Abstract

We present saturation absorption spectroscopy of transitions in Te2 near 444.4nm. These spectra were taken using a blue diode laser locked to a Fabry–Perot (FP) cavity that is in turn locked to a Zeeman-stabilized helium–neon laser. Tuning of the diode laser frequency is accomplished by N2 pressure tuning of the FP cavity. The result is a tuning frequency that is proportional to the dispersion of the index of refraction between the helium neon and diode laser wavelengths. We assess the stability of the blue laser frequency by scanning over a single Te2 absorption line repeatedly over a 48h period. This work is motivated by our desire to produce a versatile frequency-locked source of radiation for use in molecular optical polarization experiments.

© 2011 Optical Society of America

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References

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  1. R. N. Hall, G. E. Fenner, J. D. Kingsley, T. J. Soltys, and R. O. Carlson, “Coherent light emission from GaAs junctions,” Phys. Rev. Lett. 9, 366–368 (1962).
    [CrossRef]
  2. M. I. Nathan, W. P. Dumke, G. Burns, F. H. Dill Jr., and G. Lasher, “Stimulated emission of radiation from GaAs p-n junctions,” Appl. Phys. Lett. 1, 62–64 (1962).
    [CrossRef]
  3. C. Bradley, J. Chen, and R. G. Hulet, “Instrumentation for the stable operation of laser diodes,” Rev. Sci. Instrum. 61, 2097–2101 (1990).
    [CrossRef]
  4. D. Wang, L. Xie, and Y. Wang, “GaAlAs laser diode frequency locked at the D2 line of Cs atoms in an atomic beam,” Opt. Lett. 13, 820–822 (1988).
    [CrossRef] [PubMed]
  5. P. Gill, “Optical frequency standards,” Metrologia 42, S125–S137(2005).
    [CrossRef]
  6. J. I. Thorpe, K. Numata, and J. Livas, “Laser frequency stabilization and control through offset sideband locking to optical cavities,” Opt. Express 16, 15980–15990 (2008).
    [CrossRef] [PubMed]
  7. E. Riedle, S. H. Ashworth, J. J. T. Farrell Jr., and D. J. Nesbitt, “Stabilization and precise calibration of a continuous-wave difference frequency spectrometer by use of a simple transfer cavity,” Rev. Sci. Instrum. 65, 42–48 (1994).
    [CrossRef]
  8. P. Bohlouli-Zanjani, K. Afrousheh, and J. D. D. Martin, “Optical transfer cavity stabilization using current-modulated injection-locked diode lasers,” Rev. Sci. Instrum. 77, 093105–093109(2006).
    [CrossRef]
  9. B. G. Lindsay, K. A. Smith, and F. B. Dunning, “Control of long-term output frequency drift in commercial dye lasers,” Rev. Sci. Instrum. 62, 1656–1657 (1991).
    [CrossRef]
  10. W. Z. Zhao, J. E. Simsarian, L. A. Orozco, and G. D. Sprouse, “A computer-based digital feedback control of frequency drift of multiple lasers,” Rev. Sci. Instrum. 69, 3737–3740 (1998).
    [CrossRef]
  11. A. Rossi, V. Biancalana, B. Mai, and L. Tomassetti, “Long-term drift laser frequency stabilization using purely optical reference,” Rev. Sci. Instrum. 73, 2544–2548 (2002).
    [CrossRef]
  12. B. Burghardt, W. Jitschin, and G. Meisel, “Precise rf tuning for cw dye lasers,” Appl. Phys. 20, 141–146 (1979).
    [CrossRef]
  13. D. F. Plusquellic, O. Votava, and D. J. Nesbitt, “Absolute frequency stabilization of an injection-seeded optical parametric oscillator,” Appl. Opt. 35, 1464–1472 (1996).
    [CrossRef] [PubMed]
  14. J. Helmcke, S. A. Lee, and J. L. Hall, “Dye laser spectrometer for ultrahigh spectral resolution: design and performance,” Appl. Opt. 21, 1686–1694 (1982).
    [CrossRef] [PubMed]
  15. J. H. T. Burke, O. Garcia, K. J. Hughes, B. Livedalen, and C. A. Sackett, “Compact implementation of a scanning transfer cavity lock,” Rev. Sci. Instrum. 76, 116105 (2005).
    [CrossRef]
  16. E. R. Peck and B. N. Khanna, “Dispersion of Nitrogen,” J. Opt. Soc. Am. 56, 1059–1063 (1966).
    [CrossRef]
  17. U. Griesmann and J. Burnett, “Refractivity of nitrogen gas in the vacuum ultraviolet,” Opt. Lett. 24, 1699–1701 (1999).
    [CrossRef]
  18. A. Buckingham and C. Graham, “The density dependence of the refractivity of gases,” Proc. R. Soc. A 337, 275–291 (1974).
    [CrossRef]
  19. J. Old, K. Gentili, and E. Peck, “Dispersion of carbon dioxide,” J. Opt. Soc. Am. 61, 89–90 (1971).
    [CrossRef]
  20. E. R. Peck and D. J. Fiisier, “Dispersion of argon,” J. Opt. Soc. Am. 54, 1362–1364 (1964).
    [CrossRef]
  21. J. Cariou and P. Luc, Atlas du Spectre d’Absorption de la Molecule de Tellure (Laboratoire Aime-Cotton, 1980), pp. 23.
  22. T. J. Scholl, S. J. Rehse, R. A. Holt, and S. D. Rosner, “Absolute wave-number measurements in Te2130: reference lines spanning the 420.9–464.6 nm region,” J. Opt. Soc. Am. B 22, 1128–1133(2005).
    [CrossRef]

