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Procedia CIRP 00 (2017) 000–000 Procedia CIRP 74 (2018) 589–593 www.elsevier.com/locate/procedia th

10th CIRP 10th CIRP Conference Conference on on Photonic Photonic Technologies [LANE 2018]

Controllable spatial of optical needles withNantes, independent axial intensity 28tharray CIRP Design Conference, May 2018, France distributions for laser microprocessing A new methodology to analyze the functional and physical architecture of a, a a Orlovfor *, Alfonsas Juršėnasoriented , Ernestas product Naciusa, Justas Baltrukonis existing Sergej products an assembly family identification aa Center

Center for Physical Sciences and Technology, Industrial laboratory for photonic technologies, Sauletekio av. 3, Vilnius, LT-10257, Lithuania

Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat

* Corresponding author. Tel.: +370-5-264-9211 ; fax: +370-5-260-2317. E-mail address: [email protected]

École Nationale Supérieure d’Arts et Métiers, Arts et Métiers ParisTech, LCFC EA 4495, 4 Rue Augustin Fresnel, Metz 57078, France * Abstract Corresponding author. Tel.: +33 3 87 37 54 30; E-mail address: [email protected]

Due to their high length to width ratio nondiffracting beams are usually perceived as “optical needles”. We construct an “optical needle” with an arbitrary longitudinal intensity distribution and change the spatial position of it in the focal region of a lens. Next, we introduce a spatial Abstract array of independent “optical needles” and report on physical limitations due to mutual interference of individual beams. We employ a spatial light modulator as a toy model of an actual geometrical phase element and experimentally observe controllable spatial arrays with various Innumbers today’s business environment, towards more product andthe customization is unbroken. Due to this development, the need of and spatial separations the of trend individual beam. Lastly, we variety examine distortions caused by propagation through planar air-dielectric agile and reconfigurable emerged to cope with various products and product families. To design and optimize production interface and attempt to production compensatesystems it. systems well as to choose the by optimal product matches, product analysis areCC needed. Indeed,license most of the known methods aim to © 2018as The Authors. Published Elsevier Ltd. This is an open access articlemethods under the BY-NC-ND © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license analyze a product or one product family on the physical level. Different product families, however, may differ largely in terms of the number and (http://creativecommons.org/licenses/by-nc-nd/3.0/) (https://creativecommons.org/licenses/by-nc-nd/4.0/) nature of components. This fact impedes an efficient comparison and choice of appropriate product family combinations for the production Peer-review under responsibility of the Bayerisches Laserzentrum GmbH. Peer-review under responsibility of the Bayerisches Laserzentrum GmbH. system. A new methodology is proposed to analyze existing products in view of their functional and physical architecture. The aim is to cluster Keywords: Diffraction; Structured oriented light; Optical engineering; beams; Optical Needle; Focal assembly lines; Multiple these products in new assembly product familiesBessel for the optimization of existing linesfocal and spots the creation of future reconfigurable assembly systems. Based on Datum Flow Chain, the physical structure of the products is analyzed. Functional subassemblies are identified, and a functional analysis is performed. Moreover, a hybrid functional and physical architecture graph (HyFPAG) is the output which depicts the similarity between product families by providing design support to both, production system planners and product designers. An illustrative 1. Introduction thestudy electric (or product magnetic) fieldofinsteering the needle is the example of a nail-clipper is used to explain the proposed methodology. An control industrialofcase on two families columns of next of step engineering of focal lines suitable for thyssenkrupp Presta France is then carried out to give a first industrial evaluation the towards proposed approach. ©Nomenclature 2017 The Authors. Published by Elsevier B.V. applications, where the orientation of electromagnetic field is Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018. important. A nondiffracting Bessel beam is a common

