ECE 103 Engineering Programming Spring 2018 These are some important parameters

Question

ECE 103 Engineering Programming Spring 2018 These are some important parameters that characterize the Gaussian beam: . Rayleigh range: z Minimum beam waist (aka minimum spot size) at location z = 0: Beam width at position z along the beam ax is: Beam angular spread (radians): ?-29, where ? = w? the beam axis: w(z) Note: ? is the beam wavelength . To make a functioning laser, curved mirrors are placed along the axis to create a resonant cavity that reflects the beam back and forth. If the two mirrors have radii of curvature Ri and R2, respectively, they need to be placed at specific locations z1 and z2 along the axis to exactly match the wavefront's radius at those locations (Figure 3). Figure 3: Two-mirror resonant cavity Suppose you are given two mirrors with radii R and R2. They are to be placed a distance L apart. Where are the mirror locations zi and z2? The locations can be calculated from these equations: L (R,-L) R R2-2L 2221L The Rayleigh length zg is then: (R1 + R2-2L)" Assuming index n-1, the minimum beam waist wo is given by: wo =JLA! gl82(1-8182) +82-2881 where gl =l-L and g, =i-L RI where g,-|-_ and g,-|-- Source: Laser Physics, M. Sargent III, M. I. Scully, W. E. Lamb Jr, Addison-Wesley (1977)

Explanation / Answer

/******************************************************************************

You need to declare the variables as float.
scanf is used for the user input.
print is used for printing the output.
for float upto 3 deimal place with no trailing zeros %0.3g is used.

*******************************************************************************/

#include <stdio.h>
#include <math.h>

int main()
{
float R1, R2, L, lambda;
float z1, z2, g1, g2, w0, bas, zr, bw, pai=3.141592654;
printf("Enter radius of mirror 1 (cm): ");
scanf("%f", &R1);
printf("Enter radius of mirror 2 (cm): ");
scanf("%f", &R2);
printf("Enter distance between mirrors (cm): ");
scanf("%f", &L);
printf("Enter wavelength in the medium (nm): ");
scanf("%f", &lambda);
z1 = -1*L*(R2-L)/(R1+R2-2*L);
z2 = z1 + L;
g1 = 1-L/R1;
g2 = 1-L/R2;
w0 = sqrt(L*lambda/(1e7*pai))*sqrt(sqrt((g1*g2*(1-g1*g2))/((g1+g2-2*g1*g2)*(g1+g2-2*g1*g2))));
bas = 2*lambda/(pai*w0*1e7);
zr = 1e-5*sqrt((L*(R2-L)*(R1-L)*(R1+R2-L))/((R1+R2-2*L)*(R1+R2-2*L)));
bw = 1e-5*w0*sqrt(1+(35786/zr)*(35786/zr));
printf(" Laser system characteristic:");
printf(" z1 = %0.3g cm", z1);
printf(" z2 = %0.3g cm", z2);
printf(" w0 = %0.3g cm", w0);
printf(" Beam angular spread = %0.3g radians", bas);
printf(" Beam width at geostationary distance = %0.3g km", bw);
return 0;
}

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