Characterizing the Production of Polarized Light From a Liquid Crystal Variable Retarder

Ian Wojtowicz Author

07/27/2021 Added

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By applying a voltage to a liquid crystal variable retarder, it can produce different polarization states of light, by introducing a phase shift, or a retardance. It is necessary to understand the behavior of the LCVR as the applied voltage varies across it. First, a retardance curve is experimentally calculated for two different wavelengths, and then the deflection of light is measured at different retardances. It was found that the retardances produced by the variable retarder is wavelength dependent, and there appears to be no measurable deflection in the direction of the light at different retardances.

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[00:00:01.890]Hi there.
[00:00:02.723]My name is Ian Wojtowicz
[00:00:03.790]and I'm a rising junior majoring in physics
[00:00:05.950]at Carleton College.
[00:00:07.500]Today, I will be focusing on
[00:00:08.760]the production of polarized light
[00:00:10.130]from a liquid crystal variable retarder, an optical device,
[00:00:13.430]which when connected to a power source can be used to change
[00:00:16.570]the polarization of light.
[00:00:18.510]Before diving into specifics,
[00:00:20.070]we'll go into some information on light polarization and how
[00:00:23.100]a retarder works.
[00:00:25.530]Some light sources such as the sun give off unpolarized
[00:00:28.550]light, which oscillates in multiple directions around
[00:00:30.810]the axis of propagation as seen here.
[00:00:33.610]However, if the light passes through a linear polarizer,
[00:00:36.408]then only one direction of light will be led through,
[00:00:39.010]and so the light is said to be linearly polarized.
[00:00:42.170]This direction is called the past axis of the linear
[00:00:44.727]polarizer.
[00:00:46.643]On the other hand, if a retarder lets through a light
[00:00:48.540]in all orientations,
[00:00:50.130]but introduces a phase shift between components of the
[00:00:52.192]electromagnetic wave that are parallel to a set of
[00:00:54.643]perpendicular axes.
[00:00:56.960]This is a difference in how quickly light is transmitted
[00:00:59.240]along these axes
[00:01:00.390]because the index of refraction varies with respect
[00:01:02.950]to the angle at which light is transmitted.
[00:01:05.770]The axes along which light travels,
[00:01:07.360]the slowest and fastest are respectfully called the slow
[00:01:09.694]and fast axes.
[00:01:11.820]Because of the speed difference, these light components are
[00:01:14.390]out of phase when they exit the other side of the retarder.
[00:01:17.560]The phase shift is referred to as the retardance,
[00:01:19.530]which is 90 degrees in this example.
[00:01:22.410]Because the wave components are out of phase by 90 degrees,
[00:01:24.904]the oscillation direction will appear to rotate
[00:01:28.580]above the propagation axis with time,
[00:01:31.430]this results in the production of circularly polarized
[00:01:33.780]light.
[00:01:34.613]If rotating clockwise, as seen in this image, it is called
[00:01:37.530]the right-hand circularly polarized or counter-clockwise
[00:01:40.230]would be left-hand circularly polarized.
[00:01:43.230]Usually retarders need to be physically rotated
[00:01:45.490]to change the outgoing lights polarization,
[00:01:47.770]but this can cause issues if optical imperfections are
[00:01:50.030]present.
[00:01:51.420]And if the entrance of the liquid crystal variable
[00:01:53.003]retarder or LCVR for short is the absence of moving parts.
[00:01:57.200]Retardances change by applying a voltage across a liquid
[00:02:00.190]crystal film.
[00:02:01.470]It is important to understand how the applied voltage
[00:02:03.720]changes the retardance in order to see if the LCVR is a
[00:02:06.940]viable device for reliable production of given polarization
[00:02:10.660]states.
[00:02:11.790]To effectively use this quality of LCVR, is first necessary
[00:02:15.250]to understand how its retardance varies for different
[00:02:17.650]voltages and thus build up a retardance curve.
[00:02:20.690]To do this, laser light must first pass through
[00:02:22.810]a linear polarizer
[00:02:23.934]and rotated such that it produce horizontally polarized
[00:02:26.850]light.
[00:02:27.683]This light then passed through the LCVR,
[00:02:29.700]which applied some phase shift at some set voltage,
[00:02:32.220]and then it passed through another linear polarizer.
[00:02:35.260]The final intensity of the light was then measured up by
[00:02:37.320]detector.
[00:02:38.540]The voltage was varied by point one volt increments
[00:02:40.890]from zero to six volts,
[00:02:42.080]and then by one volt increments up to 10 volts.
[00:02:45.260]The entire process was repeated with two lasers
[00:02:48.200]with different wavelengths, one that was 632.8 nanometers
[00:02:52.280]and another that was 801.7 nanometers.
[00:02:55.470]Initially the 633 nanometer laser was used
[00:02:58.540]because it is easily visible to the naked eye,
