Introduction to Ellipsometer
2. Light and Polarization

Light can be imagined as electromagnetic waves, and can be expressed using its electrical field by following equations:


where u1 and u2 are two unit vectors to indicated the direction of two orthogonal components, w is the angular frequency of the  wave; k is the wave number whose absolute value is 2p/l (l is the wavelength of light in medium), and the directional part indicate the propagating direction of the light; s is the directional distance for study the amplitude of electrical field; A1 and A2 are amplitude and d1 and d2 are phases.

The trace of the end of electrical field is normally used to describe the polarization state. As we can see from following graph, ellipse is the general case of polarization.

To specify polarized wave, q (azimuth angle, the direction of long axis of the ellipse), e (ellipticity - the ratio the short to the long axis), A (amplitude, the half of the diagonal of the most tighten rectangle box), directional wave number k, handness and the exact phase.  Normally, A, wave number and the exact phase are not concerned in the study.  The parameters under interest can be converted to amplitude ratio and phase difference between the two components, and vice versa.

When the two components of the electrical field are exactly in phase to each other, the ellipticity will be 0 and the light is linearlly polarized.  Another special case is circular polarization, where the ellipticity is 1 and the phase difference is 90 or 270 degree.

The equations above supposed a single wavelength, which indicates a strict monochromatic light.  Commonly, light is superposition of many waves, each of which can be expressed by the equation in the part of their lifetime.  They might differ in the frequency (color), and amplitudes and phases (polarization).  Polarization is an indication of how the light spirally propagates in the space. If all the waves followed the same rule of polarization (same ratio of amplitude and phase difference), the light is said to be polarized.  Sunlight, which is composed of light wave with different wavelength and polarization style, can be polarized after reflected from surface of water.  Photographer normally need an analyzer to get rid of the strong reflection from the surface and catch the fishes in the water.

Data Analysis and Data Aquisition Reflection and Fresnel's Equation