The Raman effect is the appearance of weak lines in the spectrum of light scattered by a substance which has been illuminated by a monochromatic light (with angular frequency w). The lines occur close to, and on each side of, the incident light frequency, and hence are optical sidebands. The sidebands arise from the nonlinear interaction of the light with atomic or molecular quantum states in the scattering material. In a classical picture, the light induces a dynamic (time dependent) response in the polarizability of the substance, and then the product of the polarizability with the original light field results in the optical sidebands. In a quantum mechanical picture, the nonlinearity is equivalent to second order time-dependent perturbation theory. In this case, one encounters a product involving a quantum state a with time dependence exp(-iwat) , the complex conjugate of a quantum state b with time dependence exp(iwbt) , and the electromagnetic field with time dependence cos(wt). Using simple trig identities, one obtains a resultant time dependence cos[(w - (wb - wa)) t] and cos[(w + (wb - wa)) t] . By analogy with the terminology used in fluorescence, the lines corresponding to a lower frequency are called Stokes lines and those corresponding to a higher frequency are called Anti-Stokes lines. By measuring the frequency shifts and wb - wa, the structure of the system can be determined. [1-8]
Recalling that second order perturbation theory involves a sum over virtual states, a pictorial mnemonic for Raman scattering may be viewed as in Fig. 1.
1. The first step is to check the status of the PMT thermoelectric cooler. The cooler is based on the thermoelectric effect, in which a DC electric potential difference generates a temperature gradient; by anchoring the high end of the gradient near room temperature with a flowing water heat exchanger, the low temperature end of the gradient can be used to cool the PMT. The thermoelectric effect is reversible, so that a temperature gradient can generate a potential difference. There are some potential diffculties with this cooler, so that it cannot be turned on until two checks are performed. The reason is that the cooler may have been used earlier, and the heat exchange water may have been stopped when the cooler was turned off. This may result in two problems. The first problem is that parts of the cooler which remain cold after shut-down may cause the water (no longer flowing) to freeze and plug the heat exchanger. The second problem is that the residual temperature gradient may establish an electric potential across the leads connected to the cooler power supply, with the consequence that when the power supply is turned on, the extra potential causes too much current to flow, and a fuse is blown. The steps to check the status of the cooler are as follows: (a) Turn on the DMM connected to the PMT cooler power supply (which should be off), and set it to measure DC voltage. The absolute value of the voltage should be less than 0.1V; if not, there may be a residual temperature gradient on the thermoelectric cooler, and you must wait until it reduces.
(b) Follow the rubber tubing from the PMT housing to the source of the heat exchanger water at a green-handled ball valve on a back wall near the floor. Turn on the water by rotating the green handle until it is parallel to the outlet pipe. Do not alter the round-handled throttling valve which is upstream from the green-handled ball valve. Water should exit the other rubber tube into a drain pipe, and the lights on a safety flow switch mounted on the wall near the PMT housing should change from red to green. If water does not flow, the PMT cooler may be plugged with ice, and you will have to wait until it melts. If the water does flow, turn it off by rotating the green handle until it is perpendicular to the outlet pipe. Note that the water is filtered, and that the filter should be replaced if it appears dirty.
If the checks indicate that the PMT cooler is operational, do not turn on the power supply at this point. Also do not turn on the water at this point.
2. Check that the spectrometer exit slit shutter (at the PMT unit) is closed. Turn on the PMT high voltage power supply and set it at 900 V (the actual output voltage is negative). Turn on the PMT preamp and set its gain to 64. The PMT preamp output should be kept connected to the computer. You may check the PMT preamp output by inserting a BNC tee and viewing the output with an oscilloscope [How should the connection be terminated?]; negative pulses should be observed. The pulses have about the same amplitude (a few hundred mV); the magnitude of the signal from the PMT is taken as the rate that the pulses occur in time, expressed as counts-per-second (cps). When taking data with the computer, disconnect the PMT preamp output from the oscilloscope.
3. Turn on the computer and make sure no anti-virus software is running; such software may disable the computer's data acquisition hardware driver. Start the raman computer program by double-clicking its icon on the desktop, or by running the program Check the Settings menu, and make sure the Timeinterval is set at 0.8 s. Use File -> Open to open a new file and at the prompt “How long do you want to measure?,” enter the value 2000s; proceed to step 2, and at the prompt “Enter counter value,” accept the default (0); finally, Start the data acquisition. The data presentation will default to a graph display of PMT pulse rate (in cps, determined from the number of counts occurring over the time interval given by the “Timeinterval” setting) versus time. Using the View menu, turn on the Listview display; you should see a list of numbers scrolling up. The pulse count rate from the PMT will show up as numbers in a column labeled as “Frequency (Hz);” the numbers should have values of approximately 200 to 300 cps. This is the room temperature PMT dark current count rate. The data acquisition mode may be exited at the end of the run (or at any earlier time) by clicking the Stop button. Leave it running for now.
