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Laser Resources

Optics Handling & Cleaning

Great care should be taken when handling infrared optics. Please note the following precautions:

  • Always wear powder-free finger cots or rubber/latex gloves when handling optics. Dirt and oil from the skin can severely contaminate optics, causing a major degradation in performance.
  • Do not use any tools to manipulate optics — this includes tweezers or picks.
  • Always place optics on supplied lens tissue for protection.
  • Never place optics on a hard or rough surface. Infrared optics can be easily scratched.
  • Bare gold or bare copper should never be cleaned or touched.
  • All materials used for infrared optics are fragile, whether single crystal or polycrystalline, large or fine grained. They are not as strong as glass and will not withstand procedures normally used on glass optics.

Due to the problems encountered when cleaning mounted optics, it is recommended that the cleaning procedures described here be performed only on unmounted optics. If cleaning must be performed on a mounted optic, refer to the instructions printed in italics and in brackets [ ]. These are additional steps that must be performed when cleaning mounted optics.

Except for Step 1 and Step 2, the cleaning procedures described here should not be used for new optics. New optics are cleaned and packaged prior to leaving II-VI to ensure their high quality condition upon receipt. If you suspect a problem with contamination, or other cosmetic defects with a new optic, please contact II-VI Infrared immediately.

Step 1 – Mild Cleaning for Light Contamination (dust, lint particles)

Use an air bulb to blow off any loose contaminants from the optic surface before proceeding to the cleaning steps. If this step does not remove the contamination, continue to Step 2.

Note:Avoid using shop air lines because they usually contain significant amounts of oil and water. These contaminants can form detrimental absorbing films on optical surfaces.

[No additional steps necessary for mounted optics.]



Step 2 – Mild Cleaning for Light Contamination (smudges, fingerprints)

Dampen an unused cotton swab or a cotton ball with acetone or isopropyl alcohol. Gently wipe the surface with the damp cotton. Do not rub hard. Drag the cotton across the surface just fast enough so that the liquid evaporates right behind the cotton. This should leave no streaks. If this step does not remove the contamination, continue to Step 3.

Note: Use only paper-bodied 100% cotton swabs and high-quality surgical cotton balls.

Reagent grade acetone and isopropyl alcohol are recommended.

[No additional steps necessary for mounted optics.]

Step 2 (alternative method) “Drop and Drag“ – Mild Cleaning for Light Contamination

(Note: The “Drop and Drag” method is not a preferred cleaning method of II-VI Infrared.)

Lay the lens tissue on the optic’s surface. Using an eyedropper, squeeze a few drops of acetone onto the lens tissue, wetting the complete optic’s diameter.

Without lifting the lens tissue, drag the lens tissue across the optic just fast enough so that the liquid evaporates behind the tissue. This should leave no streaks. If this step does not remove the contamination, continue to Step 3.

Note:Use only the lens tissue supplied in the optics cleaning kit or another high-quality lens tissue.

Reagent grade acetone is recommended.

[This method cannot be used for mounted optics.]

Step 3 – Moderate Cleaning for Moderate Contamination (spittle, oils)

Dampen an unused cotton swab or cotton ball with white distilled vinegar. Using light pressure, wipe the optic’s surface with the damp cotton. Wipe excess distilled vinegar with a clean dry cotton swab. Immediately dampen a cotton swab or cotton ball with acetone. Gently wipe the optic’s surface to remove any acetic acid. If this step does not remove the contamination, continue to Step 4.

Note:Use only paper-bodied 100% cotton swabs.

Use only high-quality surgical cotton balls that have been sorted to remove any with embedded abrasives.

White distilled vinegar with a 6% acetic acid content should be used.

[No additional steps necessary for mounted optics.]

Step 4 – Aggressive Cleaning for Severely Contaminated Optics (splatter)

Caution: Step 4 should NEVER be performed on new or unused laser optics. These steps are to be done only on optics that have become severely contaminated from use and have no acceptable results yielded from Steps 2 or 3 as previously noted.

If the thin-film coating is removed, the optic’s performance will be destroyed. A change in apparent color indicates the removal of the thin-film coating.

