Abstract

We present the results of our theoretical and experimental investigation of the pulsed heterodyne of an electro-optically Q-switched radio-frequency-excited CO2 waveguide laser with two channels. We used a six-temperature model for CO2 lasers to describe the process of dynamic emission in an electro-optically Q-switched laser. The calculated pulse waveforms are in good agreement with the experiment, which we used as the basis for our theoretical study of a pulsed laser heterodyne and its Fourier transform frequency spectrum. The experimental results are consistent with the theoretical analyses.

© 2001 Optical Society of America

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References

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  1. H. Ahlberg, S. Lundqvist, D. Letalick, I. Renhorn, O. Steinvall, “Imaging Q-switched CO2 laser radar with hetrodyne detection: design and evaluation,” Appl. Opt. 25, 2891–2898 (1986).
    [CrossRef]
  2. G. N. Pearson, B. J. Rye, “Frequency fidelity of a compact CO2 Doppler lidar transmitter,” Appl. Opt. 31, 6475–6484 (1992).
    [CrossRef] [PubMed]
  3. D. Wen, J. Guo, “Analysis of signal of infrared laser heterodyne gas analyzer,” Acta Opt. 3(2), 138–145 (1983) in Chinese.
  4. W. S. Read, R. G. Turner, “Tracking heterodyne detection,” Appl. Opt. 4, 1570–1573 (1965).
    [CrossRef]
  5. M. C. Teich, “Infrared heterodyne detection,” Proc. IEEE 56, 37–46 (1968).
    [CrossRef]
  6. K. Smith, R. M. Thomson, Computer Modeling of Gas Laser (Plenum, New York, 1978).
    [CrossRef]
  7. M. Soukieh, B. A. Ghani, M. Hammadi, “Mathematical modeling of CO2 TEA laser,” Opt. Laser Technol. 30, 451–457 (1999).
    [CrossRef]
  8. C. G. Parzzoli, K.-R. Chen, “Numerical analysis of a CW RF pumped CO2 waveguide laser,” IEEE J. Quantum Electron. 22, 479–488 (1986).
    [CrossRef]
  9. J. J. Degnan, H. E. Walker, J. H. McElroy, “Gain and saturation intensity measurements in a waveguide CO2 laser,” IEEE J. Quantum Electron 9, 489–491 (1973).
    [CrossRef]
  10. D. Letalick, I. Renhorn, A. Widen, “CO2 waveguide laser with programmable pulse profile,” Opt. Eng. 28, 172–179 (1989).

1999 (1)

M. Soukieh, B. A. Ghani, M. Hammadi, “Mathematical modeling of CO2 TEA laser,” Opt. Laser Technol. 30, 451–457 (1999).
[CrossRef]

1992 (1)

1989 (1)

D. Letalick, I. Renhorn, A. Widen, “CO2 waveguide laser with programmable pulse profile,” Opt. Eng. 28, 172–179 (1989).

1986 (2)

C. G. Parzzoli, K.-R. Chen, “Numerical analysis of a CW RF pumped CO2 waveguide laser,” IEEE J. Quantum Electron. 22, 479–488 (1986).
[CrossRef]

H. Ahlberg, S. Lundqvist, D. Letalick, I. Renhorn, O. Steinvall, “Imaging Q-switched CO2 laser radar with hetrodyne detection: design and evaluation,” Appl. Opt. 25, 2891–2898 (1986).
[CrossRef]

1983 (1)

D. Wen, J. Guo, “Analysis of signal of infrared laser heterodyne gas analyzer,” Acta Opt. 3(2), 138–145 (1983) in Chinese.

1973 (1)

J. J. Degnan, H. E. Walker, J. H. McElroy, “Gain and saturation intensity measurements in a waveguide CO2 laser,” IEEE J. Quantum Electron 9, 489–491 (1973).
[CrossRef]

1968 (1)

M. C. Teich, “Infrared heterodyne detection,” Proc. IEEE 56, 37–46 (1968).
[CrossRef]

1965 (1)

Ahlberg, H.