2008 (1)

2006 (1)

P. Bohlouli-Zanjani, K. Afrousheh, and J. D. D. Martin, “Optical transfer cavity stabilization using current-modulated injection-locked diode lasers,” Rev. Sci. Instrum. 77, 093105–093109(2006).
[CrossRef]

2005 (3)

P. Gill, “Optical frequency standards,” Metrologia 42, S125–S137(2005).
[CrossRef]

J. H. T. Burke, O. Garcia, K. J. Hughes, B. Livedalen, and C. A. Sackett, “Compact implementation of a scanning transfer cavity lock,” Rev. Sci. Instrum. 76, 116105 (2005).
[CrossRef]

T. J. Scholl, S. J. Rehse, R. A. Holt, and S. D. Rosner, “Absolute wave-number measurements in Te2130: reference lines spanning the 420.9–464.6 nm region,” J. Opt. Soc. Am. B 22, 1128–1133(2005).
[CrossRef]

2002 (1)

A. Rossi, V. Biancalana, B. Mai, and L. Tomassetti, “Long-term drift laser frequency stabilization using purely optical reference,” Rev. Sci. Instrum. 73, 2544–2548 (2002).
[CrossRef]

1999 (1)

1998 (1)

W. Z. Zhao, J. E. Simsarian, L. A. Orozco, and G. D. Sprouse, “A computer-based digital feedback control of frequency drift of multiple lasers,” Rev. Sci. Instrum. 69, 3737–3740 (1998).
[CrossRef]

1996 (1)

1994 (1)

E. Riedle, S. H. Ashworth, J. J. T. Farrell Jr., and D. J. Nesbitt, “Stabilization and precise calibration of a continuous-wave difference frequency spectrometer by use of a simple transfer cavity,” Rev. Sci. Instrum. 65, 42–48 (1994).
[CrossRef]

1991 (1)

B. G. Lindsay, K. A. Smith, and F. B. Dunning, “Control of long-term output frequency drift in commercial dye lasers,” Rev. Sci. Instrum. 62, 1656–1657 (1991).
[CrossRef]

1990 (1)

C. Bradley, J. Chen, and R. G. Hulet, “Instrumentation for the stable operation of laser diodes,” Rev. Sci. Instrum. 61, 2097–2101 (1990).
[CrossRef]

1988 (1)

1982 (1)

1979 (1)

B. Burghardt, W. Jitschin, and G. Meisel, “Precise rf tuning for cw dye lasers,” Appl. Phys. 20, 141–146 (1979).
[CrossRef]

1974 (1)

A. Buckingham and C. Graham, “The density dependence of the refractivity of gases,” Proc. R. Soc. A 337, 275–291 (1974).
[CrossRef]

1971 (1)

1966 (1)

1964 (1)

1962 (2)

R. N. Hall, G. E. Fenner, J. D. Kingsley, T. J. Soltys, and R. O. Carlson, “Coherent light emission from GaAs junctions,” Phys. Rev. Lett. 9, 366–368 (1962).
[CrossRef]

M. I. Nathan, W. P. Dumke, G. Burns, F. H. Dill Jr., and G. Lasher, “Stimulated emission of radiation from GaAs p-n junctions,” Appl. Phys. Lett. 1, 62–64 (1962).
[CrossRef]

Afrousheh, K.

