|MadSci Network: Physics|
This is a good question. I will try to answer. I hope I can help you.. Firstly, we should explain how wave plates (oblique incidence phase retarder) works to convert light of one polarization state to another. The first step is the understanding polarization. The light is accepted as an electromagnetic wave, composed of an electric field(E) and a magnetic field (H) that travel together at the same velocity and in the same direction, k E and H are vector quantities. Thus we usually deal only with E and define a wave’s polarization as the orientation of its E- field. There are basically three polarization states: linear, circular, and elliptical. These terms describe the path traced out by the tip of the electric-field vector as it propagates in space. The output light from a laser is typically highly polarized, that is, it consists almost entirely of one linear polarization. On the other hand, un-polarized light, such as light from a light bulb, an LED, or the sun, is a random superposition of all possible polarization states. A linearly polarized wave has two components of electric field(E), which are in phase with each other. In circularly polarized wave E field vector tip forms a helix or corkscrew shape. It can be either left-handed or right handed, depending on the clockwise or counter-clockwise nature of the rotation. For a circular wave, two linear e-field components must be of the same magnitude. If they are not equal in magnitude, the result is an elliptically polarized wave. Indeed elliptical polarization is the most general case of polarization, For instance, you can think of a circle as being a special ellipse with equal major and minor axes. In general, an elliptically polarized wave will be of the form: E=Ex.(cos(wt))+Ey.cos(wt+T) Notice that the ellipse degenerates into a linear wave when T=-….360,-180, 0, 180, 360… (0 and 180 degrees) The polarization is circular when T=…-270, -90, 90, 270…. (90 degrees) and Ex and Ey is equal in magnitude. In here we should review the properties of uniaxial crystals. When light travels through a transparent material such as a crystal, it interacts with the atoms in the lattice. Consequently, the speed of light inside the crystal is slower than that in a vacuum or air, typically by a factor between 1 and 3. The speed v varies inversely with the crystal’s refractive index n. That is, v=c/n. The larger the refractive index, the more the light is retarded. The amount of phase retardation (or delay) T that a monochromatic wave acquires from traveling through the crystal is related to its speed (n, refractive index), wavelength, and the path length L inside the crystal. T=(360.n.L)/wavelength (T in radians) The simplest class of crystals is those with cubic symmetry. In a cubic crystal, all 3 crystallographic directions or axes are equivalent. nx=ny=nz, and the crystal is optically isotropic. Regardless of how the light is polarized with respect to the crystal, it will experience the same refractive index and phase delay. Therefore, any polarized light, aside from accumulating a constant phase delay, remains unchanged after traveling through a defect-free, isotropic crystal. The Phase Retarder is extremely useful for applications where you want to synthesize and analyze light of different polarization states. For example, using a quarter-wave plate, you can convert an input beam from linear polarization to circular (or elliptical) polarization and vice versa. Using a half-wave plate, you can continuously adjust the polarization angle of a linearly-polarized beam. An input beam that is normally incident on the wave plate will be resolved into ordinary and extraordinary axis components, each with a different refractive index. The beam that emerges has a phase-delay difference or retardation between the axes of T=(360.(ne-n0).L)/wavelength (T in radians) If the wave plate thickness L is chosen, the retardation corresponds to 90 radians (or 90o) then it is called a quarter-wave plate. A phase shift of T=90 will convert linearly polarized light to circular and vice versa. Half-wave plates have 180 radians of retardation. A retardation of T=180o will flip linearly polarized light. If the incoming beam is at angle theta with respect to the fast axis, the light will be flipped 2.theta around fast axis. This is especially convenient since your laser or apparatus is often too large to rotate. Quarter and half wave are not measures of physical thickness, rather they are in reference to a specific wavelength. Therefore, all fixed-thickness wave plates should be properly labeled with the wavelength of light they were designed for. In table 1, the most common applications of phase retarders is given. In order to follow the prescriptions in Table , you need to find the fast and slow axes of your wave plate and then rotate the retarder so that the input or output polarization is at the correct angle. Table 1: Common polarization conversions using phase retarder Input Output Quarter-wave Linear, theta=45o Right circular Linear, theta=-45o Left circular Right circular Linear, theta=-45o Left circular Linear, theta=45o Linear, any theta but not 45o Elliptical Half-wave Linear, angle theta Linear, angle theta Left circular Right circular Right circular Left circular Any wave plate Linear, angle=0o or 90o Unchanged I hope you can find an answer to your question above. References Hecht, E. 1987, Optics, 2nd ed. Reading, MA: Addison-Wesley Publishing Co. Born, M.; Wolf, E. 1980, Principles of Optics. Oxford: Pergammon Press Yariv, A.; Yeh P. 1984, Optical Waves in Crystals, New York: John Wiley and Sons. Best Wishes
Try the links in the MadSci Library for more information on Physics.