# Beam expansion - A unique system made of aspheric lenses

Conventional beam expansion systems can only be adapted with great effort, are relatively large and only suitable for a certain wavelength. The world’s first use of an aspheric lens for beam expansion opens completely new possibilities. Spherical aberrations are corrected and an afocal system for large input beam diameters is realized. The aspheric optic reduces the system size up to 50% compared to currently available optical components on the market. The asphericon system covers a wide wavelength spectrum. Design wavelengths of 355, 532, 632 and 780 to 1064 nm. An intelligent assembly concept saves time-consuming adjustments and ensures precision and flexibility. Discover the advantages of aspherical beam expansion for your application!

## a|BeamExpander

Discover the world‘s first aspheric and diffraction-limited beam expander. The a|BeamExpander is a monolithic laser accessory with just one aspheric lens for the highest level of precision. Experience nearly endless possibilities with up to 32× beam magnification and optimized performance for different design wavelengths (355, 532, 632, 780, 1064 nm) - individually measured and certified. The a|BeamExpander works completely diffraction limited, both as a single element and in cascades with up to five additional coated elements. Three magnification levels are available (1.5, 1.75, 2.0), which can achieve up to 32x expansion.

• Available in five design wavelengths [355 nm / 532 nm / 632 nm / 780 nm / 1064 nm]
• Max. input aperture 10.6 – 14.7 mm, max. output aperture 22.5 mm
• Available with magnifications of 1.5 | 1.75 | 2.0
• Possibility of combining up to five expander for up to 32 times beam expansion and over 230 intermediate stages
• Completely diffraction-limited – individually measured and guaranteed by an original asphericon certificate
• Laser induced damage threshold (Coating):  12 J/cm², 100 Hz, 6 ns, 532 nm

The design of the Kepler telescope represents the simplest principle of a beam expansion system. Here, two converging lenses with different focal lengths are combined. The expansion or reduction of the beam crosssection results from the quotient of the focal length

(1) $$V = \frac{f_2}{f_1}$$

The overall length of the optical system is essentially determined by distance of the two lenses, which can be estimated over the sum of the focal length,

(2) $$e = f_1 + f_2$$

In the Galilean telescope, the converging lens is replaced by a diverging lens, which decreases the construction lengths while maintaining the magnification level. Figure 1 shows both: Kepler telescope (a) and Galilean telescope (b) with 10x magnification (V=10).

### Asperization and flexible magnification levels

Spheric single lenses are used in classic beam expansion systems. Thus, spheric aberrations become visible. This can be remedied by asperization of one of the lens surfaces, particular where a high quality of wave front is required. The shape of the lens surface can be described by

(3) $$z(h) = \frac {h^2}{R(1+\sqrt{(1-(1+k) \frac{h^2}{R^2}}} + \sum_{i=2}^{n} A_{2i} h^{2i}$$

These beam expansion systems are typically optimized for one wavelength in terms of the shape of optical surface and lens distance. Spheric aberrations can be reduced to a minimum.

By adding an additional optical group, the beam expansion system receives additional flexibility with regard to the adjustable magnification levels. This can be done most easily with a symmetrical zoom system, which consists of three single optical lenses (converging lens-diverging lens-converging lens). Therby two lenses must be able to change their position so that an afocal beam path is ensured for each magnification level. Depending on requirements, such a system can become very complex, whereby the demands increas in terms of the mechanical mount.

### Monolithic beam expansion systems

A slightly different approach is taken by monolithic beam expansion systems that are similar in operating principle to a Galilean telescope, but consists only of one optical element – a meniscus lens. The two optically active surfaces have a common center of curvature. The principle of this so-called zero lenses has been known for a very long time, but they show strong spherical aberration in their original design with two spherical surfaces and thus are only suitable for very small beam diameters and very low magnifications.

In Figure 2 (a) the beam path in such a spherical lens is shown schematically. If these optical elements are aspherized to one of the two surfaces, the spherical aberration can be corrected and an afocal system for large beam diameters can be implemented.

The improvement in the optical properties can be clearly seen in comparison to Figure 1. The magnification in both cases corresponds to V = 2, whereby the beam diameter is different by the factor 2. The maximum attainable magnification of such a single element is V = 2. This is estimated by the paraxial magnification

(4) $$V = \frac {d}{r} * \frac {n-1}{n}$$

whereby n is the refractive index of the glass, r is the radius of the concave side, and d is the center thickness.

It turns out that the single element magnifications of the monolithic Galilean telescopes are comparatively low due to the overall length limitation. Since it is an afocal beam expansion systems, they can gradually increase the input beam while they are “connected in series” in succession in the beam path (Figure 3c).

Various magnification levels allow both, high magnifications with minimum space requirements (use V = 2) as well as finer increments (use V = 1.5 and V = 1.75). Due to the afocal design of the single elements, the meniscus lenses can arbitrarily oriented inside the beam path.

The use of monolithic beam expansion systems in cascade involves much more optical surfaces than the conventional optical systems (see Figure 3). Moreover, each second surface is aspheric! For such a cascade system for flexible beam expansion very high surface qualities of the single elements are required. Prerequisite for a variety of combinations during the subsequent use is that every single element over the entire clear aperture must be significantly better than the requirement “diffraction limited”, that is wavefront error RMS< λ/14.

If, at the same time, center thickness and decentering of the surfaces are very accurately manufactured, one can speak of a completely adjustment-free beam expansion system, since all degrees of freedom required for adjustment are fixed at an optimum by the manufacturing as monolithic element. Also, the introduction of further monolithic elements for changing the magnification level will be completely adjustment-free and therefore quick and easy.

