Flexible and robust beam shaping concepts with aspherical surfaces Ulrike Fuchs* and Jens Moritz asphericon GmbH, Stockholmer Str. 9, D-07747 Jena, Germany ABSTRACT The potpourri of aspherical surfaces offers many possibilities in optical design, even the chance for flexible beam shaping setups. Since these are refractive optical elements the beam shaping is robust with respect to wavelength changes. Keywords: laser beam shaping, axicon, asphere, Bessel beams, ring focus
1. INTRODUCTION The generation of Bessel beams with axicons is the most noted application for this uncommon type of aspherical surfaces. Even though this is already some kind of beam shaping, the case becomes more interesting when more axicons are involved and above that, combined with other aspherical elements or even merged within a single element. Due to refraction all these set-ups are quite insensitive to changes in wavelength or fluctuations of the incoming beam profile.
2. AXICONS There are several ways to describe the surface sag of aspherical surfaces. The oldest one was introduced by Ernst Abbe and reads in its most general version +∑
z(h) = (
A h,
(1)
)
a conic section and polynomial terms. Axicons are a very special type of conic surface and sometimes described by employing really large values for the conic constants k. Since perfect axicons have a tip in the center of rotation, this is not the best way. Simplifying Eq. (1) with R → ∞ and just A ≠ 0 leads to a mathematically exact description with z(h) = A ∙ h .
(2)
The surface is a rotational symmetric cone and sometimes referred to as rotational symmetric prism. Figure 1 shows a photo of an axion with diameter 25.4 mm and an axicon angle of 10° fabricated by asphericon.
Figure 1. Photo of an axicon fabricated by asphericon. The surface is rotational symmetric and described by Eq. (2).
*
[email protected]; www.asphericon.com International Optical Design Conference 2014, edited by Mariana Figueiro, Scott Lerner, Julius Muschaweck, John Rogers, Proc. of SPIE-OSA Vol. 9293, 92930B · © 2014 SPIE CCC code: 0277-786X/14/$18 · doi: 10.1117/12.2072613 SPIE-OSA/ Vol. 9293 92930B-1 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 02/16/2015 Terms of Use: http://spiedl.org/terms
The physical properties off an axicon arre determinedd by the so-caalled axicon anngle, which is given by 18 80° 2α withh w a collimaated beam. Ass one can seee, α = arctan A . Figure 3 shhows a basic layout of an axicon being illuminated with there are twoo regions of innterest. The fiirst one, markked as section (a), in the intterference areea for Bessel beams b and thee second one, marked as seection (b), whhere a ring shhaped light distribution d w a diamtetter d = 2l tan with n α(n 1) iss created. How the lenggth of region (a) ( depends on o the axicon angle and thee diameter of the t incoming beam, is disccussed next, ass well as the lateral size of thhe Bessel beam m. As one cann see from Fig g. 3 the diameeter of the ringg shaped light distribution iss section (b) deepends on thee distance l frrom the axicoon surface and d increases with w longer disstances l. Theereby, the ringg width is abouut have the diaameter of the incoming beaam. It will be shown later on o how this prroperty can bee used for veryy flexible and definitely d robuust beam shapping.
Figure 2. Layout, L axicon anngel = 180° - 2α with w α = arctan A1, (a) interferencce area for Bessell beam, (b) ring shhaped light distriibution d=2l tan (α(n-1)) ))
3. BEAMS SHAPING WITH W ASPH HERICAL SURFACES S S t followingg optical elem ments are invo olved: A beam m The first exaample is depiccted in Fig. 3, going from left to right the expansion sysstem made off four monolithhical aspherical elements [1 1] to adapt thee beam diametter from the laaser source forr beam shapingg without intrroducing noteeworthy waveefront errors. The followingg beam shapeer (Gauss to top-hat t [2]) iss depicted as a black box siince it can bee either a diffrractive opticaal element (DO OE) or a bi-aasphere based on refractionn. Later one is way less senssitive to variaations in waveelength or thee entrance beam profile annd therefore more m robust inn handling. Sinnce both kindss of beam shapping elementss are calculated d for a certainn entrance beaam diameter and a profile, thee magnificationn afterwards is i limited andd it can be neecessary to en nlarge the beaam diameter bbehind even further. fu By thee way, dependiing on the kinnd of beam shhaper used, specific sizes caan be cheaperr than others aand therefore it is necessaryy to be able to split s up the beeam expansionn in two or even more interm mediate steps. Adding a lenns behind the axicon createss a ring focus, as shown in Fig. 3. The size and distannce of this rin ng focus is deetermined by the focal leng gth of the lenss involved. Em mploying an asspherical lenss in this set-upp leads to a sm moother shape of the ring bbecause especcially for highh numerical apeertures an aspphere has way less aberratioons, which cou uld cause distoortion of the liight distributio on.
beam haper
4---* 75m rn
20mm
Figure 3. Scheme S of a beam m shaping set-up involving beam diameter scaling for the incomingg laser beam (leftt), beam shaping from Gauss to top-hat, enlargement of thhe beam for optim mized use of the axicon a and generaating a ring focuss with an asphere.
