Surface Plasmons Edited 6/6/2016 by Stephen Albright & DGH & ETS

Transcription

1 Surface Plasmons Edited 6/6/2016 by Stephen Albright & DGH & ETS Purpose The purpose of this experiment is to measure the dispersion relation of surface plasmons and the electron density in a thin silver film. Note: This manual is not intended to be all-inclusive. You are expected to reference the equipment manuals and technical resources provided in the lab, on the lab wiki, etc. However, you may not consult with students who have done this lab before or refer to their write-ups. Introduction At the interface of a metal and dielectric (in this case air), Maxwell s theory predicts that coherent charge density oscillations, called surface plasmons (SPs), can exist in the metal. From Maxwell s equations, SPs must be polarized so their magnetic field is parallel to the interface. This polarization is called transverse magnetic (TM). SPs can be induced in metal films by one of two methods incident electrons (by scattering metallic electrons on the metal surface) or photons (by coupling with surface electrons to transfer momentum). This experiment will rely on photon excitation. Solving Maxwell s equations for the relevant boundary conditions, we arrive at an expression for the dispersion of surface plasmons excited by incoming light of frequency ω: k!" =!(!)!!!!!!! k!, where k SP and k 0 are the wavevectors of the surface plasmons and incident light, respectively, with k 0 = ω/c (c = speed of light). The dielectric constant of the dielectric medium and the metal are given by ε d and ε(ω), respectively. Recall ε d = 1 for air. The dielectric constant of the metal is defined as ε(ω) = ε 1 + iε 2, where in general ε 1 >> ε 2. Drude theory predicts ε 1 = 1 (ω p /ω) 2. The bulk plasma frequency, ω p, is defined as ω p = (ne 2 /ε 0 m * ) 1/2, where n is the electron density, e is the electron charge, ε 0 is the permittivity of free space and m * is the effective mass of electrons in the metal. From the dispersion relation above, we can see that SPs have a nonlinear dispersion with wavevectors greater than the incoming photons (see Figure 1). Because of this property, SPs cannot be directly excited by shining light onto a metal surface. For a given frequency of incoming Figure 1: Dispersion relation of surface plasmons (light blue), incident light (red) and light from prism (dark blue)

2 photon, the corresponding SP would have a larger wavevector and therefore momentum than the photon. Therefore, the momentum of the incident photon is insufficient to generate the SP. In 1968 A. Otto developed a method for exciting SPs with photons. He showed that when light through a prism undergoes total internal reflection, the wavevector of the photons along the base of the prism k would be k = k! n sin α, where n is the refractive index of the prism and α is the angle of incidence from vertical. Clearly, n sin(α) can be greater than unity, in which case the wavevector of the photons in the prism would be greater than in air. Under total internal reflection, no light propagates into the air. However, so that the fields are continuous at the interface, the fields do extend a short distance into the air and decay from the surface exponentially. This extension of the fields is called an evanescent wave. See Figure 2. Figure 2: Total internal reflection at a glass/air interface. Black lines are wavefronts. Otto then proposed harnessing the increased wavevector of the evanescent wave by placing a metal so close to (but not in contact with) the prism that the evanescent wave reaches the metal. At the correct frequency and wavevector, the evanescent wave could induce SPs in the metal surface. There is another case to consider that could induce SPs: when the incoming photons hit the prism/air interface at its critical angle, refracting the photons along the surface of the interface. In this case, evanescent waves do not play a significant role, 1 but the fields from the refracted photons could still interact with a metal surface close to the prism and form SPs. This can be seen in Figure 3. 1 Even though total internal reflection does not occur in the case of critical refraction, some light does reflect. Because the majority of the light is refracted, the evanescent waves would play little role in SP excitation. This reflection and evanescent wave are not displayed in Figure 3 for clarity.

