Materials Research Laboratory, Center for Thin Film Devices, and Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802 USA
R. W. Collins and Joohyun Koh, "Dual rotating-compensator multichannel ellipsometer: instrument design for real-time Mueller matrix spectroscopy of surfaces and films," J. Opt. Soc. Am. A 16, 1997-2006 (1999)
We describe the design of a high-speed multichannel ellipsometer in the optical configuration having frequency-coupled rotating compensators ( and ) and a fixed polarizer and analyzer (P and A) symmetrically placed about the sample (S) on the polarization generation and detection arms of the instrument. For this instrument the frequency-coupled compensators rotate continuously at
and where π/ω is the fundamental optical period. Although the dual rotating-compensator configuration has been proposed and demonstrated earlier, we focus on its extension to real-time Mueller matrix spectroscopy of surface modification and thin-film growth utilizing high-speed multichannel detection with a wide spectral range. The proposed instrument design provides the capability of extracting all 16 elements of the unnormalized Mueller matrix of an evolving sample at 1024 points from 1.5 to 6.5 eV with potential acquisition and repetition times of 0.2 s. Techniques of data acquisition, data reduction, and instrument calibration are described for the general case of arbitrary compensator retardances and polarizer and analyzer angles. We expect that the proposed instrument will have important applications in studies of surfaces and thin films that exhibit anisotropy and inhomogeneity.
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
The parameters tabulated include the frequency ratio of the first and second compensators (column 1); the fundamental or base frequency, defined by (column 2); the frequencies of the first and second compensators (columns 3 and 4); the highest-order Fourier coefficient (F.C.) in the detector irradiance waveform, with 2ω used as the fundamental optical frequency (column 5); the minimum number of waveform integrals required to extract all Fourier coefficients (column 6); a convenient encoder increment (referenced to the fundamental mechanical rotation) for driving the multichannel detector scans (column 7); the fundamental optical period π/ω (column 8); and the detector waveform integration time for the given encoder increment (column 9).
Table 2
Listing of the Nonzero, dc-Normalized Fourier Coefficients and Calibration Phase Angles of Eq. (3), Where and
Freq. Term (dc,
or )
Phase
Fourier Coefficient of
( or )
dc
—
Table 3
Product of the Square of the dc Term and the Amplitude Function of Eq. (7a), Where and
Freq. Term
Table 4
Phase Functions in the Measured Fourier Coefficients of Eq. (7b)
Freq. Term
Phase Function
Tables (4)
Table 1
System Design Parameters for a Dual Rotating-Compensator Multichannel Ellipsometera
The parameters tabulated include the frequency ratio of the first and second compensators (column 1); the fundamental or base frequency, defined by (column 2); the frequencies of the first and second compensators (columns 3 and 4); the highest-order Fourier coefficient (F.C.) in the detector irradiance waveform, with 2ω used as the fundamental optical frequency (column 5); the minimum number of waveform integrals required to extract all Fourier coefficients (column 6); a convenient encoder increment (referenced to the fundamental mechanical rotation) for driving the multichannel detector scans (column 7); the fundamental optical period π/ω (column 8); and the detector waveform integration time for the given encoder increment (column 9).
Table 2
Listing of the Nonzero, dc-Normalized Fourier Coefficients and Calibration Phase Angles of Eq. (3), Where and
Freq. Term (dc,
or )
Phase
Fourier Coefficient of
( or )
dc
—
Table 3
Product of the Square of the dc Term and the Amplitude Function of Eq. (7a), Where and
Freq. Term
Table 4
Phase Functions in the Measured Fourier Coefficients of Eq. (7b)