Abstract

The relative changes in refractive index of the amplifying medium in a waveguide CO2 laser have been measured as a function of the inlet and outlet pressures, discharge current, gas flow rate, and intracavity power using an interferometric technique. The experiments have been made for two gas mixing ratios over a wide range of the inlet pressure. Saturated phenomena of the refractive index have been observed for increasing inlet pressure. The output power and the varitaion in impedance of the amplifying medium have been simultaneously measured. The dependence of the refractive index on the inlet pressure in the absence of the discharge, the electron density, and the estimation of errors in measurements are discussed.

© 1986 Optical Society of America

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  1. E. A. J. Marcatili, R. A. Schmeltzer, “Hollow Metallic and Dielectric Waveguides for Long Distance Optical Transmission and Lasers,” Bell Syst. Tech. J. 41, 1783 (1964).
  2. P. W. Smith, “A Waveguide Gas Laser,” Appl. Phys. Lett. 19, 132 (1971).
    [CrossRef]
  3. T. J. Bridges, E. G. Burkhardt, P. W. Smith, “CO2 Waveguide Lasers,” Appl. Phys. Lett. 20, 403 (1972).
    [CrossRef]
  4. For a review of waveguide lasers see J. J. Degnan, “The Waveguide Laser: A Review,” Appl. Phys. 11, 1 (1976).
    [CrossRef]
  5. H. W. Mocker, “Pressure and Current Shifts in the Frequency of Oscillation of the CO2 Laser,” Appl. Phys. Lett. 12, 20 (1968).
    [CrossRef]
  6. A. Van Lerberghe, S. Avrillier, C. J. Borde, “High Stability CW Waveguide CO2 Laser for High Resolution Saturation Spectroscopy,” IEEE J. Quantum Electron QE-14, 481 (1978).
    [CrossRef]
  7. Y. Ohwada, T. Tako, “A New Counting Method in Wavelength Measurement Utilizing the Tuning Curve of Laser Output,” Kogaku 3, 305 (1974), in Japanese.
  8. J. J. Degnan, D. R. Hall, “Finite-Aperture Waveguide-Laser Resonators,” IEEE J. Quantum Electron. QE-9, 901 (1973).
    [CrossRef]
  9. For example, W. Demtroder, Laser Spectroscopy (Springer-Verlag, Berlin, 1981), p. 292.
  10. D. E. Gray, Ed., American Institute of Physics Handbook, (McGraw-Hill, New York, 1972), p. 6–110.
  11. M. Lyszyk, F. Herlemont, J. Lemaire, “On the Tuning Range of a CW Double-Discharge Pyrex Waveguide 12C16 O2 Laser,” J. Phys. E 10, 1110 (1977).
    [CrossRef]
  12. T. Kurosawa, T. Sakurai, K. Tanaka, “DC Bias Dependence of W-Ni and W-Co Point-Contact Diodes as Harmonic Generators and Mixers at 9.4 μm,” Appl. Phys. Lett. 36, 751 (1980).
    [CrossRef]
  13. R. L. Abrams, “Gigahertz Tunable Waveguide CO2 Laser,” Appl. Phys. Lett. 25, 304 (1974).
    [CrossRef]
  14. R. L. Abrams, W. B. Bridges, “Characteristics of Sealed-Off Waveguide CO2 Lasers,” IEEE J. Quantum Electron. QE-9, 940 (1973).
    [CrossRef]
  15. Z. Kucerovsky, E. Brannen, “Operating Characteristics of a Fixed Alignment CO2 Waveguide Laser,” Rev. Sci. Instrum. 54, 1135 (1983).
    [CrossRef]
  16. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 96.
  17. J. B. Gerardo, J. T. Verdeyen, “The Laser Interferometer: Application to Plasma Diagnostics,” Proc. IEEE 52, 690 (1964).
    [CrossRef]
  18. P. K. Cheo, “CO2 Laser,” in Lasers: A Series of Advances, Vol. 3, A. K. Levine, A. J. DeMaria, Eds. (Marcel Dekker, New York, 1971), p. 201.
  19. W. J. Witteman, “A Sealed-Off Michelson Type CO2 Laser for Diagnostic Studies of Gaseous Plasma,” Appl. Phys. Lett. 10, 347 (1967).
    [CrossRef]
  20. A. I. Carswell, J. I. Wood, “Plasma Properties of a CO2 Laser Discharge,” J. Appl. Phys. 38, 3028 (1967).
    [CrossRef]
  21. N. Ioli, V. Panchenko, M. Pellegrino, F. Strumia, “Amplification and Saturation in a CO2 Waveguide Amplifier,” Appl. Phys. B 38, 23 (1985).
    [CrossRef]
  22. T. L. Killeen, P. B. Hays, B. C. Kennedy, D. Rees, “Stable and Rugged Etalon for the Dynamics Explorer Fabry-Perot Interferometer. 2: Performance,” Appl. Opt. 21, 3903 (1982).
    [CrossRef] [PubMed]

