In order to illustrate the process of determining whether a given laser system will damage an optic, a number of example calculations of laser induced damage threshold are given below. For assistance with performing similar calculations, we provide a spreadsheet calculator that can be downloaded by clicking the button to the right. To use the calculator, enter the specified LIDT value of the optic under consideration and the relevant parameters of your laser system in the green boxes. The spreadsheet will then calculate a linear power density for CW and pulsed systems, as well as an energy density value for pulsed systems. These values are used to calculate adjusted, scaled LIDT values for the optics based on accepted scaling laws. This calculator assumes a Gaussian beam profile, so a correction factor must be introduced for other beam shapes (uniform, etc.). The LIDT scaling laws are determined from empirical relationships; their accuracy is not guaranteed. Remember that absorption by optics or coatings can significantly reduce LIDT in some spectral regions. These LIDT values are not valid for ultrashort pulses less than one nanosecond in duration.

A Gaussian beam profile has about twice the maximum intensity of a uniform beam profile.

CW Laser Example
Suppose that a CW laser system at 1319 nm produces a 0.5 W Gaussian beam that has a 1/e² diameter of 10 mm. A naive calculation of the average linear power density of this beam would yield a value of 0.5 W/cm, given by the total power divided by the beam diameter:

However, the maximum power density of a Gaussian beam is about twice the maximum power density of a uniform beam, as shown in the graph to the right. Therefore, a more accurate determination of the maximum linear power density of the system is 1 W/cm.

An AC127-030-C achromatic doublet lens has a specified CW LIDT of 350 W/cm, as tested at 1550 nm. CW damage threshold values typically scale directly with the wavelength of the laser source, so this yields an adjusted LIDT value:

The adjusted LIDT value of 350 W/cm x (1319 nm / 1550 nm) = 298 W/cm is significantly higher than the calculated maximum linear power density of the laser system, so it would be safe to use this doublet lens for this application.

Pulsed Nanosecond Laser Example: Scaling for Different Pulse Durations
Suppose that a pulsed Nd:YAG laser system is frequency tripled to produce a 10 Hz output, consisting of 2 ns output pulses at 355 nm, each with 1 J of energy, in a Gaussian beam with a 1.9 cm beam diameter (1/e²). The average energy density of each pulse is found by dividing the pulse energy by the beam area:

As described above, the maximum energy density of a Gaussian beam is about twice the average energy density. So, the maximum energy density of this beam is ~0.7 J/cm².

The energy density of the beam can be compared to the LIDT values of 1 J/cm² and 3.5 J/cm² for a BB1-E01 broadband dielectric mirror and an NB1-K08 Nd:YAG laser line mirror, respectively. Both of these LIDT values, while measured at 355 nm, were determined with a 10 ns pulsed laser at 10 Hz. Therefore, an adjustment must be applied for the shorter pulse duration of the system under consideration. As described on the previous tab, LIDT values in the nanosecond pulse regime scale with the square root of the laser pulse duration:

This adjustment factor results in LIDT values of 0.45 J/cm² for the BB1-E01 broadband mirror and 1.6 J/cm² for the Nd:YAG laser line mirror, which are to be compared with the 0.7 J/cm² maximum energy density of the beam. While the broadband mirror would likely be damaged by the laser, the more specialized laser line mirror is appropriate for use with this system.

Pulsed Nanosecond Laser Example: Scaling for Different Wavelengths
Suppose that a pulsed laser system emits 10 ns pulses at 2.5 Hz, each with 100 mJ of energy at 1064 nm in a 16 mm diameter beam (1/e²) that must be attenuated with a neutral density filter. For a Gaussian output, these specifications result in a maximum energy density of 0.1 J/cm². The damage threshold of an NDUV10A Ø25 mm, OD 1.0, reflective neutral density filter is 0.05 J/cm² for 10 ns pulses at 355 nm, while the damage threshold of the similar NE10A absorptive filter is 10 J/cm² for 10 ns pulses at 532 nm. As described on the previous tab, the LIDT value of an optic scales with the square root of the wavelength in the nanosecond pulse regime:

This scaling gives adjusted LIDT values of 0.08 J/cm² for the reflective filter and 14 J/cm² for the absorptive filter. In this case, the absorptive filter is the best choice in order to avoid optical damage.

Pulsed Microsecond Laser Example
Consider a laser system that produces 1 µs pulses, each containing 150 µJ of energy at a repetition rate of 50 kHz, resulting in a relatively high duty cycle of 5%. This system falls somewhere between the regimes of CW and pulsed laser induced damage, and could potentially damage an optic by mechanisms associated with either regime. As a result, both CW and pulsed LIDT values must be compared to the properties of the laser system to ensure safe operation.

