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Lec13 Inelastic-Scattering.Pdf Inelastic Scattering Ken Voss, Ocean Optics Summer class, 2017 Introduction Remember your freshman physics class and all that time you spent learning about collisions? Two types of collisions: elastic and in-elastic. What was the difference? Introduction Remember your freshman physics class and all that time you spent learning about collisions? Two types of collisions: elastic and in-elastic. What was the difference? Elastic collisions conserved Kinetic energy and momentum, inelastic just momentum….was energy lost? Introduction So elastic scattering: photons come in and out of the process with the same energy (wavelength) In-elastic scattering: photons come in with one wavelength and leave with another wavelength. (remember Compton scattering of photons?). Difference between this and fluorescence is basically a short intermediate time for the event (which leads to other effects). prepared samples (see Fig. 1). All measurements were when recording Raman and luminescence spectra. done at a temperature of 21°C. This background-correcting spectrum was sub- A schematic for the experimental setup is shown in tracted from the raw experimental data. In the case Fig. 1. Laser light of wavelength 532 nm with a of Raman spectra, a straight line has been fitted in polarization controlled through the λ∕2 waveplate the spectral region from 700 to 745 nm. This straight was reflected by a dichroic mirror and focused onto line is shown in Fig. 2 and has been also subtracted the sample by a microscope objective. The degree from the spectrum. This subtraction has affected the of linear polarization of the incoming laser light is final estimate for the scattering coefficient by less at least better than 99.9%. The Raman scattering than 0.5%. Relating the total scattered light to the from pure water (impurity concentration <1 ppb) light collected from the cone intercepted by the mi- and luminescence of R6G were collected through the croscope objective requires knowledge of the angular same 0.55 NA microscope objective. A low-pass filter distribution of the scattered light. Generally the scat- (Semrock LP03-532RS25, optical density larger than tering from a single molecule is complex and must be 7 at 532 nm) removed laser light and a polarizer was described by a tensor [28]. We consider a geometry used to examine the polarization dependence of the where the exciting laser light, polarized along the sample’s radiation spectrum. The light was then x-axis travels along the y-axis through a bulk sample. focused into a spectrometer (SpectraPro 2300i) The optical axis of the microscope objective lies along with resolution 2 nm. The wavelength-dependent the z-axis of this coordinate system. The radiation transmissions of the optical collection system were scattered from a source much smaller than the wave- measured using a spectral lamp (Optronic Laborato- length of light but still containing a large number of ries Model: OL 200M) by comparing the measured randomly oriented molecules, which creates spheri- spectrum to the actual spectrum. The spectral lamp cal symmetry, can be described as the radiation manufacturer providesRaman a Scattering dataset for its spectrum of three orthogonal dipoles, with corresponding and the absolute intensities of the lamp have errors of less than 1% over a wider wavelength range than 1 1 covered in our experiment.Strongest, We assume most a generous (A) 0.5% error in the relative intensities of the lamp over ) 1 the spectral range ofevident our interest. in natural − 0.8 0.8 nm The objective collects a cone of the scattered light 1 with an opening angle θ (the NA of the objective used − 0.6 0.6 seawater, in-elastic (m in this experiment was 0.55). For each sample, six 5 spectra were measured,scattering corresponding process to all combi- is 0.4 0.4 nations of horizontal and vertical input and output Depolarization ratio 0.2 0.2 lights. For example,RamanSHV labels the scattering, spectrum of the vertically polarized component of the scattered light 0 0 obtained with horizontallyalthough polarized by laser most light. In 620 630 640 650 660 670 680 690 700 addition, spectra measured without any polarizers Wavelength (nm) are labeled by N. Weaccounts, measured the polarization water andhas intensity of laser light just in front of the cuvette. We 0.05 found that for H polarizationa weak the Raman light was slightly (B) attenuated and depolarized. We corrected this by Differential scattering coefficient x 10 adding weighting factors to the measured spectra. 