RU2583959C1 - Method of determining muller matrix - Google Patents

Abstract

FIELD: measuring equipment.

SUBSTANCE: invention relates to optical measurements and can be used for complete polarisation state determination of light reflected from surface of analysed sample. To determine Muller matrix, analysed sample is illuminated with polarised light beam and measuring change in polarization using separation of reflected beam on p- and s-component with decomposition of amplitude and phase to obtain at outlet of four light beams with intensities I_Ψ1, I_Ψ2, I_Δ1, I_Δ2, wherein azimuth angles of optical elements receiving fixed values in certain combinations, polariser is fixed in positions P = 0°, -45°, +45°, analyzer in amplitude channel A_Ψ= 0°, 45°, phase channel A_Δ= 45°, Fresnel rhombus R = 0 and measurements corresponding to following configurations: A: P45SR0W_Ψ45W_Δ45; B: P45SR0W_Ψ0W_Δ45; F: P0SR0W_Ψ45W_Δ45; E: P0SR0W_Ψ0W_Δ45. Change state of polarisation of incident light on specimen with linear on circular, each optical channel before sample retarder in position D = 0° and measurements corresponding configurations C: P-45D0SR0W_Ψ0WΔ45; D: P-45D0SR0W_Ψ45W_Δ45, while components of Muller matrix S_ij is determined by solving system of linear equations.

EFFECT: invention enables complete determining polarisation state of light reflected from surface of analysed sample, for location of all components of Muller matrix.

1 cl, 1 dwg

Description

The invention relates to the field of optical measurements and can be used to fully determine the state of polarization of light reflected from the surface of the sample. The method allows the use of standard instruments that measure the state of polarization, commercially available ellipsometers, built on the basis of a four-channel photometric circuit. To implement the invention, it is necessary to make minor changes to the optical path of the device. Moreover, the ability to bring the optical circuit to its original form is an integral part of the proposed method, which allows you to use the ellipsometer in the normal mode for measuring ellipsometric angles Ψ and Δ at any time of a physical experiment.

Known Stokes ellipsometer [KR 20030049473 (A), IPC G01J 4/00, publ. 06/25. 2003], consisting of a non-monochromatic light source, collimators, a polarization generator, an analyzing unit based on CCD matrices and allowing to measure the components of the Mueller matrix of the sample under study.

The disadvantages of this device are the low resolution in spectrum, as well as the difficulty of alignment in case of use in situ, for example, as a diagnostic tool on a high-vacuum chamber.

In the invention [US 5757494 A, IPC G01 21/21, publ. 05.26.1998] it is also possible to measure the Mueller matrix, however, the presence of rotating elements significantly increases the measurement time, which is a serious drawback in the study of dynamic processes.

A known method of measuring the state of polarization with an ellipsometer [pm RF №16314, IPC G01N 21/21, publ. 20.12.2000], constructed according to the photometric scheme, which consists in splitting the light beam reflected from the surface of the test sample into two components, which measure the amplitude and phase changes in light during reflection, respectively, for p and s polarizations.

The disadvantages of this method are the low accuracy of the measurements and the narrow spectral range of the measurements, as well as the inability to measure the total polarization state (Stokes vector) of the light reflected from the test sample.

The closest technical solution to the claimed is a method of measuring the state of polarization with an ellipsometer [RF patent No. 2302623, IPC: 6 G01N 21/21, publ. July 10, 2007 (prototype)], which consists in the fact that the design also uses a photometric four-channel scheme, which allows minimizing the number of optical configurations for measuring the Mueller matrix, which will accelerate the time of one experiment.

The technical result consists in the possibility of a complete determination of the state of polarization of light reflected from the surface of the sample (Stokes vector) to find all the components of the Mueller matrix.

The technical result is achieved by the fact that in the method of determining the Mueller matrix, which consists in the fact that the test sample is illuminated with a polarized light beam and the change in polarization upon reflection is measured using separation of the reflected beam into p and s components with expansion in amplitude and phase, obtaining four output light beams with intensities _{I Ψ1, I Ψ2, I Δ1} , I Δ2, wherein the azimuth angles of the optical elements take fixed values in certain combinations, the polarizer is fixed to P = 0 °, -45 °, +45 Analyzer in amplitude channel A _Ψ = 0 °, 45 °, phase channel A _Δ = 45 °, Fresnel rhomb R = 0 and measured, corresponding to the following configurations:

A: P45SR0W _Ψ 45W _Δ 45

In: P45SR0W _Ψ 0W _Δ 45

F: P0SR0W _Ψ 45W _Δ 45

E: P0SR0W _Ψ 0W _Δ 45,

new is that they change the polarization state of the incident light from linear to circular, installing a phase plate in the optical path in front of the sample in the position D = 0 °, and carry out measurements corresponding to the configurations:

C: P-45D0SR0W _Ψ 0W _Δ 45

D: P-45D0SR0W _Ψ 45W _Δ 45,

and the components of the Mueller matrix S _{ij are} determined by solving the following system of linear equations:

- интенсивности р- и s-компонент в амплитудном измерительном канале Ψ плеча анализатора,

- в фазовом измерительном канале Δ для различных конфигураций оптических элементов.Where

- the intensity of the p and s components in the amplitude measuring channel Ψ of the analyzer arm,

- in the phase measuring channel Δ for various configurations of optical elements.

