LETTERS. Three-dimensional optical metamaterial with a negative refractive index

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1 Vol Septemer 28 doi:1.138/nture7247 LTTRS Three-dimensionl optil metmteril with negtive refrtive index Json Vlentine 1 *, Shung Zhng 1 *, Thoms Zentgrf 1 *, ri Ulin-Avil 1, Dentho A. Genov 1, Guy Brtl 1 & Xing Zhng 1,2 Metmterils re rtifiilly engineered strutures tht hve properties, suh s negtive refrtive index 1 4, not ttinle with nturlly ourring mterils. Negtive-index metmterils (NIMs) were first demonstrted for mirowve frequenies 5,6,ut it hs een hllenging to design NIMs for optil frequenies nd they hve so fr een limited to optilly thin smples euse of signifint frition hllenges nd strong energy dissiption in metls 7,8. Suh thin strutures re nlogous to monolyer of toms, ming it diffiult to ssign ul properties suh s the index of refrtion. Negtive refrtion of surfe plsmons ws reently demonstrted ut ws onfined to two-dimensionl wveguide 9. Three-dimensionl (3D) optil metmterils hve ome into fous reently, inluding the reliztion of negtive refrtion y using lyered semiondutor metmterils nd 3D mgneti metmteril in the infrred frequenies; however, neither of these hd negtive index of refrtion 1,11.erewereport3Doptilmetmteril hving negtive refrtive index with very high figure of merit of 3.5 (tht is, low loss). This metmteril is mde of sded fishnet strutures, with negtive index existing over rod spetrl rnge. Moreover, it n redily e proed from free spe, ming it funtionl for optil devies. We onstrut prism mde of this optil NIM to demonstrte negtive refrtive index t optil frequenies, resulting unmiguously from the negtive phse evolution of the wve propgting inside the metmteril. Bul optil metmterils open up prospets for studies of 3D optil effets nd pplitions ssoited with NIMs nd zero-index mterils suh s reversed Doppler effet, superlenses, optil tunnelling devies 12,13, ompt resontors nd highly diretionl soures 14. NIMs, first desried y Veselgo more thn 4 yers go 1 nd reently disussed in the frmewor of metmterils 2, rise from the ft tht oth the permittivity nd the permeility of the mterils re simultneously negtive. In the pst severl yers, muh effort hs een dedited to the engineering nd extension of the funtionlities of metmterils t terhertz nd optil frequenies 7,8,1, Metl dieletri metl fishnet strutures were mong the erliest demonstrtions of optil NIMs. These strutures, however, onsist of single funtionl lyer long the diretion of propgtion. This is equivlent to n tomi monolyer, ming it diffiult to explore phenomen in three dimensions nd develop devie pplitions. Moreover, s result of their resonnt nture, these systems suffer sustntil loss t optil frequenies. On the sis of the ove, it is therefore impertive to relize low-loss ul optil NIMs if we re to demonstrte unmiguously the unique effets ssoited with negtive index of refrtion. Reently, it hs een suggested theoretilly tht sting up multiple fishnet funtionl lyers long the propgtion diretion onstitutes promising pproh for hieving 3D optil NIM 22 (Fig. 1). This sding leds to strong mgneto-indutive oupling etween neighouring funtionl lyers 23. As demonstrted reently 24, the tight oupling etween djent LC resontors through mutul indutne results in rodnd negtive index of refrtion with low loss, whih is similr to the mteril response of left-hnded trnsmission lines 25,26. In ddition, the loss is further redued owing to the destrutive interferene of the ntisymmetri urrents ross the metl film, effetively nelling out the urrent flow in the entre of the film 23. ere we experimentlly demonstrte the first 3D optil NIM y diretly mesuring the ngle of refrtion from prism mde of sded fishnet metmteril. The experimentl results, long with numeril lultions, serve s diret evidene of zero nd negtive phse index in the metmteril. The 3D fishnet metmteril is frited on multilyer metldieletri st y using foused ion-em milling (FIB), whih is ple of utting nnometre-sized fetures with high spet rtio. Figure 1 shows the snning eletron mirosopy (SM) imge of the proposed 3D fishnet pttern, whih ws milled