3 Figure 3: Waves incoming at the critical angle, α c, refract along the interface. The EM fields from the refracted light could reach a nearby metal and induce SPs. Otto found that the latter case induced SPs. This makes intuitive sense evanescent waves from total internal reflection only exist in the neighborhood around the reflection point and therefore have a minimum spatial effect on the metal. The critically refracted light however shines along the metal surface, greatly increasing the surface area over which the metal is affected. Otto s configuration relies entirely on the EM fields from the critically refracted light reaching the metal surface. Due to the rapid decay of these fields far from the photons, the metal and prism must be maintained at a distance of approximately 100 nm (actually 200 nm in Otto s experiment). The distance required to generate SPs in Otto s experiment is very difficult to maintain in reality. In 1971, E. Kretschmann presented an alternate configuration, one that was more easily experimentally realized. Kretschmann deposited a thin metal film directly to a prism and found he could generate SPs at the metal/air interface just as Otto had. One can easily see however that the mechanism for plasmon formation has changed significantly. With metal at the edge of the prism, light is not refracted along the bottom edge of the prism the light undergoes total internal reflection. What is generating the SPs then? In Kretschmann s case, evanescent waves do play an important role. At the reflection point on the glass/metal interface, evanescent waves are formed, extending into the metal. If the metal is made thin enough, the evanescent waves can reach air on the other side. When this happens, the evanescent wave forms a new light wave that propagates through the air! This is called frustrated total internal reflection (FTIR). 2 One can quickly see the parallels between FTIR and quantum tunneling it is in fact just the optical analog of quantum tunneling. In Kretschmann s experiment, the reflected light tunnels through the silver via its evanescent wave and emerges on the other side. 2 Unlike evanescent waves, newly formed propagating waves can transmit energy and information. Because of this, special care must be paid to avoiding FTIR when manufacturing bundles of fiber-optic cables. If the fibers are too close together, the light from one could jump to another.

4 Upon emerging in the air, this new light refracts. However, because it doesn t propagate, only tunnels, through the silver, the angle of refraction is found using the refractive indices of the glass and air. The index of refraction of silver does not play a role. Therefore, if the photons hit the glass/metal surface at the critical angle for glass and air, the newly generated light wave will propagate on the other side of the metal exactly along the metal/air interface (see Figure 4). These new waves still maintain the wavevector calculated above, so their EM fields induce SPs on the metal/air interface. Figure 5 shows Otto s and our variation of Kretschmann s experimental setups instead of depositing a thin metal film directly to a prism, we deposited the film to a glass slide and attached that to a prism. Using the explanations above, convince yourself that the locations of the refracted light and surface plasmons in Figure 5 are accurate. Figure 4: The Kretschmann configuration for generating plasmons. The metal film is thin enough for FTIR to occur, which generates new refracted light in the air. This new wave can be seen as the clear wavefronts bordered in purple. Figure 5: The Otto (a) and our variation of the Kretschmann (b) configurations for generating surface plasmons in metal films. The 2000Å air gap in (a) refers to the gap used by Otto in his original experiment.