1985

N. Ioli, V. Panchenko, M. Pellegrino, F. Strumia, “Amplification and Saturation in a CO2 Waveguide Amplifier,” Appl. Phys. B 38, 23 (1985).
[CrossRef]

1983

Z. Kucerovsky, E. Brannen, “Operating Characteristics of a Fixed Alignment CO2 Waveguide Laser,” Rev. Sci. Instrum. 54, 1135 (1983).
[CrossRef]

1982

1980

T. Kurosawa, T. Sakurai, K. Tanaka, “DC Bias Dependence of W-Ni and W-Co Point-Contact Diodes as Harmonic Generators and Mixers at 9.4 μm,” Appl. Phys. Lett. 36, 751 (1980).
[CrossRef]

1978

A. Van Lerberghe, S. Avrillier, C. J. Borde, “High Stability CW Waveguide CO2 Laser for High Resolution Saturation Spectroscopy,” IEEE J. Quantum Electron QE-14, 481 (1978).
[CrossRef]

1977

M. Lyszyk, F. Herlemont, J. Lemaire, “On the Tuning Range of a CW Double-Discharge Pyrex Waveguide 12C16 O2 Laser,” J. Phys. E 10, 1110 (1977).
[CrossRef]

1976

For a review of waveguide lasers see J. J. Degnan, “The Waveguide Laser: A Review,” Appl. Phys. 11, 1 (1976).
[CrossRef]

1974

Y. Ohwada, T. Tako, “A New Counting Method in Wavelength Measurement Utilizing the Tuning Curve of Laser Output,” Kogaku 3, 305 (1974), in Japanese.

R. L. Abrams, “Gigahertz Tunable Waveguide CO2 Laser,” Appl. Phys. Lett. 25, 304 (1974).
[CrossRef]

1973

R. L. Abrams, W. B. Bridges, “Characteristics of Sealed-Off Waveguide CO2 Lasers,” IEEE J. Quantum Electron. QE-9, 940 (1973).
[CrossRef]

J. J. Degnan, D. R. Hall, “Finite-Aperture Waveguide-Laser Resonators,” IEEE J. Quantum Electron. QE-9, 901 (1973).
[CrossRef]

1972

T. J. Bridges, E. G. Burkhardt, P. W. Smith, “CO2 Waveguide Lasers,” Appl. Phys. Lett. 20, 403 (1972).
[CrossRef]

1971

P. W. Smith, “A Waveguide Gas Laser,” Appl. Phys. Lett. 19, 132 (1971).
[CrossRef]

1968

H. W. Mocker, “Pressure and Current Shifts in the Frequency of Oscillation of the CO2 Laser,” Appl. Phys. Lett. 12, 20 (1968).
[CrossRef]

1967

W. J. Witteman, “A Sealed-Off Michelson Type CO2 Laser for Diagnostic Studies of Gaseous Plasma,” Appl. Phys. Lett. 10, 347 (1967).
[CrossRef]

