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Additive manufacture of photonic components for the terahertz bandEnrique Castro-Camus,1 Martin Koch,2 and Arturo I. Hernandez-Serrano31)Centro de Investigaciones en Optica A.C., Loma del Bosque 115, Lomas del Campestre, Leon, Guanajuato 37150,Mexico.a)2)Faculty of Physics and Material Sciences Center, Philipps-Universitat Marburg, Renthof 5, 35032 Marburg,Germany.3)Physics Department, University of Warwick, Coventry CV4 7AL, United Kingdom

(Dated: 18 May 2020)

In this Perspective contribution we present a brief review of the literature available on opticaldevices for terahertz frequencies, followed by an analysis of the challenges faced by thistechnology and its future potential to generate complex photonic systems, and in principlethe possibilities of this technique for the production of components for the infrared and visibleband.

This is a pre-print. The final version will appear at The Journal of Applied Physics (2020).

PACS numbers: Valid PACS appear hereKeywords: 3D printing, terahertz, optical, photonic, components

I. CONTEXT

The development of the fused deposition modelling(FDM) method has allowed the use of affordable andreliable three-dimensional printers over the last decade,to the point that a good number of research laborato-ries have them within their toolboxes, and even “am-ateur” developers have access to this technology athome. The capacity of making a computer assisted three-dimensional design and having it fabricated within min-utes has revolutionized the way prototypes are conceivedand developed. While it might be obvious that 3D print-ing can be used to produce components that would tra-ditionally be made in a mechanical workshop, opticalcomponents might not, a priori, be natural candidatesfor 3D printer based fabrication. Yet, if we take theterm “optical” in a broad sense, i.e. not restricted tothe visible band of the electromagnetic spectrum, theresolution of these printers is enough to produce opti-cal and photonic components for wavelenghts falling inthe terahertz regime.1 Yet, materials which are beingused for optical elements need to be largely transpar-ent over the frequency range in which they should beused. Many standard materials that are being used for3D printing show a considerabe absorption and cannotbe used to print THz lenses or waveguides. As a rule-of-thumb one can state that, just like liquids,2–4 polarpolymers are absorbing while non-polar polymers show areasonable transparency in the THz range. Polyethyleneand polypropylene show a very good transparency in thelower THz frequency range as shown in Fig. 1, but un-fortunately they are inappropriate for 3D printers basedon fused material deposition. In fact any thermoplasticmaterial can be used for printing, however, the print-ing quality varies considerably depending on the meltingpoint, thermal expansion coefficient, and elasticity, of thematerial. Fortunately several materials, appropriate for3D printing, such as polystyrene (ps), TOPAS and Bend-ley have low enough absorption in the terahertz band to

a)Electronic mail: enrique@cio.mx

FIG. 1. Refractive index and absorption coefficient ofvaripous thermoplastics used in FMD 3D-printing.5,13 Theacronyms and abreviations are: HDPE=High DensityPolyethylene, Polyprop.=Polypropylene, ABS=AcrylonitrileButadiene Styrene, PLA=Polyactic acid. Data from5,13.

be considered transparent,5–12 opening the possibility toproduce geometrically complex dielectric devices, whichwould be hard, if not impossible, to produce in the moretraditional visible or near infrared regions.

With the ideas mentioned in the previous paragraphsin mind, many groups around the world have testedthis technique for the production of components thatrange from very conventional mirrors 6,16, lenses 5,17,18,prisms 19, gratings 13,20–29 and antireflection structures 30

to optical components that are less conventional such asGRIN lenses14,31–33 (see Fig. 2a and Fig.4) and diffractivedevices 34–36. In addition some beam modifier compo-nents such as Airy 37,38 or Bessel 39–41 beam generatorshave been introduced such as the ones shown in Fig. .Furthermore, designs of variable or active optical com-ponents like an Alvarez lens 42 have been published.

Since 3D printing opens the possibility of creatingrather complex geometrical structures a possibility thatseems very appealing is to produce rectangular di-electric 43–46, plasmonic 47, metal-dielectric 48 and other

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(a)

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FIG. 2. Two examples of 3D printed optical components. (a)Is a Gradient-Refractive-INdex (GRIN) lens,14 which benefitsfrom the sub-wavelength resolution, at a few hundred GHz, ofthe printer, in order to produce a quasi-continuous variationof the effective refractive index as function of the radial coor-dinate, which induces the lens behaviour, althogh the compo-nent has flat faces in the plane of the page. (b) Is a topologicalwaveplate,15 which also uses the sub-wavelenth resolution ofthe printer in order to generate form-birefringence at 150GHz,yet the direction of the slow and fast axes of the material area function of the position,this component can be used in or-der to generate exotic polarization modes such as radial orazimuthal “polarization”.

