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

= πr^{2}

= 3.14 x (0.4 mm)^{2}

= 3.14 x (0.04 cm)^{2}

= 5.024 x 10^{-3}cm^{2}

Next, calculate the power density or power per unit area:

Power Density

= Power / Area

= 50 mW / (5.024 x 10^{-3}cm^{2})

= 9.95 W/cm^{2}

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/cm^{2} 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/cm^{2}).

Expressing laser damage threshold (LDT) in equation form:

LDT (y) = LDT (x) * (y/x)^{½}

In the example above, x = 1 µsec or 10^{-6} sec, and y = 10 nsec or 10 x 10^{-9} sec

= 2 J/cm^{2}* (10^{-6}sec/ 10 x 10^{-9}sec)^{½}

= 2 J/cm^{2}* (100)^{½}

= 20 J/cm^{2}

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. Therefore, a safety factor of 2 or 3 applied to the calculations should be considered in order to accommodate for hot spots. Also a factor of 2 is typically applied for Gaussian shaped beams.