radius vector  x, y, z  in Cartesian coordinates example of the optical field, which can be perceived as an optical needle, and is widely used in such applications as laser angle between the z axis and the direction of the wave vector micromachining [3-5] and optical tweezers [6]. In practical applications one needs to eliminate spherical wave vector  k , 0, k zz  k aberration caused by and planar dielectric material interface (e.g. 1.mIntroduction of the product range characteristics manufactured and/or , n integer number, order of the Bessel function focusing from air into the volume of bulk material) [7]. assembled in this system. In this context, the main challengeWe in p integer number, number of the “optical needle” in the investigateand thisanalysis problemisnumerically and demonstrate the Due array to the fast development in the domain of modelling now not only to cope withhow single spherical aaberration may range be eliminated byproduct using modified communication and beam an ongoing products, limited product or existing families, f ( z ) desired axial profile trend of digitization and spectral mask of superimposed Bessel beams. digitalization, manufacturing enterprises are facing important but also to be able to analyze and to compare products to define A  k zz  Fourier transform of the axial intensity profile shaping can beclassical implemented in challenges in today’s market environments: a continuing newVarious product beam families. It cantechniques be observed that existing order to produce complex structures – ranging from a spatial tendency towards reduction of product development times and product families are regrouped in function of clients or features. light modulator (a SLM, in product short, which is flexible buttocannot A combination of beamsInexhibiting long isfocal lines and However, shortened product lifecycles. addition, there an increasing assembly oriented families are hardly find. sustain high laser powers) to a geometrical phase elements small focal spot sizes are strongly desired in a variety of demand of customization, being at the same time in a global On the product family level, products differ mainly in two (which are static (i) butthe usable laser microprocessing applications.with A competitors good example laser of main competition all is over the micromachining world. This trend, characteristics: number in of components and (ii) the applications), see an example in Ref. [8]. structures with dimensions comparable (or even smaller) to which is inducing the development from macro to micro type of components (e.g. mechanical, electrical, electronical). We aimmethodologies here for optical needles in laser the wavelength lightlot [1].sizes Optical exhibiting markets, results of in incident diminished duebeams to augmenting Classical considering mainlyusable single products micromachining but we need to test experimentally our this property are called optical needles [2]. Polarization product varieties (high-volume to low-volume production) [1]. or solitary, already existing product families analyze the To cope with this augmenting variety as well as to be able to product structure on a physical level (components level) which 2212-8271possible © 2018 The Authors. Published by Elsevier Ltd. This is an opencauses access article under theregarding CC BY-NC-ND license definition and identify optimization potentials in the existing difficulties an efficient (http://creativecommons.org/licenses/by-nc-nd/3.0/) production system, it is important to have a precise knowledge comparison of different product families. Addressing this Peer-review under responsibility of the Bayerisches Laserzentrum GmbH.

r 

Keywords: Assembly; Designthe method; identification angle between z axisFamily and the direction 

Peer-review under responsibility of the Bayerisches Laserzentrum GmbH.

2212-8271 © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) 2212-8271 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of scientific the Bayerisches Laserzentrum GmbH. Peer-review under responsibility of the committee of the 28th CIRP Design Conference 2018. 10.1016/j.procir.2018.08.081

Sergej Orlov et al. / Procedia CIRP 74 (2018) 589–593 Author name / Procedia CIRP 00 (2018) 000–000

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theoretical model, so we are using a SLM as a toy model of an actual geometrical phase element. Here we consider various superpositions of non-diffracting Bessel beams with controlled axial intensity patterns and positions in the transverse plane and experimentally implement them.

The spatial spectrum of a shifted optical needle is obtained from Eqns. (3) and (4) using angular Fourier transformation

ˆ (k , k ) 





m  

J m (k 12 )e

 im  12

im e

im  k

 (k sin   k ) k

.

(5)

2. Bessel-like beam translation and axial intensity control Consider a scalar Bessel beam propagating in the direction

 z .Complex amplitude of ideal scalar Bessel beam in this

case in cylindrical coordinates is given by

 (  ,  , z)  J m (k  )eim izk ,

(1)

z

2 where  ,  , z - cylindrical spatial coordinates, k kx2  k y2 

radial wavenumber, k z - axial wavenumber. For the sake of the brevity we consider further only zeroth - order Bessel beams. 2.1. Bessel-like beam axial intensity control The axial intensity control of Bessel beam superposition is achieved as follows. Let us assume a continuous spectral representation of the axial beam profile via the axial beam spectrum

A(k z ) 

1 2







f ( z )e i kz z dz ,

(2)

where f ( z ) is a desired axial beam profile. We assume, that

k kz 0  K z , where k z 0 is a carrier wave vector. If z kz 0  K z , we can rewrite (2) as a Fourier transform 

(r)   A(K z  kz 0 ) (r; kz )dK z .

(3)



Thus, the monochromatic superposition of Bessel beams in Eq. (3) enables to freely engineer the axial intensity distribution of the “optical needle”, which is described here by a freely chosen function f ( z ) . We note, that the case of a discreet Fourier transform with a Talbot effect was presented elsewhere [9].