5 Apparatus Light Source: The lamp housing contains a 12V, 100 W tungsten bulb and is powered by a large, highly regulated DC power supply more than capable of blowing out the lamp. 12V is not required to do this experiment so please be sure to stay below 12V. ~8A should be adequate for wavelengths > 500nm, though shorter wavelengths may require a slightly higher current. Monochromator: The Jarrell-Ash , ¼ meter Ebert Monochromator is a high precision monochromator containing two 1180 grooves/mm high dispersion gratings, one blazed to 300 nm, the other blazed to 600 nm. The entrance and exit slits are 500 µm wide. See the instruction manual on the lab wiki. Corner reflector: A 90 isosceles prism is used as a corner reflector. Light entering the prism through the vertical face of the hypotenuse will reflect through the prism and be sent back in the opposite direction at the same angle. See Figure 9. Assorted: Adjustable Polarizer, Mounted Mirror, Mineral Oil, Double Convex Lens, 2 Optical Rails (1 long, 1short), and various Optical Holders. Photometer: The Optec SSP-3 photometer has been sold since Recently the manufacturer upgraded it to include a PIC microcontroller and a serial computer interface. The model in this experiment predates these upgrades. The manual on the lab wiki is for the upgraded model - referred to as SSP-3 (generation 2) however, the information it contains is also accurate for earlier models such as ours. Evaporator: The Edwards Auto 306 evaporator, located in B&H 203, will be used to make the silver and aluminum slides needed for this experiment. Making slides is the last step of this experiment and you must receive special training before using the evaporator and liquid nitrogen. A film thickness of ~1/10th the wave length of light is necessary. Spectrometer: The heart of this experiment is the AO Spence 3700 spectrometer. This is a very delicate and precise instrument with many small controls that allow very fine & accurate adjustments. To avoid damaging this valuable instrument, please study Figure 6 and the 3700 Spectrometer manual, on the wiki, before proceeding. Note: some of the spectrometers parts are labeled separately in the light path schematic. The spectrometer has a graduated circle that moves with the telescope and a 30 minute vernier scale that moves with the center table. Both can be locked independently. See Appendix A for a guide on how to read a vernier scale.

6 A Slit L Eyepiece Ring, B Collimator Objective M Telescope Focusing Ring, C Dispersing Prism N Divided Circle Dust Cover D Telescope Objective O Prism Table Leveling Screws E Position of Cross Hairs P Collimator & Telescope Leveling Screws I - Prism Table Clamping Screw Q Telescope Bearing Front Screw J Prism Table Clamping & Tangent Screws R Telescope Bearing Side Screws K Telescope Arm Clamping & Tangent Screws Figure 6: The Spencer Spectrometer Figure 7: Schematic of the experimental setup used for excitation and measurement of surface plasmons

7 The experimental setup for generating and measuring SPs appears in Figure 7. Light is generated in a broadband lamp and passed through a monochromator to select a single frequency of light. From there, the light passes through a polarizer, adjustable slit and collimator. The slit varies the width and intensity of the slit image a narrower slit gives better resolution but less intensity. SPs will be excited on a thin silver film deposited on a microscope slide. The silver slide will be attached to the prism on one of the short sides using mineral oil as an adhesive, with the silver film on the side opposite the prism. Mineral oil is used because it has a refractive index very near that of glass no light is refracted at the mineral oil interfaces. An aluminum film, also deposited on a glass slide, is attached to the other short side of the prism to help reflect the light to the silver film. The aluminum film is attached with mineral oil as well, but with the aluminum facing the prism. Due to its orientation, SPs cannot be generated in the aluminum, so you can be confident you are measuring SPs in silver. From the silver, the light is reflected into a photometer which measures its intensity. Experiment To measure the dispersion relation of SPs excited in the silver film, you will be looking for an SP absorption resonance in the setup above. When SPs are generated at a particular frequency and wavevector, the light reflected off of the silver film will decrease dramatically as momentum is transferred into generating surface plasmons. The frequency and wavevector at resonance can then be plotted as one point of the dispersion relation, which can be found completely by finding resonances at several different frequencies. The first part of this experiment is aligning and calibrating the optics. Careful alignment and calibration of the optics is time consuming but critical to success in this experiment. Due to silver s high oxidation rate, silver slides have a very short useable lifetime; therefore, slides are made only after all of the optics has been setup. Alignment and calibration can be done without metal films attached to the prism. I. Measuring the Index of Refraction To calculate the wavevector at a particular resonance, you must know the index of refraction of the prism at all wavelengths of light measured. You will calculate the index of refraction by the minimum angle deviation method. The deviation angle, δ m, appears in Figure 8 and is minimized when the light beam entering and exiting are symmetric (as in Figure 8). Recall Snell s Law:!!"#$%!!"# =!"#!!!"#!!. By simple geometry, you can verify θ! =!! and the minimum deviation δ! = 2θ! α. From these, the index of refraction of the prism can be calculated (with δ m in radians): n!"#$% = sin δ! + α 2 sin α 2 sin δ! 2 + π 8 = sin π 8

