Transcription of 17. Jones Matrices & Mueller Matrices - Brown University
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17. Jones Matrices & Mueller Matrices - Brown University
17. Jones Matrices & Mueller MatricesJones MatricesRotation of coordinates - the rotation matrixStokes Parameters and unpolarized lightMueller MatricesR. Clark Jones (1916 - 2004)Sir George G. Stokes(1819 - 1903)Hans Mueller (1900 - 1965)2211 xxxyyxyxyEEEEEEEEEED efine the polarization state of a field as a 2D vector Jones vector containing the two complex amplitudes: Jones vectors describe the polarization state of a waveA few examples: 0 linear (x) polarization: Ey/Ex = 0linear (arbitrary angle) polarization: Ey/Ex= tan right or left circular polarization: Ey/Ex= j10 1tan 1j (normalized to length of unity)To model the effect of a medium on light'spolarization state, we use Jones A11101201210220xxyyxyEaEaEEaEaE This yields:1000x AFor example, an x-polarizer can be written:0010010000xxxyEEEEE ASo:Since we can write a polarization state as a ( Jones ) vector, we use Matrices , A, to transform them from the input polarization, E0, to the output polarization, aaaaAThis should be thought of as a transfer Jones matricesA y-polarizer:0001y A1001 HWP AA half-wave plate.
0 = the total irradiance S 1 = the excess in intensity of light transmitted by a horizontal polarizer over light transmitted by a vertical polarizer S 2 = the excess in intensity of light transmitted by a 45° polarizer over light transmitted by a 135° polarizer S 3 = the excess in intensity of light transmitted by a RCP filter over light
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