EXERCISE 1: THE TEM MODE: “LINE CUTS”

The irradiance  (power per unit area) of a laser oscillating in the TEM mode can be expressed as

where  is the maximum irradiance of the beam and  is a parameter that describes the width (i.e., the spatial extent) of the beam. You can show that when , the locations  at which  are . Show that when  and , the irradiance is  and show that the above expression for the irradance is equivalent to

where the “scaled variables”  and  are defined as . We can relate this expression to the total power  transmitted by the beam:

(a) Assume  mW and  mm to generate a line plot of the irradiance  on the vertical axis versus  on the horizontal axis for  for different values of  and .

(b) Repeat (a) but now plot the irradiance divided by the maximum irradiance for that particular value of  (in other words, plot ) versus  on the horizontal axis. Comment on the resulting plot.