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Surface Plasmons
Edited 4/5/2016 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:
𝑘𝑆𝑃 = √
𝜀(𝜔)𝜀𝑑
𝜀(𝜔)+𝜀𝑑
𝑘0 ,
where kSP and k0 are the wavevectors of the surface plasmons and incident light, respectively,
with k0 = ω/c (c = speed of light). The dielectric constant of the dielectric medium and the metal
are given by εd and ε(ω), respectively. Recall εd = 1 for air.
The dielectric constant of the metal is defined as ε(ω) = ε1
+ iε2, where in general |ε1| >> |ε2|. Drude theory predicts ε1
= 1 – (ωp/ω)2. The bulk plasma frequency, p, is defined
as p = (ne2/0m*)1/2, where n is the electron density, e is
the electron charge, 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)
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 = 𝑘0 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.
Figure 3: Waves incoming at the critical angle, αc, 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.
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.
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 82-410, 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 1983. 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.
A – Slit
B – Collimator Objective
C – Dispersing Prism
D – Telescope Objective
E – Position of Cross Hairs
I - Prism Table Clamping Screw
J – Prism Table Clamping & Tangent Screws
K – Telescope Arm Clamping & Tangent Screws
L – Eyepiece Ring,
M – Telescope Focusing Ring,
N – Divided Circle Dust Cover
O – Prism Table Leveling Screws
P – Collimator & Telescope Leveling Screws
Q – Telescope Bearing Front Screw
R – Telescope Bearing Side Screws
Figure 6: The Spencer Spectrometer
Figure 7: Schematic of the experimental setup used for excitation and measurement
of surface plasmons
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, δm, appears in Figure 8 and is minimized
when the light beam entering and exiting are symmetric (as in Figure 8).
Recall Snell’s Law:
𝑛𝑝𝑟𝑖𝑠𝑚
𝑛𝑎𝑖𝑟
=
sin 𝜃1
sin 𝜃2
.
𝛼
By simple geometry, you can verify 𝜃2 = 2 and the minimum deviation 𝛿𝑚 = 2𝜃1 − 𝛼.
From these, the index of refraction of the prism can be calculated (with δm in radians):
𝛿𝑚 + 𝛼
𝛿𝑚 𝜋
2 ) sin ( 2 + 8 )
=
𝛼
𝜋
sin ( 2 )
sin ( 8)
sin (
𝑛𝑝𝑟𝑖𝑠𝑚 =
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 180o 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 δm. 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 90o 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
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, αc, at which total internal reflection
begins, for light of 400, 450, 500, 550, 600 and 650 nm. This angle should be the angle at
which surface plasmons form. Use this rearrangement of Snell’s law, αc =
arcsin(nair/nprism), to find αc for each of these wavelengths. See Figure 9.
d. Set the monochromator to 650nm and the prism hypotenuse to approximately αc 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.
Figure 9: Path of light through the prism
III. Metal Film Preparation
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
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 = 𝑘0 𝑛 sin 𝛼 = 𝑛𝑝𝑟𝑖𝑠𝑚 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. Fix the prism table near the calculated critical angle, look at the photometer reading and
rotate tangent screw of the prism table slowly. You should see a resonance (drop in
intensity) at a particular wavelength that corresponds to SP excitation.
f. Measure and record the angle of reflection at resonance.
g. 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.
h. Repeat above for TE polarization (0°) and wavelengths 600, 550, 500, 450 and 400 nm.
i. Plot the measured dispersion relation over this range of wavelengths.
j. 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?
k. 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
1. Kretschmann, E. & Raether, H. “Radiative decay of nonradiative surface plasmons
excited by light.” Z. Naturforsch. A 23, 2135–2136 (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, 824-830 (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 0-360 which measures the angle and one from -60-0-60 (or -30-0-30) 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 28° 15’. Figure 10.b shows a vernier scale you’re
more likely to see in real life; read that scale and convince yourself it reads 86° 30’.
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
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 28° 15’.