For severely contaminated and dirty optics, an optical polishing compound may need to be used to remove the absorbing contamination film from the optic.

A.Shake the container of polish thoroughly before opening. Pour four or five drops of polish onto a cotton ball. Gently move the cotton ball in circular patterns across the surface to be cleaned. Do not press down on the cotton ball! Let the cotton ball drag lightly across the surface under its own weight. If too much pressure is applied, the polish will quickly scratch the optic’s surface. Rotate the optic frequently to avoid excessive polishing in any one direction. Clean the optic in this manner for no more than 30 seconds. If, at any time during this step, you notice the optic’s surface change color, stop polishing immediately. This color change indicates that the outer portion of the thin-film coating is being eroded.

[For a mounted optic, a fluffed cotton swab may have to be substituted for the cotton ball if the entire optic’s surface is to be uniformly cleaned. This is especially true with small diameter optics. Be careful not to apply pressure when using a cotton swab!

For a fluffed cotton swab, take the unused cotton swab and rub it back and forth on a soft piece of foam that is free of foreign particles.]

Step 4 (continued)

B.After using the polish, wet an unused cotton ball with distilled water and gently swab the optic’s surface. Thoroughly wet the surface to remove as much of the polish residue as possible. Do not let the optic’s surface dry! This will make the remaining polish removal much more difficult.

[For a mounted optic, a fluffed cotton swab may be substituted. Try to remove as much polish residue as possible, especially near the mount’s edges.]



Step 4 (continued)

C.Quickly wet a fluffed cotton swab with isopropyl alcohol and gently clean the optic surface thoroughly. Cover the entire surface with the swab to dislodge as much polish residue as possible.

NOTE:If the optic is 2.00” or larger, a cotton ball may be substituted for the cotton swab in this step.

[For a mounted optic, place the cotton swab in the optic’s center and clean outwards in a spiral motion toward the optic’s edges.]


Step 4 (continued)

D. Wet a fluffed cotton swab with acetone and clean the optic’s surface, removing any remaining isopropyl alcohol and polish residue in the process. When performing the final cleaning with acetone, lightly drag the cotton swab across the optic, overlapping strokes until the entire surface has been wiped. Move the swab very slowly for the final strokes to assure that the acetone on the optic’s surface dries immediately behind the swab. This will eliminate streaks on the surface.

[For a mounted optic, start in the optic’s center and work outward in a spiral pattern toward the edge with a fluffed swab dampened with acetone. Use a new cotton swab dampened with acetone and run it around the outside of the optic against the mount to remove the polish residue. Repeat this step several times if necessary to assure that no polish residue is left on the optic’s edges when the cotton swab is lifted from the surface.]

[For a mounted optic, it may be impossible to remove every trace of residue from the surface, especially near the outer edge. Try to be certain any remaining residue is along the optic’s outermost edge only, and not in the center.]


The final step is to carefully examine the optic’s surface under good light in front of a black background. Any visible polish residue should be removed by repeating steps 4B-4D as many times as required.


Contamination and damage types, such as metal splatter, pits, etc, cannot be removed. If the optic shows the contamination or damage mentioned, it will probably need to be replaced.


Handling & Cleaning Procedure

1 Micron Laser Optics Cleaning Kit
CO2 Laser Optics Cleaning Kit







Laser Marked


As Generated








Angle of Incidence




Anti-Reflection Coating








Broadband Anti-Reflection Coating


Outside Diameter


Beam Combiner


Oxygen Free High Conductivity




Optical Grade


Clear Aperture (coated)