P. Bohlouli-Zanjani, K. Afrousheh, and J. D. D. Martin, “Optical transfer cavity stabilization using current-modulated injection-locked diode lasers,” Rev. Sci. Instrum. 77, 093105–093109(2006).
[CrossRef]

Ashworth, S. H.

E. Riedle, S. H. Ashworth, J. J. T. Farrell Jr., and D. J. Nesbitt, “Stabilization and precise calibration of a continuous-wave difference frequency spectrometer by use of a simple transfer cavity,” Rev. Sci. Instrum. 65, 42–48 (1994).
[CrossRef]

Biancalana, V.

A. Rossi, V. Biancalana, B. Mai, and L. Tomassetti, “Long-term drift laser frequency stabilization using purely optical reference,” Rev. Sci. Instrum. 73, 2544–2548 (2002).
[CrossRef]

Bohlouli-Zanjani, P.

P. Bohlouli-Zanjani, K. Afrousheh, and J. D. D. Martin, “Optical transfer cavity stabilization using current-modulated injection-locked diode lasers,” Rev. Sci. Instrum. 77, 093105–093109(2006).
[CrossRef]

Bradley, C.

C. Bradley, J. Chen, and R. G. Hulet, “Instrumentation for the stable operation of laser diodes,” Rev. Sci. Instrum. 61, 2097–2101 (1990).
[CrossRef]

Buckingham, A.

A. Buckingham and C. Graham, “The density dependence of the refractivity of gases,” Proc. R. Soc. A 337, 275–291 (1974).
[CrossRef]

Burghardt, B.

B. Burghardt, W. Jitschin, and G. Meisel, “Precise rf tuning for cw dye lasers,” Appl. Phys. 20, 141–146 (1979).
[CrossRef]

Burke, J. H. T.

J. H. T. Burke, O. Garcia, K. J. Hughes, B. Livedalen, and C. A. Sackett, “Compact implementation of a scanning transfer cavity lock,” Rev. Sci. Instrum. 76, 116105 (2005).
[CrossRef]

Burnett, J.

Burns, G.

M. I. Nathan, W. P. Dumke, G. Burns, F. H. Dill Jr., and G. Lasher, “Stimulated emission of radiation from GaAs p-n junctions,” Appl. Phys. Lett. 1, 62–64 (1962).
[CrossRef]

Cariou, J.

J. Cariou and P. Luc, Atlas du Spectre d’Absorption de la Molecule de Tellure (Laboratoire Aime-Cotton, 1980), pp. 23.

Carlson, R. O.

R. N. Hall, G. E. Fenner, J. D. Kingsley, T. J. Soltys, and R. O. Carlson, “Coherent light emission from GaAs junctions,” Phys. Rev. Lett. 9, 366–368 (1962).
[CrossRef]

Chen, J.

C. Bradley, J. Chen, and R. G. Hulet, “Instrumentation for the stable operation of laser diodes,” Rev. Sci. Instrum. 61, 2097–2101 (1990).
[CrossRef]

Dill, F. H.

M. I. Nathan, W. P. Dumke, G. Burns, F. H. Dill Jr., and G. Lasher, “Stimulated emission of radiation from GaAs p-n junctions,” Appl. Phys. Lett. 1, 62–64 (1962).
[CrossRef]

Dumke, W. P.

M. I. Nathan, W. P. Dumke, G. Burns, F. H. Dill Jr., and G. Lasher, “Stimulated emission of radiation from GaAs p-n junctions,” Appl. Phys. Lett. 1, 62–64 (1962).
[CrossRef]

Dunning, F. B.

B. G. Lindsay, K. A. Smith, and F. B. Dunning, “Control of long-term output frequency drift in commercial dye lasers,” Rev. Sci. Instrum. 62, 1656–1657 (1991).
[CrossRef]

Farrell, J. J. T.

E. Riedle, S. H. Ashworth, J. J. T. Farrell Jr., and D. J. Nesbitt, “Stabilization and precise calibration of a continuous-wave difference frequency spectrometer by use of a simple transfer cavity,” Rev. Sci. Instrum. 65, 42–48 (1994).
[CrossRef]

Fenner, G. E.

