Question

A Gaussian laser beam is incident on the interface between two dielectric media with refractive indices of n1=2 and n2=1.5. a) If the beam is at normal incidence to the interface and its waist location coincides with it, what is the reflection coefficient? If the spot size is 0.5μm, plot the reflected energy in percentage vs. wavelength from 300nm – 800nm. b) If the wavelength is fixed at 630nm and the waist diameter is still 0.5μm, but incident angle gradually increases from 0 to 60 degree, plot the reflected energy vs. incident angle. c) If the laser beam is in vacuum, with a waist diameter of 0.1 μm and a wavelength of 630nm. What is the Rayleigh range and the beams divergence. If any of the answers appear to be  unusual, explain the result.

Answer 1

a) at normal incidence, the reflection coefficient is given by

r = (n₁ – n₂) / (n₁ + n₂) = 2-1.5 / 2+1.5 = 0.5/3.5

Therefore, r = 0.14

c) The divergence of the beam is given by

Here λ = 630 nm = 630 ×10^-9 m and 2w_o = 0.1 ×10^-6 m

So,

= 8.02 rad = 459.5^o

The rayleigh range is given by

So

= 1.25 × 10^-8 m

Here we found that beam divergence and Rayleigh range are 459.5^o or 99.5^o and 1.25 × 10^-8 m, respectively. These values appear to be unusual in case of laser beam because the laser beam has a minimum possible divergence value.