on 21 lternting films of silver nd mgnesium fluoride, resulting in ten funtionl lyers. To mesure the index of refrtion of the 3D metmteril experimentlly, prism ws reted in the multilyer st (Fig. 2, ). Mesurements of the refrtive index of these strutures were performed y oserving the refrtion ngle of light pssing through the prism y Snell s lw. This provides diret nd unmiguous Ag MgF 2 p 1 µm Figure 1 Digrm nd SM imge of frited fishnet struture., Digrm of the 21-lyer fishnet struture with unit ell of p 5 86 nm, nm nd nm., SM imge of the 21-lyer fishnet struture with the side ethed, showing the ross-setion. The struture onsists of lternting lyers of 3 nm silver (Ag) nd 5 nm mgnesium fluoride (MgF 2 ), nd the dimensions of the struture orrespond to the digrm in. The inset shows ross-setion of the pttern ten t 45u ngle. The sidewll ngle is 4.3u nd ws found to hve minor effet on the trnsmittne urve ording to simultion. 1 NSF Nno-sle Siene nd ngineering Center (NSC), 3112 theverry ll, University of Cliforni, Bereley, Cliforni 9472, USA. 2 Mteril Sienes Division, Lwrene Bereley Ntionl Lortory, Bereley, Cliforni 9472, USA. *These uthors ontriuted eqully to this wor Mmilln Pulishers Limited. All rights reserved

2 NATUR Vol Septemer 28 LTTRS Lser em 5 µm Qurtz Lens 1 Smple Lens 2 Prism n = 1 n < Cmer determintion of the refrtive index, euse the refrtion ngle depends solely on the phse grdient tht the light em experienes when refrted from the ngled output fe. We used femtoseond synhronously pumped optil prmetri osilltor s tunle f 2 f 2 f 2 d n = 1.5 n = 1 Figure 2 SM imge of NIM prism nd shemtis of experimentl setup., SM imge of the frited 3D fishnet NIM prism. The unit ell size is identil to tht shown in Fig. 1. The inset shows mgnified view with the film lyers visile in eh hole., Geometry digrm of the ngle mesurement; d orresponds to the position differene of the em pssing through window in the multilyer struture (n 5 1) nd prism smple. By mesuring d, the solute ngle of refrtion n e otined., xperimentl setup for the em refrtion mesurement. The fol length of lens 1 is 5 mm nd tht of lens 2 is f mm. Lens 2 is pled in 2f onfigurtion, resulting in the Fourier imge t the mer position. Imge light soure to determine the refrtive index t different wvelengths. The em ws foused on the smple, nd hrge-oupled devie (CCD) mer ws pled in the Fourier plne (Fig. 2). Figure 3 shows the em shift d resulting from the ending of light t the prism output t different wvelengths, rnging from 1,2 to 1,7 nm. The mesurement ws performed on prism of ngle 5 5.u nd the em shift is plotted long with referene mesurements of trnsmission through window, without the presene of the prism (left pnel). Clerly, s the wvelength inreses, the em shift resulting from the prism refrtion is hnging from positive to negtive, inditing trnsition from positive index in the shorter wvelengths to negtive index in the longer wvelengths. At wvelength l of 1,475 nm, the index of refrtion is pprohing zero; tht is, the em does not quire ny phse while propgting in the metmteril. Consequently there is no phse grdient t the ngled output fe nd the exiting em is extly norml to the output fe (see dshed lines in Figs 2 nd 3). Figure 3 depits the mesured refrtive index of the 3D fishnet metmteril t vrious wvelengths. The refrtive index vries from n t 1,2 nm to n t 1,775 nm. The refrtive index ws determined from multiple mesurements of two fishnet prisms with ngles of 5 5.u nd 4.7u nd for wvelengths rnging from 1,2 to 1,8 nm. Although there is orreltion etween the em spot positions shown in Fig. 3 nd the refrtive index in Fig. 3, it should e noted tht Fig. 3 shows the verge of mesurements on different prisms with the stndrd devition s error rs, wheres Fig. 3 shows n individul mesurement. The experimentl results re found to e in good greement with the theoretil preditions (l line in Fig. 3) on the sis of rigorous oupled-wve nlysis (RCWA). The mesured negtive refrtion ngle is diret result of negtive phse evolution for light propgting inside the smple used y negtive refrtive index. This is illustrted in Fig. 3 y numeril