A. I. Carswell, J. I. Wood, “Plasma Properties of a CO2 Laser Discharge,” J. Appl. Phys. 38, 3028 (1967).
[CrossRef]

1964

J. B. Gerardo, J. T. Verdeyen, “The Laser Interferometer: Application to Plasma Diagnostics,” Proc. IEEE 52, 690 (1964).
[CrossRef]

E. A. J. Marcatili, R. A. Schmeltzer, “Hollow Metallic and Dielectric Waveguides for Long Distance Optical Transmission and Lasers,” Bell Syst. Tech. J. 41, 1783 (1964).

Abrams, R. L.

R. L. Abrams, “Gigahertz Tunable Waveguide CO2 Laser,” Appl. Phys. Lett. 25, 304 (1974).
[CrossRef]

R. L. Abrams, W. B. Bridges, “Characteristics of Sealed-Off Waveguide CO2 Lasers,” IEEE J. Quantum Electron. QE-9, 940 (1973).
[CrossRef]

Avrillier, S.

A. Van Lerberghe, S. Avrillier, C. J. Borde, “High Stability CW Waveguide CO2 Laser for High Resolution Saturation Spectroscopy,” IEEE J. Quantum Electron QE-14, 481 (1978).
[CrossRef]

Borde, C. J.

A. Van Lerberghe, S. Avrillier, C. J. Borde, “High Stability CW Waveguide CO2 Laser for High Resolution Saturation Spectroscopy,” IEEE J. Quantum Electron QE-14, 481 (1978).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 96.

Brannen, E.

Z. Kucerovsky, E. Brannen, “Operating Characteristics of a Fixed Alignment CO2 Waveguide Laser,” Rev. Sci. Instrum. 54, 1135 (1983).
[CrossRef]

Bridges, T. J.

T. J. Bridges, E. G. Burkhardt, P. W. Smith, “CO2 Waveguide Lasers,” Appl. Phys. Lett. 20, 403 (1972).
[CrossRef]

Bridges, W. B.

R. L. Abrams, W. B. Bridges, “Characteristics of Sealed-Off Waveguide CO2 Lasers,” IEEE J. Quantum Electron. QE-9, 940 (1973).
[CrossRef]

Burkhardt, E. G.

T. J. Bridges, E. G. Burkhardt, P. W. Smith, “CO2 Waveguide Lasers,” Appl. Phys. Lett. 20, 403 (1972).
[CrossRef]

Carswell, A. I.

A. I. Carswell, J. I. Wood, “Plasma Properties of a CO2 Laser Discharge,” J. Appl. Phys. 38, 3028 (1967).
[CrossRef]

Cheo, P. K.

P. K. Cheo, “CO2 Laser,” in Lasers: A Series of Advances, Vol. 3, A. K. Levine, A. J. DeMaria, Eds. (Marcel Dekker, New York, 1971), p. 201.

Degnan, J. J.

For a review of waveguide lasers see J. J. Degnan, “The Waveguide Laser: A Review,” Appl. Phys. 11, 1 (1976).
[CrossRef]

J. J. Degnan, D. R. Hall, “Finite-Aperture Waveguide-Laser Resonators,” IEEE J. Quantum Electron. QE-9, 901 (1973).
[CrossRef]

Demtroder, W.

For example, W. Demtroder, Laser Spectroscopy (Springer-Verlag, Berlin, 1981), p. 292.

Gerardo, J. B.

J. B. Gerardo, J. T. Verdeyen, “The Laser Interferometer: Application to Plasma Diagnostics,” Proc. IEEE 52, 690 (1964).
[CrossRef]

Hall, D. R.

J. J. Degnan, D. R. Hall, “Finite-Aperture Waveguide-Laser Resonators,” IEEE J. Quantum Electron. QE-9, 901 (1973).
[CrossRef]

Hays, P. B.

Herlemont, F.

