Polarization of Light and Birefringence of Materials

Polarization of Light and Birefringence of Materials Ajit Balagopal (Team Members Karunanand Ogirala, Hui Shen) ECE 614- PHOTONIC INFORMATION PROCESSING LABORATORY Abstract-- In this project, we study the polarization of light and the effects of polarizers on a beam of light. In the first part of the experiment, light from a beam of He-Ne laser was passed through a polarizing crystal and the output from this polarizer was sent through another polarizer to find the polarizing effects. The output from the second polarizer was measured at various angles of the polarizers with respect to each other. The expected result of observing maximum light when the polarizers' axes are aligned together and minimum light when they are aligned orthogonal to each other, was observed and the readings were tabulated and plotted, and were found to meet the expected criteria. In the next part of the experiment, we performed the Brewster s angle test on a thin microscopic glass slide. Here, we passed the light through the polarizer and the output was incident on the glass slide. The reflection of the light from the slide was observed at different angles and the glass was found not to reflect any light when the angle of incidence of the light was around 56, the Brewster's angle for glass. In the second part of the experiment, we observe the effects of birefringent materials on the polarized beam of light. We align a beam splitter in such a way that the transmitted and reflected rays are orthogonal to each other. We then inserted quarter wave plate in between the polarizers to generate a circularly polarized beam, and this was observed on the analyzer. Another quarter wave plate was inserted so as to make a half wave plate and the polarization of the light beam was shifted by 90. This was also verified by rotating the analyzer. We also built an optical isolator, the effects of which were verified, by using the polarizer and the quarter wave plate. (ii) To measure the Brewster's angle for a glass slide and check it with the theoretically expected value (iii) To observe the effect of birefringent materials on a laser beam (iv) To rotate the angle of polarization by 90 by making a half wave plate using two quarter wave plates (v) To build an optical isolator using quarter wave plate and polarizer Polarization Index terms Polarization, half-wave plate, quarter-wave plate, Brewster s angle, birefringence I. INTRODUCTION This report discusses an experiment to study the phenomena of polarization and birefringence of light. The objectives of the experiment are (i) To observe the effect of polarization on a beam of light and to measure the output power as a function of the angular separation between the axes of the two polarizers Figure 1 By polarized light we mean optical radiation with its electric field vibrating in a specific regular mode. Any generally polarized electric field can be resolved into two orthogonally polarized components, namely the electric 1

Figure 2 field vector and the magnetic field vector. [4]Polarization is of different types and is determined by the vibration of the tip of the electric field vector. In other words, the direction of electric field of a light wave is used to specify the direction of polarization of the light. Light is said to be linearly polarized if the orientation of the electric field vector doesn t change with respect to time. If the light is plane polarized then the electric field vibrates in a single plane - the plane of polarization. If the two components have a constant phase difference, and the tip of the electric field vector follows a three dimensional ellipse as the beam propagates, the light beam is said to be elliptically polarized. Circularly polarized light is a special case of elliptically polarized light in which the two components have a 90 phase difference and the electric field vector describes a circular cross section spiral. When viewed looking towards the source, a right circularly polarized beam has a light vector that describes a clockwise circle, while left circularly polarized light describes an anticlockwise circle.[1] If the direction of polarization of light does not follow a specific pattern, it is said to be unpolarized, or more descriptively, randomly polarized[2]. The different types of polarization are illustrated in Figure 1. Figure 3 surface.[2] The degree of polarization depends on the angle the light hits and the refractive indexes of the air and refractive medium. The angle of maximum polarization is called BREWSTER'S ANGLE. This angle is given by tan θ B = n 2 /n 1 where θ B is the Brewster s angle and n 1 and n 2 are the refractive indices of the two media. The angle between the refracted and reflected rays is 90 at Brewster's angle. So, if the light that is incident on a sheet of glass is already polarized and the direction of polarization is perpendicular to the face of the plate, then if the angle of incidence is equal to the Brewster s angle, then we do not observe any light reflected from the sheet. (see Figure 3) Birefringence Certain crystalline substances have a refractive index which depends upon the state of incident polarization. This is known as birefringence or double refraction. Unpolarized light entering a birefringent crystal is therefore split into two linearly polarized beams which are refracted by different amounts. Brewster s Angle When light reflects from a non-metallic surface, the reflected light will be polarized in the plane of the Figure 4 The direction within the crystal along which there is no double refraction is known as the optic axis or the axis of the crystal.[2] There are two refractive indices 2