FIG. 3. Height profiles (a, c) and photos (b, d) of of two3D-printed elements which, in conbination, generate an Airybeam.38 Reproduced with permission from Optics express 24,29342 (2016). Copyright 2016 The Optical Society.

forms of waveguides 49 and waveguide-based filters 50, aswell as Bragg 51–53, photonic crystal 54–57, such as theones depicted in Fig. 5, and hollow core optical fibers 58–62

as well as various preforms for optical fibers 63–65. Addi-tionally, photonic crystals 44,55,66–69 among other meta-materials 70–73 appear in recent publications, that includesome engineered corrugated surfaces to couple electro-magnetic radiation with polaritons 74. All these compo-nents can open the possibility to interconnect various de-vices and, in principle, create integrated optical circuitryat terahertz frequencies. In fact, the first experiments to

FIG. 4. A 3D terahertz gradient-refractive index lens designedby transformation optics is achieved by fabricating “wood-pile” structures with varying dimensions of subwavelength di-electric unit cells using the projection microstereolithographytechnique. Both simulation and experimental investigationsconfirm that the lens delivers an imaging resolution very closeto the diffraction limit over a frequency range from 0.4 to 0.6THz.31 Reproduced with permission from Advanced OpticalMaterials 4, 1034 (2016). Copyright 2016 Wiley-VCH VerlagGmbH & Co. KGaA.

transfer waveguide “wire”-based data streams at a fewhundred GHz have recently been carried out.75,76 Yet,very recently it was also found that the humidity in theambient air leads to a water film to form on bare polymerwires.77 This water film is highly absorbing and limits thetransmission distances for polymer wire-bound transmis-sion. This shows that THz waveguides will require acladding or other more complex inner structures. Here,3D printed waveguides or 3D printed preforms for pulledwaveguides could be a solution.

Polarization handling and modifying components havealso been introduced. For instance polarizers 78–80, po-larization splitters 81, waveplates 82, topologica plates15

(see Fig. 2b), vortex beam generators 83–86 and polarizedgrids 79 have been explored and reported. In addition,the use of 3D printing technology has allowed to demon-strate waveguides that act as focusing probes 87 for nearfield microscopy or for endoscopic purposes 88. Variousholograms have also been reported26,27,89–93.

A quick inspection of the list of references cited in theprevious paragraphs allows us to realize that most of theinvestigation in this field has happened in the last 5 years,therefore it can still be considered an emerging researchtopic with enormous potential in the near future for tworeasons. Firstly, the number and complexity of photoniccomponents for the THz band is expected to quickly growin the next decade driven by the imminent shift of wire-less communications, that currently use the 3 GHz band,to higher frequencies.94 Secondly because with the im-provement of resolution of the printers, 3D printing willsoon be able to produce components for the mid infrared,and eventually for the visible band. As a matter of fact,a few 3D printed components for the infrared have al-ready been explored,95–97 such as the one shown in Fig. 6.

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FIG. 5. (a) Photograph and (b) calculated fundamentalguided mode structure at 1 THz for a “large” mode area fiber,and (c) photograph and (d) calculated fundamental modestructure at 1 THz of a “small” mode area (SMA) fiber. (e)Photograph of fibers shaped into 90◦ bends.54 Reprinted withpermission from Optics Express 17, 8592 (2009). Copyright2009 The Optical Society.

Therefore, the experience gained a at terahertz frequen-cies, will be crucial to exploit this technology on otherbands of the electromagnetic spectrum.

II. LIMITATIONS

The main two limitations for this technique are the,still, relatively poor resolution of economical FDM 3Dprinters, and the limited number of highly transpar-ent printable polymers, all with refractive indices in thevicinity of 1.5.

The consequence of the poor resolution of FDM print-ers is that devices operate in the few hundred gigahertzregion, which is only the low frequency end of the THzband. This can be overcome by using other 3D print-ing techniques, which unfortunately are currently not aswidely available, or as accessible in terms of cost. Fur-thermore, those printers use a completely different set ofmaterials, which are sometimes sold in sealed cartridgesby the printer manufacturers only, and little, or no in-formation about their composition is available. Yet theFMD technology is expected to still evolve, and perhapsit will reach the desired resolutions in the future.

The limited number of THz-transparent polymers thatcan be 3D printed, which all have very similar opticalproperties (n∼1.5) prevents the possibility of fabricatingseveral interesting components, such as photonic crystalswith large bandgaps, where a significant refractive indexcontrast is required.

(a)

(b)

(c)

(d)

FIG. 6. Spiral phase plates have been fabricated by 3D print-ing on the tip of optical fibers, demonstrating the possibil-ity of using additive manufacture of components, in this casefor the near-infrared region. (a) Shows an scanning-electron-micrograph, (b) an optical-micrograph (c) an optical profilom-etry reconstruction of the device after fabrication. (d) Illus-trates how this device can be used to modify the angular mo-mentum state of optical beams.97 Reproduced with permis-sion from Opt. Express 25, 19672 (2017). Copyright (2017)The Optical Society.

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FIG. 7. (a) Number of articles per year (circles) as reported byWeb of Science on 21-10-2019 for the search chain “terahertz3D print”, the square is an estimation for the end of 2019. (b)Number of citations to the articles in (a) per year (circles) asreported by Web of Science on 21-10-2019, the square is anestimation for the end of 2019.