M. Lyszyk, F. Herlemont, J. Lemaire, “On the Tuning Range of a CW Double-Discharge Pyrex Waveguide 12C16 O2 Laser,” J. Phys. E 10, 1110 (1977).
[CrossRef]

Ioli, N.

N. Ioli, V. Panchenko, M. Pellegrino, F. Strumia, “Amplification and Saturation in a CO2 Waveguide Amplifier,” Appl. Phys. B 38, 23 (1985).
[CrossRef]

Kennedy, B. C.

Killeen, T. L.

Kucerovsky, Z.

Z. Kucerovsky, E. Brannen, “Operating Characteristics of a Fixed Alignment CO2 Waveguide Laser,” Rev. Sci. Instrum. 54, 1135 (1983).
[CrossRef]

Kurosawa, T.

T. Kurosawa, T. Sakurai, K. Tanaka, “DC Bias Dependence of W-Ni and W-Co Point-Contact Diodes as Harmonic Generators and Mixers at 9.4 μm,” Appl. Phys. Lett. 36, 751 (1980).
[CrossRef]

Lemaire, J.

M. Lyszyk, F. Herlemont, J. Lemaire, “On the Tuning Range of a CW Double-Discharge Pyrex Waveguide 12C16 O2 Laser,” J. Phys. E 10, 1110 (1977).
[CrossRef]

Lyszyk, M.

M. Lyszyk, F. Herlemont, J. Lemaire, “On the Tuning Range of a CW Double-Discharge Pyrex Waveguide 12C16 O2 Laser,” J. Phys. E 10, 1110 (1977).
[CrossRef]

Marcatili, E. A. J.

E. A. J. Marcatili, R. A. Schmeltzer, “Hollow Metallic and Dielectric Waveguides for Long Distance Optical Transmission and Lasers,” Bell Syst. Tech. J. 41, 1783 (1964).

Mocker, H. W.

H. W. Mocker, “Pressure and Current Shifts in the Frequency of Oscillation of the CO2 Laser,” Appl. Phys. Lett. 12, 20 (1968).
[CrossRef]

Ohwada, Y.

Y. Ohwada, T. Tako, “A New Counting Method in Wavelength Measurement Utilizing the Tuning Curve of Laser Output,” Kogaku 3, 305 (1974), in Japanese.

Panchenko, V.

N. Ioli, V. Panchenko, M. Pellegrino, F. Strumia, “Amplification and Saturation in a CO2 Waveguide Amplifier,” Appl. Phys. B 38, 23 (1985).
[CrossRef]

Pellegrino, M.

N. Ioli, V. Panchenko, M. Pellegrino, F. Strumia, “Amplification and Saturation in a CO2 Waveguide Amplifier,” Appl. Phys. B 38, 23 (1985).
[CrossRef]

Rees, D.

Sakurai, T.

T. Kurosawa, T. Sakurai, K. Tanaka, “DC Bias Dependence of W-Ni and W-Co Point-Contact Diodes as Harmonic Generators and Mixers at 9.4 μm,” Appl. Phys. Lett. 36, 751 (1980).
[CrossRef]

Schmeltzer, R. A.

E. A. J. Marcatili, R. A. Schmeltzer, “Hollow Metallic and Dielectric Waveguides for Long Distance Optical Transmission and Lasers,” Bell Syst. Tech. J. 41, 1783 (1964).

Smith, P. W.

T. J. Bridges, E. G. Burkhardt, P. W. Smith, “CO2 Waveguide Lasers,” Appl. Phys. Lett. 20, 403 (1972).
[CrossRef]

P. W. Smith, “A Waveguide Gas Laser,” Appl. Phys. Lett. 19, 132 (1971).
[CrossRef]

Strumia, F.

N. Ioli, V. Panchenko, M. Pellegrino, F. Strumia, “Amplification and Saturation in a CO2 Waveguide Amplifier,” Appl. Phys. B 38, 23 (1985).
[CrossRef]

Tako, T.

