In many areas of science and technology that utilize the

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1 pubs.acs.org/journal/apchd5 Planar, Ultrathn, Subwavelength Spectral Lght Separator for Effcent, Wde-Angle Spectral Imagng Yasn Buyukalp,* Peter B. Catrysse,* Wonseok Shn, and Shanhu Fan* E. L. Gnzton Laboratory and Department of Electrcal Engneerng, Stanford Unversty, Stanford, Calforna 94305, Unted States ABSTRACT: We propose a planar, ultrathn, subwavelength spectral lght separator that enables effcent, angularly robust, spatally coregstered decomposton of lght nto ts spectral components. The devce conssts of a collecton of spectrally tuned meta-atoms and acheves spectral selectvty by utlzng strong localzed resonance supported by each ndvdual meta-atom. The three-dmensonal meta-atoms are formed by resonant subwavelength-sze rectangular apertures n a planar metallc flm of deepsubwavelength thckness. The overall physcal cross-sectonal area of the devce s subwavelength, and ts thckness s deepsubwavelength. Dfferent spectral components of lght are smultaneously separated and collected n dfferent subwavelength-sze aperture pars, where each aperture par s composed of two perpendcularly orented, same-sze apertures; and dfferent aperture pars collect ther lght from overlappng cross-sectonal regons. Hence, spatal coregstraton errors between dfferent spectral channels are qute reduced, whch s an attractve feature for multspectral magng systems. The operaton of the devce s polarzaton-ndependent; however, the devce also smultaneously separates dfferent lnear polarzaton components of lght and collects ther power n dfferent apertures of aperture pars. The devce also exhbts angular robustness for oblquely ncdent lght, that s, spectral selectvty s largely angle-ndependent. Both features are appealng for magng applcatons. KEYWORDS: multspectral magng, snapshot systems, polarmetrc magng, subwavelength, Fabry-Peŕot, nanocavtes, apertures, metallc structure, funnelng In many areas of scence and technology that utlze the spectrum of lght, such as spectroscopy, multspectral magng, hyperspectral magng, and wavelength demultplexng, t s desred to decompose lght nto ts spectral components wth mnmum photon loss Especally, n snapshot magng applcatons, where the goal s to smultaneously collect full spatal and spectral nformaton, one needs to perform the spectral decomposton n a photon-effcent manner, wthout sacrfcng spatal resoluton, whch s conventonally lmted by dffracton. 5,21,22 Furthermore, magng systems are ncreasngly mnaturzed, and pxels n mage sensors or focal plane arrays tend to shrnk down to the (sub)wavelength scale, whch are drven n part by the small form factor requrement on moble platforms. 8,22 27 Hence, there s an urgent need for a photoneffcent, compact, subwavelength-sze spectral lght separator to buld hgh-resoluton, low-cost, low-power, and lghtweght multspectral snapshot magng systems. 1 8,21,26 One class of snapshot systems acheves spectral selectvty by utlzng hard-to-mnaturze devces that are larger than ther operatng wavelength n sze. 5,11,17 19,28 40 Tradtonally, these systems nclude ether spectral decomposton systems based on prsms or guded-mode resonance flters based on phasematchng elements such as dffracton gratngs. 5,8,11,28,29 Novel devces have also been proposed, such as photon sorters or other plasmonc structures ,30 40 Ther operaton depends on surface plasmon polarton exctaton by usng perodc hole arrays, groove arrays, or gratngs, where the perod s comparable to the operaton wavelength. To operate, these devces requre at least a few perods; therefore, they are necessarly larger than the operaton wavelength. 41 As an alternatve approach, spectral selectvty can be acheved wth structures supportng localzed resonances. 7,13,42,43 Recently, the concept of assemblng several deepsubwavelength resonant structures ( meta-atoms ), each supportng a sngle resonance at a dfferent wavelength, to acheve spectral separaton at the subwavelength scale n a sngle solated (.e., nonperodc) devce was demonstrated. 7,13 Ths concept does not rely on any perodcty effect to acheve spectral separaton. It s therefore compatble wth the current trend n constructng detector arrays wth smaller, (sub)- wavelength-sze pxels. Unlke spectral flter arrays, where only a sngle spectral component s selected n a wavelength-sze pxel area, the devces based on ths concept select and separate multple spectral components n a subwavelength-sze area; therefore, ths concept also provdes a more photon effcent way for magng than the concept of usng spectral flter arrays. The subwavelength-sze devces that have been demonstrated so far, 7,13 however, reman polarzaton-dependent, whch s not deal for many magng applcatons. Moreover, for spectral separaton, they utlze ether strong nterference between dfferent spectral bands 13 or nonplanar structures. 7 The former lmts spectral selectvty, angular robustness, and hence Receved: September 16, 2016 Publshed: January 17, Amercan Chemcal Socety 525

