-mode pulse energies were also predicted and good agreement was found with experimentally measured values. An analysis of the thermal frequency drift of the resonator is also presented.

© 1991 Optical Society of America

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References

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  1. T. W. Carman, P. E. Dyer, “Continuous Tuning Characteristics of a Small High Pressure UV Preionised CO2 Laser,” Opt. Commun. 29, 218 (1979).
    [CrossRef]
  2. J. L. Bruneau, “A Tunable Single Longitudinal Mode CO2 Oscillator for Efficient Optical Pumping,” Opt. Commun. 41, 443 (1979).
    [CrossRef]
  3. P. Mathieu, J. R. Izatt, “Narrow-Band CO2 TEA Laser for Efficient FIR Laser Pumping,” IEEE J. Quantum Electron. QE-13, 465 (1977).
    [CrossRef]
  4. B. K. Deka, M. A. Rob, J. R. Izatt, “Mode Contol and High Energy Operation of a Multi-Atmosphere CO2 Laser Using a Three Mirror Resonator,” Opt. Commun. 57, 111 (1986).
    [CrossRef]
  5. P. E. Dyer, D. N. Raouf, “Continuously Tunable, Line Narrowed TE CO2 Laser Using a Near Grazing Incidence Grating,” Appl. Opt. 24, 3152–3154 (1985).
    [CrossRef] [PubMed]
  6. J. R. Izatt, “Tunable Far-Infrared Laser,” Proc. Soc. Photo. Opt. Instrum. Eng. 666, 15 (1986).
  7. B. K. Deka, P. E. Dyer, R. J. Winfield, “Single Mode Operation of a Continuously Tunable TE CO2 Laser Using a Three Mirror Resonator,” Opt. Commun. 39, 255 (1981).
    [CrossRef]
  8. G. J. Ernst, J. Witteman, “Transition Selection with Adjustable Outcoupling for a Laser Device Applied to CO2,” IEEE J. Quantum Electron. QE-7, 484 (1971).
    [CrossRef]
  9. J. E. Bjorkholm, T. C. Damen, J. Shah, “Improved Use of Gratings in Tunable Lasers,” Opt. Commun. 4, 283 (1971).
    [CrossRef]
  10. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).
  11. A. Yariv, Quantum Electronics (Wiley, New York, 1975).
  12. O. Judd, “High Power Gas Lasers,” Inst. Phys. Conf. Ser. 20, (1975).

1986

B. K. Deka, M. A. Rob, J. R. Izatt, “Mode Contol and High Energy Operation of a Multi-Atmosphere CO2 Laser Using a Three Mirror Resonator,” Opt. Commun. 57, 111 (1986).
[CrossRef]

J. R. Izatt, “Tunable Far-Infrared Laser,” Proc. Soc. Photo. Opt. Instrum. Eng. 666, 15 (1986).

1985

1981

B. K. Deka, P. E. Dyer, R. J. Winfield, “Single Mode Operation of a Continuously Tunable TE CO2 Laser Using a Three Mirror Resonator,” Opt. Commun. 39, 255 (1981).
[CrossRef]

1979

T. W. Carman, P. E. Dyer, “Continuous Tuning Characteristics of a Small High Pressure UV Preionised CO2 Laser,” Opt. Commun. 29, 218 (1979).
[CrossRef]

J. L. Bruneau, “A Tunable Single Longitudinal Mode CO2 Oscillator for Efficient Optical Pumping,” Opt. Commun. 41, 443 (1979).
[CrossRef]

1977

P. Mathieu, J. R. Izatt, “Narrow-Band CO2 TEA Laser for Efficient FIR Laser Pumping,” IEEE J. Quantum Electron. QE-13, 465 (1977).
[CrossRef]

1975

O. Judd, “High Power Gas Lasers,” Inst. Phys. Conf. Ser. 20, (1975).

1971

G. J. Ernst, J. Witteman, “Transition Selection with Adjustable Outcoupling for a Laser Device Applied to CO2,” IEEE J. Quantum Electron. QE-7, 484 (1971).
[CrossRef]

J. E. Bjorkholm, T. C. Damen, J. Shah, “Improved Use of Gratings in Tunable Lasers,” Opt. Commun. 4, 283 (1971).
[CrossRef]

Bjorkholm, J. E.

J. E. Bjorkholm, T. C. Damen, J. Shah, “Improved Use of Gratings in Tunable Lasers,” Opt. Commun. 4, 283 (1971).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).

