Polarisation of THz synchrotron radiation: from its measurement to control
Meguya Ryu, Denver Linklater, William Hart, Armandas Balcytis, Edvinas Skliutas, Mangirdas Malinauskas, Dominique Appadoo, Yaw-Ren Eugene Tan, Junko Morikawa, Saulius Juodkazis
PPolarisation of THz synchrotron radiation: from its measurement to control
Meguya Ryu, Denver Linklater, William Hart, Armandas Balˇcytis, Edvinas Skliutas, Mangirdas Malinauskas, Dominique Appadoo, Yaw-Ren Eugene Tan, Junko Morikawa, and Saulius Juodkazis
2, 6 Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8550, Japan Swinburne University of Technology, John st., Hawthorn, Victoria 3122, Australia Laser Research Center, Department of Quantum Electronics, Faculty of Physics,Vilnius University, Saul˙etekio Ave. 10, Vilnius LT-10223, Lithuania Infrared Microspectroscopy Beamline, Australian Synchrotron, Clayton, Victoria 3168, Australia Australian Synchrotron, Clayton, Victoria 3168, Australia Melbourne Center for Nanofabrication, Australian National Fabrication FacilityClayton,Victoria 3168, Australia (Dated: September 24, 2018)Polarisation analysis of synchrotron THz radiation was carried out with a standard stretchedpolyethylene polariser and revealed that the linearly polarised (horizontal) component contributesup to 22 ±
5% to the circular polarised synchrotron emission extracted by a gold-coated mirror witha horizontal slit inserted near a bending magnet edge. Comparison with theoretical predictionsshows a qualitative match with dominance of the edge radiation. Grid polarisers 3D-printed out ofcommercial acrilic resin were tested for the polariser function and showed spectral regions where thedichroic ratio D R > < PACS numbers: polarisation, FT-IR, synchrotron, anisotropy of absorbance, 3D printing
I. INTRODUCTION
Methods of terahertz generation are evolving fast us-ing ultra-short laser pulses, electrically driven 2D elec-tron gas in semiconductor junctions, and photo-mixing,laser-driven electron plasmas to facilitate number of ap-plications which require smaller and portable devices .The highest intensity THz sources are available at freeelectron laser and synchrotron facilities . With a high-brilliance synchrotron THz radiation it is possible touse imaging arrays and monitor in situ temporal evo-lution, e.g., of a phase transition in real time. Polarisa-tion of synchrotron THz radiation becomes important inabsorbance spectroscopy and for investigation of orien-tational anisotropy . Even for non-absorbing trans-parent materials at THz spectral range, a birefringencewould cause polarisation changes due to a purely refrac-tive phase delay which is important for interpretationof spectroscopical data. Synchrotron THz wavelengthsare spanning wavenumber range 7-700 cm − (or 0.2 -21 THz), which in terms of wavelengths are 1.43 mm -14.3 µ m. With a widely accessible 3D printing technologyreaching tens-of-micrometers resolution of plastic compo-nents, there is a potential to make optical elements forTHz applications. Rough surfaces on ∼ − µ m scaleon 3D printed surfaces can be smoothed by controlledreflow using strongly absorbed UV post-illumination ofthe plastic workpieces and are reaching required sub-wavelength λ/
10 min-max roughness even for the visible-IR spectral range applications. Plastics have refrac-tive index of ∼ . . Molecular ordering in σ π e - e - Dipole radiationEdge radiation Edge radiationDipole magnetto IR beamline mirror