2 effcency. The latter results n thckness that s not deepsubwavelength and poses fabrcaton challenges. RESULTS AND DISCUSSION In ths work, we numercally demonstrate a planar subwavelength spectral lght separator that overcomes all the above-mentoned lmtatons assocated wth prevously demonstrated spectral separaton devces. We present here a threedmensonal (3D), surface-thn, planar, subwavelength-sze nanophotonc devce that can decompose lght nto ts spectral components n a very photon-effcent way. Our spectral lght separator acheves spectral selectvty by utlzng the strong localzed resonances of 3D meta-atoms formed by subwavelength resonant apertures n a metallc flm of deepsubwavelength thckness. These apertures have electromagnetc cross sectons far exceedng ther physcal sze at ther resonance wavelengths. 44 We show that one can assemble these apertures, each tuned to a dfferent wavelength, n a subwavelength-wde and deep-subwavelength-thck devce wthout causng sgnfcant nterference among them. The overall transmsson through our devce s polarzaton-ndependent, but the devce can be used to separate the dfferent lnear polarzaton components of lght as well, whch mght be useful for polarmetrc magng. 17,38 We also show that our devce has angular robustness, that s, a clear spectral separaton can stll be acheved for oblquely ncdent lght. Furthermore, snce the apertures collect lght comng from overlappng cross-sectonal regons, spatal coregstraton errors between dfferent spectral channels are qute reduced, whch s a very attractve feature for multspectral magng. 7,45,46 Fgure 1 llustrates a planar subwavelength spectral lght separator desgned to operate at nfrared wavelengths. The Fgure 1. Geometry of the proposed planar subwavelength spectral lght separator. The devce conssts of three rectangular aperture pars where each aperture par s composed of two perpendcularly orented, same-sze, ar-flled apertures n a deep-subwavelength-thck alumnum flm. The structure s solated (non-perodc). The flm thckness s 50 nm. Each aperture has a wdth and heght of 50 nm. Each of the apertures of the frst aperture par (1 1 ) has the length of 1 μm, of the second aperture par (2 2 ) has the length of 1.25 μm, and of the thrd aperture par (3 3 ) has the length of 1.5 μm. The separaton between adjacent parallel apertures s 200 nm. The devce s surrounded by ar. k nc represents the ncdent lght. λ mn s 1.8 μm, whch corresponds to the mnmum free-space wavelength sze n the nvestgated spectral range. structure s a sngle solated (.e., nonperodc) devce. It conssts of three subwavelength-sze rectangular aperture pars (1 1, 2 2, and 3 3 ) n an ultrathn metallc flm. The flm thckness s 50 nm, whch s deep-subwavelength compared to the operatng wavelength range. The apertures have a wdth of 50 nm, and ther lengths are chosen such that each aperture exhbts a resonant behavor at a sngle spectral band n the wavelength range between 1.8 and 5 μm. Each of the apertures of the frst aperture par (1 1 ) has the length of 1 μm, of the second aperture par (2 2 ) has the length of 1.25 μm, and of the thrd aperture par (3 3 ) has the length of 1.5 μm, whch allows separatng three dfferent spectral components of lght such that each spectral component s transmtted through a dfferent aperture par. For each aperture par, one aperture s orented along the x-drecton, and the other aperture s orented along the y-drecton, whch enables a polarzatonndependent response when usng aperture pars as detected elements. The separaton between adjacent parallel apertures s 200 nm. The overall structure s symmetrc wth respect to the x = y plane. The total physcal cross-sectonal area of the devce s n the subwavelength range. Wthout loss of generalty, we choose alumnum 47 (Al) as the metal, choose