lultion of the in-plne eletromgneti field distriution in the fishnet prism t Window Prism 1,2 nm n = 1 n = 1 n = 1,35 nm 1,475 nm 1,59 nm 1,7 nm Position (mm) Position (mm) Index of refrtion ,2 1,4 1,6 1,8 Wvelength (nm) l = 1,763 nm n = 1.4 Figure 3 xperimentl results nd finite-differene time-domin simultions., Fourier-plne imges of the em for the window nd prism smple for vrious wvelengths. The horizontl xis orresponds to the em shift d, nd positions of n 5 1 nd n 5 re denoted y the white lines. The imge intensity for eh wvelength hs een normlized for lrity., Mesurements nd simultion of the fishnet refrtive index. The irles show the results of the experimentl mesurement with error rs (s.d., 28 Mmilln Pulishers Limited. All rights reserved n 5 4 mesurements). The mesurement grees losely with the simulted refrtive index using the RCWA method (l line)., Left: simultion of the in-plne eletri field omponent for the prism struture t 1,763 nm, showing the phse front of the light. Negtive-phse propgtion resulting from the negtive refrtive index leds to negtive refrtion ngle s mesured y the em shift in the experiment. Right: mgnified plot of the field distriution in the prism. 377

3 LTTRS NATUR Vol Septemer 28 l 5 1,763 nm, where the struture shows refrtive index of n A movie of the evolution of the eletri field generted with ommeril finite-differene time-domin softwre t the sme wvelength is lso presented in Supplementry Informtion. Beuse of the negtive phse propgtion inside the metmteril, the eletromgneti wve emerging from the thier prt of the prism experienes phse dvne ompred with tht pssing through the thinner prts, using the light to end in the negtive diretion t the exit interfe. We note tht the refrtive index remins onsistent for the fishnet metmteril with three or more funtionl lyers long the propgtion diretion, whih leds to uniform wvefront exiting from the prism (see Supplementry Informtion). To quire ler understnding of the 3D metmteril s optil response, we seprte the fishnet into two susets nd lulte the dispersion urves with RCWA. The first onstituent is 3D rry of metl wires ligned with the polriztion diretion of the inident eletri field (Fig. 4). This rry serves s n effetive medium with lowered volumetri plsm frequeny (22 Tz), elow whih wve propgtion is not llowed euse of negtive effetive permittivity 27. The seond onstituent is 3D rry of metl strips long the diretion of the mgneti field (Fig. 4), in whih indued ntisymmetri ondutive urrents ross the dieletri lyers give rise to mgneti ndgp etween 135 nd 21 Tz. This is further onfirmed y the plots of the mgneti fields t two frequenies, elow nd ove the ndgp. Aove the ndgp the mgneti response is positive, s shown in Fig. 4d, where the mgneti field omponent etween the strips is in phse with the externl field. Aove the letri nd gp Mode 2 Mgneti nd gp Mode 1 Overlp region Phse dvne (deg) d e f Trnsmittne (%) Mode 1 Mode xperiment Simultion n< x4 1, 1,4 1,8 2,2 Wvelength (nm) Figure 4 Dispersion reltions, field plots nd trnsmission for the 3D fishnet struture. In ll plots the grey re orresponds to the negtiveindex region s determined y simultions., Dispersion reltion for 3D rry of metl wires ligned long the eletri field, where denotes the inident propgtion vetor. The dotted lines in the digrm mr the unit ell size, whih is identil in e, nd orrespond to Fig. 1., Dispersion reltion of 3D rry of metl strips long the mgneti field., The dispersion for the 3D fishnet struture. A dispersion urve with negtive slope ppers within the overlpped region of the eletri ndgp nd mgneti ndgp if oth strutures re omined. d, Mgneti field plot elow the ndgp. e, Mgneti field plot ove the ndgp. f, xperimentl trnsmittne urve (red line) of unit ell fishnet struture ( mm 2 totl ptterned re), whih hs een multiplied y four for lrity. The simulted trnsmittne (l dotted line) ws otined with RCWA. 378 ndgp, the metl strips hve modertely negtive response, s shown in Fig. 4e, where the mgneti field etween the strips is out of phse. Finlly, these two strutures re merged to form the 3D fishnet metmteril, for whih the dispersion reltion is