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πShaper 6_6 Application Notes

Description of πShaper_6_6 (models _852, _1064, _532/1064, _1319, _1550, _VIS, _410/820, _TiS, _350)

Beam shaping systems of πShaper_6_6 series present optical components to convert input single mode beams (TEM00) or multimode beams, which intensity profile is similar to a Gaussian one, to flattop beams with uniform intensity distribution. Because of many same features there is applied a common denomination πShaper_6_6 below, when necessary the differences between models will be noted additionally.

Most important features and basic principles of πShaper_6_6 are:

- πShaper are refractive optical systems that transform Gaussian, or close to Gaussian intensity distribution of source laser beam to a flattop (or top-hat, or uniform) one;

- The initial laser beam can have either a TEM00 one of Gaussian intensity profile or a multimode beam which intensity distribution is described by a Bell-like function having peak intensity in the center of a beam and steadily decreasing of intensity towards the beam periphery;

- The uniform intensity is kept after the πShaper over a large distance;

- The development technology lets it possible to provide other output intensity profiles, however most asked is flattop one;

- The πShaper_6_6 are implemented as: o a Telescopes, when both input and output beams are collimated, or o a Collimator, when divergent input and collimated output;

- Achromatic design provides the transformation for a certain wavelength range; - Galilean design, thus there is no intermediate focusing of a beam.

Angular Magnification of the telescopic system is about 0.65, thus, from the point of view of paraxial optics the diameter of output beam is increased by factor 1/0.65 while field angle is reduced by factor 0.65.

The optical system of πShaper_6_6 consists of 2 components.

Input side, left at the picture, has a clear diameter 9 mm, and “smaller” size of mechanical cabinet; output side, right at the picture, has a clear diameter 7,6 mm.

Input Side

πShaper_6_6_1064 Adjustment Rings

Input, Clear Diameter 9 mm Side view Output, Clear Diameter 7,6 mm

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Technical Specifications: Common for all πShaper 6_6 models:

Input beam TEM00 or multimode with Gaussian or similar intensity profle

Output beam - Collimated - Flat-top, uniformity within 5% - Diameter 6 mm - High edge steepness

Other features - Achromatic for design wavelengths - Compact design suitable for scientific and industrial applications - Long working distance

Overall dimensions - Diameter 39 mm - Length 133 mm

Weight < 250 g Mounting External Thread M 27x1, at Input and Output

πShaper 6_6 features Model _852 _1064 _532/1064 _1319 _1550

Type Telescope of Galilean type ( without internal focus)

Input beam features Collimated, Diameter 5,9-6,0 mm (1/e2)

Optimum spectral range*, nm 800-900 1020-1100 520-550, 1020-1100 1200-1400 1500-1600

Design wavelengths, nm 1064 (Nd:YAG) 852 nm (Ti:Sapphire)

1064 (Nd:YAG) 632.8 (He-Ne)

1064 (Nd:YAG) 632.8 (He-Ne)

1064 (Nd:YAG) 1319 (Laser Diode)

1064 (Nd:YAG) 1550 (Laser Diode)

Applications based on Ti:Sapphire laser, other near-IR lasers

Nd:YAG, Fiber and other near IR-lasers

1st (1064) / 2nd (532) Harmonics of Nd:YAG laser

near IR lasers, laser diodes

near IR lasers, laser diodes

Model _VIS _410/820 _TiS _350 _350_C

Type Telescope of Galilean type ( without internal focus) Collimator w/o internal focus

Input beam features Data for 1/e2 Collimated, Diameter 5,9-6,0 mm

- Divergent - Div. 75 mrad - Input Dia 6 mm

Optimum spectral range*, nm 420-680 400-420, 800-840 700-900 330-370

Design wavelengths, nm 442 (He-Cd), 632.8 (He-Ne)

442 (He-Cd), 632.8 (He-Ne)

1064 (Nd:YAG) 632.8 (He-Ne) 350

Applications based on He-Ne, He-Cd, other VIS lasers

1st (820) / 2nd (410) Harmonics of

Ti:Sapphire laser

Ti:Sapphire laser, other near-IR lasers

3rd (355) Harmonics of Nd:YAG laser

* - according to coatings applied

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Input beam. The optical design of πShaper_6_6 models, excluding the πShaper_6_6_350_C, presumes the input TEM00 or multimode beam is collimated and has 1/e2 intensity diameter 2ω=5.9-6.0 mm (ω is a waist of laser beam).