Y. Ohwada, T. Tako, “A New Counting Method in Wavelength Measurement Utilizing the Tuning Curve of Laser Output,” Kogaku 3, 305 (1974), in Japanese.

Tanaka, K.

T. Kurosawa, T. Sakurai, K. Tanaka, “DC Bias Dependence of W-Ni and W-Co Point-Contact Diodes as Harmonic Generators and Mixers at 9.4 μm,” Appl. Phys. Lett. 36, 751 (1980).
[CrossRef]

Van Lerberghe, A.

A. Van Lerberghe, S. Avrillier, C. J. Borde, “High Stability CW Waveguide CO2 Laser for High Resolution Saturation Spectroscopy,” IEEE J. Quantum Electron QE-14, 481 (1978).
[CrossRef]

Verdeyen, J. T.

J. B. Gerardo, J. T. Verdeyen, “The Laser Interferometer: Application to Plasma Diagnostics,” Proc. IEEE 52, 690 (1964).
[CrossRef]

Witteman, W. J.

W. J. Witteman, “A Sealed-Off Michelson Type CO2 Laser for Diagnostic Studies of Gaseous Plasma,” Appl. Phys. Lett. 10, 347 (1967).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 96.

Wood, J. I.

A. I. Carswell, J. I. Wood, “Plasma Properties of a CO2 Laser Discharge,” J. Appl. Phys. 38, 3028 (1967).
[CrossRef]

Appl. Opt.

Appl. Phys.

For a review of waveguide lasers see J. J. Degnan, “The Waveguide Laser: A Review,” Appl. Phys. 11, 1 (1976).
[CrossRef]

Appl. Phys. B

N. Ioli, V. Panchenko, M. Pellegrino, F. Strumia, “Amplification and Saturation in a CO2 Waveguide Amplifier,” Appl. Phys. B 38, 23 (1985).
[CrossRef]

Appl. Phys. Lett.

W. J. Witteman, “A Sealed-Off Michelson Type CO2 Laser for Diagnostic Studies of Gaseous Plasma,” Appl. Phys. Lett. 10, 347 (1967).
[CrossRef]

H. W. Mocker, “Pressure and Current Shifts in the Frequency of Oscillation of the CO2 Laser,” Appl. Phys. Lett. 12, 20 (1968).
[CrossRef]

P. W. Smith, “A Waveguide Gas Laser,” Appl. Phys. Lett. 19, 132 (1971).
[CrossRef]

T. J. Bridges, E. G. Burkhardt, P. W. Smith, “CO2 Waveguide Lasers,” Appl. Phys. Lett. 20, 403 (1972).
[CrossRef]

T. Kurosawa, T. Sakurai, K. Tanaka, “DC Bias Dependence of W-Ni and W-Co Point-Contact Diodes as Harmonic Generators and Mixers at 9.4 μm,” Appl. Phys. Lett. 36, 751 (1980).
[CrossRef]

R. L. Abrams, “Gigahertz Tunable Waveguide CO2 Laser,” Appl. Phys. Lett. 25, 304 (1974).
[CrossRef]

Bell Syst. Tech. J.

E. A. J. Marcatili, R. A. Schmeltzer, “Hollow Metallic and Dielectric Waveguides for Long Distance Optical Transmission and Lasers,” Bell Syst. Tech. J. 41, 1783 (1964).

IEEE J. Quantum Electron

A. Van Lerberghe, S. Avrillier, C. J. Borde, “High Stability CW Waveguide CO2 Laser for High Resolution Saturation Spectroscopy,” IEEE J. Quantum Electron QE-14, 481 (1978).
[CrossRef]

IEEE J. Quantum Electron.

