# Laser Damage Threshold

## Continuous Wave Lasers

For continuous wave (CW) lasers the damage threshold can be calculated from the peak power and beam diameter. For example, to calculate the power density of a 50 mW Nd:YAG laser at 1064 nm with a 0.8 mm beam diameter, first calculate the beam area in terms of centimeters:
Beam Area
= πr2
= 3.14 x (0.4 mm)2
= 3.14 x (0.04 cm)2
= 5.024 x 10-3 cm2
Next, calculate the power density or power per unit area:
Power Density
= Power / Area
= 50 mW / (5.024 x 10-3 cm2)
= 9.95 W/cm2
For laser beams with a Gaussian intensity profile, multiplying the power density by two for safety is required to accommodate the peak power density at the center of the beam. Remember, damage threshold scales with wavelength, so the damage threshold at 532 nm will be half that at 1064 nm.

## Pulsed Lasers

For pulsed lasers in the range of µsec to nsec, the energy density varies as a function of the square root of the time domain. As a rule of thumb, an optic can withstand 10 times more energy when used with a 1 µsec pulsed laser than a 10 nsec pulsed laser. Suppose, for instance, that the damage threshold is rated at 2 J/cm2 for 10 nsec pulses, but your laser has a 1 µsec pulse length. This means that at the 1 µsec time domain (10-6 sec compared to 10 x 10-9 sec), the optic can withstand 10 times more energy (20 J/cm2).
Expressing laser damage threshold (LDT) in equation form:
LDT (y) = LDT (x) * (y/x)1/2
as in the example above, x = 1 microsec or 10-6 sec, and y = 10 nsec or 10 x 10-9 sec
= 2 J/cm2 * (10-6 sec/ 10 x 10-9 sec)1/2
= 2 J/cm2 * (100)1/2
= 20 J/cm2
In the realm in between pulsed and CW applications (in the msec range), compare both the average power with the CW threshold and the pulse energy density with the energy specification.
In the millisecond range, there is a crossover between pulse and CW regimes where you should try to satisfy both criteria.
Please note that for pulsed lasers, there may be hot spots in the output beam. Typically, there is a safety factor of 2 or 3 applied to the calculations in order to accommodate for hot spots. Also a factor of 2 is typically applied for Gaussian shaped beams.

## Ultrafast Lasers

For Ultrafast pulsed lasers in the psec to fsec regime, the electric field of the pulse attacks the electronic bonds of the dielectric coating. Peak powers can be quite high. Our UF.25 Ultrafast 45° mirror has been laboratory tested and found to have a damage threshold of 1 TW/cm2 with 100 fsec pulses at 5 Hz at 800 nm.