ar as the materal surroundng the devce, and use ar-flled apertures. We also examne the case where the metal s perfect electrc conductor (PEC) to compare ts performance wth that of the realstc Al devce and to provde a smpler understandng of the operaton prncple. We demonstrate the operaton of our devce by smulatng ts nteracton wth electromagnetc waves va the fnte-dfference frequency-doman (FDFD) method Fgure 2 shows the transmsson cross secton spectra, σ T (λ), calculated when the ncdent lght s a normally ncdent plane wave wth ts electrc feld along the x-drecton (x-polarzed). The ndvdual transmsson cross secton spectra of the alumnum structure n Fgure 2a c show clear resonance behavor at three dfferent nfrared wavelengths, whch are 2688, 3328, and 3936 nm. As can be seen n the fgure, these resonances are assocated wth the frst (aperture 1), second (aperture 2), and thrd (aperture 3) aperture orented along the y-drecton, respectvely. Thus, dfferent resonances occur n the dfferent apertures, meanng that the spectral separaton s acheved. Note that these resonances correspond to the three resonance peaks n the overall transmsson cross secton spectra shown n Fgure 2d. We observe that the peak wavelengths of the transmsson cross secton resonances depend drectly on the lengths of the apertures orented along the y-drecton. Also, the ratos of the resonance wavelengths are approxmately equal to the ratos of the lengths of the correspondng resonant apertures. Ths s because the resonances are assocated wth Fabry-Peŕot-lke cavty modes that are supported by the subwavelength rectangular apertures for ncdent lght havng an electrc feld component pontng along the apertures short axs. 51,52 Ths behavor can be clearly notced by nvestgatng the transmsson cross secton spectra of the PEC structure, where each resonance wavelength s approxmately twce the length of the correspondng resonant aperture, wth a small redshft due to the electromagnetc couplng to free-space modes. 51,53 In the case where the metal s alumnum, there s an addtonal redshft n each resonance wavelength. Ths s attrbuted both to the penetraton of the electromagnetc felds nto the alumnum flm due to the fnte delectrc constant of the alumnum, and to the coupled surface waves that are supported 526

3 Fgure 2. Transmsson cross secton spectra of both alumnum and PEC planar subwavelength spectral lght separators for a normally ncdent x-polarzed plane wave. The ndvdual transmsson cross secton spectra for the aperture par 1 1 n a), 2 2 n b), and 3 3 n c). The blue lne corresponds to the ndvdual transmsson cross secton spectrum of the Aperture 1 n a), 2 n b), and 3 n c) for the PEC structure whereas the red lne corresponds to the ndvdual transmsson cross secton spectrum of the Aperture 1 n a), 2 n b), and 3 n c) for the alumnum structure. In each of a), b) and c), there are two separate dotted-gray lnes concdng almost on top of each other, and they show the ndvdual transmsson cross secton spectra of the Aperture 1 n a), 2 n b), and 3 n c) for the PEC structure and the alumnum structure. (d) The overall transmsson cross secton spectra for the entre structure. The blue lne corresponds to the PEC structure whereas the red lne corresponds to the alumnum structure. at the alumnum-ar nterfaces on the long edges of the resonant apertures. 52,54 The peak transmsson cross secton of each resonant aperture s much larger than the physcal sze of the aperture. The peak transmsson cross sectons of the alumnum structure are 0.971, , and μm 2 for the frst, second, and thrd resonant aperture, respectvely. The physcal szes of these apertures are 0.05, , and μm 2 respectvely. Thus, the peak transmsson cross sectons are more than 19 tmes the physcal area of the apertures. For the PEC structure, the peak transmsson cross sectons are , , and μm 2 for the frst, second, and thrd resonant aperture, respectvely. Each of these values s very close to the maxmum theoretcal transmsson cross secton of a sngle deep-subwavelength rectangular aperture n a PEC flm, whch s approxmately 3λ 2 /4π. 51,53,55 Ths lmt arses from the fact that a sngle deepsubwavelength rectangular aperture has a radaton pattern very close to a dpole radaton pattern. Compared to the PEC structure, the alumnum structure has about 32.4%, 34%, and 22.5% less peak transmsson cross secton for the frst, second, and thrd resonant aperture, respectvely. Ths