Bruneau, J. L.

J. L. Bruneau, “A Tunable Single Longitudinal Mode CO2 Oscillator for Efficient Optical Pumping,” Opt. Commun. 41, 443 (1979).
[CrossRef]

Carman, T. W.

T. W. Carman, P. E. Dyer, “Continuous Tuning Characteristics of a Small High Pressure UV Preionised CO2 Laser,” Opt. Commun. 29, 218 (1979).
[CrossRef]

Damen, T. C.

J. E. Bjorkholm, T. C. Damen, J. Shah, “Improved Use of Gratings in Tunable Lasers,” Opt. Commun. 4, 283 (1971).
[CrossRef]

Deka, B. K.

B. K. Deka, M. A. Rob, J. R. Izatt, “Mode Contol and High Energy Operation of a Multi-Atmosphere CO2 Laser Using a Three Mirror Resonator,” Opt. Commun. 57, 111 (1986).
[CrossRef]

B. K. Deka, P. E. Dyer, R. J. Winfield, “Single Mode Operation of a Continuously Tunable TE CO2 Laser Using a Three Mirror Resonator,” Opt. Commun. 39, 255 (1981).
[CrossRef]

Dyer, P. E.

P. E. Dyer, D. N. Raouf, “Continuously Tunable, Line Narrowed TE CO2 Laser Using a Near Grazing Incidence Grating,” Appl. Opt. 24, 3152–3154 (1985).
[CrossRef] [PubMed]

B. K. Deka, P. E. Dyer, R. J. Winfield, “Single Mode Operation of a Continuously Tunable TE CO2 Laser Using a Three Mirror Resonator,” Opt. Commun. 39, 255 (1981).
[CrossRef]

T. W. Carman, P. E. Dyer, “Continuous Tuning Characteristics of a Small High Pressure UV Preionised CO2 Laser,” Opt. Commun. 29, 218 (1979).
[CrossRef]

Ernst, G. J.

G. J. Ernst, J. Witteman, “Transition Selection with Adjustable Outcoupling for a Laser Device Applied to CO2,” IEEE J. Quantum Electron. QE-7, 484 (1971).
[CrossRef]

Izatt, J. R.

B. K. Deka, M. A. Rob, J. R. Izatt, “Mode Contol and High Energy Operation of a Multi-Atmosphere CO2 Laser Using a Three Mirror Resonator,” Opt. Commun. 57, 111 (1986).
[CrossRef]

J. R. Izatt, “Tunable Far-Infrared Laser,” Proc. Soc. Photo. Opt. Instrum. Eng. 666, 15 (1986).

P. Mathieu, J. R. Izatt, “Narrow-Band CO2 TEA Laser for Efficient FIR Laser Pumping,” IEEE J. Quantum Electron. QE-13, 465 (1977).
[CrossRef]

Judd, O.

O. Judd, “High Power Gas Lasers,” Inst. Phys. Conf. Ser. 20, (1975).

Mathieu, P.

P. Mathieu, J. R. Izatt, “Narrow-Band CO2 TEA Laser for Efficient FIR Laser Pumping,” IEEE J. Quantum Electron. QE-13, 465 (1977).
[CrossRef]

Raouf, D. N.

Rob, M. A.

B. K. Deka, M. A. Rob, J. R. Izatt, “Mode Contol and High Energy Operation of a Multi-Atmosphere CO2 Laser Using a Three Mirror Resonator,” Opt. Commun. 57, 111 (1986).
[CrossRef]

Shah, J.

J. E. Bjorkholm, T. C. Damen, J. Shah, “Improved Use of Gratings in Tunable Lasers,” Opt. Commun. 4, 283 (1971).
[CrossRef]

Winfield, R. J.

B. K. Deka, P. E. Dyer, R. J. Winfield, “Single Mode Operation of a Continuously Tunable TE CO2 Laser Using a Three Mirror Resonator,” Opt. Commun. 39, 255 (1981).
[CrossRef]

Witteman, J.

G. J. Ernst, J. Witteman, “Transition Selection with Adjustable Outcoupling for a Laser Device Applied to CO2,” IEEE J. Quantum Electron. QE-7, 484 (1971).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, New York, 1975).

Appl. Opt.

IEEE J. Quantum Electron.

