March 1, 2000 / Vol. 25, No. 5 / OPTICS LETTERS
347
Experimental verification of Rayleigh scattering cross sections
Hans Naus and Wim Ubachs
Department of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
Received November 4, 1999
The cavity-ringdown technique is applied to measure Rayleigh extinctions of Ar, N2, and SF6 in the 560–
650-nm region at 294 K. It is shown that experimental and calculated Rayleigh scattering cross sections
agree within an experimental uncertainty of 1% (for SF6, 3%).
2000 Optical Society of America
OCIS codes: 290.5870, 290.5840.
A century ago Lord Rayleigh formulated a theory of
light scattering by ideal gases that not only explained
the molecular origin of atmospheric scattering and the
blue color of the clear sky but also provided a quantita-
tive expression for the amount of light scattered.1
In
modern formulation the Rayleigh scattering cross sec-
tion sn cm2 for a single molecule is given by2– 4
sn
24p3n4
N2
n2n 2 12
n2n 1 22
Fkn ,
(1)
where n is the frequency cm21, N is the molecular
density cm3, nn is the refractive index, and Fkn is
the King correction factor. The factor n2
n 2 1n
2
n 1
2, an effect of the local electrostatic field that is known
as the Clausius–Mossotti or the Lorentz–Lorenz fac-
tor, is proportional to N . Because of this proportion-
ality one must be consistent in choosing the values of
nn and N . The King correction factor is defined as
Fkn 6 1 3rn6 2 7rn, where rn is the depolariza-
tion ratio of natural or unpolarized light and accounts
for the anisotropy of nonspherical molecules.5
Equation (1) includes effects of nonresonant scatter-
ing that were unknown to Rayleigh; the fine structure
on the Rayleigh line is related to vibrational and rota-
tional Raman scattering, the inf luence of the modes of
hypersound is known as Brillouin scattering, and the
effects of collisional redistribution give rise to Rayleigh
wing scattering.
Hence Rayleigh scattering cross