reducton s due to the fnte and lossy delectrc constant of alumnum. Stll, the alumnum structure mantans the resonant behavor. Hence, our devce composed of the realstc metal s capable of funnelng and collectng lght at the selected wavelengths. Another mportant fgure of mert n magng applcatons s the ratos of the ndvdual transmsson cross sectons to the overall actve devce area. These ratos also correspond to the ndvdual transmttances. In a perodc devce, the overall actve devce area of each perod can be clearly defned as the area of the perod. However, the solated structure smulaton we performed here corresponds to a metal flm that has an nfnte sze n x- and y-drecton wth only sx apertures on t, and therefore, the actve devce regon cannot be chosen unambguously. Hence, for the solated planar subwavelength spectral lght separator shown n Fgure 1, we prefer to dscuss the transmsson cross secton spectra, and later n the paper, we dscuss the transmttance spectra of the alumnum planar subwavelength spectral lght separator array shown n Fgure 4. The ndvdual transmsson cross secton spectra of the apertures orented along the x-drecton (apertures 1, 2, and 3 ) show neglgble transmsson n Fgure 2a c because the operaton wavelength range s above the cutoff wavelengths of these apertures for x-polarzed ncdent lght. Above the cutoff wavelength, felds nsde these apertures are evanescent and the couplng of the apertures wth the ncdent wave s very poor; thus, the transmsson through these apertures decreases strongly wth an ncrease n wavelength above the cutoff wavelength. 51 Our structure s symmetrc wth respect to the x = y plane. Thus, by dong addtonal smulatons, we observed that the ndvdual transmsson cross secton response of an aperture orented along the y-drecton when llumnated by x-polarzed lght and the response of the same-sze aperture orented along the x-drecton when llumnated by y-polarzed lght are the same. Also, the overall transmsson cross secton spectra obtaned for x-polarzed lght and y-polarzed lght are dentcal, meanng that the overall transmsson propertes of the devce are ndependent of the lght polarzaton n the case of normal ncdence. Although the apertures are physcally very close to each other compared to ther operaton wavelengths, dfferent apertures effcently collect lght wth dfferent wavelengths and polarzatons. To make a quanttatve statement, we defne the spectral crosstalk between a resonant aperture and an offresonant aperture as the rato of the mean absolute transmsson cross secton of the off-resonant aperture to the mean absolute transmsson cross secton of the resonant aperture n the spectral band of the resonant aperture. The spectral band of the resonant aperture s defned as the wavelength range correspondng to the full wdth at half-maxmum (fwhm) of the transmsson cross secton spectrum of the resonant aperture. If we defne λ 1, and λ 2, such that they correspond to the wavelengths at whch the transmsson cross secton of the resonant aperture has half of ts peak value and λ 2, > λ 1,, the dfference of those wavelengths (λ 2, λ 1, ) corresponds to the full wdth at half-maxmum (fwhm) of the transmsson cross secton spectrum of the resonant aperture. Then, the spectral 527

4 Table 1. Spectral Crosstalk (ω,j ) between a Resonant Aperture and an Off-Resonant Aperture j for the Alumnum Subwavelength Spectral Lght Separator Excted by a Normally Incdent x-polarzed Plane Wave off-resonant aperture j resonant aperture crosstalk (ω,j ) between the resonant aperture and the offresonant aperture j s gven by the formula below. ω j, = 1 λ2, λ2, λ1, λ1, 1 λ2, λ2, λ1, λ1, σtj, ()d λ λ = σ ()d λ λ T, λ2, λ1, λ2, λ1, σ ()d λ λ Tj, σ ()d λ λ T, For the alumnum structure, the spectral band of the aperture 1 s the wavelength range between 2433 and 2844 nm; the spectral band of the aperture 2 s the wavelength range between 3074 and 3558 nm, and the spectral band of the aperture 3 s the wavelength range between 3702 and 4425 nm. The spectral crosstalk values for the alumnum structure are gven n Table 1. Table 1 shows that the spectral crosstalk between the apertures orented along y-axs and x-axs are almost zero as expected from the fact that the ncdent lght s x-polarzed. Also, the maxmum spectral crosstalk between any resonant aperture and off-resonant aperture s less than 15.4%. Thus, only the resonant aperture effectvely transmts lght n ts spectral