shown in Fig. 4. A propgtion nd with negtive slope ppers in the overlpped region of the foridden gps of oth eletri nd mgneti medi, demonstrting tht the negtive-index ehviour in the 3D sded fishnet does indeed result from the ft tht oth the eletri permittivity nd the mgneti permeility re negtive. In ddition, trnsmittne mesurements were performed on the 3D fishnet metmteril mde of 21 lyers with the use of Fouriertrnsform infrred mirosope (Niolet Ni-Pln IR mirosope). Figure 4f shows the mesured trnsmittne spetrum long with the numerilly lulted trnsmittne. The simultion predits rod negtive-index nd spnning from 1.45 mm to 2.2 mm (shded region), whih oinides with the high trnsmission nd from 1.5 mm to 1.8 mm. As mentioned previously, this wide nd of negtive index results from the strong oupling etween neighouring lyers. The mesured trnsmittne hs similr fetures to those of the lultion, nmely two pes imposed over the trnsmission nd tht re slightly red-shifted with respet to the numeril results. These fetures re due to the Fry Pérot effet, in whih the impedne mismth leds to refletne t the metmteril/ir nd metmteril/glss interfes. Although the pes re visile t lower refrtive index vlues owing to the lower loss, the Fry Pérot effet nnot e lerly seen in the trnsmission spetr for lrger negtive index t longer wvelength where the loss is higher, resulting in rodening nd extintion of spetrl fetures. We note tht the trnsmittne in the negtive-index nd is one-qurter of the numerilly lulted vlue, whih is proly due to imperfetions in the frition. Nevertheless, our simultions show tht the presene of loss in the oupled fishnet metmteril hs miniml impt on the dispersion reltion (see Supplementry Informtion). This is euse the 3D fishnet struture opertes fr from the nd edge (Fig. 4), where resonne is not signifint. This explins the good greement etween the experimentlly mesured nd simulted refrtive indies despite the frition imperfetions. Finlly, we estimte the figure of merit (FOM 52Re(n)/jIm(n)j) of our fishnet multilyer struture. The mteril loss (tht is, Im(n)) is onservtively estimted from the mesured trnsmittne nd refletne dt of the 21-lyer smple, ssuming single pss of light through the metmteril, s Im(n) 5 (l/4pd)ln[(1 2 R)/T], where l, d, R nd T re the wvelength, smple thiness, refletne nd trnsmittne, respetively. The dispersion of the simulted Figure of merit 28 Mmilln Pulishers Limited. All rights reserved Simultion xperiment 1,2 1,4 1,6 1,8 Wvelength (nm) Figure 5 Figure of merit for the 3D fishnet struture. Plot of FOM ginst wvelength for the simultion (dshed line) nd experiment (squres). The lower experimentl FOM is due to redued trnsmission resulting from frition imperfetions. The experimentl FOM rehes 3.5 t 1,775 nm, where Re(n)

4 NATUR Vol Septemer 28 LTTRS nd experimentl FOM is plotted in Fig. 5. The FOM is 3.5 t l 5 1,775 nm (where Re(n) ), whih is mong the highest experimentl vlues so fr reorded t optil frequenies 19. For idel frition onditions, the FOM ould rise s high s out 2, s determined from theoretil lultions. We emphsize tht our results re different from reent reports of negtive refrtion 11,28 in nisotropi medi with hyperoli dispersion (equivlent to negtive group index ) ut positive phse veloity. The fishnet metmteril hs period out l/2 in the vertil diretion. The propgtion of light trvelling long this diretion or within some ngulr rnge is dominted y this deep su-wvelength period nd not y the in-plne period, s long s the wvevetor projetion on the in-plne diretions is smll ompred with the in-plne reiprol lttie vetor of the fishnet metmteril. There is only single propgting mode in the negtive-index frequeny region, justifying the desription of the fishnet metmteril with n effetive index. In ontrst, if higher dieletri mterils suh s silion (n < 3.6) re used to serve s the dieletri lyer, the rtio etween the wvelength nd in-plne period n e signifintly inresed euse of the lrger pitne in the LC iruit. Unlie the negtive index otined from photoni rystls 29, the negtive index presented here results from simultneous negtive mgneti nd eletri responses nd shows