FIG. 1: Source of dipole and edge radiation which both have σ (horizontal along the slit) and π (vertical) components col-lected for the use at the IR beamline. Further along the beam-line there is a beam splitter box that then directs the dipoleradiation to the mid-IR branch of the beamline and the edgeradiation to the far-IR branch. Pickup of THz radiation ismade with the first mirror (photo). Intensity shows distribu-tion of IR-THz radiation at the first mirror reflection. polymers cause birefringence and an anisotropy of ab-sorbance, which can be determined by the four polarisa-tion method used in this study.Polarisation of synchrotron THz radiation has a com-plex structure which has to be well understood whenbeam is focused (or imaged) onto the sample with spotsizes down to sub-1 mm from the first mirror where thebeam has cross sections of ∼ a r X i v : . [ phy s i c s . i n s - d e t ] J u l THz radiation is created by relativistic electrons travel-ing through a dipole magnet.The observed radiation from a dipole magnet in the or-bital plane of the electron is referred to as σ -polarisationmode radiation and is typically horizontally polarised. Inthe perpendicular plane with a non-zero vertical observa-tion angle, ψ , we have the π -polarisation mode radiationand is typically vertically polarised. The combination ofthe σ and π modes results in elliptically polarised radia-tion above and below the deflection plane of the electronbeam (Fig. 1). The proportion of the integrated powerof the σ mode to π mode radiation is, P σ = P tot and P π = P tot for typical dipole radiation .The THz spectrum of the synchrotron radiation usedby the far-IR branch of the IR beamline at the Aus-tralian Synchrotron (AS) has a horizontal acceptance of-14 mrad to +14 mrad and focuses on using the radiationcreated by the electron beam just as it exits and entersthe magnetic field of the dipole magnet . This is re-ferred to as edge radiation. The spatial and wavelengthdependent distribution of the linearly and elliptically po-larised radiation is more complex at the edge than inthe body of the dipole magnet and is discussed inSec. III B.In THz spectral range, it is possible to use linear po-larisers to set polarisation at the sample with metallicgrid or metallic gratings with high extinction ratio de-fined by transmission for the transverse magnetic andelectric modes E r = T T M /T T E (cid:39)
45 dB at 1 THz .This is achieved at the cost of a reduced intensity. Byphase and polarisation control with 3D-printed optical el-ements with small absorption losses, it would be possibleto create more efficient optical elements for polarisationcontrol.Here, we report results of a polarisation study of THzsynchrotron radiation and characterisation of 3D-printedacrilic grid waveplate polarisers. Simulation of polarisa-tion at the bending magnet edge is compared with ex-perimental measurements at the sample location. II. METHODS
Polarisation analysis of synchrotron radiation wascarried out at the IR Beamline on Australian Syn-chrotron, Melbourne with a standard linear stretchedpolyethylene (PE) polariser (Bruker No. F251; 45 − µ m-thick PE). Figure 2 shows schematics of experimentsfor polarisation analysis and absorbance anisotropy mea-surements of the 3D-printed micro-gratings. A. 3D-printed THz optical elements
Plastic gratings of varying aspect ratio (the depth-to-width) AR = d/w , duty cycle DR = w/P and period P (see geometry in Fig. 2(b)) were fabricated using the Em-ber 3D printer (AutoDesk). The Ember printer possesses (a) (b) (c) z y x mirror A A p /2 A A p /2 A FIG. 2: (a) Geometry of experiment designed to characterisepolarisation of the THz radiation by mirror with 3-mm-widemid-gap. (b) 3D printed grating used as polarisers. (c) Ex-pected angular dependence of the absorbance, A = − lg T ,from sample with orientational anisotropy. a 405 nm wavelength light emitting diode (LED) sourceand a Texas Instruments digital micro-mirror (DMD)projection system which facilitates the UV-curing of anentire s = (10 − µ m layer over a single exposure. TheEmber 3D printer is capable of an xy-resolution of 50 µ m,and a z-resolution of 10-100 µ m. Gratings were set in aframe to allow them to be fixed to a polarisation filtermount. Grating width w ranged between 100-200 µ m,period P varied between 100-400 µ
100 200 300 400 500 600 70090450-45-90