Beam Expander are primary used for research in the optics laboratory, where they are used for example to amplify the laser or to improve the usability of the optical assembly. Also in the research and development departments of aerospace, biotechnology, imaging, materials research and materials processing, particularly of laser material processing, beam expander systems are used.

The quality of the BeamTuning elements is guaranteed by asphericon based on a high-resolution wavefront or beam proﬁle measurement for selected components, also through certiﬁcation.

Find the right a|BeamExpander for your application? Use our configurator to quickly and easily scan for the desired expansion and/or the number of a|BeamExpanders and match the calculated results with your own requirements.

Wavefront and divergence deviations as well as the influence on ultrashort laser pulses can be calculated with our BeamTooling App. The app is available for free download in the Apple and Google App Stores.

## a|Waveλdapt

Using an a|BeamExpander at a wavelength, which differs from its design wavelength? No problem with the a|Waveλdapt. It covers the complete spectral range from 500 nm to 1600 nm, corrects wavefront deformation and adjusts divergence while retaining the beam diameter. This laser device is very flexible in usage – especially, since the overall length of the system is very short compared to conventional systems. Due to it‘s  metric fine thread the a|Waveλdapt, like all BeamTuning elements, can be easily integrated into any optical system.

• Available for the four a|BeamExpander design wavelengths  [532 nm / 632 nm / 780 nm / 1064 nm]
• Optimized adaptation to wavelength range  from 500 nm to 1600 nm
• Compensation of divergent incoming beams up to 1 mrad
• Combinable with up to five BeamTuning elements – completely diffraction-limited
• Max. input aperture 22.5 mm, max. output aperture 22.5 mm
• Easy and flexible handling

The outgoing beam is either divergent or convergent, when an a|BeamExpander is used at a different wavelength than the design wavelength. Additionally, higher order wavefront aberrations occur since the asphere and the center thickness do no longer match the design intention. A suitable a|Waveλdapt can easily set these problems within its range of use and thus increases the flexibility of the a|BeamExpander. By using a 780 nm a|Waveλdapt, for example, beams with a wave length of 850 nm can be collimated by an a|BeamExpander 780 nm. The diffractionlimited performance is achieved by collimating the outgoing beam at the new wavelength.

Covered range of wavelengths for the design wavelengths [nm] 532, 632, 780, 1064 when using the corresponding a|Waveλdapt.

## a|AspheriColl

The a|AspheriColl, an adjustable fiber collimation device, enables the perfect connection of FC/PC patch fibers to your set-up. Combine the only off-the-shelf fiber collimator for NA's from 0.12 to 0.5 on the market with BeamTuning or other beam shaping elements to obtain any desired output beam while maintaining a diffraction-limited wavefront.

• Fiber collimator covering for NA's from 0.12 to 0.35 (f = 20 mm) and from 0.12 to 0.5 (f = 10 mm)
• Focal length f = 10 mm, with Øe= 10 mm and f = 20 mm, with Øe= 14 mm
• Optimized for wavelength range 500 nm – 1600 nm
• Perfectly aligned lateral position
• Completely diffraction-limited performance (Strehl > 0.95) when used with FC/PC patch fibers
• Thanks to matching adapters also usable for APC fibers
• No truncation effects compared to other available fiber couplers
• Thanks to bigger output beam diameters, no additional expansion might be needed (shorter system length)

The diameter of the collimated output beam generated by an a|AspheriColl depends on the NA. This is a function of the wavelength. The basic diameter is set as shown in the graph on the left. Pre-aligned for the wavelengths [nm] 532, 632, 780 and 1064, the a|AspheriColl collimates the output of single mode ﬁbers with NA's between 0.12 and 0.275.

Covered range of wavelengths of the a|AspheriColl for the design wavelengths [nm] 532, 632, 780, 1064.

Cross-system and intra-system a|Adapters conveniently connect all BeamTuning elements to any optical set-up - without additional adjustment.

Intra-system a|Adapters allow to combine all BeamTuning elements, e.g. to use a|BeamExpander in both functional directions, to expand or reduce the beam diameter.

Easy integrate all BeamTuning elements into any optical system (e.g. Qioptiq, OWIS or Edmund Optics) through a variety of mounting concepts by using the cross- system a|Adapters (C-Mount, SM1). Thanks to its outer diameter, the 1.2" circumference can be used both as intra-system and as cross-system a|Adapter.

## a|BeamBox Essential

Compile asphericon's BeamExpansion products with MountedOptics and/or BeamShaping products flexibly for your individual application.
For a quick and easy overview, asphericon has already developed various standard combinations of the a|BeamBoxes. The “Essential” series includes five boxes for beam expansion at different wavelengths.

• Combines up to eight a|BeamExpanders with an a|AspheriColl, a|Waveλdapt and matching a|Adapters
• Optimized for wavelengths 355, 532, 632, 780 and 1064 nm
• Quality: diffraction-limited wavefront
• Multi element sets with attractive cost savings

## Beam expansion products with short delivery times.

### Precise expansion and shaping of laser beams – asphericon BeamTuning

In addition to the aspheric beam expanders (a|BeamExpander) for expanding and reducing lasers, asphericon has developed further optical modules within the BeamTuning line. The product range includes a fiber collimator for FC/PC laser patch fibers (a|AspheriColl), an element for using a|BeamExpanders outside their design wavelength (a|Waveλdapt), intra- and cross-system adapters (a|Adapters),and mounted aspherical optics (MountedOptics). Supplementary – also based on an aspheric optic – we offer beam shapers for a wide range of applications. Learn more about shaping a collimated laser beam into a Top-Hat beam and/or different focused beam profiles at the aspheric beam shaping optics site.

Contact Person
Sabrina Matthias

+49 (0) 3641 3100 560
sales@asphericon.com