Second-order Material Characterization
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Characterization
β, the first nonlinear polarizability depends on molecular structure, environment and measurement frequency. There are several tools that help us characterize the materials.
Hyper Rayleigh Scattering (HRS)
Hyper Rayleigh Scattering (aka Harmonic Light Scattering) is one method for measuring β.
An incident laser generates a second harmonic signal, specifically the frequency double signal. This can be related to the beta of the sample using this formula:
- <math>\frac {I_{sample}} {I_{solvent}} = \frac {N_{sample} \langle \beta^2 _{sample} \rangle + N_{solvent} \langle \beta^2_{solvent}\rangle} {N_{solvent} \langle \beta^2_{solvent}\rangle}\,\!</math>
See Firestone 2004 [1].
See also Density Functional Theory
Electro-optic coefficient measurements
We use the Teng - Man method to measure R33. R33 is an elipsometric measurement. You apply a voltage to the film while making the elipsometric measurements and looking for changes in the signal. You have to be careful with the kind of glass and the kind of tin oxide that is used. These measurements are made with the materials in a device configuration. The formula for R33
- <math>r_{33}= \frac {3\lambda I_m (n^2 - sin^2 \theta) ^{1/2}} {4 \pi V_{poly}I_c n^2 sin^2 \theta}
\,\!</math> where
- <math>I_m\,\!</math> is the amplitude of modulation
- <math>V_{poly}\,\!</math> is the modulation voltage across EO polymer
- <math>I_c\,\!</math> is the half intensity point
- <math>n\,\!</math> is the refractive index of the polymer
and
- <math>V_{poly}= V_{ACtot} \frac {d_{poly}} {d_{poly} + d_{clad}} \cdot \sqrt {\frac {\epsilon_{clad}} {\epsilon _{poly}}}\,\!</math>
See Khanarian 1996 [2]
See STC-MDITR research project 1.1 Measuring R33 with Interferometry
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