The optical design of πShaper_6_6_350_C presumes the input TEM00 or multimode beam is divergent and has a full angle divergence of 75 mrad (1/e2); the Focal point of the collimator is located at a distance approximately 80 mm in front of the πShaper, thus at the πShaper input the beam diameter is 2ω = 5.9 - 6.0 mm at 1/e2 level (ω is a waist of laser beam).

Input beam divergence could be provided by setting an appropriate negative lens used to adapt the πShaper to a collimated beam, which diameter is smaller than 6 mm.

Clear diameter of input optical components is 9 mm, thus 1,5 times bigger than 2ω, hence theoretically 99% of Gauss beam is inputted. Changing the diameter of input beam effects changing the intensity profile at the output of πShaper_6_6. Comparison of output intensity profiles is presented in Appendix in chapter “Behavior of πShaper 6_6_VIS when changing the diameter of input beam”.

Usually, the tolerance for input beam diameter ∆(2ω) = +/-0.1 mm.

Deviation of intensity distribution of input beam from perfect Gaussian again effects changing the intensity profile at the output of πShaper_6_6. To provide uniform output intensity distribution it is necessary to adapt the size of input beam, examples of such adaptation are presented in Appendix in chapter “Behavior of πShaper 6_6_VIS when changing the shape of input beam”.

Output beam. According to principle of operation of πShaper_6_6 output beam is collimated and has uniform intensity profile, theoretical deviation from uniformity is less than 2%.

Wavefront error (wave aberration) is below λ/10. That uniform profile is kept stable over a distance about 0,5 - 1 meter, later due to diffraction the intensity

profile is transformed to non-uniform one like an Airy distribution.

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Mounting. All πShaper_6_6 models have Mounting Thread M27x1 at both ends. It is supposed the πShapers to be mounted in an optical system by means of these threads; other means of mounting should be discussed with the Supplier.

Features of Mechanical design. One of components of πShaper_6_6, at output side, is movable; this possibility is provided to adapt a unit to real conditions of operation like working wavelength, divergence of input beam, etc. A range of motion is +/-10 mm (+/-5 mm in obsolete version), the motion of the component is provided through step-by-step turning of two adjustment wheels. These wheels are used, also, for fixation of the movable component, see the picture. The πShaper has signs in form of 1 mm step ruler on the case and strokes on one of adjustment wheels, these signs could be used as reference of position of the movable component.

Original position of components with respect to each other is optimized for one of the basic wavelengths; see the data for original setting wavelength in the table of next chapter “Spectral Range”.

Thus, a general suggestion while working with a πShaper 6_6 is to start to work from the original position. By turning the adjustment wheel (internal thread of 0.5 mm pitch is used) it is possible to move the component. This adjustment tool could be used either to compensate the divergence of source laser beam or to provide a certain optical power of the πShaper 6_6.

Please, note, the possibility of moving the output component is provided for correction purposes only - in terms of divergence the compensation is provided for a range maximum +/-4 mrad (+/-2 mrad in obsolete version) !

Spectral range. The optical components of πShaper_6_6 are made of optical glasses or fused silica,

these materials have different dispersion and the optical design is developed in such a way that the system can work in wide spectral range. Thus, πShaper_6_6 is achromatic system and can be applied with different lasers.

πShaper_6_6_852 - Ti:Sapphire laser, or other near-IR lasers of close wavelengths

πShaper_6_6_1064 - Nd:YAG, Fiber lasers or other near-IR lasers of close wavelengths

πShaper_6_6_532/1064 - Nd:YAG-lasers, 1st (1064) and 2nd (532) Harmonics, or other laser of close wavelengths

πShaper_6_6_1319 - near-IR lasers, laser diodes

πShaper_6_6_1550 - near IR lasers, laser diodes

πShaper_6_6_VIS - He-Ne, He-Cd and other lasers of visual spectrum

πShaper_6_6_410/820 - Ti-Sapphire-lasers, 1st (820) and 2nd (410) Harmonics, or other laser of close wavelengths

πShaper_6_6_TiS - Ti-Sapphire lasers or other laser of close wavelengths

πShaper_6_6_350, πShaper_6_6_350_C

- Nd:YAG-lasers, 3rd (355) Harmonics, or other laser of close wavelengths

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Coatings. AR-coatings of each version of πShaper_6_6 are optimized for corresponding wavelength range:

Coating type Optimum band, nm Working band, nm (acceptable performance)

