Abstract

We investigate laser emission from optically-pumped rotationally excited molecular gases confined in a metallic cavity. To this end, we have developed a theoretical framework able to accurately describe, both in the spatial and temporal domains, the molecular collisional and diffusion processes characterizing the operation of this class of lasers. The effect on the main lasing features of the spatial variation of the electric field intensity and the ohmic losses associated to each cavity mode are also included in our analysis. Our simulations show that, for the exemplary case of methyl fluoride gas confined in a cylindrical copper cavity, the region of maximum population inversion is located near the cavity walls. Based on this fact, our calculations show that the lowest lasing threshold intensity corresponds to the cavity mode that, while maximizing the spatial overlap between the corresponding population inversion and electric-field intensity distributions, simultaneously minimizes the absorption losses occurring at the cavity walls. The dependence of the lasing threshold intensity on both the gas pressure and the cavity radius is also analyzed and compared with experiment. We find that as the cavity size is varied, the interplay between the overall gain of the system and the corresponding ohmic losses allows for the existence of an optimal cavity radius which minimizes the intensity threshold for a large range of gas pressures. The theoretical analysis presented in this work expands the current understanding of lasing action in optically-pumped far-infrared lasers and, thus, could contribute to the development of a new class of compact far-infrared and terahertz sources able to operate efficiently at room temperature.

©2011 Optical Society of America

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References

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  1. T. Y. Chang and T. J. Bridges, “Laser actions at 452, 496, and 541 μm in optically pumped CH3F,” Opt. Commun. 1, 423–426 (1970).
    [Crossref]
  2. T. K. Plant, L. A. Newman, E. J. Danielewicz, T. A. DeTemple, and P. D. Coleman, “High power optically pumped far infrared lasers,” IEEE Trans. Microwave Theory Tech. MT22, 988–990 (1980).
  3. W. H. Matteson and F. C. De Lucia, “Millimeter wave spectroscopic studies of collision-induced energy transfer processes in the 13CH3F laser,” IEEE J. Quantum Electron. 19, 1284–1293 (1983).
    [Crossref]
  4. M. S. Tobin, “A review of optically pumped NMMW lasers,” Proc. IEEE 73, 61–85 (1985).
    [Crossref]
  5. P. K. Cheo (ed.), Handbook of Molecular Lasers (Marcel Dekker, Inc., 1987), pp. 495–569.
  6. H. O. Everitt, D. D. Skatrud, and F. C. De Lucia, “Dynamics and tunability of a small optically pumped CW far-infrared laser,” Appl. Phys. Lett. 49, 995–997 (1986).
    [Crossref]
  7. R. I. McCormick, H. O. Everitt, F. C. De Lucia, and D. D. Skatrud, “Collisional energy transfer in optically pumped far-infrared lasers,” IEEE J. Quantum Electron. QE-23, 2069–2077 (1989).
  8. H. O. Everitt and F. C. De Lucia, “A time-resolved study of rotational energy transfer into A and E symmetry species of 13CH3F,” J. Chem. Phys. 90, 3520–3527 (1989).
    [Crossref]
  9. H. O. Everitt and F. C. De Lucia, “Rotational energy transfer in CH3F: The ΔJ = n, ΔK = 0 processes,” J. Chem. Phys. 92, 6480–6491 (1990).
    [Crossref]
  10. R. L. Crownover, H. O. Everitt, D. D. Skatrud, and F. C. DeLucia, “Frequency stability and reproductibility of optically pumped far-infrared lasers,” Appl. Phys. Lett. 57, 2882–2884 (1990).
    [Crossref]
  11. D. Dangoisse, P. Glorieux, and J. Wascat, “Diffusion and vibrational bottleneck in optically pumped submillimeter laser,” Int. J. Infrared Milimeter Waves 2, 215–229 (1981).
    [Crossref]
  12. J. O. Henningsen and H. G. Jensen, “The optically pumped far-infrared laser: Rate equations and diagnostic experiments,” IEEE J. Quantum Electron. QE-11, 248–252 (1975).
    [Crossref]
  13. R. J. Temkins and D. R. Cohn, “Rate equations for an optically pumped, far-infrared laser,” Opt. Commun. 16, 213–217 (1976).
    [Crossref]
  14. H. O. Everitt, “Collisional Energy Transfer in Methyl Halides,” PhD Thesis (Department of Physics, Duke University, 1990).
  15. H. O. Everitt and F. C. De Lucia, “Rotational energy transfer in small polyatomic molecules,” in Advances in Atomic and Molecular Physics (Academic Press, 1995), Vol. 35, pp. 331–400.
  16. L. E. Reichl, A Modern Course in Statistical Physics (John Wiley & Sons Inc., 1998).
  17. A. E. Siegman, Lasers (Univ. Science Books, 1986).
  18. R. Bansal (ed.), Handbook of Engineering Electromagnetics (Marcel Dekker, Inc., 2004).
    [Crossref]
  19. I. Shamah and G. Flynn, “Vibrational relaxation induced population inversions in laser pumped polyatomic molecules,” Chem. Phys. 55, 103–115 (1981).
    [Crossref]
  20. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University Press, 2007).
  21. S. L. Chua, Y. D. Chong, A. D. Stone, M. Soljac̆ić, and J. Bravo-Abad, “Low-threshold lasing action in photonic crystal slabs enabled by Fano resonances,” Opt. Express 19, 1539–1562 (2011).
    [Crossref] [PubMed]

