Question

2. [40 pts] Gaussian Beam (Based on Textbook problem 1.4 and 1.5) A diode laser emits a Gaussian beam. The minimum waist diameter is 1 mm. The lasing wavelength is 514 nm. Find (a) Divergence angle 6div (b) The Rayleigh range (c) The diameter of the beam after propagating 10 m (d) 10 m away from the laser output aperture, you want to place a spherically curved mirror to reflect 1.0 mmthe beam back perfectly. Find the radius of curvature of the mirror. Use the R(2) formula given in class. R.о.С. Radius of curvature R(z) Z 0 spherical

Answer 1

Minimum wait diameter (w_0) = 1mm wavelength (lambda) = 514nm (a) theta_div = lambda/pi w_0 (divergence angle) theta_div = 514nm/3.14 times 1mm = 514 times 10^-9 m/3.14 times 10^-3 m theta_div = 0.167 m rad (b) Rayleigh range Z_R = pi w^2_0 /lambda = pi(1mm)^2 /514nm = 6112.04mm (c) diameter of the beam after propagating 10m diameter of the beam w_R (Z_R) = 2 squareroot 2w_0 Z_R = b/2 implies 2Z_R b = 2 times Z_R = 2 times 6112.04 mm w_R (b) = 2 squareroot 2w_0 w_R = 2.0mm (d) Radius of curvature R(z) = z[1 + (Z_R /Z)^2] [z = axial distance z_R = Rayleigh range] = 10[1 + (6112.04mm/10m)^2] R(z) = 3735663.17 R(z) = 3.7356 times 10^-6 m