resemlne to the left-hnded trnsmission line due to the tight oupling etween the djent LC resontors. The negtive index ours in the first propgtion nd nd with smooth negtive-phse evolution long the light propgtion diretion, whih differs from the negtive refrtion otined in photoni rystls. ere we hve experimentlly demonstrted the first 3D NIM t optil frequenies nd diretly mesured the refrtive index of NIM prism in the free spe. The 3D optil metmterils my offer the possiility to explore lrge vriety of optil phenomen ssoited with zero nd negtive refrtive index, s well s pplitions in the sling down of photonis nd imging. MTODS SUMMARY In the numeril studies of the 3D fishnet metmteril, the intrinsi losses of the metl re inluded 3. The multilyer st ws deposited y eletron-em evportion of lternting lyers of silver (3 nm) nd mgnesium fluoride (5 nm) resulting in totl thiness of 83 nm. Two different onfigurtions of the fishnet smples were frited on the multilyer st. Smples of the first onfigurtion onsist of in-plne fishnet unit ells nd were used for the hrteriztion of the trnsmittne. The seond onfigurtion (prism smple) ws formed y ething the film t n ngle to the film surfe, using FIB. The ext ngle ws mesured with n tomi fore mirosope nd ws found to vry slightly etween smples. A fishnet pttern ws susequently milled in the prism. To otin the solute ngle of refrtion, window with n re equl to tht of the prism ws ethed through the multilyer st to serve s referene. The window nd prism Fourier imges were mesured for ll wvelengths on n indium gllium rsenide infrred mer nd the totl em shift d of the spot entre ws lulted. Consequently, the ngle of refrtion t the surfe of the prism is given s 5 2 rtn(d/f 2 ). Snell s lw (n 5 sin/sin) ws used to lulte the rel prt of the refrtive index of the smple. The imginry prt of the refrtive index of the smple ws otined from trnsmittne nd refletne dt quired with 21-lyer smple of the first onfigurtion (s desried ove). Full Methods nd ny ssoited referenes re ville in the online version of the pper t Reeived 2 Mrh; epted 11 July 28. Pulished online 11 August Veselgo, V. G. The eletrodynmis of sustnes with simultneously negtive vlues of e nd m. Sov. Phys. Usp. 1, (1968). 2. Smith, D. R., Pendry, J. B. & Wiltshire, M. C. K. Metmterils nd negtive refrtive index. Siene 35, (24). 3. Pendry, J. B. Negtive refrtion mes perfet lens. Phys. Rev. Lett. 85, (2). 4. Tsmidis, K. L., Bordmn, A. D. & ess, O. Trpped rinow storge of light in metmterils. Nture 45, (27). 5. Shely, R. A., Smith, D. R. & Shultz, S. xperimentl verifition of negtive index of refrtion. Siene 292, (21). 6. Przzoli, C. G., Greegor, K., Li, K., Koltenh, B.. C. & Tnielin, M. xperimentl verifition of negtive index of refrtion using Snell s lw. Phys. Rev. Lett. 9, 1741 (23). 7. Pnoiu, N. C. & Osgood, R. M. Numeril investigtions of negtive refrtive index metmterils t infrred nd optil frequenies. Opt. Commun. 223, (23). 8. Shlev, V. M. et l. Optil negtive-index metmterils. Nture Photonis 1, (27). 9. Leze,. J., Dionne, N. A. & Atwter,. A. Negtive refrtion t visile frequenies. Siene 316, (27). 1. Liu, N. et l. Three-dimensionl photoni metmterils t optil frequenies. Nture Mter. 7, (28). 11. offmn, A. J. et l. Negtive refrtion in semiondutor metmterils. Nture Mter. 6, (27). 12. Silveirinh, M. & nghet, N. Tunneling of eletromgneti energy through suwvelength hnnels nd ends using epsilon-ner-zero mterils. Phys. Rev. Lett. 97, (26). 13. dwrds, B. et l. xperimentl verifition of epsilon-ner-zero metmteril oupling nd energy squeezing using mirowve wveguide. Phys. Rev. Lett. 1, 3393 (28). 14. noh, S. et l. A metmteril for diretive emission. Phys. Rev. Lett. 89, (22). 15. Yen, T. J. et l. Terhertz mgneti response from rtifiil mterils. Siene 33, (24). 16. Pdill, W. J. et l. Dynmil eletri nd mgneti metmteril response t terhertz frequenies. Phys. Rev. Lett. 96, 1741 (26). 17. Chen,. T. et l. Ative terhertz metmteril devies. Nture 444, (26). 18. Linden, S. et l. Mgneti response of metmterils t 1 terhertz. Siene 36, (24). 19. Sououlis, C. M., Linden, S. & Wegener, M. Negtive refrtive index t optil frequenies. Siene 315, (27). 