Partial Reflector






Cadmium Telluride




Customer Supplied Mount








Center Thickness














Single Crystal


Dual Wavelength Anti-Reflection Coating










Sufficient Material to Yield


Diamond-Like Coating


Single Point Turned






Effective Focal Length




Edge Thickness




Edge Thickness Variation


View Polished


Fine Grind








Focal Length


Working Distance


Fine Shine




Gallium Arsenide






Witness Sample


Inside Diameter


Width and/or Length




Zinc Selenide




Zinc Sulfide



Zinc Sulfide MultiSpectral



The industry’s lowest-absorption CO2 laser lens.Since its beginning in 1971, II-VI has played a key role in developing optical materials and coatings that enabled the CO2 laser to emerge into a leading technology for materials processing, and for applications in fields as diverse as laser surgery, laser imaging, target acquisition, and surveillance.CO2 laser technology advancements allowed lasers — with power levels exceeding 1 kW — to develop in the early 1970s. The corresponding need in understanding optical materials and optical coatings was evident.High-power infrared lasers performance, including high-energy density waveguide lasers, depends heavily upon the absorption control levels in optical substrates, their thin-film coatings, and interfaces. II-VI is the leader in infrared laser optics technology.

Absorption in Laser Optics

Contamination due to foreign materials on the optic’s surface includes dust, oil, grease, fingerprints, and hydrocarbons. These contaminants, if deposited on the optic’s surface, may lead to absorption and shorten optic lifespans and efficiency.Localized heating, caused by contamination, can lead to “thermal runaway” in high-power laser optics. High temperatures create an increase in free carriers within the bulk material which increases absorption. This process reaches an avalanche state, and thermal runaway commences at > 50° C for Ge, and > 200° C for ZnSe and GaAs.Surface imperfections also cause absorption and can include:

  • Scratches
  • Pits or digs
  • Imbedded polishing abrasives
  • Pinholes in coatings
  • Inclusions in coatings

These surface defects act as damage sites which suffer degradation due to intense perturbations in the electric field surrounding the sites.

Absorption Effects in CO2 Lasers

The CO2 wavelength absorption level coupled with the optic thermal conduction characteristics and its mount are important in determining the laser system’s performance and optic’s lifespan.While the source and control of factors contributing to absorption are complex, the results are clear and include:

  • Decreased output power
  • Fluctuations in output power
  • Mode instability
  • Focal point drifting
  • Coating failures
  • External cavity optics failures (due to output coupler thermal lensing or beam delivery system contamination)

All these failure mechanisms are the result of thermal lensing (the actual change of an optic’s physical characteristics due to absorption).The thermal lensing effect on the beam mode is increased further by a change in the material’s refractive index due to temperature. This latter and more significant effect induces additional optical distortion in the transmitted beam.

Testing to Ensure Low Absorptivity

II-VI was the first IR optics manufacturer to establish a laser vacuum calorimetry test facility for measuring absorption in commercial CO2 laser optics.In laser calorimetry, optic samples are mounted in a vacuum for thermal isolation. The sample is then irradiated with a CO2 laser beam, while thermocouples monitor the sample temperature rise. The laser beam is then turned off and the sample is cooled. By precisely measuring the sample mass, the laser beam incident power, and the heating and cooling slopes generated during the test, the total sample absorption (as a percentage of incident laser power) is determined.To maintain the leadership in quality and low-absorption coatings, the laser calorimetry system regularly undergoes calibration testing and refinement by II-VI’s technical staff.This test facility was the first of a number of industry leading innovations which keeps II-VI at the forefront of CO2 laser optics technology.

Factors Affecting Absorption

  • Substrate bulk absorption
  • Coating absorption
  • Surface contamination
  • Surface deterioration
Aspheric Lens Reference

The use of aspheric surfaces in the optical systems design allows the designer to achieve better spot size performance, or alternatively achieve similar performance while using fewer elements in the system. These aspheric surfaces are extremely difficult to fabricate using conventional polishing processes. Our diamond-turning facility at II-VI includes two-axis machines which can produce precision optical finishes with aspheric geometry. Infrared materials suitable for this machining process are germanium, zinc selenide, zinc sulfide, and silicon.The sketch below shows a plano-convex aspheric lens element with the aspheric curve parameters definition.Asperic Lens Parameterswhere,

  • R is radius of curvature at vertex(base radius)
  • K is conic constant
  • A4…A20 is Aspheric coefficient

For single element lens designs, the designer may use an aspheric surface to correct for spherical aberration, thus the theoretical spot size is limited only by diffraction. The table below shows the theoretical spot size for 2.50” focal length lenses and a 21 mm diameter Gaussian beam at 1/e2 points and an M2 value of 1.

