Question

a. Consider a laser radar emitting a Gaussian beam of diameter 20 cm with a wavelength of 2.1 μm. At distances of 50, 500, 5000, and 50,000 meters, what is the focused beam diameter, and what is the depth of field? Remember the depth of field is twice the Rayleigh range of the waist diameter. Remember that in some cases the solution may be impossible. Also re- member that there may be two solutions, and it makes sense to pick the one with the smaller beam diameter.

b. In view of your answers, comment on the feasibility of using a focusing to select a range with this laser radar.

Answer 1

a) For a beam of wavelength λ , at a distance Z, the size is given by

w(z) =                     

   Zr =  

Where r is the distance from the center of the beam, w0 is the radius at which the amplitude is 1/e of its value on the axis. Zr is the Rayleigh range.

   Zr =

           = = 14959.9m

1) Z = 50m

w(z)    = 0.1000005585m

Diameter = 0.200001117m

2) Z = 500m

w(z) =   0.1000558m

Diameter = 0.2001116m

3) Z = 5000m

w(z)   0.105437m

Diameter = 0.210874m

4) Z = 50000m

w(z) = 0.34886m

Diameter = 0.69772m

b)  

b) Depth of field = 2Zr =

                                  = 29919.9m

c) Gaussian beams are the simplest and often most desirable type of beam provided by a laser source.

At larger distances the diameter of the source beam is increasing.