2011 (1)

1990 (2)

H. O. Everitt and F. C. De Lucia, “Rotational energy transfer in CH3F: The ΔJ = n, ΔK = 0 processes,” J. Chem. Phys. 92, 6480–6491 (1990).
[Crossref]

R. L. Crownover, H. O. Everitt, D. D. Skatrud, and F. C. DeLucia, “Frequency stability and reproductibility of optically pumped far-infrared lasers,” Appl. Phys. Lett. 57, 2882–2884 (1990).
[Crossref]

1989 (2)

R. I. McCormick, H. O. Everitt, F. C. De Lucia, and D. D. Skatrud, “Collisional energy transfer in optically pumped far-infrared lasers,” IEEE J. Quantum Electron. QE-23, 2069–2077 (1989).

H. O. Everitt and F. C. De Lucia, “A time-resolved study of rotational energy transfer into A and E symmetry species of 13CH3F,” J. Chem. Phys. 90, 3520–3527 (1989).
[Crossref]

1986 (1)

H. O. Everitt, D. D. Skatrud, and F. C. De Lucia, “Dynamics and tunability of a small optically pumped CW far-infrared laser,” Appl. Phys. Lett. 49, 995–997 (1986).
[Crossref]

1985 (1)

M. S. Tobin, “A review of optically pumped NMMW lasers,” Proc. IEEE 73, 61–85 (1985).
[Crossref]

1983 (1)

W. H. Matteson and F. C. De Lucia, “Millimeter wave spectroscopic studies of collision-induced energy transfer processes in the 13CH3F laser,” IEEE J. Quantum Electron. 19, 1284–1293 (1983).
[Crossref]

1981 (2)

D. Dangoisse, P. Glorieux, and J. Wascat, “Diffusion and vibrational bottleneck in optically pumped submillimeter laser,” Int. J. Infrared Milimeter Waves 2, 215–229 (1981).
[Crossref]

I. Shamah and G. Flynn, “Vibrational relaxation induced population inversions in laser pumped polyatomic molecules,” Chem. Phys. 55, 103–115 (1981).
[Crossref]

1980 (1)

T. K. Plant, L. A. Newman, E. J. Danielewicz, T. A. DeTemple, and P. D. Coleman, “High power optically pumped far infrared lasers,” IEEE Trans. Microwave Theory Tech. MT22, 988–990 (1980).

1976 (1)

R. J. Temkins and D. R. Cohn, “Rate equations for an optically pumped, far-infrared laser,” Opt. Commun. 16, 213–217 (1976).
[Crossref]

1975 (1)

J. O. Henningsen and H. G. Jensen, “The optically pumped far-infrared laser: Rate equations and diagnostic experiments,” IEEE J. Quantum Electron. QE-11, 248–252 (1975).
[Crossref]

1970 (1)

T. Y. Chang and T. J. Bridges, “Laser actions at 452, 496, and 541 μm in optically pumped CH3F,” Opt. Commun. 1, 423–426 (1970).
[Crossref]

Bravo-Abad, J.

Bridges, T. J.

T. Y. Chang and T. J. Bridges, “Laser actions at 452, 496, and 541 μm in optically pumped CH3F,” Opt. Commun. 1, 423–426 (1970).
[Crossref]

Chang, T. Y.

