10 Things to Consider When Buying Plano Concave Cylindrical Lens

Laser Induced Damage Threshold Tutorial

The following is a general overview of how laser induced damage thresholds are measured and how the values may be utilized in determining the appropriateness of an optic for a given application. When choosing optics, it is important to understand the Laser Induced Damage Threshold (LIDT) of the optics being used. The LIDT for an optic greatly depends on the type of laser you are using. Continuous wave (CW) lasers typically cause damage from thermal effects (absorption either in the coating or in the substrate). Pulsed lasers, on the other hand, often strip electrons from the lattice structure of an optic before causing thermal damage. Note that the guideline presented here assumes room temperature operation and optics in new condition (i.e., within scratch-dig spec, surface free of contamination, etc.). Because dust or other particles on the surface of an optic can cause damage at lower thresholds, we recommend keeping surfaces clean and free of debris. For more information on cleaning optics, please see our Optics Cleaning tutorial.

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Testing Method

Thorlabs' LIDT testing is done in compliance with ISO/DIS  and ISO specifications.

First, a low-power/energy beam is directed to the optic under test. The optic is exposed in 10 locations to this laser beam for 30 seconds (CW) or for a number of pulses (pulse repetition frequency specified). After exposure, the optic is examined by a microscope (~100X magnification) for any visible damage. The number of locations that are damaged at a particular power/energy level is recorded. Next, the power/energy is either increased or decreased and the optic is exposed at 10 new locations. This process is repeated until damage is observed. The damage threshold is then assigned to be the highest power/energy that the optic can withstand without causing damage. A histogram such as that below represents the testing of one BB1-E02 mirror.

The photograph above is a protected aluminum-coated mirror after LIDT testing. In this particular test, it handled 0.43 J/cm2 ( nm, 10 ns pulse, 10 Hz, Ø1.000 mm) before damage. Example Test Data Fluence # of Tested Locations Locations with Damage Locations Without Damage 1.50 J/cm2 10 0 10 1.75 J/cm2 10 0 10 2.00 J/cm2 10 0 10 2.25 J/cm2 10 1 9 3.00 J/cm2 10 1 9 5.00 J/cm2 10 9 1

According to the test, the damage threshold of the mirror was 2.00 J/cm2 (532 nm, 10 ns pulse, 10 Hz, Ø0.803 mm). Please keep in mind that these tests are performed on clean optics, as dirt and contamination can significantly lower the damage threshold of a component. While the test results are only representative of one coating run, Thorlabs specifies damage threshold values that account for coating variances.

Continuous Wave and Long-Pulse Lasers

When an optic is damaged by a continuous wave (CW) laser, it is usually due to the melting of the surface as a result of absorbing the laser's energy or damage to the optical coating (antireflection) [1]. Pulsed lasers with pulse lengths longer than 1 µs can be treated as CW lasers for LIDT discussions.

When pulse lengths are between 1 ns and 1 µs, laser-induced damage can occur either because of absorption or a dielectric breakdown (therefore, a user must check both CW and pulsed LIDT). Absorption is either due to an intrinsic property of the optic or due to surface irregularities; thus LIDT values are only valid for optics meeting or exceeding the surface quality specifications given by a manufacturer. While many optics can handle high power CW lasers, cemented (e.g., achromatic doublets) or highly absorptive (e.g., ND filters) optics tend to have lower CW damage thresholds. These lower thresholds are due to absorption or scattering in the cement or metal coating.

Pulsed lasers with high pulse repetition frequencies (PRF) may behave similarly to CW beams. Unfortunately, this is highly dependent on factors such as absorption and thermal diffusivity, so there is no reliable method for determining when a high PRF laser will damage an optic due to thermal effects. For beams with a high PRF both the average and peak powers must be compared to the equivalent CW power. Additionally, for highly transparent materials, there is little to no drop in the LIDT with increasing PRF.

In order to use the specified CW damage threshold of an optic, it is necessary to know the following:

1. Wavelength of your laser
2. Beam diameter of your beam (1/e2)
3. Approximate intensity profile of your beam (e.g., Gaussian)
4. Linear power density of your beam (total power divided by 1/e2 beam diameter)

Thorlabs expresses LIDT for CW lasers as a linear power density measured in W/cm. In this regime, the LIDT given as a linear power density can be applied to any beam diameter; one does not need to compute an adjusted LIDT to adjust for changes in spot size, as demonstrated by the graph to the right. Average linear power density can be calculated using the equation below. 

