7.1 Gaussian beamDeveloping MatlabIn the program, ABCD law for passing Gaussian beam trough an optical system, is exploited. Entering wavelength, radius of the beam W1, and radius of the equiphase surface R1, complex curvature at the beginning of the system q1 is evaluated, which consists of a real component a1 and of an imaginary one b1:
a1 = k^2 * R1 * W1^4 / (k^2 * W1^4 + 4*R1^2);
b1 = -2*k * R1^2 * W1^2 / (k^2 * W1^2 + 4*R1^2); This complex parameter is used for evaluating beam curvature behind the optical element
q2 = (A*q1 + B) / (C*q1 + D);
Here, A, B, C, D are elements of the matrix of the optical element. In order to determine the beam radius W2 and the equiphase surface radius R2 behind the optical element, following relations are used:
W2 = sqrt( (2*(A*a1+B)^2 + (A*b1)^2) / (k*b1*((A*a1+B)*C - A*(C*a1+D))));
R2 = ((A*a1+B)^2+(A*b1)^2)/((A*a1+B)*(C*a1+D)-A*(C*a1+D)); Next, variation of parameters W and R in a given distance behind the optical elements is computed using the following relations:
W2z(zz) = sqrt((W2)^2*(1+zn/R2)^2+(2*zn/(k*W2))^2);
R2z(zz) = ((R2+zn)^2*(k*W2^2)^2+4*zn^2*R2^2)/((R2+zn)*(k*W2^2)^2+4*zn*R2^2);
Evaluated parameters W and R are shown for single equiphase surfaces depending on the distance from the optical element. |
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