n o ordinary index, for components of E perpendicular to optic axis n e extraordinary index, for components of E parallel to optic axis In a transparent material, anisotropism of the refractive index, varies as a function of polarization as well as orientation with respect to the incident ray. The term "birefringence" means, literally, "double refraction." All crystals except those of cubic lattice structure exhibit some degree of anisotropy with regard to their physical properties, including refractive index. Other materials, such as glasses or plastics, become birefringent when subjected to mechanical strain.[3] Birefringent materials, including crystals, have the ability to refract an unpolarized incident ray into two separate, orthogonally polarized rays, which in the general case take different paths, depending on orientation of the material with respect to the incident ray. The refracted rays are referred to as the "ordinary," or "O" ray, which obeys Snell's Law, and the "extraordinary," or "E" ray, which does not.(see Figure 4) Quarter Wave Plate This plate consists of a birefringent crystal of a specific thickness d, cut so that the optic axis is parallel to the plane of the plate and perpendicular to the edge. The plate is oriented so that its plane is perpendicular to the beam direction and its fast and slow axes are at 45 to the polarized direction of the incident linearly polarized light. Because of this 45 geometry, the incident light is split into slow and fast components of equal amplitude travelling through the crystal. The plate is cut so that the components which were in phase at the entrance to the crystal, travel at different speeds through it and exit at the point when they are 90, or a quarter wave, out of phase. This output of equal amplitude components, 90 out of phase, is then circularly polarized.[2] If the 45 input geometry is not maintained, the output is elliptically polarized, the eccentricity of the ellipse being determined by the angle between the input polarization and the optic axis. Half wave plate If a crystal is cut that has twice the thickness of a quarter wave plate, we get a half wave plate. In this case, linearly polarized light at any angle θ with respect to the optic axis provides two perpendicular components which end up 180 out of phase upon passage through the crystal.[2] This means that relative to one of the polarizations, the other polarization is 180 from its original direction. These components can be combined to give a resultant whose direction has been rotated 2θ from the original polarization. Sometimes a half wave plate is called a polarization rotator. Figure 6 In the second part of the project, randomly polarized light is sent through a polarizer and then through a quarter wave plate to create circularly polarized light. When circularly polarized light is reflected off a reflecting surface, its handedness is reverse. When the light passes through the quarter wave plate a second time, the circularly polarized light is turned into linearly polarized light but rotated 90 with respect to the incident polarization. Upon passage through the linear polarizer a second time, the light is absorbed. Figure 5 II. PROCEDURE (i) Project Sequence The first part of the project deals with analyzing the effects of a polarizer on a beam of light and the orientation and directional effects of aligning the polarizers. To begin with the experiment the initial arrangement had to be setup. A laser assembly was mounted on the optical bench and was aligned so that the laser beam was along a 3