band, and the transmsson cross secton of each aperture s very small for all of ts off-resonance condtons. As a result of these, we can see that the transmsson cross secton spectra shown n Fgure 2 exhbt very small spectral crosstalk. As a further evdence of the lack of a major spectral crosstalk n ths structure, Fgure 3 shows the electrc feld ntensty ( E 2 ) dstrbuton of the alumnum structure at the resonance wavelength and the resonance polarzaton of each aperture. In each case, the feld ntensty s predomnantly concentrated n only one aperture. Thus, lght s funneled nto a sngle aperture at each par of resonance wavelength and polarzaton. As an addtonal note, the ndvdual transmsson cross secton spectra n Fgure 2a c show that negatve transmsson occurs through off-resonant apertures n some parts of the spectral regon. Near the resonance wavelength of each aperture, there s negatve power flow through the off-resonant apertures. Thus, some transmtted power through the resonatng apertures flows back to the nput sde through the off-resonant apertures. We observed a smlar phenomenon n our prevous work 7 on a nonplanar spectral lght separator, and we beleve that ths phenomenon s related to the observatons of negatve power flow n perodc arrays of compound apertures. 56 On the other hand, as can be seen n Fgure 2d, the values of the overall transmsson cross secton spectra are all above zero. Hence, these results show that even when there s negatve power flow through off-resonant apertures, the total transmtted power flow through the entre structure remans postve, as expected. In general, by tunng the geometrcal propertes and the orentaton of the apertures, one can control ther resonance behavor. For the structure shown n Fgure 1, the wdth, length, and heght of each aperture control the aperture s resonance wavelength, whle the orentaton of each aperture controls ts polarmetrc response. We have observed that an ncrease n the length of a resonatng aperture causes a major redshft n the resonance wavelength of the aperture due to Fabry-Peŕot-lke nature of the resonance whereas an ncrease n the wdth of a resonatng aperture causes a mnor redshft n the resonance wavelength of the aperture as well as t ncreases the bandwdth and decreases the qualty factor of the resonance of the aperture. We have also observed that the resonance behavor of the apertures depends on the lght polarzaton, and a resonance occurs only for the lght havng an electrc feld component pontng along the apertures short axs. In addton, one may observe that apertures placed n a thcker lossy metal flm have reduced transmsson. Also, sgnfcant redshft n the resonance wavelength can be expected by addng a delectrc nsde the apertures. Fnally, whle the felds are concentrated n the nteror of the resonant apertures n ths structure, the felds can be concentrated at the ext of the apertures by placng the structure on a hgh-ndex materal. 57 These observatons lead to a seres of very straghtforward desgn rules for constructng addtonal planar spectral lght separators based on the approach shown here. So far, we have shown that our 3D planar subwavelength spectral lght separator can acheve spectral decomposton at a subwavelength scale by showng the smulaton results of an solated structure. Gven the trend n a detector pxel scalng toward (sub)wavelength sze, our devce naturally fts wthn a sngle pxel. In real-lfe applcatons, such as for mage sensor or photodetector arrays, our devce would most lkely be used n an array confguraton. Thus, now, we show that an array formed by subwavelength-sze unt cells ncludng our structures also acheves a very effcent spectral lght separaton. The perod of the array s not a major desgn parameter for the operaton of our devce snce the devce operaton s based on the localzed cavty resonances assocated wth Fabry-Peŕot-lke modes. 