Characterizing Dielectric Tensors of Anisotropic Materials From a Single Measurement

Persistent Link:
http://hdl.handle.net/10150/293464
Title:
Characterizing Dielectric Tensors of Anisotropic Materials From a Single Measurement
Author:
Smith, Paula Kay
Issue Date:
2013
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Ellipsometry techniques look at changes in polarization states to measure optical properties of thin film materials. A beam reflected from a substrate measures the real and imaginary parts of the index of the material represented as n and k, respectively. Measuring the substrate at several angles gives additional information that can be used to measure multilayer thin film stacks. However, the outstanding problem in standard ellipsometry is that it uses a limited number of incident polarization states (s and p). This limits the technique to isotropic materials. The technique discussed in this paper extends the standard process to measure anisotropic materials by using a larger set of incident polarization states. By using a polarimeter to generate several incident polarization states and measure the polarization properties of the sample, ellipsometry can be performed on biaxial materials.Use of an optimization algorithm in conjunction with biaxial ellipsometry can more accurately determine the dielectric tensor of individual layers in multilayer structures. Biaxial ellipsometry is a technique that measures the dielectric tensors of a biaxial substrate, single-layer thin film, or multi-layer structure. The dielectric tensor of a biaxial material consists of the real and imaginary parts of the three orthogonal principal indices (nₓ + ikₓ, n(y) +ik(y) and n(z) + ik(z)) as well as three Euler angles (α, β, and γ) to describe its orientation. The method utilized in this work measures an angle-of-incidence Mueller matrix from a Mueller matrix imaging polarimeter equipped with a pair of microscope objectives that have low polarization properties. To accurately determine the dielectric tensors for multilayer samples, the angle-of-incidence Mueller matrix images are collected for multiple wavelengths. This is done in either a transmission mode or a reflection mode, each incorporates an appropriate dispersion model. Given approximate a priori knowledge of the dielectric tensor and film thickness, a Jones reflectivity matrix is calculated by solving Maxwell's equations at each surface. Converting the Jones matrix into a Mueller matrix provides a starting point for optimization. An optimization algorithm then finds the best fit dielectric tensor based on the measured angle-of-incidence Mueller matrix image. This process can be applied to polarizing materials, birefringent crystals and the multilayer structures of liquid crystal displays. In particular, the need for such accuracy in liquid crystal displays is growing as their applications in industry evolve.
Type:
text; Electronic Dissertation
Keywords:
Optical Sciences
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Optical Sciences
Degree Grantor:
University of Arizona
Advisor:
Chipman, Russell

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleCharacterizing Dielectric Tensors of Anisotropic Materials From a Single Measurementen_US
dc.creatorSmith, Paula Kayen_US
dc.contributor.authorSmith, Paula Kayen_US
dc.date.issued2013-
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractEllipsometry techniques look at changes in polarization states to measure optical properties of thin film materials. A beam reflected from a substrate measures the real and imaginary parts of the index of the material represented as n and k, respectively. Measuring the substrate at several angles gives additional information that can be used to measure multilayer thin film stacks. However, the outstanding problem in standard ellipsometry is that it uses a limited number of incident polarization states (s and p). This limits the technique to isotropic materials. The technique discussed in this paper extends the standard process to measure anisotropic materials by using a larger set of incident polarization states. By using a polarimeter to generate several incident polarization states and measure the polarization properties of the sample, ellipsometry can be performed on biaxial materials.Use of an optimization algorithm in conjunction with biaxial ellipsometry can more accurately determine the dielectric tensor of individual layers in multilayer structures. Biaxial ellipsometry is a technique that measures the dielectric tensors of a biaxial substrate, single-layer thin film, or multi-layer structure. The dielectric tensor of a biaxial material consists of the real and imaginary parts of the three orthogonal principal indices (nₓ + ikₓ, n(y) +ik(y) and n(z) + ik(z)) as well as three Euler angles (α, β, and γ) to describe its orientation. The method utilized in this work measures an angle-of-incidence Mueller matrix from a Mueller matrix imaging polarimeter equipped with a pair of microscope objectives that have low polarization properties. To accurately determine the dielectric tensors for multilayer samples, the angle-of-incidence Mueller matrix images are collected for multiple wavelengths. This is done in either a transmission mode or a reflection mode, each incorporates an appropriate dispersion model. Given approximate a priori knowledge of the dielectric tensor and film thickness, a Jones reflectivity matrix is calculated by solving Maxwell's equations at each surface. Converting the Jones matrix into a Mueller matrix provides a starting point for optimization. An optimization algorithm then finds the best fit dielectric tensor based on the measured angle-of-incidence Mueller matrix image. This process can be applied to polarizing materials, birefringent crystals and the multilayer structures of liquid crystal displays. In particular, the need for such accuracy in liquid crystal displays is growing as their applications in industry evolve.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectOptical Sciencesen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineOptical Sciencesen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorChipman, Russellen_US
dc.contributor.committeememberDereniak, Eustaceen_US
dc.contributor.committeememberFalco, Charlesen_US
dc.contributor.committeememberChipman, Russellen_US
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