The calculation above assumes a uniform beam intensity profile. You must now consider hotspots in the beam or other non-uniform intensity profiles and roughly calculate a maximum power density. For reference, a Gaussian beam typically has a maximum power density that is twice that of the uniform beam (see lower right).

Now compare the maximum power density to that which is specified as the LIDT for the optic. If the optic was tested at a wavelength other than your operating wavelength, the damage threshold must be scaled appropriately. A good rule of thumb is that the damage threshold has a linear relationship with wavelength such that as you move to shorter wavelengths, the damage threshold decreases (i.e., a LIDT of 10 W/cm at nm scales to 5 W/cm at 655 nm):

While this rule of thumb provides a general trend, it is not a quantitative analysis of LIDT vs wavelength. In CW applications, for instance, damage scales more strongly with absorption in the coating and substrate, which does not necessarily scale well with wavelength. While the above procedure provides a good rule of thumb for LIDT values, please contact Tech Support if your wavelength is different from the specified LIDT wavelength. If your power density is less than the adjusted LIDT of the optic, then the optic should work for your application. 

Please note that we have a buffer built in between the specified damage thresholds online and the tests which we have done, which accommodates variation between batches. Upon request, we can provide individual test information and a testing certificate. The damage analysis will be carried out on a similar optic (customer's optic will not be damaged). Testing may result in additional costs or lead times. Contact Tech Support for more information.

Pulsed Lasers

As previously stated, pulsed lasers typically induce a different type of damage to the optic than CW lasers. Pulsed lasers often do not heat the optic enough to damage it; instead, pulsed lasers produce strong electric fields capable of inducing dielectric breakdown in the material. Unfortunately, it can be very difficult to compare the LIDT specification of an optic to your laser. There are multiple regimes in which a pulsed laser can damage an optic and this is based on the laser's pulse length. The highlighted columns in the table below outline the relevant pulse lengths for our specified LIDT values.

Pulses shorter than 10-9 s cannot be compared to our specified LIDT values with much reliability. In this ultra-short-pulse regime various mechanics, such as multiphoton-avalanche ionization, take over as the predominate damage mechanism [2]. In contrast, pulses between 10-7 s and 10-4 s may cause damage to an optic either because of dielectric breakdown or thermal effects. This means that both CW and pulsed damage thresholds must be compared to the laser beam to determine whether the optic is suitable for your application.

Pulse Duration t < 10-9 s 10-9 < t < 10-7 s 10-7 < t < 10-4 s t > 10-4 s Damage Mechanism Avalanche Ionization Dielectric Breakdown Dielectric Breakdown or Thermal Thermal Relevant Damage Specification No Comparison (See Above) Pulsed Pulsed and CW CW

When comparing an LIDT specified for a pulsed laser to your laser, it is essential to know the following:

1. Wavelength of your laser
2. Energy density of your beam (total energy divided by 1/e2 area)
3. Pulse length of your laser
4. Pulse repetition frequency (prf) of your laser
5. Beam diameter of your laser (1/e2 )
6. Approximate intensity profile of your beam (e.g., Gaussian)

The energy density of your beam should be calculated in terms of J/cm2. The graph to the right shows why expressing the LIDT as an energy density provides the best metric for short pulse sources. In this regime, the LIDT given as an energy density can be applied to any beam diameter; one does not need to compute an adjusted LIDT to adjust for changes in spot size. This calculation assumes a uniform beam intensity profile. You must now adjust this energy density to account for hotspots or other nonuniform intensity profiles and roughly calculate a maximum energy density. For reference a Gaussian beam typically has a maximum energy density that is twice that of the 1/e2 beam.

Now compare the maximum energy density to that which is specified as the LIDT for the optic. If the optic was tested at a wavelength other than your operating wavelength, the damage threshold must be scaled appropriately [3]. A good rule of thumb is that the damage threshold has an inverse square root relationship with wavelength such that as you move to shorter wavelengths, the damage threshold decreases (i.e., a LIDT of 1 J/cm2 at nm scales to 0.7 J/cm2 at 532 nm):

You now have a wavelength-adjusted energy density, which you will use in the following step.