R. N. Hall, G. E. Fenner, J. D. Kingsley, T. J. Soltys, and R. O. Carlson, “Coherent light emission from GaAs junctions,” Phys. Rev. Lett. 9, 366–368 (1962).
[CrossRef]

Fiisier, D. J.

Garcia, O.

J. H. T. Burke, O. Garcia, K. J. Hughes, B. Livedalen, and C. A. Sackett, “Compact implementation of a scanning transfer cavity lock,” Rev. Sci. Instrum. 76, 116105 (2005).
[CrossRef]

Gentili, K.

Gill, P.

P. Gill, “Optical frequency standards,” Metrologia 42, S125–S137(2005).
[CrossRef]

Graham, C.

A. Buckingham and C. Graham, “The density dependence of the refractivity of gases,” Proc. R. Soc. A 337, 275–291 (1974).
[CrossRef]

Griesmann, U.

Hall, J. L.

Hall, R. N.

R. N. Hall, G. E. Fenner, J. D. Kingsley, T. J. Soltys, and R. O. Carlson, “Coherent light emission from GaAs junctions,” Phys. Rev. Lett. 9, 366–368 (1962).
[CrossRef]

Helmcke, J.

Holt, R. A.

Hughes, K. J.

J. H. T. Burke, O. Garcia, K. J. Hughes, B. Livedalen, and C. A. Sackett, “Compact implementation of a scanning transfer cavity lock,” Rev. Sci. Instrum. 76, 116105 (2005).
[CrossRef]

Hulet, R. G.

C. Bradley, J. Chen, and R. G. Hulet, “Instrumentation for the stable operation of laser diodes,” Rev. Sci. Instrum. 61, 2097–2101 (1990).
[CrossRef]

Jitschin, W.

B. Burghardt, W. Jitschin, and G. Meisel, “Precise rf tuning for cw dye lasers,” Appl. Phys. 20, 141–146 (1979).
[CrossRef]

Khanna, B. N.

Kingsley, J. D.

R. N. Hall, G. E. Fenner, J. D. Kingsley, T. J. Soltys, and R. O. Carlson, “Coherent light emission from GaAs junctions,” Phys. Rev. Lett. 9, 366–368 (1962).
[CrossRef]

Lasher, G.

M. I. Nathan, W. P. Dumke, G. Burns, F. H. Dill Jr., and G. Lasher, “Stimulated emission of radiation from GaAs p-n junctions,” Appl. Phys. Lett. 1, 62–64 (1962).
[CrossRef]

Lee, S. A.

Lindsay, B. G.

B. G. Lindsay, K. A. Smith, and F. B. Dunning, “Control of long-term output frequency drift in commercial dye lasers,” Rev. Sci. Instrum. 62, 1656–1657 (1991).
[CrossRef]

Livas, J.

Livedalen, B.

J. H. T. Burke, O. Garcia, K. J. Hughes, B. Livedalen, and C. A. Sackett, “Compact implementation of a scanning transfer cavity lock,” Rev. Sci. Instrum. 76, 116105 (2005).
[CrossRef]

Luc, P.

J. Cariou and P. Luc, Atlas du Spectre d’Absorption de la Molecule de Tellure (Laboratoire Aime-Cotton, 1980), pp. 23.

Mai, B.

A. Rossi, V. Biancalana, B. Mai, and L. Tomassetti, “Long-term drift laser frequency stabilization using purely optical reference,” Rev. Sci. Instrum. 73, 2544–2548 (2002).
[CrossRef]

Martin, J. D. D.

P. Bohlouli-Zanjani, K. Afrousheh, and J. D. D. Martin, “Optical transfer cavity stabilization using current-modulated injection-locked diode lasers,” Rev. Sci. Instrum. 77, 093105–093109(2006).
[CrossRef]

Meisel, G.

B. Burghardt, W. Jitschin, and G. Meisel, “Precise rf tuning for cw dye lasers,” Appl. Phys. 20, 141–146 (1979).
[CrossRef]

Nathan, M. I.

M. I. Nathan, W. P. Dumke, G. Burns, F. H. Dill Jr., and G. Lasher, “Stimulated emission of radiation from GaAs p-n junctions,” Appl. Phys. Lett. 1, 62–64 (1962).
[CrossRef]

Nesbitt, D. J.

