Nonlinear response function for anisotropic polaritons in an orthorhombic crystal

Abstract

In this article we consider the intensity distribution of the light scattering by anisotropic (nonordinary) polaritons in the wave number -wave vector coordinates. We propose formulae for polariton spectra numerical calculation which are adequate for any wave vector direction and for resonant and nonresonant frequency areas. The case of polariton branch splitting along the wave vector coordinate when this vector directs close to optical axis of orthorhombic crystal is discussed as an illustration of the method availability. Keywords: light scattering by polaritons, Raman scattering, infrared optics 1. POLARITON SPECTRA OF ORDINARY POLARITONS The spontaneous light scattering by polaritons (PS) is also called small-angle Raman scattering. In the process of spontaneous light scattering by polaritons in a nonlinear crystal without center of symmetry, laser (pumper) wave with wavenumber ill decays into signals waves (wide continious range of wavenumbers v,) and idler, or polariton ( v = LIj -z.') waves. Polariton wavelengths are in infrared range. Vectors of interacting waves make the triangle: k1=k+k(1) Angles i9 between k1 and k are small, and values of k are almost equal to wave vectors of infrared light waves. PS spectroscopy not only combines advantages and possibilities of Raman and infrared (IR) spectroscopy methods but also contains additional information and is more sensitiveThe main difference of the PS spectrum from the Raman one is that the intensity P(zi, Ic) is the function frofri two coordinates, wavenumber and wavevector k = Iki . The wave vectors k actual range in eq. (1) may be wide.It corresponds to scattering angles t9 from zero to maximum value, which is defined by the optical elements and height of spectrograph sleet and is usually of 4 -120 . The points which correspond to the peaks of wave vector (or angular) line shapes P(k) at given wavenumbers ii we will call polariton modes k. The curve ii(k) connecting these peaks on the ii -k plane is called here a polariton mode curve. The area where P(k) is not less then 1% from peak value is called a polaritorz branch.If polariton waves are transversely polarized, the scattering intensity is defined by the nonlinear response function being proportional to gain factor1 G: P(u, ) G = Im(4irD2 + 0) = Im[4ir2/(jt2 -6*) + 8] (2) Here spectrum coordinates are wavenumber ii and = fkI/v. Formula contains complex values of dielectric function 6, qudratic x and cubic ® susceptibilities. The inverse wave vector mismatch function D = (p2 _ describes an area of the infrared equilibrium fluctuations existence on the ii -p plane (the polariton branch) . From twodimensional PS spectra it is possible to obtain information about the phonons dynamic parameters, that is, about their contributions into linear, quadratic and cubic susceptibilities and damping constant. The method of dynamic parameters correct calqulation from intensity distribution have been rather well developed now, but only for the case when polariton wave is ordinary, that is, transverse polarized24. 2....