Eric Compain

High-frequency modulation of the four states of polarization of light with a single phase modulator

A method for light polarization modulation is described. It allows us to independently modulate, at a high frequency, the four components of the Stokes vector of light using a single phase modulator. It works in a double-pass configuration: the polarization of light is modulated a first time by the phase modulator, and is then modified by a coupling object before being modulated a second time by the same modulator. The coupling object consists of multiple glass plates, oriented at the Brewster angle, acting as a partial polarizer and in a right angle prism acting as a phase shifter and back reflector. Its polarimetric properties are obtained from refractive index contrast effects, which provides optimized and constant properties over a wide spectral range. The phase modulator can be either an electro-optic modulator providing a very high-frequency capability (up to 100 MHz) or a photoelastic modulator providing a wide spectral range capability. It is robust because there is no moving part and simple to implement because of the presence of one modulation. It displays a high level of sensitivity because all the components are high-frequency modulated. Two applications using this modulator in a polarimeter or in a polarization states generator are described. The four modulations, having the same fundamental frequency, are easily demodulated by numerical data processing. Optimized demodulation processing, adapted to the different kind of phase modulator is described. Its adaptation taking into account the bandwidth limitation and the variation of the sampling phase, are finally presented in the case of a photoelastic modulator.

Complete high-frequency measurement of Mueller matrices based on a new coupled-phase modulator

A new polarization modulator is presented. It uses two phase-locked identical electro-optic phase modulators at 50 kHz. Thanks to a coupling object introduced between the two phase modulators, the four Stokes parameters of the light beam are independently modulated on the basis of the first and second complex harmonics of the modulation signal. A Mueller matrix ellipsometer (MME) using this new modulation and a multichannel polarimeter are also described. The data processing and the feedback control of Pockels cells is based on a numerical Fourier transform system. It allows one to measure simultaneously, in one modulation period (20 μs), the 16 coefficients of any Mueller matrix. This MME takes advantage of an easy-to-operate calibration method. The high-frequency modulation of the four parameters of the polarization enables low-light-level measurements (without any chopper and lock-in) and presents spectroscopic capabilities. It provides a promising tool for the study of many subjects of growing interes...

Complete Mueller matrix measurement with a single high frequency modulation

Abstract A new Mueller matrix ellipsometer (MME) is presented. It provides the simultaneous measurement of the 16 Mueller matrix coefficients in four modulation periods (80 μs under the present conditions). This system is accurate (error≤1%), robust since there are no moving parts, enables low-light-level measurements without a chopper and lock-in amplifier and can be easily used for real time measurements. The setup is based on the polarization modulator–sample–polarization detector configuration. The polarization modulation is provided by a coupled-phase-modulator (CPM) which uses two identical phase-locked electro-optic phase modulators operating at 50 KHz. With the introduction of a coupling object between the two phase modulators, the four Stokes parameters of the light beam, including the intensity, are independently modulated on the basis of the first and second complex harmonics of the modulation signal. The polarization of light, after interaction with the sample, is measured with a multichannel division of amplitude polarimeter (DOAP). This DOAP is based on a slightly beveled amorphous-silicon (a-Si) coated glass plate. The high index of refraction contrast between a-Si and SiO2 provides an efficient polarimeter, less sensitive to the angle of incidence than usual dielectric-coated ones. The spectroscopic capability of the MME is illustrated by preliminary measurements of depolarization effects at two laser wavelengths: He–Ne at 632.8 nm and Ar at 488 nm.

Improvements of Fourier transform phase‐modulated ellipsometry

Improvements of the Fourier transform phase‐modulated ellipsometry (FTPME) technique are described. Measurements performed on the silicon oxide‐silicon wafer system are used to illustrate FTPME performances. In particular, the chemistry of Si(100) and Si(111) surfaces after hydrofluoric acid (HF) treatment is investigated. Precisions on the ellipsometric angles Ψ and Δ of ±0.003° and ±0.008°, respectively, are obtained in the SiHn stretching mode region. SiH and SiH2 vibrations are identified at the Si surface revealing that submonolayer sensitivity can be achieved with FTPME. As a consequence, FTPME appears as a promising technique to perform detailed studies of interface formation and thin‐film growth.