Wavenumber (cm -1 ) A ng l e ( deg r ee s ) -0.5000-0.250000.25000.5000 Transmittance (r ad ) I n t en s i t y ( a r b . un i t s ) Angle (rad) (a)(b) offset amplitudeEqn. 2 I n t en s i t y FIG. 3: (a) Experimental orientational dependence ofsynchrotron radiation transmission (squares) through thepolyethylene polariser and the best fit by Eqn. 2; the phasewas chosen for the best fit. (b) Spectrum-polarisation map ofsynchrotron radiation (the offset subtracted). sign files and STL model files within the design space.To print gratings with a large phase retardance or ab-sorbance along propagation of the THz beam (z-axis;Fig. 2(b)), the printing sequence followed stacked ex-posures as samples are moved along the x-axis. UsingAutodesk software, Print Studio, sample files were ori-ented perpendicular to the build-head to allow sequen-tial stacking of model layers, “growing” the grating in alayer by layer mode as the build-head is rotated acrossthe resin tray, and lifted step-wise after the exposure ofeach model layer. Gratings were printed in 25 µ m lay-ers, with a 5 s exposure time for 4 burn-in layers, 8 sexposure for the first layer and 1.4 s exposure per eachsubsequent 25 µ m layer. The print speed of 25 µ m layerswas 18 mm/h. The build head was optionally covered inKapton tape to assist removal of the samples. 3D printedgratings were detached from the build head, then rinsedin a sequence of acetone, isopropanol and water to removeuncured resin.For comparison of polariser performance, 3D-printedgrids were coated with a 100 nm sputtered gold film.Such gratings can be considered having no transmissionin the beam region for the light polarised along θ = 0azimuth (a strong extinction due to reflection and ab-sorption) and simulates performance of the gratings with AR = ∞ . B. Optical characterisation
The dichroic ratio is defined by the maximum-to-minimum absorbance ratio D r ≡ A /A π/ , where A ,π/ are absorbance values at two perpendicular orientation
100 200 300 400 500 600 7000.00.51.01.52.0
Wavelength ( m) I n t en s i t y ( a r b . un i t s )
100 200 300 400 500 600 7000.00.20.40.60.81.0 lin. pol.circular pol. A m oun t o f li nea r po l . Wavenumber (cm -1 ) polyethylene (a) (b)
15 15
FIG. 4: (a) THz radiation spectrum (unpolarised). (b) Por-tion of the linearly polarised component
Lin (Eqn. 3.) Thespectral position of the absorption band of polyethylene at2 . ± . is shown by the circular marker. Horizontalline at Lin (cid:39) .
22 defines the average contribution of the lin-early polarised (horizontal) component of E-field. The regionenclosed in the box is where transmittance of the polyethylenepolariser is constant. angles θ . The D r was determined for differently pre-pared 3D-printed grid polarisers; see, the plot is for theabsorbance, A , in Fig. 2(c). When D r = 1 material (pat-tern) has isotropic absorbance while the metallic grid po-lariser has D r > A π/ is smaller. The case of D r < A θ and only four angles withangular separation of π/ : A θ = A cos ( θ ) + A π/ sin ( θ ) . (1)This method was recently used to determine anisotro-phy of absorbance of silk at mid-IR spectral range . III. RESULTS AND DISCUSSIONA. Polarisation of synchrotron THz radiation
Synchrotron THz radiation is extracted from the edgeof a dipole magnet using a mirror with a 3-mm-wideslit (Fig. 1(b)) to allow higher energy photons to passthrough. The resulting elliptically polarised radiationcan be separated into a circularly polarised (isotropic) -20 -10 0 10 2002468 D i po l e f l u x ( , a r b . un i t s ) -20 -10 0 10 2002468 E dge f l u x ( , a r b . un i t s ) Vertical angle (mrad) -20 -10 0 10 2002468
500 cm -1
