Learn how reflection at interfaces with different indices of refraction works and how interfaces can change the polarization states of light.

Transcription

1 Slide 1 Goals of the Lab: Learn how reflection at interfaces with different indices of refraction works and how interfaces can change the polarization states of light. Learn how to measure the influence of dielectric interfaces on light polarization states. Learn how ellipsometry works and how to carry out an ellipsometry experiment. Get to know and learn how to use different polarizers such as polarizing beam splitters, Babinet-Soleil compensator In this lab, you will use ellipsometry in order to experimentally measure the real and imaginary part of the index of refraction of different insulating and conducting materials.

2 Background: Reflection at an interface between two different indices of refraction Fresnel equations for p - light: Slide 2 E i s E i p θ i θ r E r s E r p r p = E r p /Ei p t p = E t p /Ei p θ = θ i = θ r n 1 Fresnel equations for s - light: n 2 θ t E t s E t p r s = E r s /Ei s t s = E t s /Ei s θ = θ i = θ r

3 Principal sketch of the experimental setup n 1 =1 n 2 E i s 45º light source E i p 45º E i net 45 o polarizer (to plane of incidence) Babinet-Soleil compensator (introduces phase shift of Δ between s and p-light) E r s E r p s ψ detector Slide 3 analyzer polarizer with main axis angle ψ to s axis E r net E r net

4 Slide 4 Top view of the experimental setup detector analyzer Babinet-Soleil compensator phase shift shutter (to remove second reflected beam) sample holder 45º polarizer A linearly polarized laser beam with 45º angle towards the s- and p- directions may become elliptically polarized after reflection from a single optically flat interface between two isotropic, homogenous media. The phase and amplitude of the p (polarized in the plane of incidence) and s (polarized perpendicular to the plane of incidence) electric field components are in general different after reflection. An ellipsometer measures the state of polarization of the reflected beam, or more precisely it measures the complex ratio ρ of the complex reflectivities r p and r s. HeNe Laser

5 Slide 5 How does Ellipsometry work? The ratio ρ of the reflected beam is measured using a Babinet-Soleil compensator and an analyzer (polarizer). The compensator is used to eliminate (and measures) any phase delay Δ acquired by the reflection between the p and s components. This produces linearly polarized light. The analyzer (polarizer) between the compensator and the detector measures the polarization angle ψ of the resultant linearly polarized light by finding the extinguishing condition. This is a nulling method. It is based upon the fact that once the phase delay between the two components is eliminated, the angle of the resultant linearly polarized light can be measured by extinguishing the light that passes through the analyzer. A two-dimensional search must be performed to achieve extinction of the light seen by the detector. The compensator value cannot be determined alone. The experimenter must find the optimal compensator phase angle and analyzer angle for maximum extinction. Once the null is reached, the values of Δ and ψ should be recorded. They are read directly off of the Babinet-Soleil compensator Δ and the analyzer ψ. The measured values of Δ and ψ can be directly related to the complex index of refraction n 2 of the surface, the index of the ambient (assumed here to be n 1 = 1), and in incident angle θ (= 45º here) using the formula of slide 4 and the relation

6 Slide 6 Experimental procedure 1. Set up the ellipsometer. 2. Set and measure the incident angle to 45º with respect to the sample surface normal. 3. Adjust the polarization of the laser so that it is at 45º with respect to the p and s directions. 4. Place the Babinet-Soleil compensator, analyzer and detector in the reflected beam path. 5. Align the axes of the Babinet-Soleil compensator and analyzer with the p and s directions. 6. Place the optically flat glass sample in the sample holder. 7. Perform the nulling measurement, and determine Δ and ψ for the sample. 8. Calculate the value of ρ. 9. Calculate the complex index of refraction n of the sample. 10. Repeat 6-9 using a gold, platinum and aluminum sample. Analysis and Discussion comparison with optical constants 1. Compare your measured/calculated complex index of refraction results with published values for the glass, gold, platinum and aluminum samples. 2. Calculate the expected experimental values for Δ and ψ using the published optical constants using the equations shown above. Compare them with your experimental measurements. 3. Note that the aluminum results are most different from published values. Explain why this is the case, and give some reasons why the other experimentally determined optical constants might differ from those published in the literature.

7 Slide 7 Refences [1] Handbook of Optics, Vol. II, 2nd edition, M. Bass, Ed., McGraw-Hill, New York ( ), Chapter 27. [2] Polarized Light, Fundamentals and Applications, Edward Collett, Marcel Dekker, Inc., New York (1992), Chapter 25.