Raman Depolarization Ratio of Liquids Probed by Linear Polarization Coherent Anti-Stokes Raman Spectroscopy F

Research Article Received: 10 October 2008 Accepted: 9 February 2009 Published online in Wiley Interscience: (www.interscience.wiley.com) DOI 10.1002/jrs.2289 Raman depolarization ratio of liquids probed by linear polarization coherent anti-Stokes Raman spectroscopy F. Munhoz, S. Brustlein, D. Gachet†, F. Billard‡, S. Brasselet and H. Rigneault∗ We present a simple analytical model to describe the linear polarization coherent anti-Stokes Raman scattering (CARS) spectroscopy. In this scheme, the pump and Stokes beams can have arbitrary linear polarization states and the CARS emitted signal is analyzed along two perpendicular directions. We concentrate on isotropic media without electronic resonances and show that only two polarization CARS measurements performed at the peak and the dip of a CARS spectrum are sufficient to deduce the Raman depolarization ratio, the resonant versus nonresonant contribution, the Raman resonance frequency and the linewidth. We demonstrate the applicability of our scheme to toluene and cyclohexane solutions. Copyright c 2009 John Wiley & Sons, Ltd. Keywords: CARS; polarization; spectroscopy; microscopy Introduction Although we are interested in CARS micro-spectroscopy, we present here a simple approach where we neglect the spatial Among nonlinear optical processes, the specificity of the coherent confinement of the pump and Stokes focused beams. This crude anti-Stokes Raman scattering (CARS) is its coherent and resonant approximation leads to a complete analytic description of the [1] nature. The interaction of the incident fields with the sample spectral polarized CARS signal, including the ratio between the induces a third-order nonlinear polarization, whose properties resonant and nonresonant contributions. Careful inspection of depend on the vector nature and frequencies of the incident the outcomes shows that performing only two measurements electromagnetic fields, as well as the structure of the medium. The at the peak and the dip of a CARS spectral band with a (3) ◦ latterischaracterizedbyafourth-ranksusceptibilitytensorχ that 45 angle between the pump and Stokes beams leads to all (3) (3) has a resonant χ R and a nonresonant χ NR contribution. Probing spectroscopic CARS parameters (Raman depolarization ration, a medium with polarized incident fields allows the activation of resonant versus nonresonant contribution, Raman resonance different components of this tensor and can be useful to determine frequency and linewidth (HWHM)). This simple scheme is applied the spatial orientation and symmetries of the probed molecular as a proof of principle to measure the spectroscopic CARS bonds. Pioneer work in polarization CARS has been performed in parameters of toluene and cyclohexane solutions, where we [2,3] the late seventies as a powerful alternative tool to spontaneous show that this analytic approach applies well to focused beams Raman spectroscopy and polarization-resolved CARS has also conditions. been rapidly demonstrated as an efficient mean to modulate The paper is organized as follows: the first section presents an [4] the nonresonant background contribution. Polarization analysis analytic model for the polarized emitted far field CARS signal. The [5,6] has been applied successfully in electronic resonant and second section deals with the polarized signals emitted at the peak [7–10] nonresonant multiplex coherent Raman spectroscopy. The and dip of the CARS spectrum and the subsequent determination case of anisotropic photo-induced orientation of molecules has of the spectroscopic CARS parameters. Finally, the third section been also addressed when electronic resonances are present.[11] More recently, anisotropic samples, such as water molecules in phospholipid bilayer,[12] tissues[13] or liquid crystals,[14] have been ∗ Correspondence to: H. Rigneault, Institut Fresnel, Mosaic Group, CNRS UMR investigated in polarization-resolved CARS microscopy, in order 6133, UniversitePaulC´ ezanne,´ Aix-Marseille III, Domaine Universitaire Saint- to characterize molecular orientation and director structures. In Jer´ ome,ˆ 13397 Marseille cedex 20, France. E-mail: [email protected] all these works, either the different linear polarization states of the CARS emitted signal were analyzed spectrally, or the incident † Current address: Department of Physics of Complex Systems, Weizmann parallel polarizations of the pump and Stokes beams were tuned Institute of Science, Rehovot 76100, Israel. at the same time. ‡ Current address: Institut Carnot de Bourgogne, UMR CNRS 5209, Departement´ In this work, we consider a more general CARS linear polarization ‘Optique, interaction Matiere-Rayonnement’,` Universite´ de Bourgogne, 9, scheme where the pump and Stokes beams can have arbitrary Avenue Savary, B.P. 47 870, 21078 Dijon cedex, France. and independent linear polarization states and the emitted CARS Institut