100 cm -1 -20 -10 0 10 2002468 Horizontal angle (mrad) (a) (b) (c) (d) mirror FIG. 5: (a) and (c) Compares the σ and π modes for 100 cm − and 500 cm − as a function of the vertical observation angle, ψ while (b) and (d) shows the change a function of the hori-zontal observation angle (in the plane of the electron beam), θ . The comparison highlights the complex nature of the edgeradiation. Inset in (b) schematically shows the first mirrorand angular spread of the IR-THz beam extracted into thebeamline. component of the light field E I and a linear component E L aligned with the horizontal slit ( θ = 0 ◦ azimuth). Fig-ure 1(b) shows intensity distribution of the synchrotronradiation beam taken to the IR beamline. A standardlinear stretched polyethylene polariser was set into thebeam at normal incidence and its orientation, θ , waschanged by a motorized stage while measuring transmis-sion (Fig. 1(b)).Figure 3(a) shows the angular dependence of trans-mission, T ( θ ) measured with 20 ◦ orientation steps andthe best fit to the Malus law ∝ cos ( θ ) for the analysedcase as shown below. For this case of horizontally po-larised linear component E L ( θ = 0 ◦ ) mixture with theisotropically (circularly) polarised field, E I , lets establishan orthogonal base with E-fields at two azimuths θ = 0and θ = π/ E ,π/ , respectively, for the output (trans-mitted) intensity E θ : E θ = E cos ( θ ) + E π/ sin ( θ )= (cid:18) E I + E L (cid:19) cos ( θ ) + 12 E I sin ( θ )= 12 ( E I + E L ) + 12 E L cos(2 θ ) , (2)where I off = ( E I + E L ) is the offset intensity and I amp = E L is the amplitude of the transmitted light
100 200 300 400 500 6000.000.250.500.751.00 L i n = E L2 / ( E I + E L2 ) Wavenumber (cm -1 ) Dipole Edge
FIG. 6: Simulation data showing contribution of the linearpolarisation (horizontal; along the first mirror slit, Eqn. 3);modeling is shown in Fig. 5 at selected wavenumbers. Differ-ence in spectral dependencies of
Lin ratio shown for the dipoleand edge radiations. Radiation is integrated over the verticalobservation angle, ψ from -8.5 to +8.5 mrad and horizontallyover θ from -14 to 14 mrad. (through the analyser). The best fit to cos(2 θ ) depen-dence according to Eqn. 2 provides I off and I amp values.By measuring angular dependence of the transmissionspectrum, it is possible to present a map which showsspectrum in abscise and and orientation in the ordinatedirections (Fig. 3(b)). It is revealed that the used po-lariser has a spectrally broadband action over the entireTHz window (Fig. 3(b)).Exact portion of the linearly polarised light in the en-tire spectrum (Fig. 4(a)) is estimated by the factor: Lin ≡ E L E L + E I = I amp I off , (3)which is plotted in Fig. 4(b) and obtained as the bestfit to experimental data at fixed wavelength using I amp and I off parameters. At the most intense THz spectralrange it was close to 22%. The highest linearly polarisedintensity is obtained at θ = 0 ◦ , horizontally with the firstmirror slit. B. Edge radiation
A diagram of the source of synchrotron radiation forthe IR beamline is shown in Fig. 1. The spatial andspectral distribution of the synchrotron radiation from adipole magnet is well understood and using the equationsfrom ref. the integrated flux of the σ and π polarisationsof radiation were simulated.The dipole radiation is extracted with a rectangularmirror (30 × ×
460 mm; Fig. 1(b)) located ∼ .Matching of numerical apertures of the radiation gath-ering optics along the entire beamline also plays an im-portant role. The ´etendue , ε , is a measure of the fluxgathering capability of the optical system, i.e., the col-lected power is the product of ε = area × solid angle [m sr] and the radiance of the source [W/m /sr].In Fig. 5 the comparison clearly highlights the complexnature of the edge radiation and is sensitive to the ex-act profile of the magnetic field at the edge of the dipolemagnet. These simulations only account for the distri-bution of radiation from a single electron, while for ex-act simulation it would need to factor in the cross sec-tion of the electron beam ( σ x , σ x (cid:48) , σ y , σ y (cid:48) ) . Using thissingle electron model and describing the elliptical radi-ation as a combination of linear and circular polarisa-tions (as presented