Lens Type Theoretical Spot Size
Choosing the Right Focusing Lens

CASE 1: Determining the optimum input beam diameter when lens focal length is fixed.

Often, there are constraints on lens focal length due to system mechanical considerations. For instance, there may be a lower limit on the distance from the focusing lens to the workpiece. In this situation, it’s most practical to pick a lens with a focal length that meets the system’s mechanical constraints, and then alter the input beam diameter to the lens to achieve a minimum focal spot size.

For determining the input beam diameter, which will provide minimum spot size, we take the equation for spot size, differentiate it with respect to beam diameter, and then set it equal to zero to find the minimum value. This yields the following equation:

Optimum Beam Diameter

Referring back to our previous example, using a ZnSe best form meniscus lens with focal length constrained to be 5.00” or 127 mm, we get an optimum input beam diameter of 26 mm. Inserting this value into the spot size equation yields a spot size of 86µm, as we obtained by reading the graph in the “Determing Spot Size” section. If we perform the calculation for a 5.00” focal length plano-convex ZnSe lens, we get an optimum input beam diameter of 24 mm, which provides a 96µm focus spot diameter.

If the input beam diameter obtained from this calculation does not closely match the existing beam diameter in the system, then expand or contract the laser beam to this size. The beam can be expanded or contracted using a beam expander/condenser, or by constructing a beam expander/condenser using individual lenses.

CASE 2: Determining the optimum focal length when lens input beam diameter is fixed.

If it’s impossible or undesirable to alter the system’s beam diameter, then knowing what focal length to use to produce a minimum spot size is beneficial.

To determine the focal length which will provide minimum spot size, we again take the equation for spot size, this time differentiating it with respect to focal length, and then setting it equal to zero to find the minimum value. This yields the following equation:

Once the optimum focal length is chosen, choose the stock lens with the focal length closest to the optimum value, or for more critical applications, II-VI can readily fabricate an optic to the exact focal length and tolerances required.

As seen from the preceding discussion, there is a limit on the focus spot size which can be achieved when either focal length or input beam diameter is constrained. If the minimum spot size from the calculation is larger than required for the application at hand, then there is no choice but to change some optical system parameters.


With higher power CO2 lasers, it is not generally advisable to use a lens with a diameter greater than 1.5 times the beam diameter (1/e2). Ratios greater than this increase the chance of inducing thermal distortions in the lens. This is caused by too great a thermal gradient across the optic as a result of the greater distance between the heated central beam region and the cooler edge of the lens.

Determining Spot Size

Minimum spot size for a given lens is obtained by balancing the effects of diffraction and spherical aberration. As an example, the spot size due to diffraction and spherical aberration for a 5.00” focal length meniscus ZnSe lens is plotted as a input beam diameter function in the graph below. A perfectly diffraction limited input beam (M2=1) is assumed. Also plotted is the sum of the aberration and diffraction spot sizes.

Spot Size Aberration: Spot size due to aberration and diffraction
The graph shows that spot size obtained by summing the aberration and diffraction contributions reaches a minimum value about 85µm at an input beam diameter approximately 25 mm. While simply summing the aberration and diffraction contributions may not be rigorously correct, it does provide what is probably a worst case estimate for actual spot size, and is generally an adequate criteria for choosing a lens. To summarize:

Spot Size Equation
The value of k is given for several materials at 10.6µm in the following table

Spherical Aberration Table

Optical Formulas


Snell’s Law
Snell’s Law Formula
SAG (Sagitta) of a Spherical Surface
SAG (Sagitta) Formula
Thick Lens Equation
Thick Lens Equation
Displacement Through Parallel Plate
Parallel Plate Displacement Formula
Depth of Focus (DOF)
Depth of Focus Formula
Bevel Face Width (BFW)
Bevel Face Width Formula
Deviation Through Small Wedge
Wedge Displacement Formula
Converting Between Waves and Fringes
(Single Wavelength)Converting Waves and Fringes Formula (Single Wavelength)
Converting Between Waves and Fringes
(2 Different Wavelengths)
Converting Waves and Fringes Formula (Different Wavelengths)
ETV (Edge Thickness Variation) and Wedge
ETV (Edge Thickness Variation) and Wedge Formula

Spot Size
Spot Size Formula


Lens Shape

As seen from the formula for spot size, the diffraction contribution to spot size is independent of lens shape, while the aberration contribution is dependent on lens shape through the parameter k. Thus, it is mainly when the aberration contribution becomes significant, which occurs at low f-numbers, that lens shape becomes important.