Chen, K.-R.

C. G. Parzzoli, K.-R. Chen, “Numerical analysis of a CW RF pumped CO2 waveguide laser,” IEEE J. Quantum Electron. 22, 479–488 (1986).
[CrossRef]

Degnan, J. J.

J. J. Degnan, H. E. Walker, J. H. McElroy, “Gain and saturation intensity measurements in a waveguide CO2 laser,” IEEE J. Quantum Electron 9, 489–491 (1973).
[CrossRef]

Ghani, B. A.

M. Soukieh, B. A. Ghani, M. Hammadi, “Mathematical modeling of CO2 TEA laser,” Opt. Laser Technol. 30, 451–457 (1999).
[CrossRef]

Guo, J.

D. Wen, J. Guo, “Analysis of signal of infrared laser heterodyne gas analyzer,” Acta Opt. 3(2), 138–145 (1983) in Chinese.

Hammadi, M.

M. Soukieh, B. A. Ghani, M. Hammadi, “Mathematical modeling of CO2 TEA laser,” Opt. Laser Technol. 30, 451–457 (1999).
[CrossRef]

Letalick, D.

Lundqvist, S.

McElroy, J. H.

J. J. Degnan, H. E. Walker, J. H. McElroy, “Gain and saturation intensity measurements in a waveguide CO2 laser,” IEEE J. Quantum Electron 9, 489–491 (1973).
[CrossRef]

Parzzoli, C. G.

C. G. Parzzoli, K.-R. Chen, “Numerical analysis of a CW RF pumped CO2 waveguide laser,” IEEE J. Quantum Electron. 22, 479–488 (1986).
[CrossRef]

Pearson, G. N.

Read, W. S.

Renhorn, I.

Rye, B. J.

Smith, K.

K. Smith, R. M. Thomson, Computer Modeling of Gas Laser (Plenum, New York, 1978).
[CrossRef]

Soukieh, M.

M. Soukieh, B. A. Ghani, M. Hammadi, “Mathematical modeling of CO2 TEA laser,” Opt. Laser Technol. 30, 451–457 (1999).
[CrossRef]

Steinvall, O.

Teich, M. C.

M. C. Teich, “Infrared heterodyne detection,” Proc. IEEE 56, 37–46 (1968).
[CrossRef]

Thomson, R. M.

K. Smith, R. M. Thomson, Computer Modeling of Gas Laser (Plenum, New York, 1978).
[CrossRef]

Turner, R. G.

Walker, H. E.

J. J. Degnan, H. E. Walker, J. H. McElroy, “Gain and saturation intensity measurements in a waveguide CO2 laser,” IEEE J. Quantum Electron 9, 489–491 (1973).
[CrossRef]

Wen, D.

D. Wen, J. Guo, “Analysis of signal of infrared laser heterodyne gas analyzer,” Acta Opt. 3(2), 138–145 (1983) in Chinese.

Widen, A.

D. Letalick, I. Renhorn, A. Widen, “CO2 waveguide laser with programmable pulse profile,” Opt. Eng. 28, 172–179 (1989).

Acta Opt. (1)

D. Wen, J. Guo, “Analysis of signal of infrared laser heterodyne gas analyzer,” Acta Opt. 3(2), 138–145 (1983) in Chinese.

Appl. Opt. (3)

IEEE J. Quantum Electron (1)

J. J. Degnan, H. E. Walker, J. H. McElroy, “Gain and saturation intensity measurements in a waveguide CO2 laser,” IEEE J. Quantum Electron 9, 489–491 (1973).
[CrossRef]

IEEE J. Quantum Electron. (1)

C. G. Parzzoli, K.-R. Chen, “Numerical analysis of a CW RF pumped CO2 waveguide laser,” IEEE J. Quantum Electron. 22, 479–488 (1986).
[CrossRef]

Opt. Eng. (1)

D. Letalick, I. Renhorn, A. Widen, “CO2 waveguide laser with programmable pulse profile,” Opt. Eng. 28, 172–179 (1989).

Opt. Laser Technol. (1)

M. Soukieh, B. A. Ghani, M. Hammadi, “Mathematical modeling of CO2 TEA laser,” Opt. Laser Technol. 30, 451–457 (1999).
[CrossRef]

Proc. IEEE (1)

M. C. Teich, “Infrared heterodyne detection,” Proc. IEEE 56, 37–46 (1968).
[CrossRef]

Other (1)

K. Smith, R. M. Thomson, Computer Modeling of Gas Laser (Plenum, New York, 1978).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Numerical results of the electro-optically Q-switched laser pulsed waveform.