44,51,52 We also show that the devce functonalty s angularly robust, that s, the devce acheves spectral separaton for a very large range of angle of ncdence. Fgure 4 llustrates a perodc planar subwavelength spectral lght separator. The devce s agan based on a thn alumnum flm wth three pars of apertures. Except for the addton of perodcty, all dmensons are the same as the structure n Fgure 1. The perod of our perodc structure s 1.75 μm n both the x-drecton and the y-drecton. Ths s subwavelength for the operaton wavelength range, and the perodcty has only a mnor nfluence on the operaton of the devce. We agan use the FDFD method to examne ths perodc structure. Ths tme, n addton to normally ncdent plane waves, we also use oblquely ncdent plane waves to excte the structure. Each possble ncdent plane wave can be decomposed to the bass of s- and p-polarzed plane waves n ths confguraton. Therefore, we perform smulatons for both s-polarzed ncdent lght (a plane wave wth ts electrc feld beng perpendcular to plane of ncdence) and p-polarzed ncdent lght (a plane wave wth ts magnetc feld beng perpendcular to plane of ncdence). Wthout a loss of generalty, we choose the top and bottom surfaces of our planar structure to be parallel to the xy-plane 528

5 Fgure 3. Electrc feld ntensty ( E 2 ) dstrbutons of the alumnum planar subwavelength spectral lght separator excted by a normally ncdent plane wave for two dfferent polarzatons. The ncdent lght s x-polarzed n (a), and y-polarzed n (b). Subfgures ) ) show the ntensty dstrbutons when the wavelength of the lght s equal 2688 nm, 3328 nm, and 3936 nm, whch are the free-space resonance wavelengths of the frst, second, and thrd aperture par (aperture pars 1 1, 2 2, and 3 3 n Fgure 1), respectvely. The orgn of the coordnate system corresponds to the center of the structure. The structure s n the regon where 25 nm z 25 nm. The ncdent lght comes from the regon where z < 25 nm, and t goes towards the +z-drecton. In each subfgure, the feld ntensty s plotted both on the horzontal plane at z = 0 whch goes through the mddle of the structure, and on the vertcal plane whch goes through the mddle of the long sde of the resonatng aperture. The color scale s chosen such that the maxmum of each subfgure corresponds to the same color. and perpendcular to the z-axs. The plane of ncdence s defned by the z-axs and propagaton drecton. Therefore, the drecton of the electrc feld n s-polarzed lght (the magnetc feld n p-polarzed lght) s parallel to the xy-plane. In each smulaton, we excte the devce usng an ncdent plane wave wth a dfferent polar angle (θ) and azmuthal angle (φ). The polar angle s defned from the +z-axs drecton toward the drecton of propagaton vector, and hence, t also corresponds to the angle of ncdence. The azmuthal angle s defned from the +y-axs drecton toward the drecton of propagaton vector projecton on the xy-plane. Snce the electrc feld drecton, magnetc feld drecton and the propagaton drecton must be orthogonal n a plane wave, the azmuthal angle also corresponds to the angle defned from the +x-axs drecton toward the drecton of the electrc feld of the ncdent lght when the ncdent lght s s-polarzed. Smlarly, t also corresponds to the angle defned from the +x-axs drecton toward the drecton of the magnetc feld of the ncdent lght when the ncdent lght s p-polarzed. Whle an solated structure s typcally characterzed by ts transmsson cross secton, 55 a perodc structure s characterzed by ts transmttance as the overall actve area of a perodc structure can be clearly defned n each perod as the area of the perod. Here, we measure the ndvdual transmttances as a functon of wavelength. Fgure 5a shows the ndvdual transmttance spectra found for s-polarzed ncdent plane wave wth dfferent polar (θ) angle. Here, the azmuthal angle (φ) sfxed and t s 0. Thus, the drecton of the electrc feld of the ncdent lght s fxed along the x-drecton. Hence, s-polarzed plane wave here corresponds to x-polarzed plane wave. Only the angle of ncdence (θ) s changed. The ndvdual transmttance spectra n Fgure 5a, show clear resonance behavor as assocated wth the frst (aperture 1), second (aperture 2), and thrd (aperture 3) aperture orented along the y-drecton, respectvely. Ths result shows that our devce separates the dfferent spectral components of s-polarzed lght nto dfferent apertures for a very large range of angle of ncdence. In general, the transmttance values decrease wth the ncrease n the polar angle (angle of ncdence). For small angles (θ 15 ), however, the decrease s barely notceable and the transmttance spectra are nearly dentcal. Also, the resonance wavelengths for dfferent polar angles are very close to each other. These are due to the nearly dpole radaton profle of resonatng apertures n our structure, whch results n excellent angular robustness of our structure s spectral response and ncreases the effcency of our devce. We also observe that the longer resonatng apertures have hgher peak values n ther ndvdual transmttance spectra. Another observaton made from Fgure 5a s that the ndvdual transmttance spectra 529

