# Technical Notes: Laser Optics - General explanations

## Overview

> Part number

> Datasheets, technical drawings and CAD-files

> Anti-reflective and low-absorption coatings

> Design wavelength

> Absorption and thermal focus shift

> Working distance

> Diffraction value M²

> Reversed Mode

> Beam diameter

> Apodisation factor

> Spot size (1/e²)

> Rayleigh length

> Fiber imaging

## Part number

The part number is unique for every lens design. Special requests with changes to catalog lenses are assigned a new part number, so repeated purchase with the same specifications is easily possible. The complete part number consists of a 5-digit lens type declaration (e.g. S4LFT = f-theta lens), a 4-digit design identifier number and a 3-digit wavelength and coating specification. Sill Optics reserves the right to make constructional changes in the course of product improvement.

## Datasheets, technical drawings and CAD-files

Individual datasheets are available for each lens from our Homepage. Just go to "Products" on the top menu. Then click on the category "Laser optics" and then the subcategory of the needed lens, e.g. "f-Theta lenses". You see a Basic explanationabout f-Theta lenses and on the top a button calles "product overview", which leads to an interactive table with all catalog products of the specific category. On the right of each entry, you can find the download-button for the datasheet. Technical drawings, so called outlines, and 3D CAD-files are also available for the download.

## Anti-reflective and low-absorption coatings

Our anti-reflective coatings are optimized for a certain wavelength or wavelength ranges. They allow a high transmittance of the laser radiation and less absorption of energy in the lens for specific wavelengths. Low-absorption coatings are recommended for lasers with a high average power, because they minimize thermal effects. The following table shows the specifications of our standard coatings.

Most standard coatings are manufactured in Wendelstein on our own coating machines. If there is no standard coating which is suitable for your application we or our external coating suppliers are able to develop a customized coating design to match the wavelengths of your laser or observation unit.

For detailed information about damage thresholds, plaese refer to our extra lexicon chapter about LIDT.

The following coating curves show measured reflections of our typical coatings per surface. If the transmission through a complete lens is of interest, the reflection value at the specific wavelength has to be multiplied with twice the number of lens elements (each element has two surfaces) and then subtracted from 100%. The number of lens elements can be found on the datasheets.

In addition Sill Optics offers some lenses with customized coatings such as /159 for 1850 nm - 1980 nm or /008 for 1550 nm. In the following you can see a specification table for the exemplary coatings. Lenses with customized coatings can also be requested for other wavelengths in the range from 200 nm up to 2000 nm.

## Design wavelength

All optical systems, especially the coating of the lenses, are designed for a special wavelength or wavelength range. The specifications are demonstrated for a single wavelength and can deviate for a different wavelength in the wavelength transmission band. For the S4LFT4010/292, the specifications are declared for 532 nm but it is possible to use this f-Theta objective in a wavelength range from 515 nm to 545 nm without concern.

## Absorption and thermal focus shift

**Basic problem**

With the increasing powers of available lasers, commonly used optical glasses have been pushed to their limits in respect to acceptable thermal effects: Via the exposure of optical glasses to laser radiation, parts of the beam energy are absorbed into the material. This leads to a heating effect with two mayor influences onto optical properties. First, the heating changes the index of refraction of the glass and second, thermal expansion leads to changes in the surface curvatures and therefore changing the refraction of the laser beam. In the application, starting from average laser powers of about 50 W at 1064 nm, a resulting shift of the focal position can lead to decreasing process quality and make online adjustments necessary.

**Possible solution**

Another option lies in the use of fused silica as lens element material. It is a very resistive glass type which has also a very low absorption coefficient compared to optical glasses. Therefore it is commonly used to minimize thermal effects. Sill also uses special low-absorption coatings to minimize thermal effects further and increase typical damage thresholds.

**Other influences on absorption**

Cleanness of the optical components plays also an important role for absorption and therefore thermal effects. Of course there are any larger dust particles (e.g. finger prints) are an extreme absorber of laser radiation. But also time brings micro particles or other contaminations onto lens surfaces. These are not visible to the human eye, but they can be measured. Measurements show that the absorption increases with the duration to the last cleaning. A new lens cleaning resets the absorption values to the original state. Therefore regular cleaning of surfaces exposed to the environment is recommended. This effect could not be shown for internal lens elements, thus cleaning them is not necessary!

Here you can find further details on cleanness of lenses and lens elements:

**> proper lens handling and cleaning**

## Working distance

The working distance is defined as the distance from the front most mechanical edge of the lens to the focal or scanning plane of the objective. Be careful to not mix this up with the effective focal length (EFL) of an objective. This is measured from the principle plane, which is a hypothetical plane were the refraction of the complete lens system can be assumed to occur, to the focal plane of the optical system.

## Diffraction value M²

The ability of focusing laser light is defined by ISO standard 11146 and is described by the diffraction value M². This parameter is defined as the ratio of the divergence angle of the laser beam as compared to the divergence angle of an ideal Gaussian beam. An ideal Gaussian beam would provide the smallest possible focus diameter and would have an M² value of 1. Sometimes the quality of the laser beam is also described by a parameter K which is the reciprocal of M². The quality of a fiber laser is often defined by the Beam Parameter Product (BPP). This value is given by the product of the diffraction value M² and the wavelength λ divided by π. Sill assumes an M² values of 1 in all statements about spot sizes. Multiply the spot diameter by the actual laser M² value to obtain an actual spot diameter.