P. Mathieu, J. R. Izatt, “Narrow-Band CO2 TEA Laser for Efficient FIR Laser Pumping,” IEEE J. Quantum Electron. QE-13, 465 (1977).
[CrossRef]

G. J. Ernst, J. Witteman, “Transition Selection with Adjustable Outcoupling for a Laser Device Applied to CO2,” IEEE J. Quantum Electron. QE-7, 484 (1971).
[CrossRef]

Inst. Phys. Conf. Ser.

O. Judd, “High Power Gas Lasers,” Inst. Phys. Conf. Ser. 20, (1975).

Opt. Commun.

B. K. Deka, P. E. Dyer, R. J. Winfield, “Single Mode Operation of a Continuously Tunable TE CO2 Laser Using a Three Mirror Resonator,” Opt. Commun. 39, 255 (1981).
[CrossRef]

J. E. Bjorkholm, T. C. Damen, J. Shah, “Improved Use of Gratings in Tunable Lasers,” Opt. Commun. 4, 283 (1971).
[CrossRef]

B. K. Deka, M. A. Rob, J. R. Izatt, “Mode Contol and High Energy Operation of a Multi-Atmosphere CO2 Laser Using a Three Mirror Resonator,” Opt. Commun. 57, 111 (1986).
[CrossRef]

T. W. Carman, P. E. Dyer, “Continuous Tuning Characteristics of a Small High Pressure UV Preionised CO2 Laser,” Opt. Commun. 29, 218 (1979).
[CrossRef]

J. L. Bruneau, “A Tunable Single Longitudinal Mode CO2 Oscillator for Efficient Optical Pumping,” Opt. Commun. 41, 443 (1979).
[CrossRef]

Proc. Soc. Photo. Opt. Instrum. Eng.

J. R. Izatt, “Tunable Far-Infrared Laser,” Proc. Soc. Photo. Opt. Instrum. Eng. 666, 15 (1986).

Other

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).

A. Yariv, Quantum Electronics (Wiley, New York, 1975).

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Figures (7)

Fig. 1
Fig. 1

Schematic representation of a three-mirror resonator.

Fig. 2
Fig. 2

Configuration used for calculating the wavelength dependent reflection of the three-mirror resonator.

Fig. 3
Fig. 3

Wavelength dependent reflection of a three-mirror resonator. The center wavelength is 10.6 μm. The subcavity length is 0.1 m, etalon thickness R1 is 11 mm and its reflectivity is 80%, and a 150-lines/mm grating is used in the Littrow angle.

Fig. 4
Fig. 4

Calculated P30 CO2 laser pulse. The pulse energy is 34 mJ and the FWHM is 87 ns.

Fig. 5
Fig. 5

Measured P30 CO2 laser pulse. The pulse energy is 30 mJ and the FWHM is 83 ns. The time scale is 100 ns/div and the amplitude scale is 20 mV/div.

Fig. 6
Fig. 6

Example of parasitic oscillations from the 50% partial reflecting mirror. The P20 and P30 lines oscillate at the same time. The time scale is 100 nS/div and the amplitude scale is 20 mV/div.

Fig. 7
Fig. 7

Change of resonance frequency with a 1°C change in temperature for different subcavity lengths. Zero corresponds to a subcavity length of 0.1 m. These values were calculated for a 0.45-m main cavity. The subcavity length was changed from 0.1 to 0.1 + 10 μm. The cavity was supported on Invar 36 rods.

Tables (1)

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Table I Mode Discrimination of Two Modes With Different Reflectivitles and Different Gain Values

Equations (36)