6 Fgure 4. Alumnum planar subwavelength spectral lght separator array. It has the same geometry and materal as n Fgure 1, but ths structure s perodc. The perods n the x- and y-drectons are the same, both beng 1.75 μm. λ mn s 2.3 μm, whch corresponds to the mnmum free-space wavelength sze n the nvestgated spectral range. k nc represents the ncdent lght whch s an oblquely ncdent plane wave whose propagaton drecton s defned by polar (θ) and azmuthal (φ) angle. θ s defned from the +z-drecton toward the propagaton drecton, and t also corresponds to angle of ncdence. φ s defned from the +y-drecton toward the drecton of propagaton vector projecton on the xy-plane. If the ncdent lght s s-polarzed, ts electrc feld s on the xy-plane, whereas f the ncdent lght s p- polarzed, ts magnetc feld s on the xy-plane. Snce the electrc feld drecton, magnetc feld drecton and the propagaton drecton of a plane wave must be orthogonal, φ also corresponds to the angle defned from the +x-axs drecton toward the drecton of the electrc feld of the ncdent lght for s-polarzaton (the magnetc feld of the ncdent lght for p-polarzaton). assocated wth the apertures orented along the x-drecton (apertures 1, 2, and 3 ) show neglgble transmsson. Ths s expected as the wavelength range s above the cutoff wavelengths of these apertures for ncdent lght wth electrc feld along the x-drecton. Fgure 5b shows the ndvdual transmttance spectra found for s-polarzed ncdent lght wth dfferent azmuthal (φ) angles, whle the polar angle (θ) sfxed and t s 15. In ths case, the drecton of the electrc feld of the ncdent lght s changed. The ndvdual transmttance spectra n Fgure 5b, show clear resonance behavor as assocated wth the frst, second, and thrd aperture par, respectvely. At a resonance wavelength, dependng on the electrc feld drecton of the ncdent lght, ether only one aperture or both apertures of the aperture par assocated wth that resonance wavelength can resonate. For example, when φ = 0, only apertures orented along the y-drecton resonate. However, when φ ncreases toward 90, the resonance at the apertures orented along the y- drecton decreases whereas the resonance at the apertures orented along the x-drecton ncreases. When 0 φ < 45 and 135 < φ < 225 and 315 < φ 360, the apertures orented along the y-drecton have hgher transmttance values than the ones along the x-drecton. However, when 45 < φ < 135 and 225 < φ < 315, the apertures along the x-drecton have hgher transmttance values than the ones along the y- drecton. Thus, Fgure 5 shows that for a very large range of angle of ncdence (θ), our devce spectrally separates s- polarzed ncdent lght, and t collects dfferent spectral components n dfferent subwavelength-sze aperture pars. Achevng spectral separaton s ndependent of feld drectons of s-polarzed plane waves whle usng aperture pars as detected elements. Our devce further separates the dfferent lnear polarzaton components of s-polarzed ncdent lght and transmts the power of those components through dfferent apertures of aperture pars. We repeated the same smulaton cases of Fgure 5, but ths tme we used a p-polarzed ncdent plane wave nstead. The results are shown n Fgure 6. Fgure 6a shows the ndvdual transmttance spectra found for a p-polarzed ncdent plane wave wth dfferent polar angle (θ). Here, the azmuthal angle s agan fxed and t s 0. Thus, the drecton of the magnetc feld of the ncdent lght s fxed along the x-drecton. Hence, the p- polarzed plane wave here has electrc feld only n the y- and z- drectons when θ > 0 and t corresponds to y-polarzed plane wave for θ = 0. Now, we observe that the ndvdual transmttance spectra n Fgure 6a, show clear resonance behavor as assocated wth the frst (aperture 1 ), second (aperture 2 ), and thrd (aperture 3 ) aperture orented along the x-drecton, respectvely. Ths result shows that our devce separates the dfferent spectral components of p-polarzed lght nto dfferent apertures for a very large range of angle of ncdence, whch confrms the angular robustness of our structure. We notce that the transmttance spectra for the cases wth θ =0 and θ =15 are very close. But, ths tme, we see a redshft n the resonance wavelength of the small aperture wth an ncrease n the angle of ncdence. Ths s partcularly notceable for θ =30 and 