II-VI offers best form meniscus, plano-convex, and aspheric lenses. The prime advantage of plano-convex lenses is lower cost, whereas meniscus lenses can provide better performance. Thus, determining which lens shape is appropriate for a specific application is a tradeoff between the cost and performance factors. To make this evaluation, formulas are used to calculate the spot size for the two different lens shapes, shown in the example of the 5.00” focal length lens in Choosing the Right Focusing Lens.In some cases, calculating exact spot size is not possible.

This is true when the laser contains higher order modes, which can be difficult to accurately detect and analyze as to their effect on lens performance. Under these circumstances, use the general rule that when operating below f/5, the meniscus lens will yield demonstrably better performance. For f-numbers between 5 and 10, the performance differences between the two lens shapes are marginal. Above f /10, it is unlikely there is any significant difference in lens performance.

Lens Reference

All lenses, regardless of their shape, share certain common characteristics. The most important is focal length. It is critical to understand just how focal length is measured and how the lens focus point is affected through various factors.

Focal Length

As illustrated in Figure 1, three different values describe lens focal length. The most common is the effective focal length (EFL), which determines the lens magnification power and is the measure most commonly used describing a lens focal length in specification tables.

The EFL is calculated by formulae and relates to a non-physical “principal plane” in or near the lens. The non-physical plane position varies with the lens design and cannot be located from visual inspection. The back focal length (BFL) and working distance (WD) relate the focal point to physical points on the lens surface which are easily observed.

Only when presented with an object at infinity — which corresponds to a perfectly collimated input — will a lens form a spot at an image distance corresponding to its EFL. For any other object distance, the image forms further from the lens than the focal length. Ideally, image distance is related to object distance by the formula:

EFL Formula

where o is the distance from the object to the first principal point of the lens, i is the distance from the second principal point to the image, and f is the lens focal length. The geometry of this situation is shown on Figure 2. When dealing with lasers, the object is generally considered to be the beam waist. Laser manufacturers provide data on the beam waist location relative to the laser so the image distance can be readily calculated.

This relationship is important because in many laser beam delivery systems — “flying optics” systems — the lens system moves relative to the laser’s beam waist during operation. As a result, the focal spot position will also shift.

There are several real-world effects which influence focal position for a lens, especially in high-power laser systems. Laser power absorption during operation causes the lens to heat up. The temperature change leads to a change in index of refraction, the optic’s thermal expansion, and stress induced changes in index of refraction (photoelastic effects). The result is thermal lensing which causes an operational change in focal length.

Thermal Stress: Starting clockwise at the top left: The progression of a thermally stressed lens. Thermal Stress: Starting clockwise at the top left: The progression of a thermally stressed lens.



Polarization is an important optical property inherent in all laser beams. Brewster windows, reflective phase retarders, and absorbing thin-film reflectors use the advantage of polarization. On the other hand, it can cause troublesome and sometimes unpredictable results when ignored. Since virtually all laser sources exhibit some degree of polarization, understanding this effect is necessary in order to specify components properly. The following text gives a basic polarization definition and presents the polarization types most commonly encountered.

Light is a transverse electromagnetic wave; this means that the electric and magnetic field vectors point perpendicular to the direction of wave travel. (Figure 1.) When all the electric field vectors for a given wavetrain lie in a plane, the wave is said to be plane or linearly polarized. The orientation of this plane is the direction of polarization.

Unpolarized light refers to a wave collection which has an equal distribution of electric field orientations for all directions. (Figure 2.) While each individual wavetrain may be linearly polarized, there’s no preferred direction of polarization when all the waves are averaged together.