Fig. 2
Fig. 2

Heterodyne waveform of the pulsed laser and the cw laser compared with the pulsed waveform of the Q-switched laser: (a) E s = 10E L , (b) E s = E L , (c) 10E s = E L .

Fig. 3
Fig. 3

Fourier transform spectrum of the pulsed laser heterodyne.

Fig. 4
Fig. 4

Schematic of the experimental arrangement.

Fig. 5
Fig. 5

Electro-optically Q-switched pulsed laser waveform at a pulse repetition frequency of 10 kHz (200 ns/div).

Fig. 6
Fig. 6

Heterodyne waveform of the pulsed laser (500 ns/div) and the cw laser.

Fig. 7
Fig. 7

Heterodyne waveform of the pulsed laser (200 ns/div) and its Fourier transform frequency spectrum of 10 MHz/div.

Equations (20)

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dE1dt=netfnCO2X1hν1-E1-E1Tτ10T-E1-E1T2τ12T2+hν1hν3E3-E3T, T1, T2τ3T, T1, T2+hν1hν5E5-E5T, T1, T2τ5T, T1, T2+ν1ΔNWIν0,
dE2dt=netfnCO2X2hν2+hν2hν3E3-E3T, T1, T2τ3T, T1, T2-E1-E1T2τ12T2-E2-E2T2τ20T2+hν2hν5E5-E5T, T1, T2τ5T, T1, T2,
dE3dt=netfnCO2X3hν3+E4-E4T3τ43T2-E3-E3T, T1, T2τ3T, T1, T2+hν3hν5E5-E5T, T3τ53T, T3-ν3ΔNWIν0,
dE4dt=netnN2X4hν4-E4-E4T3τ43T+hν4hν5E5-E5T, T4τ54T, T4,
dE5dt=net1-fnCO2X5hν5-E5-E5T, T3τ53T, T3+E5-E5T, T1, T2τ3T, T1, T2+E5-E5T, T4τ43T, T4,
dEKdt=E1-E1Tτ10T+E2-E2Tτ20T+1-hν1hν3-hν2hν3E3-E3T, T1, T2τ3T, T1, T2+1-hν3hν5E5-E5T, T3τ53T, T3+1-hν2hν5-hν2hν5E5-E5T, T1, T2τ5T, T1, T2+1-hν4hν5E5-E5T, T4τ54T, T4,
EK=52 nN2+52 fnCO2+32 nHe+521-fnCOkT,
dδJ0dt=-2δJ0WIν0-δJ0-PJ0nu-PJ0+1nlτR,
PJ=nν,Jnν=hcBνkTgJ exp-hcBνJJ+1kT.
dIν0dt=-Iν0τc+chν0ΔNWIν0h+n001PJS,
τc=-2Lc lnr1r2,
W=Fλ24π2ν0Δνc+ΔνDτsp,
ΔN=n001PJ-2J+12J+3 n100PJ+1,
n001=nCO2 exp-hν3kT3Z,
n100=nCO2 exp-hν1kT1Z,
Z=1-exp-hν1kT1×1-exp-hν2kT221-exp-hν3kT3.
dE1dt, dE2dt, dE3dt, dE4dt, dE5dt, dEKdt, dIν0dt, dδJ0dt.
P out=AIν0LG1-αt0r2expGL-1+1-exp-GL×10-7,
Est=EsPouttPmax1/2 cosωst,
ipt=aEs2t2+EL22+EstEL cosωs-ωLt=i1t+imf,

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