Simulations of optimal light polarization state generators and analyzers configurations realized in one-way double pass Mueller polarimetric system using two twisted nematic liquid crystals working in different way

The dataset contains the results of optimizing the configurations of light polarization state generators and analyzers that can be implemented in one-way double pass Mueller polarimetric system. The same module is used as a generator (PSG) and analyzer (PSA) of different polarization states of light. In the performed numerical simulations, the PSG/PSA module is constructed from a linear polarizer and two twisted nematic liquid crystals (TNLCs).

PSG/PSA description

The elements of the system are represented by a Mueller matrices. The forms of the used Mueller matrices are included in the file: "Mueller_matrix.pdf". TNLCs are the same oriented azimuthally. It was assumed that for PSG, TNLC director axis of the first layer is aligned along the x-axis of the coordinate system. However, for PSA, TNLC directors at the input surface of the modulator is rotated by an angle π/2. Due to the configuration, TNLC in the PSG and PSA system introduce the same linear phases. The dependence between the voltage of the TNLC and the induced phase difference is not considered. At the same time TNLC elements introduce different linear phase differences.

Optimization process

The numerical PSG/PSA model were simulated and optimized to find the optimal sets of TNLC’s linear phase differences for every linear polarizer’s azimuth angle, and thereby the best set of generators and analyzers, leading to the minimum system condition number (CN). Also equally weighted variance (EWV) is calculated. The results of optimization process were generated for:

• different ranges of possible TNLC’s linear phase difference: (0;2π>, (0;3π>, (0;4π>, (0;5π>,
• different number of configurations realized by PSG/PSA (n={4:20}),
• azimuthal orientations of the polarizer from 0°-180° with a step of 0.5°.

For each azimuth angle of the polarizer randomly permuted two sets (for TNLC1 and TNLC2) n TNLC’s linear phases and determination instrumental matrices for PSG (the columns of this matrix correspond to the n Stokes vectors of the PSG) and PSA (the rows of this matrix correspond to the n Stokes vectors of the PSA). CN of the polarimeter system was calculated as product of generator’s CN and analyzer’s CN. These steps have been repeated 10 000 times and the minimum CN value corresponding to a given polarizer azimuth angle was determined. Associated with this determined minimum CN value of the system are EWV value and two sets of n TNLC’s linear phases (for TNLC1 and TNLC2), leading to n Stokes vectors for PSG and PSA.

Used software: MATLAB

File information and data format

The data are saved as text files (.txt) and MAT-files (.mat).

The resulting files are grouped according to the assumed maximum linear phase difference introduced by TNLC (PDmax):

• maximum_linear_phase_difference_2pi.zip -> TNLC’s linear phases are generated from the range (0;2π>
• maximum_linear_phase_difference_3pi.zip -> TNLC’s linear phases are generated from the range (0;3π>
• maximum_linear_phase_difference_4pi.zip -> TNLC’s linear phases are generated from the range (0;4π>
• maximum_linear_phase_difference_5pi.zip -> TNLC’s linear phases are generated from the range (0;5π>.

Inside, the folders are grouped according to the different number of configurations (n={4:20}). Names are created in this way: number_of_configurations_n.

Each folder contains:

• CN_PSA_vs_alfaP_PDmax_n.txt -> The first row is the azimuth angles of the polarizer in radians, the second row is the CN values of the PSA instrumental matrix (corresponding to the minimum CN value of the system).
• CN_PSG_vs_alfaP_PDmax_n.txt -> The first row is the azimuth angles of the polarizer in radians, the second row is the CN values of the PSG instrumental matrix (corresponding to the minimum CN value of the system).
• CN _vs_alfaP_PDmax_n.txt -> The first row is the azimuth angles of the polarizer in radians, the second row is the minimum CN values of the system.
• EWV _vs_alfaP_PDmax_n.txt -> The first row is the azimuth angles of the polarizer in radians, the second row is the EWV values of the system (corresponding to the minimum CN value of the system).
• linear_phase1 _alfaP_PDmax_n.txt -> The first row is the azimuth angles of the polarizer in radians, the second row is the set of n TNLC1’s linear phases in radians (corresponding to the minimum CN value of the system).
• linear_phase2 _alfaP_PDmax_n.txt -> The first row is the azimuth angles of the polarizer in radians, the second row is the set of n TNLC2’s linear phases in radians (corresponding to the minimum CN value of the system).
• PSA_vs_alfaP_PDmax_n.mat -> For each azimuth angle of the polarizer saved matrix formed from the Stokes vectors of the analyzers (corresponding to the minimum CN value of the system). Each column is a new Stokes vector.
• PSG_vs_alfaP_PDmax_n.mat -> For each azimuth angle of the polarizer saved matrix formed from the Stokes vectors of the generators (corresponding to the minimum CN value of the system). Each column is a new Stokes vector.

Cell array indices consistent with polarizer azimuth angle indices.

Preferred software for analyzing/interpreting results: MATLAB.