Introduction to Ellipsometer
3. Reflection and Fresnel's Equations

Polarization state of light will be changed after reflection and refraction. To describe the change, light is decomposed into two linearly polarized components:  one along the direction normal to the incident plane (called the transverse electrical field and denoted by TE, Es or E^ and the other in the incident plane (called the transverse magnetic field and denoted by TM, Ep or E//).  Subscripts i,r,t is used to indicate incident, reflected, transmitted light.  They are illustrated in the graph below, as light reflected and refracted when entering medium N1 from medium N0

The Fresnel's reflection equations specify the change of each components in the reflected and refracted light by r and t.

Most of symbols in the above equations are self explained in the graph, except the complex refractive index N = n + jk, where n = c/v (the ratio of light speed in vacuum to in medium, specifies the effect of medium on wave number k) is the refractive index and k is extinction coefficient, which is related to the absorption constant a by:

In addition, F0 and F1 follows the rule of refraction:

The measurement of both r and p involves the measurement of two lights' intensity.  This is not an easy thing in reality because of small difference in the response of individual detectors and time variation of intensity of light source.  Ellipsometry bypasses the difficulty beautifully by measuring the ratio between rs and rp (or ts and tp).

Take a close look we find that

describes the change (from incident to reflected light) in phase difference between the two components.

describes the  change (from incident to reflected light) in the amplitude ratio between the two components.

As discussed in last section, we need only to know the polarization state (determine the ellipse) of incident and reflected light respectively.  The polarization state of incident light is totally controllable by orientation of the polarizer and phase plate, therefore only the polarization state of reflected light need to be measured.

Light and Polarization Drude's Equation