Fresnel, Mosaic Group, CNRS UMR 6133, UniversitePaulC´ ezanne,´ Aix- signal is analyzed along two perpendicular directions. We restrict Marseille III, Domaine Universitaire Saint-Jer´ ome,ˆ 13397 Marseille cedex 20, ouranalysistoisotropicmediaexhibiting noelectronicresonances. France J. Raman Spectrosc. (2009) Copyright c 2009 John Wiley & Sons, Ltd. F. Munhoz et al. reports the experimental implementation of our technique and a The susceptibility tensor χ (3) couples the induced third order comparison with related measurements. nonlinear polarization with the excitation electromagnetic fields and can be written as P(3) = 3 χ (3) (−ω ; ω , ω , −ω )E (ω )E (ω )E∗ (ω )(5) Analytic model of the polarized CARS signal i ijkl AS P P S Pj P Pk P Sl S emitted from an isotropic medium jkl The CARS signal depends on the structure of the medium under where EP and ES are the pump and Stokes incident fields at angular = − investigation, that is characterized by a third order susceptibility frequencies ωP and ωS respectively and ωAS 2ωP ωS is the tensor χ (3). This tensor has 81 components but some of them angular frequency of the emitted anti-Stokes field. may vanish or be dependent on the others according to some The analytic model of the polarization-resolved CARS emission symmetry rules. For an isotropic medium where only two-photon for an isotropic medium is developed from the elements vibrational resonances are allowed, only two components are introduced above and under some simplificative assumptions. independent and the whole tensor can be described by[15]: First, the pump and Stokes fields are linearly polarized with polarizations angles αP and αS with respect to the x direction. Second, the incident fields are plane waves propagating in the z (3) = (3) + + (3) χ ijkl χ xxyy(δijδkl δikδjl) χ xyyxδilδjk (1) (3) direction. As a consequece, EPz and ESz are zero and Pz vanishes. Thisisacrudeapproximationforanimplementationinmicroscopy, where the subscripts i, j, k and l stand for the cartesian coordinates where strongly focused beams are used. Nevertheless, we will see x, y and z and δ is the Kronecker delta funcion. further that the main features for the polarization CARS signal By analogy to the spontaneous Raman spectroscopy theory, we are surprisingly well described. Under these assumptions the x can define a depolarization ratio ρCARS that links two components and y components of the CARS signal polarization can be then [2] of the susceptibility tensor as determined by introducing Eqn (3) in Eqn (5), following χ (3) χ (3) (3) = (3) 2 ∗ = xyyx = xyyx Px 3χ x EPES ρCARS (2) eff ∗ (6) (3) 2 (3) + (3) P(3) = 3χ (3) E2E χ xxxx χ xxyy χ xyyx y yeff P S (3) (3) (3) Equations (1) and (2) together show that any component of χ is where the effective susceptibilities χ x and χ y are defined as (3) eff eff a function of χ xxyy and ρCARS. (3) InEqn(1),thespectralbehaviorofχ is not taken into (3) (3) 2 χ = χ 2cosαP sin αP sin αS + sin αP cos αS account. To do so, one must consider the two contributions xeff NR +3cos2 α cos α P S to the susceptibility tensor in CARS spectroscopy, namely the (3) ρ 2 (3) + 2χ cos α sin α sin α + R sin α cos α vibrational resonant term χ and the electronic nonresonant R P P S 1−ρ P S R R (3) (3) 1 2 term χ .Theχ tensor can then be written as the sum of these + cos αP cos αS NR 1−ρR (3) = (3) + (3) two contributions χ χ R χ NR. We can insert this relation in (3) (3) 2 χ = χ 2cosαP sin αP cos αS + cos αP sin αS Eqn (1) and use Eqn (2) to obtain the complete description of χ (3), yeff NR +3sin2 α sin α following P S + (3) + ρR 2 2χ R cos αP sin αP cos αS − cos αP sin αS 1 ρR (3) = (3) + + 1 2 χ ijkl χ NR(δijδkl δikδjl δilδjk) + − sin αP sin αS 1 ρR 2ρ (7) +χ (3) δ δ + δ δ + R δ δ (3) R ij kl ik jl − il jk 1 ρR After some algebric manipulations, Eqn (7) can be recast under (3) (3) (3)NR where χ NR (respectively χ R )standsforχ xxyy χ (3) = χ (3) [2cosα + cos(2α − α )] (3)R xeff NR S P S respectively χ xxyy and ρR is the Raman depolarization + + a 1 ρR + − − cos αS cos(2αP αS) ratio. For the resonant contribution, the latter term is equal to the (δω − R) + i 1 ρR CARS depolarization ratio and its value lays between 0 and 3/4.[10] (3) = (3) + − χ y χ NR [2sinαS sin(2 αP αS)] For the nonresonant contribution, according to the Kleinman’s eff + + a 1 ρR + − [16] (3)NR = (3)NR NR = − + − sin αS sin(2αP αS) symmetry rule, χ xxyy χ xyyx and consequently ρCARS 1/3, (δω R) i 1 ρR which has been already inserted in the equation above. The (8) (3) nonresonant term χ NR is a real constant whereas the resonant term χ (3) holds the lorentzian spectral dependency given by (3) R where χ R was replaced by its expression given by Eqn (4). From (3) (3) Eqn(8),bothexpressionsofχ x and χ y have a nonresonant a eff eff (3) = term that only depends on the incident polarization direction and χ R (4) (δω − R) + i a resonant contribution that depends also on the spectral shift and the Raman depolarization ratio.

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