Randomly polarized light is exactly what it says; the light is plane polarized, but the direction is unknown, and may vary with time. Random polarization causes problems in optical systems since some components are polarization sensitive. If the polarization state changes with time, then the components’ transmission, reflection, and/or absorption characteristics will also vary with time.

Polarization is a vector that has both direction and amplitude. Like any vector, it’s defined in an arbitrary coordinate system as the sum of orthogonal components. In Figure 3, we see a plane polarized wave which points at 45° to the axes of our coordinate system. Thus, when described in this coordinate system, it has equal x and y components. If we then introduce a phase difference of 90° (or one-quarter wavelength) between these components, the result is a wave in which the electric field vector has a fixed amplitude but whose direction varies as we move down the wavetrain. (Figure 4.) Such a wave is said to be circularly polarized since the tip of the polarization vector traces out a circle as it passes a fixed point.If we have two wavetrains with unequal amplitude and with a quarter-wave phase difference, then the result is elliptical polarization. The tip of the polarization vector will trace out an ellipse as the wave passes a fixed point. The ratio of the major to the minor axis is called the ellipticity ratio of the polarization.Always state the polarization orientation when ordering optical coatings for use at non-normal incidence. If you are unsure about how to determine the polarization state of your source, please contact our applications engineers for assistance.

Polarization: Figure 3: A wave is resolved into two equal components, each at 45° to the orginal (top). Introducing a quarter-wave phase difference between these components produces a result in a wave whose amplitude is constant (bottom), but whose polarization vector rotates. Polarization: Figure 3: Polarization: Figure 4: For s-polarization, the input polarization is perpendicular to the plane (shown in color) containing the input and output beams. For p-polarization, the input polarization is parallel to the plane (shown in color) containing the input and output beams. Polarization: Figure 3: Polarization: Single Surface Reflectivity: A graph of single surface reflectance for s- and p-polarization as a function of angle of incidence for ZnSe at 10.6µm.

When light strikes an optical surface, such as a beamsplitter, at a non-perpendicular angle, the reflection and transmission characteristics depend upon polarization. In this case, the coordinate system we use is defined by the plane containing the input and reflected beams. Light with a polarization vector lying in this plane is called p-polarized, and light, which is polarized perpendicular to this plane, is called s-polarized. Any arbitrary state of input polarization can be expressed as a vector sum of these s and p components.

To understand the significance of s and p polarizations, examine the graph which shows the single surface reflectance as a function of angle of incidence for the s and p components of light at a wavelength of 10.6µm striking a ZnSe surface. Note that while the reflectance of the s component steadily increases with angle, the p component at first decreases to zero at 67° and then increases after that. The angle at which the p reflectance drops to zero is called Brewster’s Angle. This effect is exploited in several ways to produce polarizing components or uncoated windows which have no transmission loss such as the Brewster windows.

Polarization State: Polarization state is particularly important in laser cutting applications. See our reflective phase retarders, which provide the optimum polarization for laser cutting. Polarization State: Polarization Summary.
Pressure Loading

It’s not unusual to use a lens or window as the port between a vacuum chamber and the outside, or to encounter a situation where an optic must withstand pressure loading. Given the cost of most infrared optics, as well as the potential safety issues, it’s important that the optic under pressure be sufficiently thick to withstand the loading without breaking. On the other hand, since increasing thickness reduces optical transmission, it’s desirable to minimize thickness for optical considerations.

The formulae equations given in the following text show how to calculate the necessary thickness for an optic under pressure. It is assumed that the window is unclamped and supported by a flat flange around its edge. Other important factors which may affect the required thickness for a given application, but which are not included in this treatment, include:

  • Mounting flange size
  • Stress resulting from mounting or sealing
  • Flange clamping stresses
  • Mounting flange flatness
  • Stress due to thermal expansion
  • Vibration effects
  • Pressure cycling or surges
  • Thermal shock/cycling
  • Mounting surface rigidity
  • Mounting surface roughness
  • Optic edge roughness
  • Desired optical specifications

Since it’s not possible to include all these factors in our analysis, it’s common practice to include a “safety factor” in the equation which increases the predicted thickness to an amount which should be adequate for most applications. Doing this yields the following equations.For a circular window the minimum thickness is:

Polarization: Figure 2: For a rectangular window, the minimum thickness is given by:

M Values for Common II-VI Materials

Polycrystalline Optical Grade CVD Diamond
8,000 psi
10,000 psi
15,000 psi
13,500 psi
20,000 psi
29,000-145,000 psi psi
Spherical Aberration

When collimated, on-axis light is focused by an ideal lens. All light rays cross the optical axis at a single point, forming a spot with a diameter determined by the diffraction formula in the Spot Size tutorial. However, many lenses exhibit a phenomenon termed spherical aberration. This causes light rays impinging near the lens edge to cross the optical axis closer to the lens than those going through the lens center, as shown in the graphic at left.

Spherical aberration increases spot size and causes best focus to occur at a different location than the calculated effective focal length. Spherical aberration, a function of several factors, includes lens shape, orientation, and index of refraction. For example, the best shape for a crown glass lens used to focus visible light to a minimum spot size is a biconvex lens. Conversely, for a ZnSe lens used at 10.6µm, the best design for a minimum spot size is a meniscus lens.

The exact spot size for a given lens under specific circumstances is determined by ray tracing; however, a useful formula for estimating the spot size due to spherical aberration in a best form lens is:


  • f is lens focal length
  • D is input beam diameter at the lens (at the 1/e2 point)
  • k is an index of refraction function

The most important point to note from the preceding formula is that the spot size due to spherical aberration is proportional to the cube of the beam diameter and inversely proportional to the square of the focal length. Thus, as the laser beam diameter decreases for a given lens, spot size rapidly decreases due to spherical aberration. Similarly, as focal length increases for a given laser beam diameter, the spherical aberration spot size is again reduced. For all the materials listed, the k value is significantly smaller for meniscus lenses than for plano-convex lenses. Thus, when spherical aberration is significant, the meniscus lens will perform better than the plano-convex lens.

The value of k is given for several materials at 10.6µm in the following table:
Spot Size
Spot Size Spiricon (1): The image above, captured using a Spiricon® Pyrocam™ III camera, is a CO2 laser beam focused with a “Cross Hair” lens. The lens surface is divided into four quadrants. Each quadrant has a slightly tilted cylindrical parabolic shape. This surface shape resSpot Size Spiricon (2): The image above, captured using a Spiricon® Pyrocam™ III camera, is a CO2 grating tuned laser beam near the laser output. Note the beam intensity is approximately Gaussian in distribution.

Cutting applications require focusing a laser beam to a minimum spot size. This is necessary to maximize the energy density and produce precision cuts. Many factors affect spot size. The most important are:

  • Laser mode (M2)
  • Diffraction
  • Spherical aberration

Lens shape and focal length determine the latter two factors. Of course, laser mode is determined by the laser and beam delivery system. II-VI offers plano-convex, meniscus, and aspheric lenses in a wide variety of standard focal lengths and diameters. The following images show how these three factors affect spot size, and how to calculate spot size for plano-convex, meniscus, and aspheric lenses. The notes outline a simple procedure for picking the right lens for a given application.

Diffraction Diffraction, a natural and inescapable result of the wave nature of light, is present in all optical systems, and determines the ultimate theoretical limit on their performance. Diffraction causes light beams to spread transversely as they propagate. If a “perfect” lens is used to focus a collimated laser beam, the spot size is limited only by diffraction. Spot size formula:

Spot Size Formula

This equation is used to determine the spot size produced by an aspheric lens. Diffraction’s most important factor is that the spot size increases linearly with focal length but is inversely proportional to beam diameter. Thus, as the input laser beam diameter increases for a given lens, spot size decreases due to lower diffraction. Also, as focal length decreases for a given laser beam diameter, spot size again decreases.

M2 – Laser Mode Parameter

As seen in the previous formula for diffraction, focal spot size is directly proportional to the laser mode parameter, M2. M2 expresses how quickly a given beam diverges while propagating; a perfect TEM00 laser beam has M2=1. This parameter is measured by advanced instruments, or is obtained from laser manufacturers’ specifications.