T. Y. Chang and T. J. Bridges, “Laser actions at 452, 496, and 541 μm in optically pumped CH3F,” Opt. Commun. 1, 423–426 (1970).
[Crossref]

Chong, Y. D.

Chua, S. L.

Cohn, D. R.

R. J. Temkins and D. R. Cohn, “Rate equations for an optically pumped, far-infrared laser,” Opt. Commun. 16, 213–217 (1976).
[Crossref]

Coleman, P. D.

T. K. Plant, L. A. Newman, E. J. Danielewicz, T. A. DeTemple, and P. D. Coleman, “High power optically pumped far infrared lasers,” IEEE Trans. Microwave Theory Tech. MT22, 988–990 (1980).

Crownover, R. L.

R. L. Crownover, H. O. Everitt, D. D. Skatrud, and F. C. DeLucia, “Frequency stability and reproductibility of optically pumped far-infrared lasers,” Appl. Phys. Lett. 57, 2882–2884 (1990).
[Crossref]

Dangoisse, D.

D. Dangoisse, P. Glorieux, and J. Wascat, “Diffusion and vibrational bottleneck in optically pumped submillimeter laser,” Int. J. Infrared Milimeter Waves 2, 215–229 (1981).
[Crossref]

Danielewicz, E. J.

T. K. Plant, L. A. Newman, E. J. Danielewicz, T. A. DeTemple, and P. D. Coleman, “High power optically pumped far infrared lasers,” IEEE Trans. Microwave Theory Tech. MT22, 988–990 (1980).

De Lucia, F. C.

H. O. Everitt and F. C. De Lucia, “Rotational energy transfer in CH3F: The ΔJ = n, ΔK = 0 processes,” J. Chem. Phys. 92, 6480–6491 (1990).
[Crossref]

H. O. Everitt and F. C. De Lucia, “A time-resolved study of rotational energy transfer into A and E symmetry species of 13CH3F,” J. Chem. Phys. 90, 3520–3527 (1989).
[Crossref]

R. I. McCormick, H. O. Everitt, F. C. De Lucia, and D. D. Skatrud, “Collisional energy transfer in optically pumped far-infrared lasers,” IEEE J. Quantum Electron. QE-23, 2069–2077 (1989).

H. O. Everitt, D. D. Skatrud, and F. C. De Lucia, “Dynamics and tunability of a small optically pumped CW far-infrared laser,” Appl. Phys. Lett. 49, 995–997 (1986).
[Crossref]

W. H. Matteson and F. C. De Lucia, “Millimeter wave spectroscopic studies of collision-induced energy transfer processes in the 13CH3F laser,” IEEE J. Quantum Electron. 19, 1284–1293 (1983).
[Crossref]

H. O. Everitt and F. C. De Lucia, “Rotational energy transfer in small polyatomic molecules,” in Advances in Atomic and Molecular Physics (Academic Press, 1995), Vol. 35, pp. 331–400.

DeLucia, F. C.

R. L. Crownover, H. O. Everitt, D. D. Skatrud, and F. C. DeLucia, “Frequency stability and reproductibility of optically pumped far-infrared lasers,” Appl. Phys. Lett. 57, 2882–2884 (1990).
[Crossref]

DeTemple, T. A.

T. K. Plant, L. A. Newman, E. J. Danielewicz, T. A. DeTemple, and P. D. Coleman, “High power optically pumped far infrared lasers,” IEEE Trans. Microwave Theory Tech. MT22, 988–990 (1980).

Everitt, H. O.

R. L. Crownover, H. O. Everitt, D. D. Skatrud, and F. C. DeLucia, “Frequency stability and reproductibility of optically pumped far-infrared lasers,” Appl. Phys. Lett. 57, 2882–2884 (1990).
[Crossref]

H. O. Everitt and F. C. De Lucia, “Rotational energy transfer in CH3F: The ΔJ = n, ΔK = 0 processes,” J. Chem. Phys. 92, 6480–6491 (1990).
[Crossref]

R. I. McCormick, H. O. Everitt, F. C. De Lucia, and D. D. Skatrud, “Collisional energy transfer in optically pumped far-infrared lasers,” IEEE J. Quantum Electron. QE-23, 2069–2077 (1989).