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E 1 r ( t ) = E 0 r 1 exp ( i π ) exp ( i ω t ) , E 2 r ( t ) = E 0 t 1 2 t e 2 r g exp ( i π ) exp [ i ( ω t + δ ) ] , E 3 r ( r ) = E 0 t 1 2 t e 4 r g 2 r 1 exp ( i 2 π ) exp [ i ( ω t + 2 δ ) ] ,
δ = 4 π λ L .
E R = E 1 r + E 2 r + E 3 r + E 4 r + = E 0 exp ( i ω t ) ( - 1 ) [ r 1 + t 1 2 t e 2 r g exp ( i δ ) { 1 + t e 2 r g r 1 × exp ( i π ) exp ( i δ ) + [ t e 2 r g r 1 exp ( i π ) exp ( i δ ) ] 2 + } .
E R = E 0 exp ( i ω t ) ( - 1 ) { r 1 + t 1 2 t e 2 r g exp ( i δ ) × [ 1 1 - t e 2 r g r 1 exp ( i π ) exp ( i δ ) ] } .
I r = E r E r * = E 0 2 [ R 1 + 2 R 1 R g T e cos δ + T e 2 R g 1 + 2 T e R s R 1 cos δ + T e 2 R s R 1 ] ,
E R 2 = E 0 2 [ R 1 + 2 R 1 R g T e cos δ + T e 2 R g 2 1 + 2 T e R 1 R g cos δ + T e 2 R g 2 R 1 ] .
R g = [ sin ( k a p b / 2 ) k a p b / 2 ] 2 [ sin ( N k d p / 2 ) sin ( k d p / 2 ) ] 2 ,
p b = sin ( θ i - θ b ) - sin ( θ r - θ b ) ,
T e = t e 4 E 0 2 [ exp ( α l ) - r 2 exp ( - α l ) ] 2 + 4 r 2 sin 2 ( δ / 2 ) ,
δ = 4 π f l cos θ c ,
T e = E 0 2 [ exp ( α l ) - R exp ( - α l ) ] 2 1 1 + 4 R 2 2 sin 2 ( δ / 2 ) [ exp ( α l ) - exp ( - α l ) ] 2 .
I x I y = { R x R y exp [ 2 L ( α x - α y ) ] } N r ,
I x I y = ( R x / R y ) N r .
r c = - r 1 + t e 2 r g exp ( i δ ) 1 + t e 2 r g r 1 exp ( i δ ) .
ϕ 1 = arctan [ - ( t e 2 r g - t e 2 r g r 1 ) sin δ - 1 + t e 4 r g 2 r 1 + ( t e 2 r g - t e 2 r g r 1 ) cos δ ] .
θ m , n = k z + ( n + m + 1 ) arctan ( z / z 0 ) ,
2 [ θ m , n ( z 2 ) - θ m , n ( z 1 ) ] + ϕ 1 + π = 2 π q ( q is an integer ) ,
θ m , n ( z 2 ) - θ m , n ( z 1 ) = [ k z 2 - ( n + m + 1 ) arctan ( z 2 / z 0 ) ] - [ k z 1 - ( n + m + 1 ) arctan ( z 1 / z 0 ) ] .
2 { k ( z 2 - z 1 ) - ( n + m + 1 ) [ arctan ( z 2 z 0 ) - arctan ( z 1 z 0 ) ] } + ϕ 1 + π = 2 π q .
{ k ( z 2 - z 1 ) - [ arctan ( z 2 z 0 ) - arctan ( z 1 z 0 ) ] } + ϕ 1 + π = 2 π q .
λ = 2 π L π ( q - 1 / 2 ) - ϕ 1 / 2 + arctan ( L / z 0 ) .
d λ d T = 2 π d L d T π ( q - 1 / 2 ) - ϕ 1 / 2 + arctan ( L / z 0 ) + - 2 π L [ - 1 2 ( ϕ 1 T ) + ( 1 / Z 0 1 + ( L / Z 0 ) 2 ) ( d L d T ) ] [ π ( q - 1 / 2 ) - ϕ 1 / 2 + arctan ( L / z 0 ) ] 2 .
d ϕ 1 d T = ( 1 1 + ( y / x ) 2 ) ( 1 x d y d T - y x 2 d x d T ) .
x = r 1 - t e 4 r g r 1 + ( t e 2 r g r 1 - t e 2 r g r 1 2 ) cos δ ( 1 - t e 4 r g 2 r 1 2 ) ,
d x d T = t e 2 r g r 1 - t e 2 r g r 1 2 1 - t e 4 r g 2 r 1 2 sin δ d δ d T ,
y = - t e 2 r g r 1 2 - t e 2 r g r 1 1 - t e 4 r g 2 r 1 2 sin δ
d y d T = - t e 2 r g r 1 2 - t e 2 r g r 1 r 1 - t e 4 r g 2 r 1 2 cos δ d δ d T ,
d δ d T = 4 π λ d L d T .
d η d t = - ( η - z Δ ) τ x - 2 σ I h v η ,
d Δ d t = - 2 σ I h v η ,
I t + c I t = c σ η I - I τ c ,
d L d T = 2.0 × 10 - 6 × L ,
d L d T = 2.0 × 10 - 6 × L .
f λ = c .
δ f = - c λ 2 δ λ .
Δ f = - c λ 2 2 q d L d T L Δ T .

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