8 a. Using the setup in Figure 7, without the glass slides in place, select 650 nm on the monochromator. b. Remove the prism and clean with alcohol (not acetone) c. Turn on the light source and set it to a medium intensity. Remember to plug in the fan. d. With knob J locked and knob K released (see Figure 6), position the telescope to look directly into the collimator (see Figure 7). There should be a sharply focused narrow slit of light visible in the telescope. Optimize this image by adjusting the location and width of the collimator slit and the focus of the telescope. Move the telescope to position the slit image near the intersection of the crosshairs. Lock knob K and use it s fine adjustment control to position the slit image precisely at the intersection of the crosshairs. The telescope is now 180 o from the collimator. Record reading of the Divided Circle. e. Position and secure the prism on the spectrometer table as in figure 7. Release K and rotate the telescope to find the slit image. Release clamp I and rotate the table while monitoring the movement of the slit image in the telescope. Precisely identify the prism location where the angular motion of the slit changes direction lock I. Adjust the telescope to position the slit image at the intersection of the crosshairs. Record the Divided Circle reading and calculate the angle location of the telescope. f. Repeat for 600, 550, 500, 450 and 400 nm. g. For a given wavelength, the difference between the angles measured in part d. and e. is equal to the minimum deviation δ m. Calculate the wavelength dependent index of refraction for this prism. Figure 8: Diagram for measurement of the index of refraction of the prism by the minimum deviation angle method II. Alignment of Optics a. Rotate the telescope precisely 90 o CW from the location recorded in part d. of step I and lock K. Release I. While looking through the telescope, rotate the prism table until the slit image reflected off of the hypotenuse of the prism falls precisely on the intersection of the cross hairs. Lock I. Note: It may be necessary to adjust Leveling Screws O to make the slit image vertical. In this position, the hypotenuse of the prism

9 is at an angle of 45 with the incident light. Record the reading on the Divided Circle. From this point on, do not loosen I, K or remove the prism. Doing so will destroy this calibration. b. All future angles will be measured with respect to the calibration angle found in part a. To rotate the prism without losing your calibration, release or adjust J. Remember to calculate, using Snell s Law, the corresponding angle of incidence on the silver film for each angle of the hypotenuse (use Figure 9). Remember that when the hypotenuse is at an angle of 0 (45 CW from the calibration angle), the angle of incidence on the film is 45. c. Use Snell s law to determine the critical angle, α c, at which total internal reflection begins, for light of 650, 600, 550, 500, 450, and 400 nm. This angle should be the angle at which surface plasmons form. Use this rearrangement of Snell s law, α c = arcsin(n air /n prism ), to find α c for each of these wavelengths. See Figure 9. d. Set the monochromator to 650nm and the prism hypotenuse to approximately α c for that wavelength. e. Align the mirror, lens and photometer to focus the slit image on the circle in the photometer s eyepiece. Note: Only light inside the circle at the center of the viewfinder will be detected accurately. See SSP-3 Photometer on the wiki. III. Metal Film Preparation Figure 9: Path of light through the prism You will prepare the silver and aluminum films in the evaporator. The films will be deposited on clean glass microscope slides. See the Dean s List of Thin Film Fabrication Tips located on the Technical Tips & References page of the lab wiki for detailed description of the slide cleaning procedure and the operation of the evaporator. Be sure to check that the shields on the evaporator are not shorting out your metal sources, this is particularly necessary for the silver boat. Be sure to keep the deposition rate low (<10 Å/sec) so you do not overshoot the desired thickness of the