straight line, marked by a line of holes on the optical bench. At a distance of few inches from the laser, a lens chuck assembly, to which a polarizer was fitted, was mounted. The polarizer was fitted in the lens chuck assembly so that the notch (which corresponds to the optic axis of the polarizer) was aligned vertically. The second polarizer was fitted to a rotation stage assembly which was mounted to the optical bench a few inches away from the first polarizer. A photodetector was fitted in a lens chuck assembly and mounted at the end of the above arrangement so as to detect the amount of light coming out of the second polarizer. The second polarizer was rotated by 10 increments and the output of the detector as measured by the voltmeter was noted for all successive values from 0 to 180, and the values were plotted. Figure 7 The next part of the experiment was performed to find the Brewster s angle of glass and verify it with the expected value. To perform this experiment, the second polarizer was removed first and a lens chuck assembly was mounted on a rotation stage. On this lens chuck assembly a microscopic glass slide was taped. The rotation stage was aligned in such a way that the glass face was perpendicular to the beam of light. Then, the rotation stage was rotated and for every few degrees of rotation, the power of the beam reflected from the glass slide was measured by mounting the detector. By successive approximations, the stage was brought to a position where there was no reflection from the slide and when rotated further beyond that position, reflection was observed again. This position where there is no reflection of the polarized light from the slide corresponds to the Brewster s angle of the material of the slide, i.e.; glass. Figure 8 The second part of the experiment was performed to observe and analyze the effects of birefringence of a material on the polarization of a beam of light. Using the same principles, an optical isolator was built and verified. As in the first part of the experiment, a laser assembly was mounted on the edge of the optical and is aligned such that the beam is parallel to the edge and in line with the line of tapped holes in the bench. A beam splitter was fitted in a lens chuck assembly and was mounted on the bench. The beam splitter was oriented such that the surface was at an angle of 45 to the incident beam of laser. The beam splitter was observed to split the beam into two separate beams, transmitting one through and reflecting one beam off its face. The beam splitter assembly was rotated so that the reflected beam was aligned perpendicular to the originally incident beam. Target assemblies were placed on either side of the beam splitter assembly to monitor the beams reflected from the beam splitter. A lens chuck assembly fitted with a polarizer with its notch pointing up was mounted a few inches from the beam splitter assembly. A second polarizer was mounted about 7 inches away from the first polarizer. This polarizer was fitted to a rotation stage assembly mounted vertically. A quarter wave plate was then fitted to a rotation stage and the assembly was mounted between the two polarizers. The second polarizer was rotated in its chuck. The output light was verified to be circularly polarized, by observing non-varying output, with rotation of the second polarizer. The second polarizer was then replaced with a mirror. The reflections observed on the Figure 9 4

Figure 9 index card showed no reflection from the mirror. This signifies that the outgoing beam has been optically isolated from reflections after the quarter wave plate. The mirror was then removed and the second polarizer was mounted again and another quarter wave plate was mounted between the first quarter wave plate and the second polarizer. The second quarter wave plate was rotated until the light passing through the second polarizer was of maximum intensity. The second polarizer was rotated to produce minimum transmission and it was observed that it had to be rotated through 90* and also that the axes of the two polarizers were parallel. The first polarizer was then rotated by a few degrees at a time and it was found that the analyzer had to be rotated twice the same angle to extinguish the beam. (ii) Theoretical Analysis When the laser beam passes through the first polarizer, it is polarized in a direction indicated by the direction of the notch. Now, the oscillations are restricted to this single plane. When this linearly polarized light is incident upon a second polarizer, the amount of light passing through that is dependent on the difference in angle between the two polarizers. If their axes are aligned parallel to each other, maximum transmission of light is observed and if the axes are perpendicular to each other, no light passes through the second polarizer. In other words, the amount of light passing through any polarizer is proportional to the angle it makes with the axis of the polarizer. The relation governing the input intensity, output intensity and the angle between the two is given by Malus Law, which is I trans =I o cos 2 θ where I trans is the amount of light transmitted through the polarizer and I o is the amount of light incident on it and θ being the angle. Linearly polarized light in any direction can be considered to be composed of two components, one along the axis of the polarizer and the other perpendicular to the axis. The polarizer allows the component that is along its axis and blocks the component perpendicular to it. One of the methods of converting non-polarized light to polarized light is reflection, since the amount of light reflected off a tilted surface is dependent on the orientation of the incident polarization and the normal to the surface. When the propagation direction of reflected and refracted rays at an interface are perpendicular to each other, the component of light polarized parallel to the plane of incidence is transmitted totally and none of it is reflected. The angle of incidence at which this occurs is known as Brewster s angle, which is given by tan θ B = n 2 /n 1 So, by measuring the Brewster s angle, we can calculate the refractive index of a material. In the experiment conducted, we observe that as we measure the reflection from the glass at various angles, the power reduces until it reaches 0 at an incident angle of 56. This is the Brewster s angle for the glass with which the slide is made. The second part of the experiment deals with observing the effects of a beam splitter and quarter wave and half wave plates on the polarization of a beam of light. First when we mounted the beam splitter at an angle of 45 to the direction of propagation of the beam, it is observed that part of the beam is reflected and a part of it is transmitted along the path. The polarizer polarizes the light beam such that the plane of polarization lies along the vertical plane. Now, when the linearly polarized light passes through the quarter wave plate when the axis is aligned at an angle of 45 to the plane of polarization, it converts the linearly polarized light to circularly polarized light. This could be observed by rotating the second polarizer and obtaining same output at all angular positions. This is because the circularly polarized light has same amount of light on all planes. Next, when we place a mirror on the path of the beam, the beam gets reflected back to the quarter wave plate, and when it passes through the quarter wave plate for the second time, it gets linearly polarized again, but at an angle of 90 to the original plane of polarization. So when it passes through the first polarizer again, it gets blocked totally, and no reflection is observed on the index card as a result of it. Then, we insert two quarter wave plates in between the two polarizers, we effectively create a half wave plate. We observe that the polarized light has its plane of polarization shifted by 90. So when the light passes through both the quarter wave plates, its plane of polarization is shifted by 90, which is verified by rotating the second polarizer by 90 to get peak output. This can further be verified by aligning both the polarizers along the same axis, which would result in minimum output. When the quarter wave plates are not aligned perfectly with each other and have a little axial shift with respect to each other, the light coming out of the second quarter wave plate is not linearly polarized but is elliptically polarized. This can be verified by rotating the second polarizer. When it is rotated over a range of 180, it never blocks light totally and some amount of light is always transmitted, with the magnitude varying from a peak to a low. This signifies that the incident light has oscillations on all planes and hence is not 5