J. J. Degnan, D. R. Hall, “Finite-Aperture Waveguide-Laser Resonators,” IEEE J. Quantum Electron. QE-9, 901 (1973).
[CrossRef]

R. L. Abrams, W. B. Bridges, “Characteristics of Sealed-Off Waveguide CO2 Lasers,” IEEE J. Quantum Electron. QE-9, 940 (1973).
[CrossRef]

J. Appl. Phys.

A. I. Carswell, J. I. Wood, “Plasma Properties of a CO2 Laser Discharge,” J. Appl. Phys. 38, 3028 (1967).
[CrossRef]

J. Phys. E

M. Lyszyk, F. Herlemont, J. Lemaire, “On the Tuning Range of a CW Double-Discharge Pyrex Waveguide 12C16 O2 Laser,” J. Phys. E 10, 1110 (1977).
[CrossRef]

Kogaku

Y. Ohwada, T. Tako, “A New Counting Method in Wavelength Measurement Utilizing the Tuning Curve of Laser Output,” Kogaku 3, 305 (1974), in Japanese.

Proc. IEEE

J. B. Gerardo, J. T. Verdeyen, “The Laser Interferometer: Application to Plasma Diagnostics,” Proc. IEEE 52, 690 (1964).
[CrossRef]

Rev. Sci. Instrum.

Z. Kucerovsky, E. Brannen, “Operating Characteristics of a Fixed Alignment CO2 Waveguide Laser,” Rev. Sci. Instrum. 54, 1135 (1983).
[CrossRef]

Other

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 96.

P. K. Cheo, “CO2 Laser,” in Lasers: A Series of Advances, Vol. 3, A. K. Levine, A. J. DeMaria, Eds. (Marcel Dekker, New York, 1971), p. 201.

For example, W. Demtroder, Laser Spectroscopy (Springer-Verlag, Berlin, 1981), p. 292.

D. E. Gray, Ed., American Institute of Physics Handbook, (McGraw-Hill, New York, 1972), p. 6–110.

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Figures (10)

Fig. 1
Fig. 1

Changes in cavity mode position for a 10.6-μm CO2 laser and its mode spacing measured by interference fringes for a 0.633-μm He–Ne laser when the voltage was applied to the PZT.

Fig. 2
Fig. 2

Experimental apparatus used for measuring the refractive-index changes of the amplifying medium in the waveguide CO2 laser.

Fig. 3
Fig. 3

Experimental apparatus used for measuring the refractive index change of the amplifying medium in the waveguide CO2 laser.

Fig. 4
Fig. 4

(a) Refractive-index change, (b) output power, and (c) impedance change and outlet pressure measured as a function of inlet pressure with the discharge current fixed at 2.5 mA. Open circles (solid curve) are for CO2:N2:He = 1:1:4, and triangles (dotted curve) are for CO2:N2:He = 1:0.72:2. Broken lines in (a) show the relative changes in refractive index calculated by using the Cauchy formula in the absence of discharge.

Fig. 5
Fig. 5

(a) Refractive-index change, (b) output power, and (c) impedance change and inlet pressure measured as a function of outlet pressure in the conditions of I0 = 2.5 mA, CO2:N2:He = 1:1:4. Open circles (solid curve) are for inlet pressure fixed at 10 kPa. Solid circles (dotted curve) are for variations in inlet pressure with increasing outlet pressure.

Fig. 6
Fig. 6

(a) Refractive-index change, (b) output power, and (c) impedance change measured as a function of discharge current in the conditions of pi 10 kPa and po = 2 kPa for two gas mixing ratios. Open circles (solid curve) are for CO2:N2:He = 1:1:4 and triangles (dotted curve) are for CO2:N2:He = 1:0.72:2.

Fig. 7
Fig. 7

(a) Refractive-index change, (b) output power, and (c) impedance change and outlet presure measured as a function of gas flow rate with pi = 10 kPa, I0 = 2.5 mA, and CO2:N2:He = 1:1:4.

Fig. 8
Fig. 8

(a) Refractive-index change, (b) output power, and (c) impedance change and outlet pressure measured as a function of inlet pressure with gas flow rate fixed at (7 ± 0.5) liters/min for I0 = 2.5 mA and CO2:N2:He = 1:1:4.