Beam diameter is also important to know when comparing damage thresholds. While the LIDT, when expressed in units of J/cm², scales independently of spot size; large beam sizes are more likely to illuminate a larger number of defects which can lead to greater variances in the LIDT [4]. For data presented here, a <1 mm beam size was used to measure the LIDT. For beams sizes greater than 5 mm, the LIDT (J/cm2) will not scale independently of beam diameter due to the larger size beam exposing more defects.

The pulse length must now be compensated for. The longer the pulse duration, the more energy the optic can handle. For pulse widths between 1 - 100 ns, an approximation is as follows:

Use this formula to calculate the Adjusted LIDT for an optic based on your pulse length. If your maximum energy density is less than this adjusted LIDT maximum energy density, then the optic should be suitable for your application. Keep in mind that this calculation is only used for pulses between 10-9 s and 10-7 s. For pulses between 10-7 s and 10-4 s, the CW LIDT must also be checked before deeming the optic appropriate for your application.

Please note that we have a buffer built in between the specified damage thresholds online and the tests which we have done, which accommodates variation between batches. Upon request, we can provide individual test information and a testing certificate. Contact Tech Support for more information.

[1] R. M. Wood, Optics and Laser Tech. 29, 517 ().
[2] Roger M. Wood, Laser-Induced Damage of Optical Materials (Institute of Physics Publishing, Philadelphia, PA, ).
[3] C. W. Carr et al., Phys. Rev. Lett. 91, ().
[4] N. Bloembergen, Appl. Opt. 12, 661 ().

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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 LIDT Calculator button. 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.

Figure 71A  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 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 Figure 71A. 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 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 ( nm / 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 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.

Plano-Convex Lenses are the best choice for focusing parallel rays of light to a single point, or a single line in the case of cylindrical lenses. This lens can be used to focus, collect and collimate light. It is the most economical choice for demanding applications. The asymmetry of these lenses minimizes spherical aberration in situations where the object and image are located at unequal distance from the lens. The optimum case is where the object is placed at infinity (parallel rays entering lens) and the final image is a focused point. Although infinite conjugate ratio (object distance/image distance) is optimum, plano-convex lenses will still minimize spherical aberration up to approximately 5:1 conjugate ratio. For the best performance, the curved surface should face the largest object distance or the infinite conjugate to reduce spherical aberration.

Bi-Convex Lenses are the best choice where the object and image are at equal or near equal distance from the lens. When the object and image distance are equal (1:1 magnification), not only is spherical aberration minimized, but also coma, distortion, and chromatic aberration are identically canceled due to the symmetry. Bi-convex lenses function similarly to plano-convex lenses in that they have a positive focal length, and focus parallel rays of light to a point. Both surface are spherical and have the same radius of curvature, thereby minimizing spherical aberration. As a guideline, bi-convex lenses perform within minimum aberration at conjugate ratios between 5:1 and 1:5. Outside this magnification range, plano-convex lenses are usually more suitable.

Plano-Concave Lenses are the best choice where object and image are at absolute conjugate ratios greater than 5:1 and less than 1:5 to reduce spherical aberration, coma, and distortion. Plano-Concave lenses bend parallel input rays so they diverge from one another on the output side of the lens and hence have a negative focal length. The spherical aberration of the Plano-Concave lenses is negative and can be used to balance aberrations created by other lenses. Similar to the Plano-Convex lenses, the curvature surface should face the largest object distance or the infinite conjugate (except when used with high-energy lasers where this should be reversed to eliminate the possibility of a virtual focus) to minimize spherical aberration.

Bi-Concave Lenses are the best choice where object and image are at absolute conjugate ratios closer to 1:1 with converging input beam. The output rays appear to be diverging from a virtual image located on the object side of the lens; the distance from this virtual point to the lens is known as the focal length. Similar to the Plano-Concave lenses, the Bi-concave lenses have negative focal lengths, thereby causing collimated incident light to diverge. Bi-Concave lenses have equal radius of curvature on both side of the lens. They are generally used to expand light or increase focal length in existing systems, such as beam expanders and projection systems.