If this relatively long-pulse laser emits a Gaussian 12.7 mm diameter beam (1/e²) at 980 nm, then the resulting output has a linear power density of 5.9 W/cm and an energy density of 1.2 x 10^-4 J/cm² per pulse. This can be compared to the LIDT values for a WPQ10E-980 polymer zero-order quarter-wave plate, which are 5 W/cm for CW radiation at 810 nm and 5 J/cm² for a 10 ns pulse at 810 nm. As before, the CW LIDT of the optic scales linearly with the laser wavelength, resulting in an adjusted CW value of 6 W/cm at 980 nm. On the other hand, the pulsed LIDT scales with the square root of the laser wavelength and the square root of the pulse duration, resulting in an adjusted value of 55 J/cm² for a 1 µs pulse at 980 nm. The pulsed LIDT of the optic is significantly greater than the energy density of the laser pulse, so individual pulses will not damage the wave plate. However, the large average linear power density of the laser system may cause thermal damage to the optic, much like a high-power CW beam.

Precision Pinholes and Slits
Thorlabs offers precision pinholes with blackened stainless steel, tungsten, or gold-plated copper foils. Our pinholes with stainless steel foils are blackened on both sides for increased absorbance and are available from stock in circles from Ø1 µm to Ø2 mm and squares from 100 µm x 100 µm to 1 mm x 1 mm. Our pinholes with tungsten foils are uncoated and available with pinhole diameters from 5 µm to 2 mm. Lastly, our pinholes with gold-plated copper foils, plated with gold on one side and black-oxide coated on the reverse, are available with pinhole diameters from 5 µm to 2 mm. We also offer slits in blackened stainless steel foils from stock with slit widths from 5 to 200 µm.

If you do not see what you need among our stock pinhole and slit offerings, it is also possible to special order pinholes and slits that are made with different foil materials, have different hole sizes and shapes, incorporate multiple holes in one foil, or provide different hole configurations. Please contact Tech Support to discuss your specific needs. For more information on the properties of the bulk materials from which the pinholes are fabricated, see the table below.

Material Properties
Depending on the application, it can be important to consider the material properties of the pinhole or slit. The material used to construct the aperture can have varying levels of melting point, density, and thermal conductivity, as detailed in the table below.

• Stainless steel pinholes and slits are blackened on both sides to increase absorbance. The material properties will be predominantly that of bulk stainless steel.
• Gold-plated copper pinholes have a thin coating of gold on one side of the bulk copper foil. With a beam incident on this side, reflectance will be that of gold (95% @ 800 nm) while thermal properties will be predominantly copper-based.

Apertures Selection Guide
Aperture Type	Representative Image (Click to Enlarge)	Description	Aperture Sizes Available from Stocka
Single Precision Pinholesa		Circular Pinholes in Stainless Steel Foils	Ø1 µm to Ø2 mm
		Circular Pinholes in Tungsten Foils	Ø5 µm to Ø2 mm
		Circular Pinholes in Gold-Plated Copper Foils	Ø5 µm to Ø2 mm
		Square Pinholes in Stainless Steel Foils	100 to 1000 µm Square
Slitsa		3 mm Long Slits in Stainless Steel Foils	Slit Widths: 5 to 200 µm
Annular Apertures		Annular Aperture Obstruction Targets on Quartz Substrates with Chrome Masks	Ø300 µm or Ø2 mm Pinholes with ε Ratiosb of 0.85,  Ø1 mm Pinholes with ε Ratiosb of 0.05 0.1, or 0.85
Pinhole Wheels		Manual, Mounted or Unmounted, Chrome-Plated Fused Silica Disks with Lithographically Etched Pinholes	Each Disk has 16 Pinholes from Ø25 µm to Ø2 mm and Four Annular Apertures (Ø100 µm Hole, 50 µm Obstruction)
		Motorized Pinhole Wheels with Chrome-Plated Glass Disks with Lithographically Etched Pinholes	Each Disk has 16 Pinholes from Ø25 µm to Ø2 mm and Four Annular Apertures (Ø100 µm Hole, 50 µm Obstruction)

• Single precision pinholes and slits can be special ordered with different aperture sizes, foil materials, shapes, and hole distributions than those offered from stock. Please contact Tech Support with inquiries.
• Ratio of the Obstruction Diameter to the Pinhole Diameter