Fig. 9
Fig. 9

Refractive-index change measured as a function of intracavity power in the operating conditions of pi = 10 kPa, I0 = 2.5 mA, Z = 1.72 MΩ, and CO2:N2:He = 1:1:4.

Fig. 10
Fig. 10

Expansion of the (a) cavity length and (b) output power when the (c) room temperature was reduced from 24.2 to 23.4°C with pi = 10 kPa, I0 = 2.5 mA, and CO2:N2:He = 1:1:4. On and Off mean that the air-conditioned apparatus is switched on (off) to reduce room temperature. Start and End mean the beginning (finish) of measurements.

Equations (21)

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q λ = 2 n 1 ( d - L ) + 2 n 2 L ,
q Δ λ = 2 n 1 Δ d + 2 Δ n 2 L .
Δ λ λ = n 1 Δ d + Δ n 2 L n 1 ( d - L ) + n 2 L .
Δ n 2 = 1 2 L ( - 2 n 1 Δ d + q λ Δ λ λ ) .
n 1 = 1 + δ n ,
Δ n 2 = - Δ d L - 1 L ( δ n · Δ d ) + q λ 2 L ( Δ λ λ ) .
q λ 2 L ( Δ λ λ ) = d L ( Δ λ λ ) .
Δ n = - Δ d L .
Δ n × 10 6 = - 0.19 ( p i - 14.1 ) 2 + 20.5 for CO 2 : N 2 : He = 1 : 1 : 4 , Δ n × 10 6 = - 0.37 ( p i - 9.75 ) 2 + 17.2 for CO 2 : N 2 : He = 1 : 0.72 : 2.
P g = - 0.55 ( p i - 13.2 ) 2 + 58.2 for CO 2 : N 2 : He = 1 : 1 : 4 , P g = - 1.05 ( p i - 9.05 ) 2 + 50.5 for CO 2 : N 2 : He = 1 : 0.72 : 2.
Δ n × 10 6 = - 0.55 I 0 3 + 4.32 I 0 2 - 11.4 I 0 + 10.9 for CO 2 : N 2 : He = 1 : 1 : 4 , Δ n × 10 6 = - 0.20 I 0 3 + 1.56 I 0 2 - 2.92 I 0 + 0.93 for CO 2 : N 2 : He = 1 : 0.72 : 2 , P g = - 1.49 I 0 3 + 14.9 I 0 2 - 41.5 I 0 + 81.2 for CO 2 : N 2 : He = 1 : 1 : 4 , P g = - 1.83 I 0 3 + 12.71 I 0 2 - 21.5 I 0 + 50.5 for CO 2 : N 2 : He = 1 : 0.72 : 2 ,
Δ n × 10 6 = 3.0 Q ,             P g = 11.3 Q + 11.1
Δ n × 10 6 = - 0.46 ( p i - 7.9 ) 2 + 7.0 , P g = - 1.64 ( p i - 8.6 ) 2 + 42.7.
P i = P w r 1 r ( 1 - r ) 2 + r 1 r ( 1 - r ) 4 = P g 1 - r 2 ,
Δ n × 10 6 = 4.97 W - 1 for P i , Δ n × 10 6 = 0.17 mW - 1 for P g .
Δ n ( P g - P g 0 ) × 10 6 = ( 0.2 - 0.3 ) mW - 1 ,
n - 1 = A 1 ( 1 + B 1 λ 2 ) ,
( n - 1 ) CO 2 = 450 × 10 - 6 , ( n - 1 ) N 2 = 300 × 10 - 6 , ( n - 1 ) He = 36 × 10 - 6 .
Δ n × 10 6 = 9.87 × Δ p ( 450 f CO 2 + 300 f N 2 + 36 f He ) ,
Δ n × 10 6 = 1.46 Δ p for CO 2 : N 2 He = 1 : 1 : 4 , Δ n × 10 6 = 1.95 Δ p for CO 2 : N 2 He = 1 : 0.72 : 2.
n - 1 = - 1 2 N e e 2 m ɛ 0 ω 2 + 2 π α m N m ,

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