The differences of the proposed method from the closest analogue are that during measurements, a phase plate is installed in the optical path, as well as in the used mathematical apparatus when calculating the values of the components of the Mueller matrix. These differences allow us to conclude that the proposed technical solution meets the criterion of "novelty." Signs that distinguish the claimed technical solution from the prototype are not identified in other technical solutions when studying this and related areas of technology and, therefore, provide the claimed solution with the criterion of "inventive step".

In FIG. 1 shows a diagram of a stokes ellipsometer.

The device for measuring the Mueller matrix (see Fig. 1) consists of a light source 1 (HeNe laser), a polarizer 2, comprising the polarizer arm, a phase 3 change module, which is a quarter-wave phase plate with the possibility of removing the test sample from the optical path 4. The shoulder of the Stokes-ellipsometer analyzer consists of a Fresnel rhombus 5, Wollaston prisms 6, 7, two-area photodetectors 8, 9.

The measurement of the Mueller matrix is as follows.

The luminous flux 10 emitted by illuminator 1 is linearly polarized by polarizer 2, passes through the phase 3 change module, and for configurations C, D changes the polarization state from linear to circular, for configurations A, B, E, F the polarization state remains unchanged, then incident on the surface of the test sample 4. An incident, linearly polarized (or circularly polarized) light beam is reflected from the surface of the sample with a change in the polarization state and becomes, in the general case, elliptically polarized and in this state enters the analyzer arm, namely, the Fresnel 5 rhombus, which simultaneously plays the role of a spatial splitter of the light beam and the phase plate, splitting the light beam reflected by the sample under study into two light components, one of which enters the amplitude measuring channel, where the Wollaston prism 6 divides the input the light beam to the p- and s-components, the intensities of which are then detected by a two-area photodetector 9. The other part of the light beam, having undergone a phase shift, falls into the phase measurement Tel'nykh channel Δ, where it also passes through a Wollaston prism 7, 8 is also registered photodetectors.

As a result, we have four intensity values I _Ψ1 , I _Ψ2 , I _Δ1 , I _Δ2 , from which the values of the components of the Mueller matrix are calculated. During such measurements, the optical polarization elements take the following fixed azimuthal positions:

A: P45SR0W _Ψ 45W _Δ 45

In: P45SR0W _Ψ 0W _Δ 45

C: P-45D0SR0W _Ψ 0W _Δ 45

D: P-45D0SR0W _Ψ 45W _Δ 45

E: P0SR0W _Ψ 0W _Δ 45

F: P0SR0W _Ψ 45W _Δ 45,

where the following notation is introduced: P - polarizer, D - tunable phase plate, S - test sample, R - Fresnel rhombus, W _Ψ and W _Δ - Wollaston prisms in the amplitude and phase measuring channels, respectively.

In order to obtain the value of the components of the Muller matrix of the test sample, it is necessary to conduct a simulation of the inventive Stokes ellipsometer. To do this, the Mueller matrices of the optical elements of the device for all the configurations (A-F) are recorded. Such matrices are described in detail in the monograph [W. Sherkliff. Polarized light // Per. from English M .: Mir, 1965]. Consider, for example, configuration C and compose a sequence of Mueller matrices for the phase measuring channel and the s-component:

Here:

I. Stokes vector of incident unpolarized light of unit intensity;

II. Mueller matrix for a linear polarizer with an azimuth of -45 °;

III. Mueller matrix for a phase plate with an azimuth of 0 °;

IV. Muller matrix of the test sample (unknown);

V. Mueller matrix for a Fresnel rhombus with an azimuth of 0 °;

VI. Matrix for the s-component of the Wollaston prism with an azimuth of 45 °;

After sequential (from right to left) matrix multiplication, we obtain the intensity value for configuration C on this channel

Similarly, we get the remaining fifteen equations that make up the system:

solving which, we get the components of the Mueller matrix.

The advantage of the proposed method for determining the Muller matrix is primarily to expand the capabilities of a standard ellipsometer for the study of samples with optical anisotropy. This optical design simplifies the alignment process and thereby allows the instrument to be mounted on an ultra-high vacuum chamber for in situ measurements.

Claims (1)

The method of determining the Muller matrix, which consists in the fact that the test sample is illuminated with a polarized light beam and the change in polarization upon reflection is measured using the separation of the reflected beam into p and s components with expansion in amplitude and phase, obtaining four light beams with intensities I at the output _Ψ1 , I _Ψ2 , I _Δ1 , I _Δ2 , while the azimuthal angles of the optical elements take fixed values in certain combinations, the polarizer is fixed in positions P = 0 °, -45 °, + 45 °, the analyzer in the amplitude channel A _Ψ = 0 ° , 45 °, fa channel A _Δ = 45 °, Fresnel rhombus R = 0 and carry out measurements corresponding to the following configurations:
A: P45SR0W _Ψ 45W _Δ 45
In: P45SR0W _Ψ 0W _Δ 45
F: P0SR0W _Ψ 45W _Δ 45
E: P0SR0W _Ψ 0W _Δ 45,
where S is the test sample, W _Ψ and W _Δ are Wollaston prisms in the amplitude and phase measuring channels, respectively,
characterized in that the polarization state of the light incident on the sample is changed from linear to circular, installing a phase plate in the optical path in front of the sample in the position D = 0 ° and performing measurements corresponding to the configurations:
C: P-45D0SR0W _Ψ 0W _Δ 45
D: P-45D0SR0W _Ψ 45W _Δ 45, and the components of the Mueller matrix S _{ij are} determined by solving the following system of linear equations:

Where

- the intensity of the p and s components in the amplitude measuring channel of the analyzer arm,

- in a phase measuring channel for various configurations of optical elements.

Images