[00:03:01.120]while the 802 nanometer laser is very dim
[00:03:03.530]and hard to detect.
[00:03:05.090]However, 802 nanometers is of particular interest
[00:03:08.090]for some planned future work with the LCVR.
[00:03:10.980]The following function was then used to calculate the
[00:03:13.040]retardance, delta is to retardance, I is the intensity,
[00:03:16.161]I max is the maximum measured intensity,
[00:03:19.570]K is an experimentally determined constant
[00:03:21.660]describing how much light makes it through
[00:03:23.340]the linear polarizers
[00:03:24.810]and V of I is the voltage corresponding to given intensity.
[00:03:28.620]The inverse cosine term is subtracted from two pie
[00:03:30.902]for voltages less than V of I max to allow solutions beyond
[00:03:35.020]a 180 degrees to be solved for.
[00:03:37.630]On its own, the inverse cosine function can only go
[00:03:40.080]from zero to 180 degrees.
[00:03:43.500]Retardance curves of both waves are shown below,
[00:03:45.951]it is clear that the retardance produced in the 802
[00:03:48.557]nanometer laser is noticeably lower
[00:03:50.900]than for the shorter wavelength laser,
[00:03:52.950]especially at smaller voltages
[00:03:54.530]where the difference is over 75 degrees.
[00:03:57.750]In both curves, there also appears to be a voltage range
[00:04:00.600]from about 1.5 to 4 volts, where the LCVRs retardance
[00:04:03.831]is most sensitive to voltage changes.
[00:04:07.680]We can now apply this retardance curve information
[00:04:09.780]to another experiment determining if different voltages
[00:04:12.500]and hence retardances can cause a spatial variation
[00:04:15.102]of movement in the laser beam,
[00:04:16.750]as it passes through the LCVR.
[00:04:19.230]The second linear polarizer, originally using the retardance
[00:04:21.880]curve set up was removed to allow free publication of the
[00:04:24.670]light to the detector.
[00:04:26.163]The detector was also replaced with one that was sensitive
[00:04:28.950]to the position of the beam upon its surface,
[00:04:31.870]separated from the LCVR by a distance of about
[00:04:34.380]25 centimeters.
[00:04:36.065]The retardances cycled through values of 90, 180, 270
[00:04:40.790]and 360 degrees, nine times.
[00:04:43.970]A measured position has taken us an average
[00:04:45.650]of 150 data points over 15 seconds, these averages were then
[00:04:49.342]further combined into a weighted average,
[00:04:52.150]displayed on the graph below for the extraction.
[00:04:55.000]The data has a spread of roughly point zero one millimeters,
[00:04:58.270]but importantly, their aero bars all overlap
[00:05:00.470]along a horizontal line to be drawn through all of them.
[00:05:03.790]This means that they can be thought of as the same value
[00:05:05.970]to within uncertainty.
[00:05:08.070]In the Y direction there's a very similar pattern,
[00:05:10.580]this indicates that in both the X and Y directions,
[00:05:12.691]the position of the beam is essentially constant
[00:05:15.180]over all four retardances.
[00:05:16.240]In this, there is no significant spatial variation
[00:05:19.170]caused by the LCVR using the 633 nanometer light.
[00:05:23.630]So what have we learned?
[00:05:25.350]First, the LCVR's retardance is dependent on the wavelength
[00:05:28.230]of light passing through it.
[00:05:29.780]Varying the retardance does not have a significant effect
[00:05:32.360]on the laser beam's deflection for the given
[00:05:34.650]retardance-detector distance
[00:05:36.310]and laser wavelength we studied.
[00:05:38.250]And finally extra care should be taken with a laser beam
[00:05:40.720]alignment during characterization to avoid back scattering
[00:05:43.490]effecting intensity measurements.
[00:05:46.130]Future directions of this work include more sensitive
[00:05:48.400]measurement of spatial beam variation by either narrowing
[00:05:51.240]the laser beam or by placing that detector farther away
[00:05:53.850]from the LCVR in order to amplify any special variation
[00:05:57.530]that may be present.
[00:05:59.070]The LCVR will also be tested it in an experiment
[00:06:01.730]for producing spin polarized electrons
[00:06:04.080]or it'll replace
[00:06:04.913]the traditional fixed retardance retarder currently in use.
[00:06:08.970]This sums up my work to characterize the production
[00:06:10.552]of polarized light from a liquid crystal variable retarder.
[00:06:14.290]This project was supported in part by the National Science
[00:06:16.640]Foundation under grant number 2 0 5 1 0 5 9.
[00:06:21.280]I would also like to extend a special thanks to my mentors,
[00:06:23.780]Dr. Timothy Gay and William Newman,
[00:06:25.650]and also to Will Burner and Carl Arendson
[00:06:27.830]and Nico Stemmers for their insights and help.
[00:06:30.760]And thank you for listening and taking an interest
[00:06:32.960]in this poster.

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Characterizing the Production of Polarized Light From a Liquid Crystal Variable Retarder

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