Final Model of Optical System for Exploiting Polarisation Changes in Strained MQW Devices

Matrix Model of Optical System

This worksheet contains the final model for the smart pixel optical system. The chip itself will be modelled by a the Jones Matrix for a rotator (of 20 degrees) and not as a half wave plate as used previously.

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INPUT POLARISATION - (HORIZONTAL) LINEARLY POLARISED LIGHT

> v1:=linalg[vector](2,[1,0]);

FIRST PASS QWP1 - ANGLE THETA

> m2:=linalg[matrix](2,2,[I*cos(theta)*cos(theta)+sin(theta)*sin(theta),(I-1)*sin(theta)*cos(theta),(I-1)*sin(theta)*cos(theta),I*sin(theta)*sin(theta)+cos(theta)*cos(theta)]);

FIRST PASS QWP2 - ANGLE PHI

> m3:=linalg[matrix](2,2,[I*cos(phi)*cos(phi)+sin(phi)*sin(phi),(I-1)*sin(phi)*cos(phi),(I-1)*sin(phi)*cos(phi),I*sin(phi)*sin(phi)+cos(phi)*cos(phi)]);

M4a IS THE DEVICE

> m4a:=linalg[matrix](2,2,[cos(2*Pi/9),sin(2*Pi/9),-sin(2*Pi/9),cos(2*Pi/9)]);

SECOND PASS QWP2

> m5:=linalg[matrix](2,2,[I*cos(phi)*cos(phi)+sin(phi)*sin(phi),(I-1)*sin(phi)*cos(phi),(I-1)*sin(phi)*cos(phi),I*sin(phi)*sin(phi)+cos(phi)*cos(phi)]);

SECOND PASS QWP1

> m6:=linalg[matrix](2,2,[I*cos(theta)*cos(theta)+sin(theta)*sin(theta),(I-1)*sin(theta)*cos(theta),(I-1)*sin(theta)*cos(theta),I*sin(theta)*sin(theta)+cos(theta)*cos(theta)]);

ANALYSER

> m7:=linalg[matrix](2,2,[1,0,0,0]);

Calculation of Signal and Contrast

> A5V:=evalm(v1&*m2&*m3&*m4a&*m5&*m6&*m7);

> A0V:=evalm(v1&*m2&*m3&*m5&*m6&*m7);

> C1:=A0V[1]^2;

> C2:=A5V[1]^2;

> Contrast:=evalm(C1/C2);

> Signal:=C2-C1;

Plots of Contrast

> plot3d(Re(Contrast),theta=0..Pi,phi=0..Pi);

> plot3d(Im(Contrast),theta=0..Pi,phi=0..Pi);

Plots of Signal

> plot3d(Re(Signal),theta=0..Pi,phi=0..Pi);

> plot3d(Im(Signal),theta=0..Pi,phi=0..Pi);

Joint Plots of Signal and Contrast

> plot3d({Re(Contrast),Re(Signal)},theta=0..Pi,phi=0..Pi);

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