D. F. Plusquellic, O. Votava, and D. J. Nesbitt, “Absolute frequency stabilization of an injection-seeded optical parametric oscillator,” Appl. Opt. 35, 1464–1472 (1996).
[CrossRef] [PubMed]

E. Riedle, S. H. Ashworth, J. J. T. Farrell Jr., and D. J. Nesbitt, “Stabilization and precise calibration of a continuous-wave difference frequency spectrometer by use of a simple transfer cavity,” Rev. Sci. Instrum. 65, 42–48 (1994).
[CrossRef]

Numata, K.

Old, J.

Orozco, L. A.

W. Z. Zhao, J. E. Simsarian, L. A. Orozco, and G. D. Sprouse, “A computer-based digital feedback control of frequency drift of multiple lasers,” Rev. Sci. Instrum. 69, 3737–3740 (1998).
[CrossRef]

Peck, E.

Peck, E. R.

Plusquellic, D. F.

Rehse, S. J.

Riedle, E.

E. Riedle, S. H. Ashworth, J. J. T. Farrell Jr., and D. J. Nesbitt, “Stabilization and precise calibration of a continuous-wave difference frequency spectrometer by use of a simple transfer cavity,” Rev. Sci. Instrum. 65, 42–48 (1994).
[CrossRef]

Rosner, S. D.

Rossi, A.

A. Rossi, V. Biancalana, B. Mai, and L. Tomassetti, “Long-term drift laser frequency stabilization using purely optical reference,” Rev. Sci. Instrum. 73, 2544–2548 (2002).
[CrossRef]

Sackett, C. A.

J. H. T. Burke, O. Garcia, K. J. Hughes, B. Livedalen, and C. A. Sackett, “Compact implementation of a scanning transfer cavity lock,” Rev. Sci. Instrum. 76, 116105 (2005).
[CrossRef]

Scholl, T. J.

Simsarian, J. E.

W. Z. Zhao, J. E. Simsarian, L. A. Orozco, and G. D. Sprouse, “A computer-based digital feedback control of frequency drift of multiple lasers,” Rev. Sci. Instrum. 69, 3737–3740 (1998).
[CrossRef]

Smith, K. A.

B. G. Lindsay, K. A. Smith, and F. B. Dunning, “Control of long-term output frequency drift in commercial dye lasers,” Rev. Sci. Instrum. 62, 1656–1657 (1991).
[CrossRef]

Soltys, T. J.

R. N. Hall, G. E. Fenner, J. D. Kingsley, T. J. Soltys, and R. O. Carlson, “Coherent light emission from GaAs junctions,” Phys. Rev. Lett. 9, 366–368 (1962).
[CrossRef]

Sprouse, G. D.

W. Z. Zhao, J. E. Simsarian, L. A. Orozco, and G. D. Sprouse, “A computer-based digital feedback control of frequency drift of multiple lasers,” Rev. Sci. Instrum. 69, 3737–3740 (1998).
[CrossRef]

Thorpe, J. I.

Tomassetti, L.

A. Rossi, V. Biancalana, B. Mai, and L. Tomassetti, “Long-term drift laser frequency stabilization using purely optical reference,” Rev. Sci. Instrum. 73, 2544–2548 (2002).
[CrossRef]

Votava, O.

Wang, D.

Wang, Y.

Xie, L.

Zhao, W. Z.

W. Z. Zhao, J. E. Simsarian, L. A. Orozco, and G. D. Sprouse, “A computer-based digital feedback control of frequency drift of multiple lasers,” Rev. Sci. Instrum. 69, 3737–3740 (1998).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. (1)

B. Burghardt, W. Jitschin, and G. Meisel, “Precise rf tuning for cw dye lasers,” Appl. Phys. 20, 141–146 (1979).
[CrossRef]

Appl. Phys. Lett. (1)

M. I. Nathan, W. P. Dumke, G. Burns, F. H. Dill Jr., and G. Lasher, “Stimulated emission of radiation from GaAs p-n junctions,” Appl. Phys. Lett. 1, 62–64 (1962).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. B (1)

Metrologia (1)

P. Gill, “Optical frequency standards,” Metrologia 42, S125–S137(2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

R. N. Hall, G. E. Fenner, J. D. Kingsley, T. J. Soltys, and R. O. Carlson, “Coherent light emission from GaAs junctions,” Phys. Rev. Lett. 9, 366–368 (1962).
[CrossRef]