In order to produce a spatial array of independent optical needles one needs to shift a single optical needle in the transverse plane to the controllable position with coordinates  2 ,2  . This can be achieved using the so called addition theorem for Bessel function [10]. In this way the Bessel beam with origin at shifted point O2 may be expanded as a superposition of Bessel beams in the unshifted origin O1 (see Fig.1) 

J

m  

m

(k 12 ) J n  m (k 1 )e

Finally, for numerical purposes and for the sake of simplicity we replace delta functions with Kronecker’s delta  (k  k sin  )  k , k sin  , where  k , k sin  is Kronecker’s delta. 2.3. Parallel spatial array of optical needles Let us assume, we would like to have a number p  1,2, P of independent parallel optical needles each with its own axial profile and position ( x p , y p ) in the transverse plane. We use the superposition principle and express the resulting spatial spectrum as a sum

ˆ (k , k )    A ( K  k )ˆ (k , k ; x , y )dK ,  x y  p z z0 x y p p z p



where Ap (k z )  1 2 





(6)

f p ( z)eikz z dz is the Fourier transform

of the individual axial intensity profile

f p  z  , and

ˆ (kx , k y ; x p , y p ) is a Bessel beam’s spatial spectrum, when it is shifted in the transverse plane to the point ( x p , y p ) . 3. Experimental setup and results

2.2. Bessel beam translation

J n (k 2 )ei n 2 

Fig. 1. Scheme of notations in the translation of cylindrical coordinates.

im ( 1  12 )

.

(4)

3.1. Experimental setup Numerical simulations were verified experimentally using a phase-only spatial light modulator (SLM) and an optical setup depicted in Fig. 2. An expanded linearly polarized Gaussian



Sergej Orlov et al. /CIRP Procedia CIRP 74 (2018) 589–593 Author name / Procedia 00 (2018) 000–000

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3.2. Experimental results

Fig. 2. Principal setup of the experiment. Experiment

Modeling

Firstly, we compare two experimentally generated arrays of five parallel “optical needles” (each of them is L=2.5 mm long) with different spatial separations d between individual needles, see Fig. 3. As d gets lower, individual beams interfere and transverse profiles of the individual needles become distorted. Nevertheless, this does not seem to be the experimental artefact as our numerical simulations predict such distortions. Moreover, we observe a good agreement between our numerical approach and our experimental implementation as the numerically expected transverse intensity profiles closely match experimental results. At the next step, we keep the same distance d between the individual needles as in Fig. 3(b) and investigate how the destructive interference is affected by the length L. It seems, that in general the reduction of the length L has a positive effect, see Fig. 4(a) – destructive interference is much weaker for shorter beams. We also demonstrate the possibility to control length L of

(a)

(b)

(a) Fig. 4. Experimentally obtained intensity distributions (a) in (x, y) plane of five 1.25 mm length optical needles (d = 0.27 mm), and (b) in (x, z) plane of an array of 5 optical needles with different lengths (L1 = 5 mm, L2 = 4 mm, L3 = 3 mm, L4 = 2 mm, L5 = 1 mm, d = 0.27 mm).

(b) Fig. 3. Intensity distribution of experimentally obtained and numerical calculated parallel arrays of five “optical needles”. The axial length L of individual needle is L= 2.5 mm. The spatial separation between the needles in the transverse plane is (a) d= 0.49 mm, (b) d = 0.27 mm.

beam of the wavelength 532 nm reflects from the SLM at zero degree angle and the phase of the beam is modified by a phase delays induced in the matrix of the SLM (a). The reflected beam propagates through Fourier lens and, as the result, a number of independent “optical needles” are formed in the focal plane. The moving linear translation stage with mounted imaging system is used for scanning along z axis. While the stage moves, the transverse intensity data (b) at different distances from focal plane is imaged onto the CCD matrix of the camera, this image is recorded and processed afterwards by a personal computer. We note that we achieve a x25 transverse magnification and approximately a x5 longitudinal magnification in our setup.

each individual „optical needle”. An array of five different length „optical needles” is depicted in Fig. 4(b). Lastly, in order to celebrate the Centennial of the restored Lithuania, we build a complex array of optical needles positioned as historical Lithuanian symbol “Pillars of Gediminas” [11], see Fig. 5. The spatial spectral phase and amplitude of this structure is depicted in Fig. 6. Thus, we have demonstrated here the possibility to control not only the individual position in the array, but also the individual length and position (x,y,z) of each individual „optical needle”. 4. Numerical simulation of focusing into planar airdielectric interface In this chapter we examine the problem of focusing trough air-dielectric interface by using the methodology described in [7]. The focal field in the second medium [7] can be expressed as an integral of focusing angles

Sergej Orlov et al. / Procedia CIRP 74 (2018) 589–593 Author name / Procedia CIRP 00 (2018) 000–000

592 4

We can effectively compensate axial intensity pattern distortions due to transmission trough the air-glass interface, if we make some adjustments to the spatial spectra of the incident field in the first media (in our case it’s air). The expression for the spatial spectra should be rewritten

V  2 ,    e2  V  2 ,    e  1  V  1 ,    ( s ) e  e1  2 ( p) t 1   t 1   n

cos 1 cos  2 (8)

Fig. 5. Three dimensional intensity distribution of experimentally generated structure “Pillars of Gediminas”.

where we have assumed that the Snell’s law is expressed as sin 1  n sin 2 and spatial angles in Eq. (8) were transformed according to the law. (a)

(b)

(b)

(a)

Fig. 6. Amplitude (a) and phase in radians (b) of the angular spectra of “Pillars of Gediminas” built from an array of “optical needles”. Fig. 8. Amplitude of the angular spectra for two cases: a) after and b) before the spherical aberration was compensated.

