Geometrical optics may be employed to determine the beam waist location in Gaussian problems.
Consider a HeNe laser with λ = 0.63 μm. Calculate the radius of curvature for mirrors in the figure below.
Calculate beam width at mirrors from the previous example and at a distance of 1m, 1 km, and 1,000 km from center of laser (assuming that mirrors do not deform beam)
Consider a colliminated Nd:YAG laser beam (λ=1.06 μm) with a diameter to e -2 relative power density of 10 cm at the beam waist with z 0 = 0. What is the beam half width to e -2 relative power density at z = 1m, 100 m, 10 km, and 1,000 km?
From the previous example, what is power density on beam axis at each distance, assuming the total power is 5 W? What is the divergence angle of beam to e -2 and e -4 relative power density?
Two identical thin lenses with f = 15 cm and D = 5 cm are located in plane z = 0 and z = L. A Gaussian beam of diameter 0.5 cm to e -2 relavtive power density for λ = 0.63 μm is incident on the first lens. The value of L is constained such that the e -2 relative power density locus is contained within the aperture of the second lens.
(a) For what value of L will the smallest spot be obtained for some value of z 0 > 0? What is the value of z 0 corresponding to the location of that spot? What is the diameter of that spot?
(b) For what value of L will the smallest spot size be obtained on the surface of the moon at a distance of 300,000 km? What is the beam diameter on the moon surface?