Homework 5

um=(10^(-6));mm=(10^(-3));cm=(10^(-2));W=1;

Problem 1: pump laser optics

A Ti:sapphire laser (wavelength 800nm) is pumped with a collimated green laser beam (532nm, diameter d=2mm). To get good pump overlap with the laser mode, the pump beam is focused (with lens (Subscript[L, P])) through the curved dielectric mirror ((Subscript[F, 1])) that is near the laser crystal. This curved optic is coated to reflect 100% at 800nm, but is transparent at 532nm. Therefore it acts like a negative lens for the pump beam. The substrate of the curved mirror has a refractive index of 1.5.

a. If the curved mirror radius is 100mm, and the pump lens focal length is 75mm, determine the distance the lens must be from the curved mirror to place the pump beam focus at the focal point of the curved mirror.  Treat both optics as “thin”, so you can use paraxial approximations.  You can solve this either with ABCD or the imaging equation.

b. What is the f-number of the final beam focus? (f-number = dist to focus/beam diameter). If we now treat the beam as a Gaussian laser beam (d = 1/(e^2) diameter), what would the diffraction-limited focal spot diameter be? You can use geometric optics to get the beam size at the curved mirror.

Problem 2:

a. A CW laser beam has a Gaussian intensity profile I(r)=(Subscript[I, pk])exp(-2(r^2)/((Subscript[w, 0])^2)). Calculate the power in the beam, in terms of (Subscript[I, pk]) and (Subscript[w, 0]).

b. Suppose we set up a 1W laser beam (λ=514nm) here in Golden to signal to a team at DIA airport 35 miles away. To get the minimum spread in the beam, we would have a slight focus to put the beam waist at half of the distance.  What is the smallest initial beam size that we can use under this condition?

c. What is the intensity of the beam at the target?

Problem 3

Suppose you know the complex q beam parameter at a given position. Derive expressions for the location and size of the beam waist from the q parameter.

Problem 4
Svelto 5.3. You can work through 5.2 as a guide (5.2 solutions in book).

Hemiconfocal resonator (L = R/2)
L = 2 m
λ = 10.6 um
a. location of the beam waist
b. spot size on each mirror
c. frequency difference between two consecutive tem00 modes
d. number of tem00 modes w/in BW of Δν = 50MHz

a. location of the beam waist

since the cavity has a flat end mirror, there must be a waist there.

b. spot size on each mirror

c. frequency difference between two consecutive tem00 mode

d. gain BW is 50MHz

Problem 5
We have a laser resonator with a flat output coupler and a concave high reflector. If the gain medium is 3mm in diameter and placed close to the high reflector, what cavity length best fills the gain medium? Aim for a 1/(e^2) beam diameter at the high reflector of 2.5mm.