H. O. Everitt and F. C. De Lucia, “A time-resolved study of rotational energy transfer into A and E symmetry species of 13CH3F,” J. Chem. Phys. 90, 3520–3527 (1989).
[Crossref]

H. O. Everitt, D. D. Skatrud, and F. C. De Lucia, “Dynamics and tunability of a small optically pumped CW far-infrared laser,” Appl. Phys. Lett. 49, 995–997 (1986).
[Crossref]

H. O. Everitt, “Collisional Energy Transfer in Methyl Halides,” PhD Thesis (Department of Physics, Duke University, 1990).

H. O. Everitt and F. C. De Lucia, “Rotational energy transfer in small polyatomic molecules,” in Advances in Atomic and Molecular Physics (Academic Press, 1995), Vol. 35, pp. 331–400.

Flynn, G.

I. Shamah and G. Flynn, “Vibrational relaxation induced population inversions in laser pumped polyatomic molecules,” Chem. Phys. 55, 103–115 (1981).
[Crossref]

Glorieux, P.

D. Dangoisse, P. Glorieux, and J. Wascat, “Diffusion and vibrational bottleneck in optically pumped submillimeter laser,” Int. J. Infrared Milimeter Waves 2, 215–229 (1981).
[Crossref]

Henningsen, J. O.

J. O. Henningsen and H. G. Jensen, “The optically pumped far-infrared laser: Rate equations and diagnostic experiments,” IEEE J. Quantum Electron. QE-11, 248–252 (1975).
[Crossref]

Jensen, H. G.

J. O. Henningsen and H. G. Jensen, “The optically pumped far-infrared laser: Rate equations and diagnostic experiments,” IEEE J. Quantum Electron. QE-11, 248–252 (1975).
[Crossref]

Matteson, W. H.

W. H. Matteson and F. C. De Lucia, “Millimeter wave spectroscopic studies of collision-induced energy transfer processes in the 13CH3F laser,” IEEE J. Quantum Electron. 19, 1284–1293 (1983).
[Crossref]

McCormick, R. I.

R. I. McCormick, H. O. Everitt, F. C. De Lucia, and D. D. Skatrud, “Collisional energy transfer in optically pumped far-infrared lasers,” IEEE J. Quantum Electron. QE-23, 2069–2077 (1989).

Newman, L. A.

T. K. Plant, L. A. Newman, E. J. Danielewicz, T. A. DeTemple, and P. D. Coleman, “High power optically pumped far infrared lasers,” IEEE Trans. Microwave Theory Tech. MT22, 988–990 (1980).

Plant, T. K.

T. K. Plant, L. A. Newman, E. J. Danielewicz, T. A. DeTemple, and P. D. Coleman, “High power optically pumped far infrared lasers,” IEEE Trans. Microwave Theory Tech. MT22, 988–990 (1980).

Reichl, L. E.

L. E. Reichl, A Modern Course in Statistical Physics (John Wiley & Sons Inc., 1998).

Shamah, I.

I. Shamah and G. Flynn, “Vibrational relaxation induced population inversions in laser pumped polyatomic molecules,” Chem. Phys. 55, 103–115 (1981).
[Crossref]

Siegman, A. E.

A. E. Siegman, Lasers (Univ. Science Books, 1986).

Skatrud, D. D.

R. L. Crownover, H. O. Everitt, D. D. Skatrud, and F. C. DeLucia, “Frequency stability and reproductibility of optically pumped far-infrared lasers,” Appl. Phys. Lett. 57, 2882–2884 (1990).
[Crossref]

R. I. McCormick, H. O. Everitt, F. C. De Lucia, and D. D. Skatrud, “Collisional energy transfer in optically pumped far-infrared lasers,” IEEE J. Quantum Electron. QE-23, 2069–2077 (1989).

H. O. Everitt, D. D. Skatrud, and F. C. De Lucia, “Dynamics and tunability of a small optically pumped CW far-infrared laser,” Appl. Phys. Lett. 49, 995–997 (1986).
[Crossref]

Soljac?ic, M.

Stone, A. D.

Temkins, R. J.

R. J. Temkins and D. R. Cohn, “Rate equations for an optically pumped, far-infrared laser,” Opt. Commun. 16, 213–217 (1976).
[Crossref]

Tobin, M. S.

M. S. Tobin, “A review of optically pumped NMMW lasers,” Proc. IEEE 73, 61–85 (1985).
[Crossref]

Wascat, J.

