Damage thresholds and Ti:Sapph lasers

Recently, a moderately expensive optical element got fried at Labrigger. During the postmortem, we revisited our power and energy calculations, and our LIDT (laser intensity damage threshold) calculations.

LIDT calculations remind me of radiation-health physics (e.g., how much radiation can a human be safely exposed to?). My nuclear physics professor, the excellent R.T. Carpenter, included a lecture on nuclear health physics in one of his courses. I suspect this was a requirement of some accreditation body, because it didn’t really fit the style he maintained over the other lectures. This is the man who famously repaired a neutron howitzer with his own hand while peaking over a radiation shield.

One of the themes of the lecture was how purely empirical the whole field is. How much radiation of a particular type can a living thing stand? Unfortunately, we can’t usually start from fundamental principles, as physicists usually like to do. However, some basic trends are clear, so by taking a few data points, we can interpolate for the intermediate values.

Thorlabs has a nice tutorial on this stuff, but it’s pretty general. Let’s go over the numbers for a bog-standard Ti:Sapph (e.g., a MaiTai or Chameleon):

Using round numbers

Rep rate: 80 MHz
Pulse width: 100 fs
Average power: 3 W

Peak power: 375 kW
Energy: 37.5 nJ
(calculation notes, more info)

If the laser intensity damage threshold (LIDT) is given as:
2 J/cm^2 at 1064 nm, 10 ns, 10 Hz

And we’re using, say 800 nm, then we first need to adjust for the wavelength:
Adjusted LIDT = LIDT Energy * sqrt(laser wavelength/LIDT wavelength)
Adjusted LIDT = 2 J/cm^2 * sqrt(800/1064) = 2 J/cm^2 * 0.867 = 1.73 J/cm^2
Not such a big deal.

Now we need to adjust for pulse duration:
Adjusted LIDT = LIDT Energy * sqrt(laser pulse duration/LIDT pulse duration)
Adjusted LIDT = 1.73 J/cm^2 * sqrt(100 fs/ 10 ns) = 1.73 J/cm^2 * 0.00316 = 5.47 mJ/cm^2
The ultrafast pulses have a much larger effect on LIDT.

If the energy, 37.5 nJ, is spread over about 1 mm^2, then that’s about 3.75 uJ/cm^2. Technically, that’s below the LIDT, but only in the domain of ns pulses.

In our case, multiphonon ionization can become a dominant process, then LIDT is proportional to (Energy density) * (1/e^2 diameter) * (pulse duration)^-1. Unfortunately, there are no helpful graphs from Thorlabs to refer to for this regime. (Labrigger can provide one data point, based on the one result pictured above.)

Corrected 18 Mar 2014. Thanks, Tony!