A Study of Evanescent Light Fields
Created by Total Internal Reflection
Bolun Liu, Marty Cohen, and John Noé
Laser Teaching Center, Stony Brook University
The behavior of light at boundaries between two medium are of interest. Most people are aware that when light hits a boundary with different indexes of refractions, it bends. The association between angle of incidence, angle of diffraction, and the index of refraction of the two prisms can be delineated using Snell's law. However, at a certain point, light entering a medium with a smaller index of refraction will be bent parallel to the medium surface. Past this "critical angle," all light is reflected back, away from the second medium. This is called total internal reflection.
What many people are unaware of is that, due to boundary conditions described by Maxwells equations, there cannot be a discontinuity in energy levels at the boundary. In total internal reflection, the light resides only on one side of the boundary. However, in actuality, an exponentially decreasing energy field propagates in the direction of light. This evanescent field is readily measurable within one or two wavelength distances away from the boundary. This makes detecting and utilizing the evanescent wave difficult for light in the visible spectrum.
Evanescent waves have a variety of uses and can be used in conjunction with other optical effects to produce interesting applications. It can be used for illumination in spectroscopy, for optical tweeing, whispering mode coupling. In this project, two phenomenon, Frustrated Total Internal Reflection and Attenuated Total Reflection will be demonstrated and quantitatively assessed
Frustrated total internal reflection and attenuated total internal reflection are two related phenomena that both deal with near-field effects. However, their fundamental propagation patterns are slightly different. Evanescent waves involved in frustrated total internal reflection exponentially decline and lose their intensity within approximately one wavelength of light. However, for the field produced by attenuated total internal reflection, the gap distance at which maximum transmittance is achieved is near one wavelength, and transmittance can still be observed at approximately two wavelengths. Both of these phenomena can be to construct optical modulators that have advantages over acousto-optic and electro optic modulators.
Using a micrometer screw and a rotating platform, it is possible to carefully maneuver a prism in between a laser beam and a photo detector. By making a wedge-shaped air gap between the prism and either another prism or, the angle of incidence can be controlled on the scale of fraction of an angle and separation distance on the scale of tens of nanometers. The intensity of the reflected/transmitted light will then be measured and checked for agreement with theoretical predictions.
I originally planned for a vertical setup with a laser pointed = up towards a prism with the piezoelectric driver pushing a film downwards, as described in the article. However, because of the lengths of the lasers and the additional complexity of the framework necessary, I settled for a simpler and more conventional build where the objects are parallel and I can use a turntable to turn my prism instead of having to adjust the angle of my laser. Here is the setup as of 7/13.
In this setup I used two brand new prisms, half-wavelength smoothness, and a piece of shim stock rolled to approximately 5 ten-thousandths of an inch thick to create my wedge. My laser had a Brewster's window in at and therefore produced polarized light, which I oriented so that the electric field was parallel to the reflected material.
The cleaning procedure is extremely important to the success of the project at this point. A huge amount of care must be taken in keeping the prisms clear of scratches and discontinuities. I unwrapped both of the prisms halfway, then place both on a piece of Styrofoam paper. After uncovering the faces where the air gap was going to reside, I took out a piece of optics cleaning paper (sold by Kodac to clean lenses), wet it with a drop or two of methanol, sandwiched it between the two faces, and gently pulled outwards. I took care not to use too much methanol, or it will cause the two prisms to optically bond.
With these procedures, the evanescent wave was readily observed and could be quantifiably assessed. However, further experimentation is necessary to measure more accurately the evanescent wave and to get more precise data.
Profiling the evanescent wave using collected data
When we fired a laser at the air gap between the prisms, and measured the transmittance distribution, we were using FTIR to see what an evanescent field looks like. However, there are multiple other complications that have to be taken into account: non-perfect triangular wedge air gap, imperfections in the prisms, and averaging of signal due to beam width.
By taking profiles of the evanescent wave on different levels of the prism, we can determine whether aberrations from exponential decay on our transmittance graphs are due to the nature of the evanescent wave, or due to discontinuities on our prism faces. This allows us to get better data from a prism that could have scratches or pieces of dust interfering with the evanescent field. Then, using data collected from the Fabry-Perot etalon we can make an estimate on the true shape of the air gap, we can get a closer approximation to the evanescent field.
One problem was that the beam was faint enough that running a power meter connected to the photodiode on milliamps still resulted in data not precise enough for my liking. Lauren assisted me and taught me how to read resistor's numbers, and how to use a power meter correctly. I added a 100k resistor in a parallel circuit and measured the voltage instead of the current, which gave me much better results.
