# Gaussian Laser Beam

## Homework Statement

A 655nm gaussian laser beam has a waist of 15mm located at a lens with focal length of 12 cm. What is the minimum beam waist and where is it located?

## Homework Equations

Beam radius w = w0*sqrt(1-(z/zr)^2)
w0 = min beam waist; z = distance, zr = Rayleigh range

## The Attempt at a Solution

I'm attempting to find the distance from where w0 is located to the focal point, so I'd be able to calculate the distance R1 to the lens. Then perhaps calculate R2 from (1/R1)-(1/R2)=(1/f), where I assume the minimum w0 is located. Problem is I have no idea how to find this initial distance along the wave front of the beam.

## Answers and Replies

Redbelly98
Staff Emeritus
Science Advisor
Homework Helper
It sounds like the beam is collimated at the lens, so the source distance would be at infinity.

It looks like you Rayleigh range is much larger than the focal length of the lens. In this case, your focused spot size will be given by f \lambda/(\pi w_i), where w_i is the initial waist size. You should find the derivation in any book on lasers (e.g. Yariv or Siegman)

Redbelly98
Staff Emeritus
Science Advisor
Homework Helper
It looks like you Rayleigh range is much larger than the focal length of the lens.
That's weird, I have calculated a much shorter Rayleigh range.