III. PERSPECTIVES

As seen in the context section many different quasi-optical/photonic devices have been demonstrated in thelast few years, some of which were only predicted theoret-ically until these reports. Some of such devices have notbeen demonstrated for the visible range or other bandsof the spectrum, mainly because of the impossibility offabricating them with conventional techniques such aspolishing of traditional materials like glass in the com-plex geometries required.

A topic search in the Web of Science using the chain

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“terahertz 3D print”(on 18-10-2019) produces the resultsshown in Fig. 7. The figure shows the number of articlespublished (a) and their citations (b) by year. The dashedline, provided as a guide-to-the-eye is the result of fittingan exponential function, while we do not expect this ex-ponential to be a very accurate model, it provides a qual-itative approximation of the past and short-term-futurebehaviour. We consider, that this area is an emergingtopic with great potential, of course, for the terahertzcommunity, but for the broad optics and photonics com-munity too. We can foresee that in the coming few years,the resolution of 3D printers will increase substantially,opening the possibility to prototype and mass producecomponents appropriate for wavelenghts from the mi-crowave to the visible bands of great complexity, thattoday can not be produced even in highly specialized re-search facilities. One can only imagine, perhaps photoniccrystals with a complex three-dimensionally distributeddefect structure, three-dimensional waveguide structuresof specifically engineered dispersion or frequency selec-tive transmission that interconnect photonic logic gatesin order to form complex integrated optical circuits, allof this fabricated in minutes from simple computer as-sisted designs. The potential applications are still to beseen. In this sense those of us working in the wavelenghtrange from ∼100µm to a few millimeters, i.e. the tera-hertz band are lucky to be the first ones to explore thisprototyping technology for photonic devices.

It is worth mentioning at this point that other 3D-printing technologies, apart from FMD, have recentlybeen explored for the fabrication of terahertz devices. Forinstance photo-polymerization based printing is an inter-esting option. This technique consists on projecting op-tical images on a reservoir of liquid polymer, which hard-ens only on the exposed regions, forming a layer of the3D model, this layer is then mechanically lifted, then thefollowing layer is exposed and the process is repeated un-til the 3D shape is completed. Initial characterization ofsome of the photo-polymer materials used have been car-ried out98 and some components have been demonstratedusing this technique99. Other examples include materialjetting99, binder jetting and selective laser melting,45 thelast two open the possibility of making metallic struc-tures, such as antennas, with complex geometries.

As for the number of 3D-printable materials avail-able, the selection of commercially available polymers hasgrown in the last few years. Yet, most of them are eithernot transparent enough or their refractive index is, for allcases, close to 1.5. This is a challenge to address in thecoming years. Finding non-conventional polymers withmelt and re-solidifying temperatures and times appropri-ate for 3D printing that show refractive indices greaterthan 2 and low absorption is highly desirable. Anotherapproach that we have tried, is the incorporation of ad-ditives to conventional 3D printable polymers that canincrease their refractive index,100 however these materi-als are not appropriate for 3D printing yet, but thereshould be interesting opportunities in that direction. Inparticular it is conceivable that new non-polar polymersappropriate for 3D printing and with a lower absorptionin the THz range than polyethylene and polypropylenewill be developed. One should recall that ordinary glass is

not very transparent at optical frequencies. A glass win-dow only a few millimeters thick is transparent, however,a block of ordinary glass with a thickness of 1 m is in factopaque. Yet the need to produce optical fibers, pushedthe development of new extremely transparent glasses inthe 1970s and 1980s which enabled the the glass fibrebased communication network in place around the globenowadays.

One additional aspect that makes printable opticalcomponents desirable is the ability to print not only theoptics, but the mounts that hold them in an optical sys-tem, this allows “makers”, low-budget laboratories indeveloping countries and even to pre-university schoolsto set up terahertz experiments.101 This effectively canmake terahertz technology and research widely accessibleto professionals and amateurs world wide.

IV. FINAL REMARKS

The possibilities that three-dimensional printing hasopened for both prototyping and production are still hardto appreciate in many fields, optical and photonic compo-nents are not the exception. A plethora of conventionaland also non-conventional optical components for the ter-ahertz band have been demonstrated recently. The trendshown by the number of publications in this area seemsto indicate that the interest in this field is growing. It isto be expected that soon the availability of new materialsand the improvement on the printing hardware will allowthe fabrication of more complex and interesting devicesin the near future. It is even possible to foresee that thistechnology will soon expand to shorter wavelenghts withpotential for the near infrared and visible regions of thespectrum.

ACKNOWLEDGEMENTS

We would like to thank the support of the Alexandervon Humboldt Fundation through an Experienced Re-search Fellowship awarded to ECC hosted by MK.

DATA AVAILABILITY

The data that support the findings of this study areavailable from the corresponding author upon reasonablerequest unless it comes from a cited reference.

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