Lab 8: Polarization of Light 1 Introduction Refer to Appendix D for photos of the appara- tus Polarization is a fundamental property of light and a very important concept of physical optics. Not all sources of light are polarized; for instance, light from an ordinary light bulb is not polarized. In addition to unpolarized light, there is partially polarized light and totally polarized light. Light from a rainbow, reflected sunlight, and coherent laser light are examples of po- larized light. There are three di®erent types of po- larization states: linear, circular and elliptical. Each of these commonly encountered states is characterized Figure 1: (a)Oscillation of E vector, (b)An electromagnetic by a di®ering motion of the electric ¯eld vector with ¯eld. respect to the direction of propagation of the light wave. It is useful to be able to di®erentiate between 2 Background the di®erent types of polarization. Some common de- vices for measuring polarization are linear polarizers and retarders. Polaroid sunglasses are examples of po- Light is a transverse electromagnetic wave. Its prop- larizers. They block certain radiations such as glare agation can therefore be explained by recalling the from reflected sunlight. Polarizers are useful in ob- properties of transverse waves. Picture a transverse taining and analyzing linear polarization. Retarders wave as traced by a point that oscillates sinusoidally (also called wave plates) can alter the type of polar- in a plane, such that the direction of oscillation is ization and/or rotate its direction. They are used in perpendicular to the direction of propagation of the controlling and analyzing polarization states. wave. The oscillating point can be considered to de- scribe the vibration of the electric ¯eld vector E of This experiment consists of a series of basic exercises, the light wave, as shown in Figure 1(a). The magnetic which will introduce important techniques for analyz- ¯eld vector B vibrates in a direction perpendicular to ing the polarization of light. We will study linear and that of the electric ¯eld vector and to the direction circular polarization, using linear polarizers and two of propagation of the wave, as shown in Figure 1(b). types of retarders: quarter-wave and half-wave. The The magnetic ¯eld is very weak and therefore it is ig- ¯rst two parts of the experiment deal with testing the nored in our study of polarization. In ¯gures 1a and polarization of a laser and analyzing it using linear 1b, only one electric ¯eld vector is shown. However, polarizers. In the third part of the experiment, you light emitted from an actual source consists of many will use quarter wave plates to produce circularly po- such electric ¯eld vectors. The polarization of light is larized light and investigate its properties. Finally, de¯ned in terms of the direction of oscillation of the you will use a half-wave plate to rotate the direction electric ¯eld vectors. An ordinary source of light (such of linear polarization. as the Sun) emits light waves in all directions. Conse- quently, the electric ¯eld vectors vibrate randomly in EXERCISES 1-5 PERTAIN TO THE BACK- all directions. Such sources of light are unpolarized GROUND CONCEPTS AND EXERCISES (Figure 2(a)). Partially polarized light occurs if 6-11 PERTAIN TO THE EXPERIMENTAL the E vectors have a preferred direction of oscillation SECTIONS. (Figure 2(b)). Light is totally linearly polarized 8.1 Figure 3: Transmission through a linear polarizer. Figure 2: Polarization of light, z is the direction of propagation. (or plane polarized) if all the electric ¯eld vectors ment. A mathematical treatment of linear and circu- oscillate in the same plane, parallel to a ¯xed direction lar polarization and their interaction with polarizers referred to as the polarization direction. The special and retarders will be presented next. case of vertically polarized light is represented by a vertical arrow (Figure 2(c)), while the special case of Linear polarizers: Certain materials have the prop- horizontally polarized light is represented by a dot in- erty of transmitting an incident unpolarized light in dicating that the E vector oscillates into and out of only one direction. Such materials are called dichroic. the page (Figure 2(d)). For linearly polarized light, Polarizing sheets (which are dichroic) are manufac- the plane of polarization is de¯ned as a plane paral- tured by stretching long-chained polymer molecules lel both to the direction of oscillation of the electric after which they are saturated with dichroic materials ¯eld vector and the direction of propagation of the such as iodine. Then they are saturating with dichroic wave. The behavior of electromagnetic waves can be materials such as iodine. The direction perpendicular studied by considering two orthogonal components to the oriented molecular chains is called the trans- of