A high-power (20 Watts) Nd:YAG laser ( l = 532 nm) is orbiting the earth at an altitude of 100 km.  It directs a laser beam towards the surface of the earth. The diameter of the Gaussian beam is 1 mm when the light exits the laser.

(a)  What is the beam diameter when the laser strikes the surface?

(b)  What is the time-averaged irradiance in W/cm² on the surface?

Problem 2:

In terms of frequency, the spacing between two successive laser modes at frequencies f_m+1 and f_m is Df = c/(2L).

(a) What is the (approximate) spacing between two modes in terms of wavelength when m is very large ( m >> 1).

(b)  For a gas laser at wavelength l = 514 nm and with a cavity length of 30 cm, what are Df (in units of MHz) and Dl, and roughly what is m, the mode number?

(c) For a diode laser at wavelength l = 670 nm and with a cavity length of 300 µm what are Df (in units of GHz) and Dl, and roughly what is m, the mode number?

Problem 3:

A He-Ne laser is 1.5 m long, l = 633 nm and the fluorescence line width is 1500 MHz.

(a)  Calculate the frequency difference between adjacent axial modes.

(b)  Explain why the coherence length is about equal to that of the incoherent fluorescence line.