in Eqn. 3) Fig. 6 compares how theratio of linear to circular polarisation changes as a func-tion of wavenumbers for the dipole and edge radiation.A larger contribution of the horizontal linear polarisa-tion at small wavenumbers is characteristic for both thedipole and edge radiation. The measured polarisation ra-tio Lin at the sample location (Fig. 4(b)) shows a smallerportion of the linear polarisation due to the ´etendue , ε ,and potentially reflects the unmatched numerical aper-tures for radiation collection. However, the same trendof larger contribution of linear (horizontal) polarisationat low wavenumbers ( <
100 cm − ) as theoretically pre-dicted was experimentally observed. C. 3D printed polariser grids
With the fully determined polarisation of the THz radi-ation, 3D-printed optical elements (Fig. 7(a)) were char-acterised using the same setup shown schematically inFig. 2 for different duty cycle and aspect ratio acrylicelements. Figure 7(b) shows dependence of the dichroicratio D r = A max /A min ∝ T min /T max vs. wavelength.The D r was increasing for longer wavelengths as wouldbe expected for a grid-type polariser where E-field com-ponent along the grid beams is absorbed stronger. Thiseffect was not very strong since P > λ , however, the ten-dency is clearly recognisable and is more expressed for thehigher aspect ratio grids (more absorbance). As the AR was increasing a tendency of D r < µ m wavelength region (Fig. 7(b)). Anisotropy inmolecular alignment is an expected cause (can be linkedto the stress in the printed grid). Similarly, the speed ofsilk formation is defining molecular alignment and me-chanical strength of silk brins . The optical birefrin-gence and activity due to an orientational anisotropy isalso linked to anisotropy of absorbance and is one of theconsequences of the molecular alignment .Usually, the optimum duty cycle for polarisation op-tics and phase retardance ∆ n × d is at DR = 0 . n is birefringence. This directly follows from the effectivemedium theory (EMT) which shows that the smallestheight structures required to effectively phase delay thebeam have the minimal height. This usually correspondsto a desired fabrication condition. Since the EMT cannot be used for the case discussed here with P > λ , the efficient phase control cannot be achieved. The dichroicratio shown in Fig. 8 is close to D r ∼ DR = 0 . D r >
1, again as wavelength is in-creased closer to the EMT range (Fig. 8(a)). By sputter-ing 100 nm of gold, the 3D-printed grating has to becomemore anisotropic since THz E-field component parallel tothe grid beams should be absorbed in metal; this can beconsidered equivalent to an increase of the aspect ratio AR → ∞ . However, the effect of D r > P > λ .Dichroic losses measured of a grating for two linearlypolarised beam orientations e − ∆ ” = (cid:112) P (cid:107) /P ⊥ providesan indirect measure whether material is suitable for fab-rication of phase elements, optical retarders to controlphase, polarisation, focusing, and orbital momentum.The achievable efficiency of an optical element, from G r i d e ff e c t A n i s o t r o p i c a b s o r p t i o n m m (a) (b) Au 100 nm m m 379 m m SEM: front-view side-view s s
20 40 60 80 100 1200.60.81.01.21.41.6 D i c h r o i c r a t i o Wavelength ( m m)AR = 2 4 6 FIG. 7: (a) SEM front- and side-view images of a 3D-printedgrating and photo images of typical samples made out of Mak-erJuice G+ (red) and SF (green) resins; s is the thickness oflayer made in one exposure. Time required to print one sam-ple was ∼ D r = A max /A min ∝ T min /T max (in other conventions D r = A /A π/ = A (cid:107) /A ⊥ )vs. wavelength for acrylic 3D-printed gratings of severalaspect ratios AR = dw ; period P = 400 µ m, duty ratio DR = wP = 0 .
33. The same spectral window is enclosedin the box in Fig. 4. The color shaded regions mark spec-tral ranges where grid effect and anisotropy of absorption arepronounced.