(a)

As the last example, we consider the focussing of the same complex “Pillars of Gediminas” through the planar air-glass interface. The interface plane is located at z= 0 , and on the left side ( z < 0 ) we see the back-reflected field, on the right side ( z > 0 , n2  2 ) the transmitted electric field is depicted, see Fig. 7 (a). In the first case, the axial intensity pattern is upscaled in the z – direction due to refraction. We employ now the Eq. (8) and adjust the spectral amplitude, so we get rid of this distortion (see Fig 8. (b) ).

(b)

Conclusion

Fig. 7. Intensity distribution of experimentally generated structures for two cases. b) The structure “Pillars of Gediminas” is focused trough planar interface air-glass without compensation (a) and with compensation (b) of the spherical aberration.

E  t

2  max

  t 0

e

s

0



(1 )[V (1 ,  )e ]e  t p (1 )[V(1 ,  )e1 ]e2 

i( k x x  k y y )  ik z 2 z

,

sin( 2 ) cos( 2 )d 2 d

(7) where Et - transmitted field in the second medium,

V(1 ,  ) e x (1 ,  ) - angular spectrum as defined in (6), e1,2 and e spherical coordinate unit vectors,  ,  - focusing s

p

angles, t , t - Fresnel coeficients, see Ref. [7].

In conclusion, we have presented a flexible technique, which enables us to create experimentally controlled arrays of parallel optical needles with independent axial intensity profiles. We have analyzed how the separation between individual optical needles interplays with the individual lengths of the optical needles. It seems, that the destructive interference is less pronounced for shorter and more spatially separated adjacent needles. Moreover, we have demonstrated the proof-of-concept implementation of the technique, which allows for compensation of various distortions due to the spherical aberration introduced by a planar interface between air and dielectric. Acknowledgements This research is/was funded by the European Social Fund according to the activity ‘Improvement of researchers’



Sergej Orlov et al. / Procedia CIRP 74 (2018) 589–593 Author name / Procedia CIRP 00 (2018) 000–000

qualification by implementing world-class R&D projects’ of Measure No. 09.3.3-LMT-K-712. References [1] Gattass R. R., Mazur E., Femtosecond laser micromachining in transparent materials, Nature photonics 2008; 2: 219–225. [2] M. Zhu, Q. Cao, H. Gao, Creation of a 50,000  long needle-like field with 0.36  width, JOSA A 2014: 31 p. 500–504. [3] Duocastella M., Arnold C. B., Bessel and annular beams for materials processing, Laser and Photonics Reviews 2015; 6: p. 607–621. [4] Bhuyan M., Courvoisier F., Lacourt P., Jacquot M., Salut R., Furfaro L., Dudley J., High aspect ratio nanochannel machining using single shot femtosecond bessel beams, Appl. Phys. Lett 2010; 97: 081102.

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[5] Courvoisier F., Zhang J., Bhuyan M., Jacquot M., Dudley J. M., Applications of femtosecond bessel beams to laser ablation, Applied Physics A 2016; 112: p. 29–34. [6] Orlov S., Stabinis A. Propagation of superpositions of coaxial optical Bessel beams carrying vortices. J. of Opt. A 2004; 6: p.259-262. [7] Novotny, Lukas, and Bert Hecht. Principles of nano-optics. Cambridge university press, 2012. [8] M. Beresna, M. Gecevičius, P. G. Kazansky, and T. Gertus, Radially polarized optical vortex converter created by emtosecond laser nanostructuring of glass. Appl. Phys. Lett., 2011; 98, p.201101. [9] Michel Zamboni-Rached, Erasmo Recami, and Hugo E. HernándezFigueroa, "Theory of “frozen waves”: modeling the shape of stationary wave fields," J. Opt. Soc. Am. A 22, 2465-2475 (2005) [10] Stratton, Julius Adams. Electromagnetic theory. John Wiley & Sons, 2007. [11] https://en.wikipedia.org/wiki/Columns_of_Gediminas