Wavelength of original setting, nm

πShaper_6_6_852 V-type, narrow band 800 - 900 750 - 1000 852

πShaper_6_6_1064 V-type, narrow band 1020 - 1100 900 - 1200 1064

πShaper_6_6_532/1064 W-type 2 narrow bands

520 - 550 1020 - 1100

500 - 580 950 - 1150 1064

πShaper_6_6_1319 V-type, narrow band 1200 - 1400 1100 - 1500 1319

πShaper_6_6_1550 V-type, narrow band 1500 - 1600 1400 - 1700 1550

πShaper_6_6_VIS Broad band 420 - 680 400 - 710 532

πShaper_6_6_410/820 W-type 2 narrow bands

400 - 420 800 - 840

390 - 450 780 - 880 820

πShaper_6_6_TiS V-type, narrow band 700 - 900 680 - 1050 790

πShaper_6_6_350 πShaper_6_6_350_C V-type, narrow band 330 - 370 310 - 390 355

When working in optimum bands total losses do not exceed 5%. Applying of πShaper_6_6 at wavelength out of the optimum band will effect increasing of losses.

Adjustments. Because of a principle of transforming the energy the πShaper_6_6 is sensitive to errors of

positioning of πShaper_6_6 with respect to input beam. Results of theoretical calculations characterizing the sensitivity of πShaper_6_6 to misalignments and tilting are described below in Appendix in separate chapter “Behavior of πShaper_6_6_1064 when misalignments”

To provide a proper result of beam profile conversion it is necessary to take care for adjustments of the πShaper_6_6 unit in optical system. Adjustments to be provided are

- Angle adjustments around axes X and Y and - Linear lateral adjustments in a plane perpendicular to optical axis, X and Y axes, - For the πShaper_6_6_350_C axial adjustment, Z axis

it is assumed that axis Z coincides with optical axis, axes X and Y are perpendicular to Z.

Mechanical design of complete optical system with πShaper_6_6 should contain opto-mechanical tools for adjustments of the πShaper_6_6, an example of such a tool is presented at the below picture.

πShaper Mount

Specifications Tilt/tip range ±2°

Sensitivity 3 arcsec

XY translation range ±2 mm

Sensitivity for XY translation 1 µm

Z translation range 10 mm

Inner Mounting Thread M 27x1

Weight 0.6 kg

Reaching of symmetric circular pattern of uniform intensity at the output of πShaper_6_6 could be used as a rough criterion of proper adjustment. Applying of Beam Profiling System is preferable.

Tolerances for the πShaper_6_6 systems are: - lateral misalignment ±0,1 mm; - tilting ±0,1o.

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Since the system is sensitive to misalignments and tilting it is recommended after turning the component to check the adjustments. A rough criterion of uniform intensity at the output could be used.

Example of the Beam Intensity Profile Transformation of a TEM00 laser beam when proper adjustment of a πShaper is presented at figure below.

a) Intensity profile of a source laser beam b) Intensity profile of a beam after πShaper One can see the πShaper is capable to provide conversion of beams of non-perfect Gaussian intensity

profile – the “tails” of the source beam have higher intensity than a “pure Gaussian”. By the way, that extra energy in “tails” is a reason of the bright rim in output intensity distribution.

Example of the πShaper_6_6_1064 operation. An illustration of the πShaper influence on the results of material processing with using the laser is

presented at left picture. Here one can see a comparison of engraving of a depression in a material with pure TEMOO laser as well as with the same laser but with a πShaper after it.

Courtesy of EO Technics

Difference is evident - irregular shape of the depression with a ragged unwished hole in the middle in case of direct engraving with the TEM00 laser, good shaped round depression with a controlled depth when applying the πShaper.

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Application Layouts with πShaper

Accurate redistribution of energy in a beam realized in field mapping optical systems of πShaper makes it possible to realize with the same πShaper unit various shapes by using additional optics before and after it; this provides users with a freedom in choosing the right beam profile for a particular technical or scientific task. Below some examples of beam shape manipulation are presented.

Beam-expanders Because of operational principle the πShaper provides an output beam which diameter is pre-determined, at the same time very often it is necessary to realize a smaller or a greater final dot. Since the output beam of the πShaper is collimated a simplest way is to use an ordinary telescopic beam-expander (or beam-reducer). This way is, undoubtedly, the best in case of expanding the output beam and is always recommended for applications.

The telescopic systems could be applied to reduce the output beam as well. It is not recommended, however, to apply reduction factor below 1/3, since the residual wave aberration of output beam is multiplied by the beam reduction and this could lead to inhomogeneity of the intensity profile.

Relay Imaging When a task requires beam reducing with a high reduction factor it is advisable to apply an approach of relay imaging of an output aperture of a πShaper with using a lens, if necessary a real aperture could be installed at the output of the πShaper as well. This way is illustrated at below figure.