2. Dolling, G., Wegener, M. & Linden, S. Reliztion of three-funtionl-lyer negtive-index photoni metmteril. Opt. Lett. 32, (27). 21. Alu, A. & nghet, N. Three-dimensionl nnotrnsmission lines t optil frequenies: A reipe for rod nd negtive-refrtion optil metmterils. Phys. Rev. B 75, 2434 (27). 22. Zhng, S. et l. Optil negtive-index ul metmterils onsisting of 2D perforted metl-dieletri sts. Opt. xpress 14, (26). 23. Li, T. et l. Coupling effet of mgneti polriton in perforted metl/dieletri lyered metmterils nd its influene on negtive refrtion trnsmission. Opt. xpress 14, (26). 24. leftherides, G. V. Anlysis of ndwidth nd loss in negtive-refrtive-index trnsmission-line (NRI TL) medi using oupled resontors. I Mirow. Wireless Components Lett. 17, (27). 25. Gri, A. & leftherides, G. V. Overoming the diffrtion limit with plnr lefthnded trnsmission-line lens. Phys. Rev. Lett. 92, (24). 26. Li, A., Crloz, C. & Itoh, T. Composite right-/left-hnded omposite trnsmission line metmterils. I Mirow. Mg. 5, 34 5 (24). 27. Pendry, J. B., oldenz, A. J., Roins, D. J. & Stewrtz, W. J. Low frequeny plsmons in thin-wire strutures. J. Phys. Condens. Mtter 1, (1998). 28. Fn, X. B. et l. All-ngle rodnd negtive refrtion of metl wveguide rrys in the visile rnge: Theoretil nlysis nd numeril demonstrtion. Phys. Rev. Lett. 97, 7391 (26). 29. Notomi, M. Theory of light propgtion in strongly modulted photoni rystls: Refrtion-lie ehvior in the viinity of the photoni nd gp. Phys. Rev. B 62, 1696 (2). 3. Johnson, P. B. & Christy, R. W. Optil onstnts of the nole metls. Phys. Rev. B 6, (1972). Supplementry Informtion is lined to the online version of the pper t Anowledgements We nowledge funding support from US Army Reserh Offie (ARO) MURI progrmme 5432-P-MUR nd prtly y the NSF Nno-sle Siene nd ngineering Center DMI We thn. Behtel nd M. C. Mrtin for ssisting in mesurements of ner-infrred trnsmission nd refletion, nd S. R. J. Brue for disussion. T.Z. nowledges fellowship from the Alexnder von umoldt Foundtion. Multilyer deposition ws performed t the Moleulr Foundry, Lwrene Bereley Ntionl Lortory, whih is supported y the Offie of Siene, Offie of Bsi nergy Sienes, of the US Deprtment of nergy under ontrt no. D-AC2-5C Author Informtion Reprints nd permissions informtion is ville t Correspondene nd requests for mterils should e ddressed to X.Z. (xing@ereley.edu). 28 Mmilln Pulishers Limited. All rights reserved 379

5 doi:1.138/nture7247 MTODS In the numeril studies of the 3D fishnet metmteril, with the exeption of Figs 3 nd 4d, e, we used RCWA, whih expnds the eletromgneti field into diffrtion orders nd mthes the oundry onditions t eh interfe. Speifilly, the numeril refrtive index in Fig. 3, the dispersion urves in Fig. 4 nd the numeril figure of merit in Fig. 5 were lulted using modl nlysis given in ref. 22. Figures 3 nd 4d, e were lulted with ommeril finite-differene time-domin softwre (CST Mirowve Studio). In the simultions, Drude model ws used for the dieletri prmeters of silver, with plsm frequeny v p 5 9. ev nd sttering frequeny 5.54 ev. The sttering frequeny is inresed y ftor of three ompred to tht of the ul silver 3 in order to ount for the dditionl loss of surfe sttering. In the experimentl setup (Fig. 2), light from the optil prmetri osilltor (Spetr-Physis) ws foused onto the prism with n hromti lens (lens 1); the seond lens (lens 2) ws pled t its fol position. The position of the em t the fol distne of lens 2 (f 2 ) ws used to lulte the ngle of refrtion. As result of limited mer imging re, only the zero-order Fourier imge ws reorded. To otin the solute ngle of refrtion, window with n re equl to tht of the prism ws ethed through the multilyer st to serve s referene. The window s Fourier imge ws mesured t ll wvelengths, giving referene position orresponding to refrtive index of 1. The entres of the em spot for oth the window nd prism smples were determined y fitting the intensity with 2D Gussin profile nd the totl em shift (d) t the position of the mer ws lulted y ting the differene etween the em spot entres. 28 Mmilln Pulishers Limited. All rights reserved