Abstract

In a previous paper [Appl. Opt. 35, 1566 (1996)] one of us presented new equations for evaluation of the phase refractive index of air over a range of wavelengths and atmospheric parameters. That paper also gave an incorrect, although sufficiently accurate, procedure for calculating the group refractive index. Here we describe the results of a more rigorous derivation of the group index that takes proper account of the Lorentz–Lorenz formula, and we demonstrate that deviations from the Lorentz–Lorenz formula are insignificant to within a foreseeable precision of dispersion measurements for atmospheric conditions. We also derive and evaluate a simplification of the resultant equation that is useful for exploratory calculations. We clarify the limits of validity of the standard equation for the group refractive index and correct some minor errors in the previous paper.

© 1999 Optical Society of America

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References

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  1. P. E. Ciddor, “Refractive index of air: new equations for the visible and the near infrared,” Appl. Opt. 35, 1566–1573 (1996).
    [CrossRef] [PubMed]
  2. J. C. Owens, “Optical refractive index of air,” Appl. Opt. 6, 51–59 (1967).
    [CrossRef] [PubMed]
  3. J. M. Rüeger, Electronic Distance Measurement—An Introduction, 4th ed. (Springer-Verlag, Berlin, 1996).
    [CrossRef]
  4. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), pp. 20–22.
  5. Y. S. Galkin, R. A. Tatevian, “Influence of resonances on the phase and group refractive indices of air,” J. Geod. 71, 680–684 (1997).
    [CrossRef]
  6. Y. S. Galkin, R. A. Tatevian, “The problem of obtaining formulae for the refractive index of air for high-precision EDM,” J. Geod. 71, 483–485 (1997).
    [CrossRef]
  7. A. N. Golubev, “On the problem of the velocity of light determination in optical distance measurement,” Proceedings Institute of Higher Education Series Geodesy and Aerial Surveying, USSR, No 5, 20–29, (1985). (In Russian; translation supplied by author.)
  8. R. J. Hill, “Refractive index of atmospheric gases,” in The Upper Atmosphere—Data Analysis and Interpretation, W. Dieminger, G. K. Hartmann, R. Leitinger, eds. (Springer-Verlag, Berlin, 1996), pp. 261–270.
  9. C. J. F. Böttcher, Theory of Electric Polarisation (Elsevier, Amsterdam, 1952).
  10. C. J. F. Böttcher, Theory of Electric Polarisation, 2nd ed. (Elsevier, Amsterdam, 1973), Vol. I.
  11. C. J. F. Böttcher, P. Bordewijk, Theory of Electric Polarisation2nd ed. (Elsevier, Amsterdam, 1978), Vol. II.
  12. L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960).
  13. K. E. Oughstun, “Pulse propagation in a linear, causally dispersive medium,” Proc. IEEE 79(10) , 1379–1390 (1991).
    [CrossRef]
  14. K. E. Oughstun, P. Wyns, D. Foty, “Numerical determination of the signal velocity in dispersive pulse propagation,” J. Opt. Soc. Am. A 6, 1430–1440 (1989).
    [CrossRef]
  15. H. Xiao, K. E. Oughstun, “Hybrid numerical-asymptotic code for dispersive-pulse propagation calculations,” J. Opt. Soc. Am. A 15, 1256–1267 (1998).
    [CrossRef]

1998

1997

Y. S. Galkin, R. A. Tatevian, “Influence of resonances on the phase and group refractive indices of air,” J. Geod. 71, 680–684 (1997).
[CrossRef]

Y. S. Galkin, R. A. Tatevian, “The problem of obtaining formulae for the refractive index of air for high-precision EDM,” J. Geod. 71, 483–485 (1997).
[CrossRef]

1996

1991

K. E. Oughstun, “Pulse propagation in a linear, causally dispersive medium,” Proc. IEEE 79(10) , 1379–1390 (1991).
[CrossRef]

1989

1967

Bordewijk, P.

C. J. F. Böttcher, P. Bordewijk, Theory of Electric Polarisation2nd ed. (Elsevier, Amsterdam, 1978), Vol. II.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), pp. 20–22.

Böttcher, C. J. F.

C. J. F. Böttcher, Theory of Electric Polarisation (Elsevier, Amsterdam, 1952).

C. J. F. Böttcher, Theory of Electric Polarisation, 2nd ed. (Elsevier, Amsterdam, 1973), Vol. I.

C. J. F. Böttcher, P. Bordewijk, Theory of Electric Polarisation2nd ed. (Elsevier, Amsterdam, 1978), Vol. II.

Brillouin, L.

L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960).

Ciddor, P. E.

Foty, D.

Galkin, Y. S.