D. Dangoisse, P. Glorieux, and J. Wascat, “Diffusion and vibrational bottleneck in optically pumped submillimeter laser,” Int. J. Infrared Milimeter Waves 2, 215–229 (1981).
[Crossref]

Yariv, A.

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University Press, 2007).

Yeh, P.

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University Press, 2007).

Appl. Phys. Lett. (2)

H. O. Everitt, D. D. Skatrud, and F. C. De Lucia, “Dynamics and tunability of a small optically pumped CW far-infrared laser,” Appl. Phys. Lett. 49, 995–997 (1986).
[Crossref]

R. L. Crownover, H. O. Everitt, D. D. Skatrud, and F. C. DeLucia, “Frequency stability and reproductibility of optically pumped far-infrared lasers,” Appl. Phys. Lett. 57, 2882–2884 (1990).
[Crossref]

Chem. Phys. (1)

I. Shamah and G. Flynn, “Vibrational relaxation induced population inversions in laser pumped polyatomic molecules,” Chem. Phys. 55, 103–115 (1981).
[Crossref]

IEEE J. Quantum Electron. (3)

J. O. Henningsen and H. G. Jensen, “The optically pumped far-infrared laser: Rate equations and diagnostic experiments,” IEEE J. Quantum Electron. QE-11, 248–252 (1975).
[Crossref]

R. I. McCormick, H. O. Everitt, F. C. De Lucia, and D. D. Skatrud, “Collisional energy transfer in optically pumped far-infrared lasers,” IEEE J. Quantum Electron. QE-23, 2069–2077 (1989).

W. H. Matteson and F. C. De Lucia, “Millimeter wave spectroscopic studies of collision-induced energy transfer processes in the 13CH3F laser,” IEEE J. Quantum Electron. 19, 1284–1293 (1983).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

T. K. Plant, L. A. Newman, E. J. Danielewicz, T. A. DeTemple, and P. D. Coleman, “High power optically pumped far infrared lasers,” IEEE Trans. Microwave Theory Tech. MT22, 988–990 (1980).

Int. J. Infrared Milimeter Waves (1)

D. Dangoisse, P. Glorieux, and J. Wascat, “Diffusion and vibrational bottleneck in optically pumped submillimeter laser,” Int. J. Infrared Milimeter Waves 2, 215–229 (1981).
[Crossref]

J. Chem. Phys. (2)

H. O. Everitt and F. C. De Lucia, “A time-resolved study of rotational energy transfer into A and E symmetry species of 13CH3F,” J. Chem. Phys. 90, 3520–3527 (1989).
[Crossref]

H. O. Everitt and F. C. De Lucia, “Rotational energy transfer in CH3F: The ΔJ = n, ΔK = 0 processes,” J. Chem. Phys. 92, 6480–6491 (1990).
[Crossref]

Opt. Commun. (2)

T. Y. Chang and T. J. Bridges, “Laser actions at 452, 496, and 541 μm in optically pumped CH3F,” Opt. Commun. 1, 423–426 (1970).
[Crossref]

R. J. Temkins and D. R. Cohn, “Rate equations for an optically pumped, far-infrared laser,” Opt. Commun. 16, 213–217 (1976).
[Crossref]

Opt. Express (1)

Proc. IEEE (1)

M. S. Tobin, “A review of optically pumped NMMW lasers,” Proc. IEEE 73, 61–85 (1985).
[Crossref]

Other (7)

P. K. Cheo (ed.), Handbook of Molecular Lasers (Marcel Dekker, Inc., 1987), pp. 495–569.

H. O. Everitt, “Collisional Energy Transfer in Methyl Halides,” PhD Thesis (Department of Physics, Duke University, 1990).

H. O. Everitt and F. C. De Lucia, “Rotational energy transfer in small polyatomic molecules,” in Advances in Atomic and Molecular Physics (Academic Press, 1995), Vol. 35, pp. 331–400.

L. E. Reichl, A Modern Course in Statistical Physics (John Wiley & Sons Inc., 1998).

A. E. Siegman, Lasers (Univ. Science Books, 1986).

R. Bansal (ed.), Handbook of Engineering Electromagnetics (Marcel Dekker, Inc., 2004).
[Crossref]

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University Press, 2007).

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Figures (6)

Fig. 1
Fig. 1 Schematic diagram of the general model used to describe the dynamics of a OPFIR molecular gas. Details on each process labeled are described in the text.

