Conventional and generalized Mueller-matrix ellipsometry using the four-detector photopolarimeter

Azzam, R. M. A.; Giardina, Kurt A.; Lopez, A.R.

doi:10.1117/12.55957

Cited by 27 publications

(10 citation statements)

References 23 publications

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“…Azzam et al . [2,3] experimentally observed polarization rotation upon reflection from a metallic grating . Bryan-Brown et al [4,5] discussed polarization conversion upon reflection from sinusoidal profile metallic gratings.…”

Section: Introductionmentioning

confidence: 97%

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Lamellar Gratings as Polarization Components for Specularly Reflected Beams

Haggans

Fujita

et al. 1993

Journal of Modern Optics

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High spatial frequency lamellar gratings are shown to function as phase compensators, quarter-wave and half-wave retarders, and polarization rotators that operate on specularly reflected (zeroth-order) beams . These gratings are designed using rigorous coupled-wave and modal grating diffraction theories . Controlling the geometrical parameters of these gratings allows for engineering the phase retardation and polarization conversion introduced to a reflected beam . Fabrication and operational tolerances for these elements are discussed . Wavelength and polar angle of incidence variation affect the performance of these elements more strongly than variations in other geometrical and operational parameters .

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Section: Introductionmentioning

confidence: 97%

“…Several authors have studied the polarization properties of beams specularly reflected from gratings [1][2][3][4][5][6][7][8][9][10] . Azzam et al .…”

Section: Introductionmentioning

confidence: 99%

Lamellar Gratings as Polarization Components for Specularly Reflected Beams

Haggans

Fujita

et al. 1993

Journal of Modern Optics

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“…1,2 The four-detector photopolarimeter ͑FDP͒ 3,4 is perhaps the simplest instrument for measuring the SOP. [5][6][7][8] The important procedure required to operate this instrument is to obtain an accurate instrument ͑calibration͒ matrix, the socalled A matrix. [5][6][7][8] The important procedure required to operate this instrument is to obtain an accurate instrument ͑calibration͒ matrix, the socalled A matrix.…”

Section: Introductionmentioning

confidence: 99%

Effect of light-beam deviation on the instrument matrix of the four-detector photopolarimeter

Liu

Azzam

1997

Opt. Eng

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Analytical geometry, ray tracing, and the Mueller-matrix calculus are used to determine the calibration matrix of the four-detector photopolarimeter (FDP) when the incident light beam deviates from the optical axis of the instrument. Detectors of the FDP are represented by their surface equations in Cartesian coordinates. The instrument matrices corresponding to angular deviations of Ϯ0.5 and Ϯ1.0 deg in reference horizontal and vertical planes, and their differences from the unperturbed matrix are given for two FDP configurations. Output Stokes parameters that correspond to several typical input states of polarization are calculated to demonstrate the effects of light-beam deviation.

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“…Except for sparse papers, this technique received little attention for several decades after Drude, but in the 1970's and 1980's, ellipsometry became widely utilized, and relevant technical papers [5][6][7] and a classical book 8 were produced during this period. In 1991, Azzam compiled a considerable number of papers on ellipsometry 9 . As a search of the literature indicates, the number of papers on experimental improvement of ellipsometers has been decreasing in the last years, because many of the problems that existed before the advance of computers have been solved, including measurement speeds and spectral range.…”

Section: Brief Historical Overviewmentioning

confidence: 99%

Fundamentals and applications of spectroscopic ellipsometry

Gonçalves¹,

Irene²

2002

Quím. Nova

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Recebido em 1/8/01; aceito em 8/11/01 This paper describes the use of ellipsometry as a precise and accurate technique for characterizing substrates and overlayers. A brief historical development of ellipsometry and the basic principles necessary to understand how an ellipsometer works are presented. There are many examples of studies performed in addressing materials science issues, and several are presented here: measurements of thickness, optical properties, and modeling of surface roughness. These selected results obtained in our laboratory for substrates, Si/SiO 2 interfaces, and polymers provide evidence that ellipsometry can play a critical role in characterizing different types of materials.Keywords: ellipsometry; polarization; films. BRIEF HISTORICAL OVERVIEWEllipsometry (reflection ellipsometry) measures the changes in the state of polarization of light upon reflection from a surface. The fact that changes are measured rather than the absolute intensity of light renders ellipsometry sensitive to submonolayer surface coverage. As a non-invasive and non-destructive tool, ellipsometry requires only a low-power light source and, consequently, it does not affect most processes, which renders ellipsometry a convenient tool for in situ studies 1,2 . P. Drude 3 was the first to build an ellipsometer even before Rothen has coined the word 'ellipsometry ' in 1945 4 . The equipment built by Drude is surprisingly very similar to many types of instruments in use today. Except for sparse papers, this technique received little attention for several decades after Drude, but in the 1970's and 1980's, ellipsometry became widely utilized, and relevant technical papers [5][6][7] and a classical book 8 were produced during this period. In 1991, Azzam compiled a considerable number of papers on ellipsometry 9 . As a search of the literature indicates, the number of papers on experimental improvement of ellipsometers has been decreasing in the last years, because many of the problems that existed before the advance of computers have been solved, including measurement speeds and spectral range. Most of the equipment used today is automated with wide band light sources, scanning monochromators, optical multichannel analyzers, and interfaces with acquisition and analysis software. Early studies on ellipsometry were performed using single wavelength equipment, usually a wide band visible light source with a filter, and later lasers. However, spectroscopic ellipsometers are commonly used nowadays in different research fields. BASIC CONCEPTSA description of ellipsometry as an optical technique would not be complete without mentioning J.C. Maxwell (1831-1879). Maxwell's theory predicts that light is a wave represented by two mutually perpendicular vectors: E, the amplitude of the electric field strength, and B, the amplitude of the magnetic field strength, and both E and B are also perpendicular to the direction of propagation, z. The electromagnetic wave is described by its amplitude and frequency in complex form:where E ...

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Conventional and generalized Mueller-matrix ellipsometry using the four-detector photopolarimeter

Cited by 27 publications

References 23 publications

Lamellar Gratings as Polarization Components for Specularly Reflected Beams

Lamellar Gratings as Polarization Components for Specularly Reflected Beams

Effect of light-beam deviation on the instrument matrix of the four-detector photopolarimeter

Fundamentals and applications of spectroscopic ellipsometry

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