10 silver film remember it is very important the silver be thin enough to allow penetration of the evanescent wave. Make the silver film approximately 250 Å so the evanescent wave can reach the far side of the film. The aluminum film only acts as a mirror, so its thickness is not as critical; somewhere between 800 & 1300 Å is fine. Due to its high oxidation rate, the silver slide is particularly short lived. Only make the silver slide once all of the other optics have been aligned, calibrated and tested. If you must store the slides for some time, keep them under vacuum or put them in the desiccator next to the evaporator. IV. Measurement of the SP Dispersion Relation Finally, you can measure the dispersion relation for the SPs excited in the silver film. Remember that the frequency can be calculated directly from the wavelength selected on the monochromator, ω = 2πc/λ. Also recall, the SP wavevector is defined as: k = k! n sin α = n!"#$% ω sin α /c. a. Attach the silver and aluminum glass slides with the films opposite and facing the prism, respectively, on the two short sides of the prism with mineral oil. Be careful with the mineral oil avoid air bubbles or dust. b. Be sure not to block airflow to the fan of the lamp. c. Set the monochromator to 650 nm. d. Set the polarizer to 90 this polarizes the light so the magnetic field is transverse to the thin film surface so-called TM polarization. e. Fully widen the collimator slit and fix the prism table near the calculated critical angle. While slowly rotating the tangent screw, look at the image through the viewfinder. You should see a dark line in the image at a particular angle that corresponds to SP excitation. f. Now reduce the slit of the collimator for better angular resolution and look at the photometer reading while rotating the tangent screw of the prism table slowly. You should again see the SP excitation, as a drop in intensity, at a similar resonance angle to part e. g. Measure and record the angle of reflection at resonance. h. Record and plot intensities for a few angles near resonance to get a sense for the quality of the peak. Be sure to take background signal as well, so it can be removed from measurements. i. Repeat above for TE polarization (0 ) and wavelengths 600, 550, 500, 450 and 400 nm. j. Plot the measured dispersion relation over this range of wavelengths. k. Assuming the effective mass in silver is simply the mass of an electron in free space (not an unreasonable assumption), fit your measured dispersion relation and solve for the density of electrons in silver. Be sure to comment on the value you calculate how reasonable is this value? l. Find the intensity ratio of TM/TE polarization as a function of light incident angle. Comment on the relative strengths of surface plasmon creation in TM and TE polarized light. References

11 1. Kretschmann, E. & Raether, H. Radiative decay of nonradiative surface plasmons excited by light. Z. Naturforsch. A 23, (1968). 2. Otto, A. Exitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection. Z. Phys. 216, 398 (1968). 3. Barnes, W, Dereux A, & Ebbesen TW. Surface plasmon subwavelength optics. Nature 424, (2003). Appendix A: Reading a Vernier Scale A vernier scale is a type of graduated scale that enables high levels of accuracy measuring lengths or angles. Examples of angular scales appear in Figure 10. Angular vernier scales have two scales, one from which measures the angle and one from (or ) which measures arcminutes. To read the scale, start with the first angle less than the 0 arcminutes line. In the case of Figure 10.a, that is 28. Now to get the number of arc minutes above 28, find the line on the arcminutes scale to the right of zero that lines up exactly with a line on the angle scale (it does not matter the value on the angle scale where the lines match up). Below, the scales line up at the 15 arcminutes line. Therefore, the angle on the scale in 10.a is Figure 10.b shows a vernier scale you re more likely to see in real life; read that scale and convince yourself it reads a. b. Figure 10: Two examples of vernier scales It should be noted that you can read the scale from the opposite direction, that is, you can find how many minutes less than a degree an angle is, rather than how many more. Look again at 10.a. The next largest angle from the 0 arcminutes line is 29. Now look to the left of 0

12 arcminutes for the line that lines up with the angle scale. We can see in this case that the 45 line to the left of 0 lines up. Subtracting the arcminutes measured from the angle measured gives your reading. Therefore the angle in Figure 10.a is 29 less 45, equal to