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Adding a seccond axicon to the previouus set-up imprroves the flex xibility even further f withouut suffering a loss of beingg robust. Figurre 4 shows thhe last three optical elemeents of this enhanced e set-uup. By movinng just the laast axicon thee diameter of the t ring focuss can be moddified. There is i a factor off five in the given g examplee. The width of the ring iss determined by the NA of the t focusing leens. Note, thaat the position n of the ring foocus stays thee same only th he last elemennt is moving, whhich makes it again a very robust r set-up.
Figure 4. Flexiblle beam shaping for f creating a ringg focus with variaable diameter. Th he diameter of thee ring is determinned by the position n where the second axicon is placed. Notice thhat the other two elements are fixeed as well as the position p of the rinng focus.
Varying the order o of the opptical elementts shown in Fig. F 4 to get a set-up as show wn in Fig. 5 pprovides anoth her interestingg utilization forr beam-shapinng with axiconns. Aligning two t axicons, which w have thhe same axicoon angle, can be b utilized forr creating a coollimated ring shaped lightt distribution after passing through this set-up. As onne can see fro om Fig. 5 thee diameter of thhis ring depennds on the disttance betweenn the axicons. Placing a focuusing lens rigght behind cau uses the axiconn set-up to worrk as a high-ppass filtering for the focusiing. Thus, onlly certain high spatial freqquencies are in ncluded in thee focusing inteerference patteern. Figure 5 shows the crross-section of o the interferrence pattern formed in th he focal planee, which is basiccally a Bessell function. 1
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -3.2
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Figure 5. left: Flexible F beam shhaping for creatinng a collimated ring shaped ligh ht distribution at 780nm used forr focusing below w diffraction limiit (asphericon asphhere, diameter = 25 2 mm and EFL= = 20 mm, NA=0.449). right: simulatted cross-section in the focal planee.
For comparisson Fig. 6 deppicts the focussing with the same s asphere and a gaussiaan intensity diistribution forr the incomingg beam. The crross-section off the intensityy distribution in i the focal plane is also gaaussian and w without any no oteworthy sidee maxima, as one o would exppect. Taking a closer look att the width of both intensityy profiles in thhe focal planes (Fig. 5 & 6)), it is obviouss that with thhe set- up inccluding the tw wo axicons the t focus diam meter can bee significantly y reduced. Too
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accomplish thhe same spot size s with a sinngle lens as inn Fig. 6 the nu umerical apertture (NA) wouuld have to go o up from 0.499 to 0.72, whichh is quite signnificant. By dooing so the Raayleigh range is reduced as well, which ccould be avoid ded with a setup as in Fig. 5. Thus, if the t applicationn involved caan handle the stronger sidee maxima andd spot diameteer is a criticaal aspect, such a two axicon set-up s should be consideredd 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
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Figure 6. left: Foocusing Gaussiann beam at 780 nm m with an aspherre (asphericon, diameter d = 25 mm m and EFL= 20 m mm, NA=0.49) to o diffraction limited spot. righht: simulated crosss-section in the focal f plane.
The optical fuunctions of axxicons and asppheres can alsoo be merged as a shown in Fiig.7, which is extremely intteresting whenn space is an isssue in opticall design. The example show wn combines beam shapingg with two axiicon surfaces with focusingg by an aspheree as introduceed above (Fig. 5). Comparedd to just focussing, this elem ment reduces tthe size of thee focal spot forr given NA. Making M use of total t internal reflection r as shhown above adds a extra chaarm because noo coating is neeeded.
Figure 7 Beam shhaper consisting of two axicon surrfaces and an aspphere for creating a focal spot beloow diffraction lim mit as introduced in i Fig. 5.
4. CONCLUSI C IONS It is demonsttrated how axiicons can be employed e for creating Bessel beams, rinng shaped lighht distribution ns, ring foci orr even sub-difffraction-limiteed foci. Due too the fact that these optical elements are made m of glasss and their mode of action iss based on refraction beam shaping s is veryy robust with respect to chaange of wavellength comparred to DOEs. The countlesss possibilities of o combinatioon of the diff fferent opticall elements shown lead to a whole new w concept of flexible beam m shaping for various applicaations, where different laserr sources or ch hanging beam m parameters aare involved.
R REFERENCE ES ocessing, Procc. [1] Fuchhs, U., “Monoolithical aspheerical beam exxpanding systeems,” in Highh Power Laserr Material Pro SPIE E 8963, (20144). [2] Čižm már, T., Dhollakia, K., “Tuunable Bessell light modes: engineering the axial proopagation,” Optics O Expresss 17(118), 15558-155570 (2009).
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