Depending on a particular task it is possible to use either a simple lens, or more complicated focusing optics, for example a combination of a beam-expander and a lens providing shortening the total length of optical system. Low divergence of the collimated output beam allows applying focusing optics of not so high numerical aperture. Essential feature of this approach is extended depth of field.

It is recommended to use this approach when reduction factor is not less than 1/100, this corresponds to size of final dots greater than 100 microns. When smaller dots are required it is recommended to use other solutions, for example the Focal-πShaper intended to manipulate the shape of focused beams.

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Roof-like intensity profile Since the πShaper requires a pre-determined input beam a resulting output beam profile would differ from a uniform one when a variation of a size of input beam as well as when source beam has intensity profile deviated from a perfect Gaussian. On the other hand just a variation of the input beam diameter could be used to adapt a πShaper to conditions of operation with a real laser beam which intensity profile differs from a perfect Gaussian - this is an often happening situation, therefore choosing of an optimum input beam diameter (for example with using zoom beam-expanders) is a routine procedure of adjusting the πShaper.

The feature of dependence of output profile from a size of an input beam could be used in some cases of realizing the beam shapes other than a uniform one. An example of such a beam profile transformation is presented at below figure. A goal is to achieve a “Roof-like” intensity profile having a uniform intensity in one direction and Gaussian one in transverse direction.

The task is solved by installing before a telescopic πShaper a beam-expander of cylinder optics squeezing a beam in a vertical direction (according to the sketch). Since the input beam size in vertical direction is smaller than a rate size the beam intensity profile in this direction stays almost untouched. At the same time, the intensity distribution in horizontal direction is transformed and a uniform beam profile is created, hence, resulting Roof-like beam shape is provided.

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Appendix Behavior of πShaper 6_6_VIS when changing the diameter of input beam.

Intensity profile at the output of πShaper_6_6_VIS under input laser beam of 6 mm diameter (1/e2) According to design the non-uniformity of the output beam intensity distribution is within +2% range.

Variation of diameter of source laser beam.

Intensity profile at the output of πShaper_6_6_VIS under input laser beam of 5 mm diameter (1/e2)

Intensity profile at the output of πShaper_6_6_VIS under input laser beam of 7 mm diameter (1/e2)

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Behavior of πShaper 6_6_VIS when changing the shape of input beam.

Left Column – data for input beam: - Diameter for 1/e2 intensity level, - Gaussian Apodisation of Factor=1 corresponds to TEM00 beam of M2=1, - Diameter is adjusted to get uniform intensity profile at output of πShaper.

Right Column – data for output beam (Full Width at Half Intensity)

Din = 6.0 Apodisation: Type Gaussian, Factor = 1 Dout = 6.0

Din = 4.4 Apodisation: Type Gaussian, Factor = 0.5 Dout = 5.4

Din = 7.3 Apodisation: Type Gaussian, Factor = 1.5 Dout =6.4

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Apodisation Type By default, the pupil is always illuminated uniformly. However, there are times when the pupil should have a non-uniform illumination. For this purpose, ZEMAX supports pupil Apodisation, which is a variation of amplitude over the pupil. Three types of pupil Apodisation are supported: uniform, Gaussian, and tangential. Uniform means rays are distributed uniformly over the entrance pupil, simulating uniform illumination. Gaussian Apodisation imparts an amplitude variation over the pupil that is Gaussian in form. The Apodisation factor refers to the rate of decrease of the beam amplitude as a function of radial pupil coordinate. The beam amplitude is normalized to unity at the center of the pupil. The amplitude at other points in the entrance pupil is given by

A(ρ) = exp(− Gρ2),

where G is the Apodisation factor and ρ is the normalized pupil coordinate. If the Apodisation factor is zero, then the pupil illumination is uniform. If the Apodisation factor is 1.0, then the beam amplitude has fallen to the 1 over e point at the edge of the entrance pupil (which means the intensity has fallen to the 1 over e squared point, about 13% of the peak). The Apodisation factor can be any number greater than or equal to 0.0.

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Behavior of πShaper 6_6_1064 when misalignments

Dependence of the intensity profile of πShaper 6_6_1064 on a value of a tilt or corresponding lateral shift (λ = 1,064 µm) Upper row relates to the plane of tilting (Y), lower row – to perpendicular plane (X).

0о

0,1о (0,0017 rad, 0,1 mm)

0,3о (0,0051 rad, 0,3 mm)

0,5о (0,0085 rad, 0,5mm)

Within 0,1о tolerance of angle alignment or 0,1 mm of lateral shift πShaper6_6 is almost insensitive to errors of alignment. Bigger errors could lead to serious changing of intensity distribution.