Double-Photon Elastic Light Scattering by Liquids Having Centrosymmetric Molecules

Abstract

First measurements of double-photon elastic scattering performed on liquids with centrosymmetric molecules yield good agreement with statistical molecular theory of nonlinear light scattering. Studies of this new scattering are shown to allow determination of the third-order molecular polarizability as well as its anisotropy, and to promise information on the structure of short-range molecular ordering and electric properties of molecules.Terhune, Maker, and Savage 1 performed the first observation of second-harmonic laser light scattering (SHLS) in liquids whose molecules lack a center of symmetry. This communication reports first measurements of double-photon elastic scattering (DPES or SHLS) by liquids consisting of molecules having a center of symmetry in their ground state. The possibility of destroying the molecular center of inversion, owing to time and space fluctuations of the molecular electric field F, led us to predict this new scattering. This is particularly predictable in the case of liquids with molecules having permanent electric quadrupole or hexadecapole moments capable of causing very strong fluctuating molecular fields in regions of shortest-range ordering in the liquid. 2 Such regions in general do not possess a center of symmetry and thus cause SHLS. This is uniquely cooperative scattering by neighboring molecules whose positions and orientations are correlated. 2 ' 3 Theoretical considerations. -Consider a laser light wave of frequency w L and propagation vector k L incident on such a liquid. The electric dipole moment M induced in the medium of volume V at frequency 2u> L is 2 ' 3is the tensor 6f third-order nonlinear polarizability induced in a molecule p at the frequency 2(x) L by the squared electric field of the light wave E UL in the presence of the molecular field ¥ ( -p) due to the AT-1 molecules surrounding molecule p with the radius vector f^.With the light beam plane polarized, propagating at velocity c along y and oscillating vertically, the intensity components of light elastically scattered at frequency 2w L with horizontal (along y) and vertical (along z) oscillations, respectively, can be written in the forms (observation along x) / y /^=#/^+i(2c^^ (2) /./"*=7^=£(2w L^^ (3 ) where I L is the incident intensity, and £=1 Q=lIn Eqs. (5) and (6) we have Ak = k 2 -2k x , where k 2 is the wave vector of the scattered second-harmonic wave and r />a = r a -"f /) is the vector connecting the centers of the two scattering molecules p and q.From Eqs.(2) and (3), we define the depolarization ratio of second-harmonic scattering byIt is obvious from the shape of the scattering factors (5) and (6) that only cooperative SHLS is present since, in the absence of molecular correlation, S 2(JJL and R 2U)L vanish. This is an important distinction with regard to SHLS by liquids consisting of molecules without centers of symmetry for which we have both a noncooperative part (isolated molecules) and a cooperative one. 2 ' 3 1295

Cooperative second harmonic laser light scattering in liquid cyclohexane, benzene and carbon disulphide

“…From (61) we derive a formula for determining the effective anisotropy of nonlinear polarisability by measuring the depolarisation ratio at frequency 2 0 : 9 D s " -1 2 = I -9 DV2O-t 1 9 D , ' " + l ' A , , = These considerations thus lead to the result DZ'2+=0.11, in agreement with our earlier [7] and present measurements.…”

“…With regard to molecules of low symmetry one is not justified in writing a nonlinear polarisability tensor of the form (21). The latter is, in fact, strictly applicable to atoms and to molecules of high e.g.…”

“…In addition liquids give rise to coherent scattering due to orientational correlations of the molecules [3, 4, 81. The part played by angular molecular correlations in nonlinear two-photon scattering is similar to the one they fulfill with regard to linear Rayleigh scattering by liquids [9, 101. Our earlier observations [7] in liquids consisting of centrosymmetric molecules revealed a co-operative double-photon scattering due to fluctuations of electric molecular fields in regions of near-range ordering [4, 111. This novel scattering permits the determination of third-order molecular polarisability [7] and near neighbourhood structure. In the present paper, we propose a complete theory of this cooperative scattering taking into account, beside radial molecular fields, the angular fields leading additionally to a nonlinear, anisotropic scattering.…”

Observing Second‐Order Nonlinear Optical Properties by Symmetry Breaking in Centrosymmetric Furan‐Containing Oligoaryl Cyclophandienes

“…[3] Hyper-Rayleigh scattering (HRS) at the doubled frequency, 2w, has been observed for centrosymmetric dichloro-and tetrachloroethenes in solution. [10] Although the intensities are relatively low, an involvement of cooperative scattering by neighboring molecules [10] including solvent molecules [11] has been suggested to account for these observations.…”

Hyper-Rayleigh scattering in centrosymmetric systems

“…Hyper-Rayleigh scattering (HRS) 1 is an incoherent variant of SHG: not subject to the rules of wave-vector matching, it leads to harmonic emission in all directions (i.e., over 4π steradians). It offers unique technical applications in the optical characterization of minerals, 2 and recently, it has been exploited in the analysis of liquid suspensions -in particular with regard to nanoparticles and nanorods.…”