0 cross section. (first 580 600 620 640 660 680 700 720 740 These factors are specified in the next section. Wavelength (nm) seen 1920’s) 1500 2000 2500 3000 3500 4000 4500 5000 3. Analysis Frequency shift (cm−1) The raw spectral data had a relative standard deviation of 0.8% for R6G and 0.7%Excitation for Raman 532 in nm, AppliedFig. 2. Panel Optics, (A) shows Bray differential et al., 52,2503-2510, Raman scattering 2013 coefficient of water as defined in Eq. (11). We show this quantity since it water. These errors have been attributed to inconsis- has no dependence on the geometry of the optical collection tency in the sample preparation. We have used system. This curve equals the spectrum measured when the scat- Student’s t-distribution [27] to estimate the 95% con- tered light is collected with high numerical aperture (NA ≈ 1) fidence interval for the mean of six measurements. optics. The S-shaped line in the middle shows the wavelength- This interval turned out to be 0.85% of relative dependent depolarization ratio. Panel (B) shows the low intensity deviation for R6G luminescence and was the largest region for better visibility of weak lines and covers a wider range of single contribution to the final estimate of the uncer- wavelengths. The units of the vertical scale are the same as in tainty (the uncertainty in the mean of the Raman panel (A). All features (except for the several sharp spikes caused signal was 0.4% because 11 spectra were measured by noise in the depolarization ratio factor) are attributed to Raman scattering in water. The dashed line shows the Gaussian fit to the for water). The measured spectra have been treated band centered at 674 nm. Stokes detuning from the laser fre- to remove background contributions. This was im- quency is shown at the bottom of the figure for convenience of portant for relatively weak Raman spectra. A spec- the reader. A thin dashed-dotted line shows the linear fit sub- trum obtained using an empty cuvette has been tracted from the spectra to correct for a small gradient in the recorded under conditions identical to ones used background. 2506 APPLIED OPTICS / Vol. 52, No. 11 / 10 April 2013 Introduction As opposed to the absorption process discussed earlier, the initial photon does not have to match an energy level to be absorbed, at least for a very short time, limited by the uncertainty principle (ΔEΔt<ħ). But the probablility of this happening is greatly enhanced if there is a nearby transistion to the virtual energy level(but if too close can cause issues of confusion with fluorescence). RAMAN SPECTROSCOPY 423 Intensity, arb. units where s is the salinity in g/l, T is the temperature in °C; 1.0 s0 = 19 g/l and T0 = 21°C are two constants. Fitting (2) to the experimental data gives the following values for the parameters: 0.8 –3 –1 A ==1.451± 0.004, B ()10.8± 0.3 × 10 °C , –3 (3) 0.6 C = ()5.6± 0.2 × 10 l/g. In Fig. 2 the experimental results with relative error bars and the fitted curves are reported. It is important to 0.4 note that the overall agreement is obtained with only three parameters. 0.2 3. RESULTS OBTAINED WITH PULSED EXCITATION 0 The idea to perform a study of the temperature 2800 3000 3200 3400 3600 3800 4000 –1 marker with pulsed experiment is twofold: to be near to Raman shift, cm the actual experimental condition in field which used a pulsed excitation and to investigate the discrepancy Fig. 1. Typical Raman spectrum obtained in cw excitation between cw and pulsed results that have been reported superimposed to the fit based on a two gaussians model. in literature. For this purpose we have also studied the Raman Scattering RAMAN SPECTROSCOPY 423 presence of stimulated Raman scattering, possibly gen- Marker R erated in pulsed experiment and which may alter the Intensity, arb. units where s1.8 is the salinity in g/l, T is the temperature in °C; detected spectrum, as compared to the weak field (cw) 1.0 s0 = 19 g/l and T0 = 21°C are two constants.Salinity Fitting 38 g/1 (2) measurement. The scheme of the setup is reported in to the experimental1.7 data gives the following values for26 Fig. 3. The laser beam, of duration of 6 ns, diameter of the parameters: 0.8 1.6 6 mm and linearly polarized was the third harmonic of –3 –1 a pulsed Nd : YAG laser. The beam was passed through A ==1.451± 0.004, B ()10.8± 0.3 × 10 °C , 13 1.5 –3 (3) a 1-m-length cell of deionized water (s = 0) whose tem- 0.6 C = ()5.6± 0.2 × 10 l/g. perature was controlled within 0.1°C in the range 17– In Fig.1.4 2 the experimental results with relative 0error 26°C. The back scattered light, collected by a pierced bars and the fitted curves are reported. It is important to mirror, and in some configuration, passed through a 1.3 0.4 note that the overall agreement is obtained with only polarizer, was focused onto the entrance slit of a 0.25 m three parameters.
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