the electric ¯eld vector. The phase relationship be- mission axis of the polarizer. A polarizing sheet has tween these two components can explain the di®erent a characteristic polarizing direction along its trans- states of polarization. For example, if the phase rela- mission axis. The sheet transmits only the com- tionship is random, light is not polarized. If the phase ponent of the electric ¯eld vector parallel to relationship is random, but more of one component is its transmission axis. The component perpendic- present, the light is partially polarized. If the phase ular to the transmission axis is completely absorbed relationship is constant, the light is completely polar- (this is called selective absorption). Therefore, light ized. More speci¯cally, if the phase di®erence is 0 or emerging from the polarizer is linearly polarized in the 180 degrees, the light is linearly polarized. If the direction parallel to the transmission axis. Figure 3 phase di®erence is 90 or 270 degrees and both compo- illustrates this idea. The linear polarizer is oriented nents have the same amplitude, the light is circularly such that its transmission axis is horizontal. Light in- polarized. If a constant phase di®erence other than 0, cident on the polarizer is unpolarized. However, the 90, 180 or 270 degrees exists and/or the amplitudes E vectors of the unpolarized light can be resolved into of the components are not equal, then the light is el- two orthogonal components, one parallel to the trans- liptically polarized. In case of circular or elliptical mission axis of the polarizer, and the other perpendic- polarization, the plane of polarization rotates, in con- ular to it. Light emerging from this linear polarizer trast to linear polarization where the plane of polar- is lineraly polarized in the horizontal direction. It is ization is ¯xed. There are two directions of circularly also worth noting that polarizers reduce the intensity (or elliptically) polarized light. Right-hand circularly of the incident light beam to some extent. polarized light is de¯ned such that the electric ¯eld is rotating clockwise as seen by an observer towards Retarders (waveplates): A retarder (or waveplate) whom the wave is moving. Left-hand circularly po- resolves a light wave into two orthogonal linear polar- larized light is de¯ned such that the electric ¯eld is ization components by producing a phase shift be- rotating counterclockwise as seen by an observer to- tween them. Depending on the induced phase di®er- wards whom the wave is moving0. ence, the transmitted light may have a di®erent type of polarization than the incident beam. Note that re- Elliptical polarization is not studied in this experi- tarders do not polarize unpolarized light and ideally 8.2 Figure 5: Conversion of linear polarization to elliptical polar- ization. Figure 4: Splitting of linearly polarized light into two compo- retarder; linear polarization is thus converted to ellip- nents as it enters a birefringent crystal. tical polarization due to the arbitrary phase shift. The phase di®erence depends on the incident wavelength, the refractive indices (along the two di®erent direc- they don't reduce the intensity of the incident light tions) and the thickness of the crystal. The phase dif- beam. ference can be expressed as a path di®erence between the two components. To understand how retarders function, it is instructive to consider the nature of the materials used in their There are many types of retarders. Some common re- construction. A material such as glass has an index tarders are quarter-wave (¸=4) plates and half-wave of refraction n, which is the same in all directions of (¸=2) plates. A quarter-wave plate is used to con- propagation through the material. Therefore when vert linear polarization to circular polarization and light enters glass, its speed will be the same in all di- vice-versa. Recall from a previous discussion that in rections (v=c/n). Such materials having one index order to obtain circular polarization, the amplitudes of refraction are called isotropic. Certain materials of the two E vector components must be equal and such as quartz exhibit double refraction or birefrin- their phase di®erence must be 90 or 270 degrees. A gence and are characterized by two indices of refrac- quarter-wave plate is capable of introducing a phase tion (along directions of crystalline symmetry): an or- di®erence of 90 degrees between the two components dinary index and an extraordinary index. These ma- of incident light. However, this is not enough to pro- terials are called anisotropic and the speed of light duce circular polarization. The direction of polariza- through them is di®erent in di®erent directions. Nor- tion of the incident light with respect to the optic mally, as light enters such a material, it splits into axis of the quarter-wave plate is equally important.