Y. S. Galkin, R. A. Tatevian, “Influence of resonances on the phase and group refractive indices of air,” J. Geod. 71, 680–684 (1997).
[CrossRef]

Y. S. Galkin, R. A. Tatevian, “The problem of obtaining formulae for the refractive index of air for high-precision EDM,” J. Geod. 71, 483–485 (1997).
[CrossRef]

Golubev, A. N.

A. N. Golubev, “On the problem of the velocity of light determination in optical distance measurement,” Proceedings Institute of Higher Education Series Geodesy and Aerial Surveying, USSR, No 5, 20–29, (1985). (In Russian; translation supplied by author.)

Hill, R. J.

R. J. Hill, “Refractive index of atmospheric gases,” in The Upper Atmosphere—Data Analysis and Interpretation, W. Dieminger, G. K. Hartmann, R. Leitinger, eds. (Springer-Verlag, Berlin, 1996), pp. 261–270.

Oughstun, K. E.

Owens, J. C.

Rüeger, J. M.

J. M. Rüeger, Electronic Distance Measurement—An Introduction, 4th ed. (Springer-Verlag, Berlin, 1996).
[CrossRef]

Tatevian, R. A.

Y. S. Galkin, R. A. Tatevian, “The problem of obtaining formulae for the refractive index of air for high-precision EDM,” J. Geod. 71, 483–485 (1997).
[CrossRef]

Y. S. Galkin, R. A. Tatevian, “Influence of resonances on the phase and group refractive indices of air,” J. Geod. 71, 680–684 (1997).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), pp. 20–22.

Wyns, P.

Xiao, H.

Appl. Opt.

J. Geod.

Y. S. Galkin, R. A. Tatevian, “Influence of resonances on the phase and group refractive indices of air,” J. Geod. 71, 680–684 (1997).
[CrossRef]

Y. S. Galkin, R. A. Tatevian, “The problem of obtaining formulae for the refractive index of air for high-precision EDM,” J. Geod. 71, 483–485 (1997).
[CrossRef]

J. Opt. Soc. Am. A

Proc. IEEE

K. E. Oughstun, “Pulse propagation in a linear, causally dispersive medium,” Proc. IEEE 79(10) , 1379–1390 (1991).
[CrossRef]

Other

J. M. Rüeger, Electronic Distance Measurement—An Introduction, 4th ed. (Springer-Verlag, Berlin, 1996).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), pp. 20–22.

A. N. Golubev, “On the problem of the velocity of light determination in optical distance measurement,” Proceedings Institute of Higher Education Series Geodesy and Aerial Surveying, USSR, No 5, 20–29, (1985). (In Russian; translation supplied by author.)

R. J. Hill, “Refractive index of atmospheric gases,” in The Upper Atmosphere—Data Analysis and Interpretation, W. Dieminger, G. K. Hartmann, R. Leitinger, eds. (Springer-Verlag, Berlin, 1996), pp. 261–270.

C. J. F. Böttcher, Theory of Electric Polarisation (Elsevier, Amsterdam, 1952).

C. J. F. Böttcher, Theory of Electric Polarisation, 2nd ed. (Elsevier, Amsterdam, 1973), Vol. I.

C. J. F. Böttcher, P. Bordewijk, Theory of Electric Polarisation2nd ed. (Elsevier, Amsterdam, 1978), Vol. II.

L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960).

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Tables (1)

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Table 1 Air Density and Group Refractive Indexa

Equations (22)

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ng=n+σdn/dσ,
Lini2-1/ni2+2=Kiσρi=Lsiρi/ρsi,
Ln2-1/n2+2=i Li=i Lsiσρi/ρsi
ng=n+σdL/dn-1iρi/ρsidLsi/dnsidnsi/dσ.
n=1+2L/1-L1/2
dL/dn=6n/n2+22,
ng=n+σn2+22/ninsi/nsi2+22×ρi/ρsidnsi/dσ.
L2/3n-11-n-1/6.
n=4-31-L1/21+3/2L+3/8L2,
dL/dn=2/94-n.
ngquad=n+σ/4-ni4-nsiρi/ρsidnsi/dσ.
ng=c/dω/dk=c dk/dω=dωnω/dω=dσnσ/dσ=nσ+σ dn(σ)/dσ.
Ez, t=-dω expikωz-iωtFω.
kω=kω0+dkωdωω0ω-ω0+12d2kωdω2ω0×ω-ω02+,
kω=up0-1ω0+iα0+ug0-1ω-ω0+iA0ω-ω0+B0ω-ω02+.
Ez, t=exp-α0zexpiup0-1z-tω0×- dω expiug0-1z - tωfω×exp-A0zω+iB0zω2+.
z  2dαωdωω0Δω-1,
z  8cΔω2dngdkk0-1.
108nsi-1=p ap/bp-σ2, p=1, 2, 3 ,
108dns/dσ=-2σ p ap/bp-σ22.
108ns-1=p apσ2p, p=0, 1, 2 ,
108dns/dσ=2 p papσ2p-1.

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