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Fig. 2
Fig. 2 (a) The OPFIR laser system considered in our numerical modeling: A cylindrical waveguide resonator of length L cell and radius R is filled with a suitable gas that lases at the desired THz frequency, while pump power at a much higher IR frequency enters the system from the front window. In our example, 13CH3F is pumped with CO2 laser at 31 THz to produce lasing at 0.245 THz. (b) Frequency dependence of the ohmic losses for the five lowest order modes (i.e. TE11, TM01, TE21, TE01, TM11) and three higher order ones with low losses (i.e. TE02, TE12, TE22). Plot is for a copper cavity with R = 0.26 cm (and assuming L cell ≫ R) so that several modes (not all shown in plot) have cut-offs below the THz lasing frequency. Despite this, only the lowest loss mode TE01 exist in the cavity near the lasing threshold. Vertical green line shows the band of frequency at which our system operates. (c) Intensity profile of the three lowest loss modes supported by the R = 0.26 cm waveguide cavity.

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Fig. 3
Fig. 3 Time dependent properties of laser system with CW pumping at P pump = 10 W. (a) Time evolution of the inversion in ν 3 state at 250 mTorr across the radial axis of the cavity until steady state behavior is observed. (b) Time evolution of the ν 3 thermal pool population at 250 mTorr across the radial axis of the cavity until steady state behavior is observed. (c) Same as in (a) except operated at 350 mTorr (using the same magnitude range for the color bar). (d) Same as in (b) except operated at 350 mTorr (using the same magnitude range for the color bar).

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Fig. 4
Fig. 4 (a) Method of threshold predictions via gain-loss balancing used in plotting (c) for every pressure point. Here, we operate at 100 mTorr with R = 0.26 cm. The blue line is the unsaturated effective gain value for a range of pump intensity predicted by the aforementioned model while the red line is the magnitude of the loss coefficient due to absorption by the metallic cavity and energy leakage from the front window. Intersection between the two lines corresponds to the lasing threshold. (b) Same as in (a) except that the pressure is at 300 mTorr. (c) Left axis depicts the relationship between the threshold intensity and pressure for a range of R values from 0.08 cm to 1 cm as predicted from numerical model. The corresponding linewidth, Δν, of the lasing transition (over which it may be tuned) is also illustrated in the top axis. A general trend exists such that the lasing threshold increases with pressure. The right axis shows the mean free path, λ MFP, within the gaseous system which at a fixed temperature, is inversely proportional to pressure. Inset is the ohmic loss [see Fig. 2(b)] of the TE01 mode at 0.245 THz, with the radii of interest marked as square markers.

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Fig. 5
Fig. 5 (a) Radial spatial variation of the excited inversion in ν 3 state of 13CH3F for a range of operating pressure from 50 to 450 mTorr. 0 cm marks the center of the cylindrical cavity while 0.5 cm marks the copper wall. All four panels in this figure assumed CW pumping at P pump = 100 W. Near the cell wall, the diffusion is ballistic allowing significant reduction of molecules from the ν 3 pool, and hence, results in a higher population inversion. (b) Same as in (a) except that the transition width at 0.245 THz is also factored in to study the gain. (c) Gain dependence on pressure for a fixed set of pump parameters. From a molecular gas physics standpoint, results clearly indicate that small R cavities are favored in terms of gain magnitude and pressure cut-off. (d) Data extracted from (c) where the left axis and right axis respectively depict the optimum operating pressure and the corresponding gain, as a function of cell radius R. Again, results here favored small sized cavity for high pressure operation.

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Fig. 6
Fig. 6 13CH3F OPFIR laser model used in this paper: results of diagnostic studies and theoretical considerations restrict the degrees of freedom so that a numerically tractable, yet physically accurate model is attained. Details on each process labeled are described in the text.