[insert circuit diagram]
One thing to be cautious of is saturating the photodetector. It has a maximum output of 10 volts, so anything above approximately 7 volts is not likely to show a linear relationship between light intensity and current produced.
Another thing my professor and I tried was to add a signal amplifier. It is important to get noise comparable to the minimum intensity that the original setup could read, otherwise an amplifier is not necessary.
[insert circuit diagram]
There are multiple ways to reduce noise. I started off by simply placing a tube of paper and taping one side to the photodetector. This was able to reduce most of the noise, but turning on and off the lights in the room still had a significant effect on the readings produced by the photodetector.
A more advanced way to do this would be to use a chopper and a lock-in amplifier. This device uses a fan like device to disrupt the laser signal, and to use the signal to subtract out noise.
However, after several data sets, I came to realize that the amount of "noise" is actually very closely related to the laser light, not the ambient light. Due to multiple reflections of the faces of the prism, there are varying amounts of diffuse monochromatic light. Therefore, I designed a new setup to isolate light with a very small angle acceptance. This is done by placing a diaphram iris very close to the prism setup, the photodetector relatively far back. Then I used several curved pieces of paper to isolate any atmospheric noise. Using this setup, I was able to get my power meter readings with a 100k resistor to be below 0.1 microvolts
Dealing with Prism Aberrations
After the first few trials it was strikingly clear that the evanescent wave was exponentially decreasing. However on certain points of the graph, there were noticeable mound-like aberrations. Unless the experimenter is working in a completely sterilized environment and has near-perfect prisms, there is always the possibility of the wedge having small pits or scratches in them.
As a result, I decided to alter my setup to allow for horizontal movement. I used two adjustable platforms to increase the height and angle of my laser. I also placed the laser on supports that consisted of a V-shaped mount, with a post and a post holder, ensuring that my laser tilts only vertically.
Using this data, we can determine if the disturbances with the evanescent field were due to a innate quality of the evanescent field, or if it was due to a localized disturbance.
Interestingly enough, from the data I collected, I could see the mound in my data move farther and farther towards the thick side of my wedge. This can explained if we consider a diagonal scratch near the 2000 to 3000 nm thickness range.
Fabry-Perot Etalon setup
In measuring the smoothness of prisms, there are different specifications, one of them, called scratch and dig, measures the frequency of "small" malformations with the prism, ones that are nanometers or micrometers in size. On the other hand, prisms also have wavelength measurements (of the form wavelength/n, where n is commonly 2, 4, 10, 50, etc.) which take into account how variation there is in larger chunk of the prism. Lastly, there is a parallelism measurement which looks at the entire face of the prism and notes how close they are to the angle they are supposed to be, e.g how close the angle between the hypotenuse and the side are to 45 degrees.
To assess the parallelism and wavelength smoothness of the air wedge, I can use a Fabry-Perot etalon. Just by rotating my prisms so that the laser light does not surpass the critical angle. This produced interference fringes that can be readily observed using the same light sensor. The maxes and minimums produced are representative of the linearity of the sides of the wedge. If the plot of the locations of the maxes against wedge number is not linear, then that means that wedge is more curved that flat.
Due to our laser having a millimeter size beam, we need to consider it after we take data for the evanescent wave. FTIR effect should give %transmission, which means that the relationship between intensity of light input and transmittance should be linear. If we multiply a standard distribution representing the beam profile centered around x, multiply it to the expected true evanescent wave profile, and take the integral from x-1 to x+1, we would expect to get something similar to the data we collect. We need to do the reverse transformation on the data.
Amazingly enough, however, the Gaussian curve thing doesn't affect the exponential component of the data at all. This is easily derived by going backwards... construct a graph that is exponentially distributed, take any average about an interval around x, and the end result is simply a shifted exponential.
Effect of Angle Change
One of the variables that can be tested using this apparatus is the angle of intercept. Obviously, the angle need not be tested above the critical angle, but the behavior of the evanescent wave in relation to angle is unintuitive.
The evanescent wave is most easily detectable close to the critical angle, and can be readily seen with approximately one degree of variation.
The quantitative method in finding the penetration depth of the evanescent wave is done by taking the maximum transmittance, dividing it by e, and using a least-squares line of best of the exponential data to solve for distance. Then, it is possible to plot the angle deviation from the critical angle against the penetration depth.