Stokes frequencies

The first observation of the stimulated Raman effect was reported by Woodbury and Ng 215) j e effect was then thoroughly studied by several authors 216-218) and its theoretical background developed 219.220) (see also the review articles by Zubov et a/.22D). The stimulated Raman effect can be described as a parametric process where the coupling between a light wave at the Stokes frequency (Os and an optical phonon (vibrational wave) at cOy is produced by a pump field at col = (Oj + ojy. 

The focal helds set up a polarization in the material. In the case of CARS, we are interested in the polarization resulting from the combined action of the pump (of frequency co ) and Stokes (of frequency coj beams, which induce motions in the electron clouds that oscillate at frequency 2co - co, the anti-Stokes frequency. The ability of the material to oscillate at the anti-Stokes frequency when the pump and Stokes helds are present is given by the third-order nonlinear susceptibility The strength of the polarization is furthermore determined by the amplitude of the pump (E ) and Stokes (E ) driving helds. In the tensorial notation, where and I denote the polarization components of the nonlinear susceptibility, the third-order polarization in the polarization direction i is given as... 

In the next sections, we shall see that by manipulating the spatial as well as temporal phase of the third-order polarization at the anti-Stokes frequency the properties of the far-field CARS signal can be favorably influenced. We will first discuss phase manipulations in terms of temporal interference in Section III and then zoom into spatial phase manipulations in Section IV. 

FIGURE 9.3 Comparison of a focal field at the anti-Stokes frequency (a) with the CARS excitation field (b). In (c) the phase difference between (a) and (b) along the optical axis is given. Note the limited phase difference within the interaction length. Calculations are for a 1.1 NA water immersion lens. The pump wavelength is 800 nm, the Stokes wavelength is 1064 nm. In the panels the lateral axis runs from -1.0 xm to 1.0 xm. 

The nonresonant contributions pertain to electron cloud oscillations that oscillate at the anti-Stokes frequency but do not couple to the nuclear eigenfrequencies. These oscillatory motions follow the driving fields without retardation at all frequencies. The material response can, therefore, be described by a susceptibility that is purely real and does not depend on the frequencies of the driving fields. The resonant contributions, on the other hand, are induced by electron cloud oscillations that are enhanced by the presence of Raman active nuclear modes. The presence of nuclear oscillatory motion introduces retardation effects relative to the driving fields i.e., there is phase shift between the driving fields and the material oscillatory response. 

FIGURE 9.7 Schematic of an in-line interferometer. The anti-Stokes local oscillator field is collinearly overlapped with the pnmp and Stokes beams on a dichroic mirror (DM). All fields are focused by a microscope objective (MO) into the sample (S), and the total signal at the anti-Stokes frequency is detected throngh a spectral bandpass filter (F) at the photodetector. 

The first term of the last equation represents Rayleigh scattering, which occurs at the excitation frequency Vex- The second and the third terms correspond to the Stokes and anti-Stokes frequencies of (vex - w) and (vex + r v). Here, the excitation frequency has been modulated by the vibration frequency of the bond. It is important to note that Raman scattering requires that the polarizability of a bond varies as a fimction of distance, that is (dajdr) must be greater than zero if a Raman line is to appear. 

Feed tank and metering pump the flow rate through such a pump can be controlled by a stroke adjusting mechanism or a variable speed drive acting on the stoke frequency. Control can be achieved by a fixed adjustment or through a flow meter. 

Figure 10.1. Comparison of normal (top) and surface-enhanced (bottom) Raman scattering. The top panel shows the conversion of incident laser light of intensity /(vl) into Stokes scattered light /NRS, which is proportional to the Raman cross section and the number of target molecules N in the probed volume. In the bottom panel

Tabulate your Stokes and anti-Stokes frequencies and also the intensity ratios Ij Hs wherever possible. According to Eq. (6), the intensity ratio for each mode can be used to determine the vibrational temperature characterizing the Boltzmann distribution. In the present experiment, the vibrational temperature should agree with the ambient temperature of the laboratory. Does it This technique of using information about spectral intensities to determine T is a very convenient method for finding the temperature of flames, shock waves, and plasmas. 

If the intensity of the Raman Stokes beam at I si is high enough, this beam itself can generate a new beam at the second Stokes frequency v 2 = si = in a man-... 

Optimum gain is found at the centre of the Raman line where ur — lol- ur. There, the gain constant for stimulated Raman scattering at Stokes frequency is given by... 

From an experimental point of view, it is quite evident that for the four nonlinear coherent Raman techniques discussed until now, one either measures the radiation generated at anti-Stokes frequency (CARS, ll)as = 2ui-cvs) or at Stokes frequency (CSRS, 2cJs - or one determines the change AS in the laser beam power (o/ z, IRS uJs -SRGS). In order to get full Raman information of the medium, it is necessary to tune the frequency difference ojl-ujs, then, successively all Raman-active vibrations (or rotations, or rotation-vibrations) will be excited and a complete nonlinear Raman spectrum is then obtained. 

Stimulated Raman gain Stimulated Raman gain (SRG) and inverse Raman scattering (IRS) are closely related. While one involves stimulated gain at a Stokes-shifted frequency, the other involves stimulated loss at an anti-Stokes-shifted frequency. SRG can be viewed as an induced emission process at the Stokes frequency. Both SRG and IRS are coherent processes. 

The detunings A/> and As are one-photon detunings with respect to the pump and Stokes frequencies respectively and... 

Coherent Anti-Stokes Raman Scattering (CARS) Thermometry is a technique for temperature measurement in high temperature environments using a third-order nonlinear optical process involving a pump and a Stokes frequency laser beam that interacts with the sample and generates a coherent anti-Stokes frequency beam. 

A photon with frequency v0 is absorbed by a Raman-active molecule that is at the time of interaction already in an excited vibrational state. If the excess energy of the excited Raman-active mode is released, the molecule returns to the basic vibrational state, and the resulting frequency of scattered light is v0 + vm. This Raman frequency is called Anti-Stokes frequency. 

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