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Tables (1)

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Table 1 Translational Cross Sections (in Å 2) of 13CH3F

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Equations (16)

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∂ N J 2 exc ( r ,   t ) ∂ t = − R pump ( r ,   t ) Δ N pump ( r ,   t ) − N J 2 exc ( r ,   t ) ∑ i = 1 3 1 τ J 2 , i + ∑ j = 1 2 N j exc ( r ,   t ) τ j , J 2 + D ∇ 2 N J 2 exc ( r ,   t )
∂ N pool exc ( r ,   t ) ∂ t = − N pool exc ( r ,   t ) ∑ k = 1 2 1 τ exc , k ( r ) + ∑ n = 1 2 N pool n ( r ,   t ) τ n , exc ( r ) + ∑ m = 1 m 0 N J m exc ( r ,   t ) τ J m swap + D ∇ 2 N pool exc ( r ,   t )
〈 γ ( λ THz ) 〉 = 〈 Δ N 〉 λ THz 2 4 π 2 n 2 τ spont Δ ν ( λ THz )
〈 Δ N ( t ∞ ) 〉 = ∫ V ACT d r | E 0 ( r ) | 2 Δ N ( r ,   t ∞ ) ∫ V ACT d r | E 0 ( r ) | 2 .
P out = f out P sat ( P in P in th − 1 )
τ eff = 1 / τ J 1 swap − 1 / τ ′ 1 / τ J 1 swap τ J 2 , J 1 − 1 / τ ′ τ J 1
1 τ ′ = τ J 3 − τ J 3 , J 2 − τ J 2 , J 3 τ J 3 , J 2 / τ J 2 swap τ J 2 , J 3 τ J 3 , J 2 , 1 τ J 1 = 1 τ J 1 , J 2 + 1 τ J 1 swap       and       1 τ J 3 = 1 τ J 3 , J 2 + 1 τ J 3 swap .
∂ N 1 ( r ,   t ) ∂ t = − N 1 ( r ,   t ) ( 1 τ 12 + 1 τ 1 A ) + N 2 ( r ,   t ) τ 21 + D ∇ 2 N 1 ( r ,   t )
∂ N 2 ( r ,   t ) ∂ t = − N 2 ( r ,   t ) ( 1 τ 21 + 1 τ 23 + 1 τ 2 A ) + N 1 ( r ,   t ) τ 12 + N 3 ( r ,   t ) τ 32 + R pump ( r ,   t ) Δ N pump ( r ,   t ) + D ∇ 2 N 2 ( r ,   t )
∂ N 3 ( r ,   t ) ∂ t = − N 3 ( r ,   t ) ( 1 τ 32 + 1 τ 3 A ) + N 2 ( r ,   t ) τ 23 + D ∇ 2 N 3 ( r ,   t )
∂ N 4 ( r ,   t ) ∂ t = − N 4 ( r ,   t )   ( 1 τ 45 + 1 τ 4 B ) + N 5 ( r ,   t ) τ 54 + D ∇ 2 N 4 ( r ,   t )
∂ N 5 ( r ,   t ) ∂ t = − N 5 ( r ,   t ) ( 1 τ 54 + 1 τ 56 + 1 τ 5 B ) + N 4 ( r ,   t ) τ 45 + N 6 ( r ,   t ) τ 65 − R pump ( r ,   t ) Δ N pump ( r ,   t ) + D ∇ 2 N 5 ( r ,   t )
∂ N 6 ( r ,   t ) ∂ t = − N 6 ( r ,   t ) ( 1 τ 65 + 1 τ 6 B ) + N 5 ( r ,   t ) τ 56 + D ∇ 2 N 6 ( r ,   t )
∂ N A ( r ,   t ) ∂ t = − N A ( r , t ) ( 1 τ A B ( r ) + 1 τ A C ( r ) ) + N B ( r ,   t ) τ B A ( r ) + N C ( r ,   t ) τ C A ( r ) + N 1 ( r ,   t ) τ 1 A + N 2 ( r ,   t ) τ 2 A + N 3 ( r ,   t ) τ 3 A + D ∇ 2 N A ( r ,   t )
∂ N B ( r ,   t ) ∂ t = − N B ( r ,   t ) ( 1 τ B A ( r ) + 1 τ B C ) + N A ( r ,   t ) τ A B ( r ) + N C ( r ,   t ) τ C B + N 4 ( r ,   t ) τ 4 B + N 5 ( r ,   t ) τ 5 B + N 6 ( r ,   t ) τ 6 B + D ∇ 2 N B ( r ,   t )
∂ N C ( r ,   t ) ∂ t = − N C ( r ,   t ) ( 1 τ C A ( r ) + 1 τ C B ) + N A ( r ,   t ) τ A C ( r ) + N B ( r ,   t ) τ B C + D ∇ 2 N C ( r ,   t )

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