polarized linearly. The variation from high to low signifies elliptical polarization. The ratio of the magnitudes of high and low would give the eccentricity of the ellipse of polarization. III. RESULTS The experiment was performed successfully and the expected results were observed. In the first part of the experiment, a beam of laser was passed through the arrangement of the two polarizers and the power output was observed at various angles between the axes of the two polarizers. The values were tabulated as in Table 1. The observed values were plotted and were found to conform almost exactly with the expected values from Malus law. The plot is shown in Figure 11, where the measured values are depicted by bullets placed on the curve for the expected values. As can be seen from the curve, the observed values coincide excellently with the expected values for the experiment. The next part of the experiment was performed to calculate the Brewster s angle of glass. The values of reflected power observed for various angles of incidence (Table 2) were measured and the results were plotted (Figure 12). It was observed that at an incident angle of 56 the glass slide did not reflect any light. This corresponds to the Brewster s angle for glass and thus this part of the experiment was completed successfully. The second part of the experiment dealt with observing the effects of birefringent materials in altering the polarization of light. The quarter wave plate was observed to convert linearly polarized light to circularly polarized light. This was verified by observing that when the light coming from the quarter wave plate was incident on the polarizer, the output remained unchanged even when the polarizer was rotated. This signifies circular polarization. Next, an optical isolator was successfully implemented and verified by placing a mirror in place of the second polarizer. The beam of light when reflected from the mirror and after passing through the quarter wave plate for a second time was blocked by the polarizer, because of the fact that its axis of polarization was shifted by 90 and hence was perpendicular to the axis of the polarizer. A half wave plate was implemented by placing two quarter wave plates in succession. These were placed in the path of the beam, between the two polarizers, so as to rotate the axis of polarization of the beam by 90. This was verified by rotating the second polarizer by 90 to get maximum output from it. When this polarizer was aligned with the first polarizer, no output was observed from it. This is because the light incident on it is polarized at an axis perpendicular to the axis of the polarizer. This confirms the half wave plate phenomena exhibited by the two quarter wave plates kept in succession. This was further verified when it was observed that for every degree of rotation of the first polarizer, the second polarizer had to be rotated twice as much to get the peak output. Table 1 Θ Power (Measured)(µW) Power(Theoretical ) (µw) 0 100 100.00 10 98 96.98 20 90 88.30 30 77 75.00 40 61 58.68 50 43 41.32 60 27 25.00 70 13 11.70 80 4 3.02 90 0 0.00 100 3 3.02 110 12 11.70 120 25 25.00 130 41 41.32 140 58 58.68 150 75 75.00 160 88 88.30 170 97 96.98 180 100 100.00 θ Table 2 12 19 16 18.2 22 16.6 28 14.2 37 10 48 3 51 0.8 54 0.2 56 0 58 0.2 61 0.8 64 3 Power(µW) 6

Figure 10 Figure 11 IV. REFERENCES [1] E. Hecht, Optics, Addison-Wesley Publishing Company, 1987. [2] D.O Shea Projects in optics: Applications Workbook, Newport Corporation [3] http://glossary.its.bldrdoc.gov/fs- 0037/dir_005/_0614.htm [4] www.halbo.com/pol_bir.htm 7