Anti-Stokes frequencies

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. 

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. 

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. 

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. 

The H2 gas acts as a nonlinear medium that converts two uq photons into one photon each at the Stokes and Anti-Stokes frequencies. Since the requirement for colinear phase matching... 

For historical reasons, the shifted frequencies that appear below the exciting frequency are called Stokes frequencies, and those that appear above the exciting frequency are called anti-Stokes frequencies. Notice that the frequency displacement (the Raman shift) of either Stokes or anti-Stokes lines from the exciting line is vi, a frequency that is characteristic of a particular molecular mode of vibration. The Stokes lines are more intense because the population of the molecular-energy levels as a function of temperature follows a Boltzmann distribution (most molecules are in the ground vibrational level at room temperature) thus the Stokes lines are recorded with a higher signal-to-noise ratio. 

The intensity of a Raman line at the Stokes or anti-Stokes frequency cos = co co is determined by the population density Ni(Ei) in the initial level Ei(v, J), by the intensity 7l of the incident pump laser, and by the Raman scattering cross section oit(( /) for the Raman transition E Ef. 

One of the most extensively used nonlinear processes for spectroscopy is coherent anti-Stokes Raman scattering (CARS). This is a four-wave mixing process of the form (Was = 2 ul — < s, where >l and >s are the laser and Stokes frequencies that are provided in the incident radiation and (Was is the anti-Stokes frequency that is generated... 

An ultrabroadband source of pulsed radiation can be used to both stimulate CARS and provide the reference pulse. The pulses from the source will be divided by a frequency-selective element such as a dichroic beam splitter into lower and higher frequency pulses. The higher frequency pulse bandwidth will correspond to the anti-Stokes frequencies emitted by the sample, and will act as the reference pulse to demodulate the anti-Stokes signal. The lower frequency pulse will be shaped to stimulate the Raman frequencies of the sample in a particular bandwidth. 

We would also like the frequency difference between the two pulses to start at Qff and end at. This best places the anti-Stokes frequencies outside of the bandwidth of the pump and Stokes frequencies ... 

In coherent anti-Stokes Raman spectroscopy (CARS) two beams of frequency co and a>2 are mixed in the sample to generate a new frequency co = 2co - a>2. If there is a Raman resonance at co - 0)2 = an amplified signal is detected at the anti-Stokes frequency (O + Q (see Figure 5). The corresponding susceptibility 1 2 3) written 5... 

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