## Reversed Mode

In some applications it is necessary to reduce the beam diameter instead of expanding it. Because of the same behavior of light in forward and reversal mode beam expanders with a magnification of x can be turned around to reach a magnification of 1/x. There are also some applications for the reversal mode of f-theta lenses. Due to the changed lens order, a beam expander or f-theta lens, which is normally free of critical back reflections, is not necessarily ghost free in reversed operation.

In the beam expander datasheet there is an information if the lens is free from internal ghosts and suitable for USP lasers for the reversed mode (“no internal ghosts, reversed usage”). If you are not sure if a lens is suitable for your application (forward or reversed usage) feel free to ask. Based on your system data (wavelength, input beam diameter, pulse duration, pulse energy and cw power) it is possible to check if lens and laser match.

## Beam diameter

The beam diameter is referenced to the drop of beam intensity to the 1/e² point, i.e. to a point where the intensity has fallen to 13.5% of the peak intensity. If the beam diameter is cut at that point, the 13.5% of the total intensity would be lost. Typically, laser beams are confined to not less than 1.5 times the 1/e² diameter to minimize losses below 1%.

## Apodisation factor

The beam shape and focused spot size after transmission through a lens is strongly dependent on its entrance profile in comparison to the entrance pupil. A common description is given by the truncation ratio T, which is the entrance beam diameter dL divided by the clear aperture dEP. Typical examples are shown in the following sketch: Below a ratio of 0.5, the beam is approximately untruncated. If the entrance beam diameter at 1/e² is equal to the clear aperture of the lens then T = 1. Typical applications are located in between those values, as a compromise between low intensity losses or small spot sizes and high costs due to large diameter lenses.

For estimating the spot size of a diffraction limited lens you need an apodisation factor (APO) which depends on the trunctation ratio T (see following figure). This factor includes the intensity distribution at the limiting surfaces, which play an important role for diffraction effects. On the one hand if you calculate a Gaussian beam which is limited at a diameter lower than 1/e², only small parts of the beam result in diffraction effects. On the other hand the part of diffraction effects is much higher if the diameter is limited at 1/e².

## Spot size (1/e²)

The minimum adjustable focal spot size is calculated by the wavelength of the laser multiplied with the focal length of the scan lens, the APO factor and the diffraction parameter M² of the laser divided by the 1/e² beam diameter dL.

**d _{F} = focal spot diameter d_{EP} = entrance pupil diameter d_{L} = beam diameter (1/e²) f' = focal length**

**Calculation example**

In this example, the focal spot size will be calculated for a Gaussian beam with dL = 6.00 mm and dL = 10.0 mm. We assume the use of a f-theta lens S4LFT4010/292 with a frequency doubled Nd:YAG laser at 532 nm and a diffraction value M² = 1.2. The lens has an effective focal length of f’ = 100 mm. Another very important value to determine in addition to the truncation ratio T, is the clear aperture or entrance pupil. This is not the clear aperture of the f-theta lens (Ø 35 mm), but typically the limiting factor is the beam entrance diameter or aperture of the scan system. Assume a very common value of dEP = 10.0 mm in this case.**Example 1**

f’ = 100 mm, λ = 532 nm, d_{EP} = 10,0 mm, M² = 1,2, d_{L }= 6,00 mm

**Example 2**

f’ = 100 mm, λ = 532 nm, d_{EP} = 10,0 mm, M² = 1,2, d_{L} = 10,0 mm

## Rayleigh length

In optics and especially laser science, the Rayleigh length or Rayleigh range is the distance along the propagation direction of a beam from the waist to the place where the area of the cross section is doubled.

The Rayleigh length is calculated by the focus area multiplied by a factor (depending on the APO-factor) divided by the wavelength and the diffraction value M² of the laser.

The depth of focus of the scan lens can be estimated by a doubled Rayleigh length. Be aware, that this is just a rough estimation and in many modern applications this value can be too large to still fulfill needed spot diameter requirements.

## Fiber imaging

A large focal spot is an advantage in many applications, like welding. Here, fiber-guided lasers are often used which, in contrast to fiber lasers, have a rather poor beam quality (M² value). As collimator aspheres are used, where Sill offers standard and custom solutions. In cutting heads the focusing is realized by aspheres, in scanning systems an f-theta optic is used.

Using the ratio of focusing focal length f2 to collimator focal length f1 provides an easy way to calculate the approximate spot size by the ratio M = f2 / f1. Usually, the fiber core is magnified. In a few applications a demagnification could be used but is limited due to physics.

**Example**

d_{fiber} = 200 µm, f_{1} = 50,0 mm, NA_{fiber} = 0,22, f_{2} = 150,0 mm

**d _{focus} = focal spot diameter**

**d**

_{fiber}= fiber core diameter**f**

_{1}= focal length of the collimator**NA**

_{fiber}= fiber NA**f**

_{2}= focal length of the focusing lensThe stated calculation is only a rough estimation that is valid when both focal length are close to each other. A more precise value can be estimated using the numerical apertures:

**α = half beam cone angle****d _{coll} = collimated beam diameter**

**NA**

_{focus}= numerical aperture on focusing side**M**

_{NA}= precise magnification (NA calculation)