Proc. R. Soc. A (1)

A. Buckingham and C. Graham, “The density dependence of the refractivity of gases,” Proc. R. Soc. A 337, 275–291 (1974).
[CrossRef]

Rev. Sci. Instrum. (7)

J. H. T. Burke, O. Garcia, K. J. Hughes, B. Livedalen, and C. A. Sackett, “Compact implementation of a scanning transfer cavity lock,” Rev. Sci. Instrum. 76, 116105 (2005).
[CrossRef]

C. Bradley, J. Chen, and R. G. Hulet, “Instrumentation for the stable operation of laser diodes,” Rev. Sci. Instrum. 61, 2097–2101 (1990).
[CrossRef]

E. Riedle, S. H. Ashworth, J. J. T. Farrell Jr., and D. J. Nesbitt, “Stabilization and precise calibration of a continuous-wave difference frequency spectrometer by use of a simple transfer cavity,” Rev. Sci. Instrum. 65, 42–48 (1994).
[CrossRef]

P. Bohlouli-Zanjani, K. Afrousheh, and J. D. D. Martin, “Optical transfer cavity stabilization using current-modulated injection-locked diode lasers,” Rev. Sci. Instrum. 77, 093105–093109(2006).
[CrossRef]

B. G. Lindsay, K. A. Smith, and F. B. Dunning, “Control of long-term output frequency drift in commercial dye lasers,” Rev. Sci. Instrum. 62, 1656–1657 (1991).
[CrossRef]

W. Z. Zhao, J. E. Simsarian, L. A. Orozco, and G. D. Sprouse, “A computer-based digital feedback control of frequency drift of multiple lasers,” Rev. Sci. Instrum. 69, 3737–3740 (1998).
[CrossRef]

A. Rossi, V. Biancalana, B. Mai, and L. Tomassetti, “Long-term drift laser frequency stabilization using purely optical reference,” Rev. Sci. Instrum. 73, 2544–2548 (2002).
[CrossRef]

Other (1)

J. Cariou and P. Luc, Atlas du Spectre d’Absorption de la Molecule de Tellure (Laboratoire Aime-Cotton, 1980), pp. 23.

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Figures (6)

Fig. 1
Fig. 1

Laser locking system. The FP etalon is fixed inside a pressure chamber. Both the He–Ne laser and the blue diode laser are resonant with the etalon, and, after filtering optics, each one is seen on its own photodiode.

Fig. 2
Fig. 2

Plot of Eq. (8) spanning roughly 3 atm of pressure for fixed T = 15 ° C and ν R = 632.8 nm .

Fig. 3
Fig. 3

Optics surrounding the tellurium cell, which is held at 650 ° C . The dashed box groups together the components that serve as an electro-optical chopper.

Fig. 4
Fig. 4

Preliminary diode laser grating scan, accurate to 50 MHz . The downward spikes are 1 GHz “markers” seen through the etalon. The alignment was set such that every other marker was diminished in amplitude.

Fig. 5
Fig. 5

Seven CDT scans of two lines, taken over a period of two days. Some data sets include 4000000 MHz sidebands. The x axis of this scan comes directly from Eq. (8).

Fig. 6
Fig. 6

Diode grating position at each point during a typical CDT scan. At this scale, one can see that a grating scan is quite nonlinear in frequency.

Tables (1)

Tables Icon

Table 1 Our Reported Intervals and Those of [21] a

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

L = λ R 2 ( N R + δ R ) = c 2 ν R n R N R
L = λ 2 ( N + δ ) = c 2 ν n N
n ν n R ν R = N R N = A constant .
n ( P 0 , T 0 ) 1 = ( 6497.378 + 3073864.9 144 k 2 ) / 10 8 α 0 ( k ) ,
α f ( k ) = α i ( k ) Γ i f ,
Γ i f = ( P f / T f ) Z i ( P i / T i ) Z f + α i Z i ( P i / T i P f / T f ) / 6 P f T f / P i T i
Z = 1 + P ( T 317.6 K ) × 10 5 760 torr
Δ ν i f = ( Γ 0 f Γ 0 i ) ( α 0 ( k R ) α 0 ( k ) ) ( 1 + α 0 ( k R ) Γ 0 i ) ( 1 + Γ 0 f α 0 ( k ) ) ν i .

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