Positive Meniscus Lenses are designed to minimize spherical aberration and are generally used in small f/number applications (f/number less than 2.5). The Positive Meniscus Lenses have a larger radius of curvature on the convex side, and a smaller radius of curvature on the concave side. They are thicker at the center compared to the edges. Positive meniscus can maintain the same angular resolution of the optical system while decreasing the focal length of the other lens, resulting a tighter focal spot size. A positive meniscus lens can be used to shorten the focal length and increase the numerical aperture of an optical system when paired with another lens. For the best performance, the curved surface should face the largest object distance or the infinite conjugate to reduce spherical aberration.

Spherical Lens Material Options

Lens Type N-BK7 UV Fused Silica CaF2 MgF2 ZnSe Crown/Flint Plano-Convex Bi-Convex Plano-Concave Bi-Concave Achromatic Doublet Cylindrical Lenses Plano-Convex Plano-Concave

Coatings

Optical coatings are generally applied as a combination of thin film layers on optical components to achieve desired reflection/transmission ratio. Important factors that affect this ratio include the material property used to fabricate the optics, the wavelength of the incident light, the angle of incidence light, and the polarization dependence. Coating can also be used to enhance performance and extend the lifetime of optical components, and can be deposited in a single layer or multiple layers, depending on the application. Newport’s multilayer coatings are incredibly hard and durable, with high resistance to scratch and stains.

Anti-Reflection Coating (AR coating)

Newport offers an extensive range of antireflection coatings covering the ultraviolet, visible, near infrared, and infrared regions. For most uncoated optics, approximately 4% of incident light is reflected at each surface, resulting significant losses in transmitted light level. Utilizing a thin film anti-reflection coating can improve the overall transmission, as well as minimizing stray light and back reflections throughout the system. The AR coating can also prevent the corresponding losses in image contrast and lens resolution caused by reflected ghost images superimposed on the desired image.

Newport offers three types of AR coating designs to choose from, the Single Layer Magnesium Fluoride AR coating, the Broadband Multilayer AR coating, and Laser Line AR V-coating. A single layer Magnesium Fluoride AR coating is the most common choice that offers extremely broad wavelength range at a reasonable price. It is standard on achromats and optional on our N-BK7 plano-convex spherical lenses and cylindrical lenses. Comparing to the uncoated surface, the MgF2 provides a significant improvement by reducing the reflectance to less than 1.5%. It works extremely well over a wide range of wavelengths (400 nm to 700 nm) at angles of incidence less than 15 degrees.

Broadband Multilayer AR coating improves the transmission efficiency of any lens, prism, beam-splitter, or windows. By reducing surface reflections over a wide range of wavelengths, both transmission and contrast can be improved. Different ranges of Broadband Multilayer AR coating can be selected, offering average reflectance less than 0.5% per surface. Coatings perform efficiently for multiple wavelengths and tunable laser, thereby eliminating the need for several sets of optics.

V-coatings offer the lowest reflectance for maximum transmission. With its high durability and high damage resistance, Laser line AR V-coating can be used at almost any UV-NIR wavelength with average reflectance less than 0.25% at each surface for a single wavelength. Valuable laser energy is efficiently transmitted through complex optical systems rather than loss to surface reflection and scattering. The trade off to its superior performance is the reduction in wavelength range. AR.33 for nm is available from stock on most Newport lenses. All other V-coating can be coated on a semi-custom basis.

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Coating Wavelength Range
(nm) Reflectance Cost Features AR.10
Broadband
245–440 Ravg <0.5% Moderate Only available on UV fused silica lenses MgF2
Broadband
Broadband
400–700 Ravg <1.5% Low Available on achromats, KPX series, and Cylindrical lenses AR.14
430–700 Ravg <0.5% Moderate Best choice for broadband visible applications AR.15
Broadband
250–700 Ravg <1.5% Moderate Great choice for broadband UV to visible applications AR.16
Broadband
650– Ravg <0.5% Moderate Excellent for NIR laser diode applications AR.18
Broadband
– Ravg <0.5% Moderate Ideal for telecom laser diode applications V-Coat Multilayer, AR.27 Laser Line
532 Rmax <0.25% High Highest transmission at a single wavelength V-Coat Multilayer, AR.28 Laser Line
632.8 Rmax <0.25% High Highest transmission at a single wavelength AR.33
Laser Line
Rmax <0.25% Moderate Highest transmission at a single wavelength