The polarization of laser light scattered by gases By N. J. Bridge* and A. D. Buckingham! Inorganic Chemistry Laboratory, Oxford University (Communicated by J. W. Linnett, —Received 23 May 1966) Measurements of the polarization of light scattered from the beam of a helium-neon gas laser at low pressures are described. The intensity, polarization and parallelism of the beam permit high accuracy, and new values for the depolarization ratios of twenty-four simple species are reported.
The polarization of laser light scattered by gases 335 Since the mean polarizability can be found from the refractive index of the gas, measurement of the depolarization ratio determines the magnitude of aB — <x±, though not its sign. The quantity a„ — ocx is of current interest through its relevance to the direct determination of molecular quadrupole moments (Buckingham & Disch 1963) and anisotropies in molecular magnetic susceptibilities by the Cotton-Mouton effect (Buckingham, Prichard & Whiffen 1965). In both cases the orientation of the gas molecules is measured through an induced birefringence proportional to an-cc±.
336 N. J. Bridge and A. D. Buckingham The radiation from an individual dipole is polarized in the plane defined by the dipole and the direction of propagation. Thus the light scattered from a polarized beam by a gas composed of spherical molecules is linearly polarized, since all the induced dipoles are parallel to the electric field of the incident wave. This is not true of anisotropic molecules, for which the direction of the dipole is influenced by the orientation of the molecule, so that the light scattered from the gas is partly depolarized.
The polarization of laser light scattered by gases 337 simplest case, suppose the directions of incident and scattered light are along the X and Y axes of a Cartesian frame; the steradiance is then a maximum when q is parallel to the Z axis and a minimum when parallel to the X axis. For incident light polarized in the Z direction the depolarization of scattered light is, from (7 a), p0 = 3/c2/(5 + 4/c2) (8 a) and for unpolarized incident light p = 6/c2/(5 + 7x2). (8b) Geometrical errors In practice, it is not possible to measure the steradiance or depolarization of light scattered in a given direction, since both detector and scattering volume must be of finite size; further, it is impossible to use an exactly parallel incident beam so that the direction of propagation and polarization vary over the sample. Thus observed values for p0 or p contain errors due to geometrical factors, whose order of magnitude must be calculated.
338 N. J. Bridge and A. D. Buckingham the ray OR diverges from the 0 Y axis, and rj the angle between the planes ROY and XOY, the steradiances for incident light polarized in the direction, and for small y,are (S0>x) = /(27rr/c)4 |-a2[3x2 + (5 + x2) |y4 sin2 (12 (S0>z) = /(27rr/c)4|a 2[3x2 + (5 + ^2)(l-y2sin2^)]. (126) If the maximum divergence accepted by the detector is (0 ^ y < (Po)obs.=Po(l + iC'2) + ^ 4+. (13) This error is small; even when C is as large as 6°, the term lp0C2 gives an error of only l % while Jj(74 produces an error of 0-04 % in a depolarization p0 of 10-2.
The 'polarization of laser light scattered by gases 339 this weak vibrational Raman scattering is excluded, and if only the internal state is present, (16) becomes < ^ > = / (^YV S ( l - ^ r ^ o p ' ^ / R, R' S ,, — ';r - 'X ^ x , SR\az,\R")(R"\aAB\R’) r", re" h(vT*T-v)[l + vR„R{vT,T-v )-ir 1 Za| /x 1 7 + F7-----K k) |J?') (17) ^ r'r + ^ l + ^ A v + t 1] 1/1 1 1 J where = S exP { — WrI^T} and aiAj3s the cosine of the angle between the A and /? directions.
340 N. J. Bridge and A. D. Buckingham so the scattering arising from a molecule in the rotational state consists of three separate frequencies, v + Vj v and v + corresponding to j_ 2, J+2, A J J' — J = — 2, 0 and 2 = and forming part of the O, Q and S branches of the rotational Raman spectrum. Their intensities in the rigid rotator approximation are J(J~ 1) < \ Xs)oj'■ <So, x}qj'■ (So,x}sj — [r + 2(2J 1) cB]4 (2 +1) * 2J(J +1) (e7 + 1) (e/ +2) : [v — 2(2 J + 3) 3(2J-l)(2J + 3) (2 J +1) (2J + 3) (24) (So,z)oj-{S0,z)Qy.(S„,z)Sj = [, + 2(2J- : 8 J (J +1) 1 4(e/ + 1) (t/ +2) > 410 : [v — 2(2 J + 3) \9k2 + 9(2J-1)(2J + 3)/ 3(2J+1) (2J+ 3) ’ where B (cm-1) is the rotational constant. The depolarization ratios of the 0 and S branches are £ and that of the Qj line 3/e2/[5(2J — 1) (2 + 3) (J2 + J)~x + 4k2].
The polarization of laser light scattered by gases 341 value. For HC1, B — 10-45 cm 1 and the reduction is 1*6 %. For gases other than hydrides and deuterides this quantum effect is negligible.
342 N. J. Bridge and A. D. Buckingham Thus the polarizabilities determined through depolarization measurements are actually those applicable to the ground state of the molecule.
The polarization of laser light scattered by gases 343 there is a change in the vibrational state of the molecule. Generally this scattering could be removed by filters; its intensity with X polarization is approximately (v = 0|a,-o L\v = times the Rayleigh scattering, and for diatomics this is (al-qpgfl which is normally only about 10-2to lO"3. For H2 this ratio is 0-060 ± 0-004 (Crawford & MacDonald 1958) and for D2 it is 2~k = 0-71 of that for H2.