20 40 60 80 100 1200.751.001.251.50 D i c h r o i c r a t i o Wavelength ( m) DR = 0.25 0.33 0.50
20 40 60 80 100 1200.751.001.251.50 D i c h r o i c r a t i o DR = 0.25 0.33 0.50 (a) (b)
FIG. 8: The dichroic ratio D r vs. wavelength for acrilic 3Dprinted grid without (a) and with (b) 100 nm gold coating forseveral duty ratios DR = wP ; period P = 400 µ m. the material point of view, is related to the smallestlosses defined by the imaginary part of refractive index( n (cid:48) + in ” ), which is linked to the retardance and dichro-ism by ∆ = ∆ (cid:48) + i ∆ ” with ∆ ( (cid:48) , ”) = k [ n ( (cid:48) , ”) (cid:107) − n ( (cid:48) , ”) ⊥ ] d ;the retardance ∆ (cid:48) and dichroism ∆ ” of the d height opti-cal element (e.g., grating) at wavevector k = 2 π/λ forthe wavelength λ governs the efficiency of the opticalelement. The amplitude of the E-field decreases expo-nentially with the hight, i.e., the intensity is given bythe Lambert-Beer’s law I ( h ) = I e − n ” ωh/c = I e − α ( ω ) h ,where α ( ω ) = 2 n ” k is the absorption coefficient. Then,the amplitude, Amp , of the cos-wave-form measured bythe 4-polarisation method (Eqn. 1) is related to thedichroism as:
Amp ≡ ( A (cid:107) − A ⊥ ) / k ( n ” (cid:107) − n ” ⊥ ) h ≡ ∆” . (4)For efficient absorbance and retardance control, 3D print-ing technology has to deliver P < λ precision of structur-ing which begin to be accessible at THz spectral band.Here we showed that open grid structures with high as-pect ratio can be fabricated at the desired DR = 0 . D r . The printingmethod demonstrated here allows 3D printing of gratingswith arbitrary depth, d , of the structure. IV. CONCLUSIONS AND OUTLOOK
Contributions of the linear and circular polarisationcomponents in THz beamline spectrum have been deter- mined using polarisation analysis of transmission.3D-printed acrylic gratings with rod width of ∼ µ m period, duty cycle 0.5, and aspect ratio up to 8were made out of standard acrylic resin. Low absorbanceof 3D-printed structures is promising for fabrication ofphase control elements (optical retarders) which wouldopen new set of polarisation control of THz beams. Theability to rapidly produce a wide range of complex op-tical elements using 3D printing from various materials(including biocompatible materials) is a key benefit of 3Dprinters such as Ember that further enhance this possi-bility. Polariser-analyser setup will be required to furtherinvestigate optical retardance due to phase delay in ad-dition to the absorbance investigated in this study.Phase control using different approaches tested forvisible and near-IR spectral ranges are transferrable tolonger IR and THz frequencies. Usual phase controlrelies of defined thickness of material (the propagationphase) , geometrical phase made by azimuthal pattern-ing of orientation of the optical axis , as well as us-ing metamaterials with phase control by spectrally over-lapping electric and magnetic dipoles in non-absorbinghigh-refractive index materials ( n > which allow toengineer polarisation, intensity, and orbital angular mo-mentum of the light. The latter two concepts can beconsidered as flat optics and can be combined with in-tensity control by axicon or Fresnel lens demonstrated re-cently for THz wavelengths with performance matchingtheoretical efficiency . 3D structuring of Si surface byfs-laser direct oxidation with subsequent plasma etchingopens new possibilities in THz optics where Si is trans-parent . Acknowledgements
Experiments were carried out via beamtime projectNo. 11615 at the Melbourne synchrotron on 8-11 March 2017.This work was performed in part at the Melbourne Centre forNanofabrication (MCN) in the Victorian Node of the Aus-tralian National Fabrication Facility (ANFF). W.H. is sup-ported by an Australian Government Research Training Pro-gram Scholarship. Partial support via NATO grant SPS-985048 “Nanostructures for Highly Efficient Infrared Detec-tion” is acknowledged. E.S. and M.M. acknowledge financialsupport by the OPTIBIOFORM (S-LAT-17-2) project fromthe Research Council of Lithuania. J.M. acknowledges thesupport of JSPS KAKENHI Grant Number 16K06768. Thiswork was supported in part by the Global University Projectat Tokyo Institute of Technology. W. R. Huang, A. Fallahi, X. Wu, H. Cankaya, A.-L. Cal-endron, K. Ravi, D. Zhang, E. A. Nanni, K.-H. Hong, andF. X. K¨artner, “Terahertz-driven, all-optical electron gun,”
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