4. Turn on the water to the PMT cooler, and turn on the PMT cooler power supply. As the PMT tube cools down, you should see its dark current count rate decrease, reaching values of only 2 or 3 cps in 30 minutes. You can monitor the PMT cool-down with either the Graphview or Listview display on the computer.
5. Near the end of the PMT cool-down, you can check for light leaks. Close the cover on the scanning spectrometer if it is open (as shown in Fig. 2), close the entrance slit, open the internal and exit slits, and finally open the shutter on the exit slit. Turn the room lights on and off; the PMT signal should remain close to 2 or 3 cps. When done with this check, close the shutter on the exit slit.
1. While the PMT is cooling down, the optical system may be aligned. Remove the two lenses from their bases. After making sure the shutter on the exit slit is closed, open the cover to the spectrometer (as shown in Fig. 2) and place a cardboard disk (with marks indicating its center) over the first mirror (opposite the entrance slit). Open the spectrometer entrance slit to almost fully open. CAUTION: Laser safety goggles must be worn from this point on. Turn on the He-Ne laser, and adjust its position so that its beam passes through the center of the entrance slit and falls on the center of the disk at the first mirror. This defines the optical axis for the spectrometer.
Before doing any Raman scattering experiment, it is necessary to become familiar with the scanning spectrometer, and to calibrate the scanning motor counter against the wavelength. The calibration can be accomplished using the He-Ne laser, the Ar laser, and the known lines from a mercury (Hg) lamp. A calibration graph should be made for future reference. The slope of the calibration line should be a ratio of two small integers. The reason is that at some point a grating inside the spectrometer was replaced; the old and new gratings had standard line densities, but they were two different standards, which differed by the ratio of two small integers.
1. Read the manual for the scanning spectrometer. The scanning is accomplished by a precision motor drive, which is controlled by a unit external to the spectrometer. Always make measurements in the same scan direction due to screw lag. Note that turning on or stopping the motor drive at high speed can ruin your calibration; always turn on or stop the drive at low speeds (approximately 10 on the control unit dial read-out), slowly accelerating or decelerating to the desired speed. Note that the scanning spectrometer needs electrical power, and it is turned on by plugging its power cord into a wall socket; lights near the scanning motor counter should turn on. When shutting down the experiment, remember to unplug this power cord. If the counter lights are off when the spectrometer is plugged in, then use a DMM to check connections, bulbs, etc. in the vicinity of the counter.
2. Using a strip of paper, trace the light from the Ar laser (which should be present as a result of the optics alignment procedure) through the first monochromator; it may be necessary to turn off the room lights. Run the spectrometer's scanning motor (rotating the gratings) so that the scattered light from the Ar laser falls on the internal slit. Note the scanning motor counter reading; this gives the “ballpark” position for the subsequent calibration at this wavelength. Note that the Ar ion laser may be tuned to produce different wavelengths of light; the possible discrete wavelengths may be found in the raman lab manual notebook. Use the table of colors and wavelengths in the lab notebook and the observed color of the Ar laser beam to determine the actual wavelength produced by the Ar laser. Do not use color charts in textbooks, because they are very inaccurate.
3. Close the cover of the scanning spectrometer, and set the internal and exit slit openings to 0.3 mm. Close the entrance slit opening to zero. The PMT cool-down data acquisition on the computer should have completed. [If you wish, you may save the cool-down data for your lab report.] Restart the computer data acquisition as for the PMT cool-down, and recheck that the PMT has cooled down so that its dark current is 2 or 3 cps. Open the shutter on the exit slit, and slowly open the entrance slit; the count rate from the PMT should increase. Use the scanning spectrometer motor drive to position the monochromator for a maximum count rate. Increase the entrance slit opening until 0.3 mm is reached, or the count rate reaches 105 cps, whichever comes first. CAUTION: Never let the PMT count rate exceed 106 cps.
4. Rewind the spectrometer scanning motor away from the “ballpark” position for the Ar laser wavelength so that the count rate drops to the background rate (near or at the dark current rate). For the calibration you will want to scan through the Ar laser wavelength to acquire a fully resolved peak. You will want to use a position where the PMT is at the background rate as your desired starting position for the scanning motor counter when initiating the calibration scan; make a note of this desired starting position. NOTE: The resolution of the spectrometer depends critically on the width of the various slits in the spectrometer and, in general, reducing the slit width will both increase the resolution and decrease the signal to the PMT. Also, weak peaks, possibly next to a strong peak, will require longer scan times. These aspects should be kept in mind when the scans for Raman lines are performed.
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