45. We agan observe that the longer resonatng apertures have hgher peak values n ther ndvdual transmttance spectra. Another observaton made from Fgure 6a s that ndvdual transmttance spectra assocated wth the apertures orented n the y-drecton (apertures 1, 2, and 3) show neglgble transmsson. Ths s expected as the wavelength range s above the cutoff wavelengths of these apertures for the ncdent lght wth magnetc feld along the x-drecton. Fgure 6b shows the transmttance spectra found for a p- polarzed ncdent lght wth dfferent azmuthal (φ) angle, whle the polar angle (θ) sfxed and t s 15. Hence, the drecton of the magnetc feld component of the ncdent lght s changed. Smlarly to the ndvdual transmttance spectra n Fgure 5b, the ndvdual transmttance spectra n Fgure 6b, also show clear resonance behavor as assocated wth the frst, second, and thrd aperture par, respectvely. But ths tme, the larger resonances for each nvestgated φ case are assocated wth the apertures orented along the x-drecton because of the use of p-polarzed ncdent lght. But, agan, by changng φ, we can ncrease the resonances n apertures orented along the y- drecton. All other man features are the same as n Fgure 5b. Thus, Fgure 6 shows that for a very large range of angle of ncdence (θ), our devce spectrally separates also p-polarzed ncdent lght, and t collects the dfferent spectral components n dfferent subwavelength-sze aperture pars. Achevng spectral separaton s ndependent of feld drectons of p- polarzed plane waves when usng aperture pars as detected elements. Our devce further separates the dfferent lnear polarzaton components of p-polarzed ncdent lght and transmts the power of those components through dfferent apertures of aperture pars. 530

7 Fgure 5. Transmttance spectra of the alumnum planar subwavelength spectral lght separator array for s-polarzed ncdent lght wth dfferent polar (θ) and azmuthal (φ) angles. (a) Indvdual transmttance spectra for the aperture par 1 1 n (), 2 2 n (), and 3 3 n (), whle φ s fxed at 0 and θ s changed. The blue, red, orange, and cyan lnes show the ndvdual transmttance spectra of the aperture 1 n (), 2 n (), and 3 n () for θ = 0, θ = 15, θ = 30, and θ = 45, respectvely. In each of (), (), and (), there are four separate gray dotted lnes concdng almost on top of each other, and they show the ndvdual transmttance spectra of the aperture 1 n (), 2 n (), and 3 n () for θ =0, θ =15, θ =30, and θ = 45. (b) Indvdual transmttance spectra for the aperture par 1 1 n (), 2 2 n (), and 3 3 n (), whle θ s fxed at 15 and φ s changed. In each of (), (), and (), the blue, red, orange, and cyan lnes show the ndvdual transmttance spectra for φ =0, φ =15, φ =30, and φ =42, respectvely. Sold lnes correspond to the aperture 1 n (), 2 n (), and 3 n (), and the dotted lnes correspond to the aperture 1 n (), 2 n (), and 3 n (). The results obtaned from Fgures 5 and Fgure 6 together show that for a very large range of angle of ncdence, achevng the decomposton of ncdent lght nto ts dfferent spectral components does not depend on the polarzaton of the lght. It also shows that the lght components havng electrc feld n the x-drecton and the lght components havng electrc feld n the y-drecton excte dfferent apertures of aperture pars, so ther power s collected n and transmtted through dfferent apertures. We also note that when θ =0 and φ =0, s-polarzed lght s the same as x-polarzed lght and p-polarzed lght s the same as y-polarzed lght, and our structure s symmetrc wth respect to a plane that s parallel to the x = y plane. Hence, as complementary to our observatons n the solated structure response, when θ =0 and φ =0, t can be seen from Fgure 5a and Fgure 6a that the transmttance response of an aperture orented along the y-drecton for s-polarzed llumnaton and the response of the same-sze aperture orented along the x- drecton for p-polarzed llumnaton are the same. Once the transmttance spectra of our devce are known for both s- and p-polarzed ncdent lght, we can obtan the transmttance spectra of our devce for unpolarzed lght. Fgure 7 shows the result for normally ncdent unpolarzed lght. The dfferent curves represent the ndvdual transmttance spectra of the dfferent aperture pars. The peak transmttance values are , , and for the frst (1 1 ), second (2 2 ), and thrd (3 3 ) aperture par, respectvely. Ths plot shows that our devce can decompose unpolarzed lght nto ts 531

8 Fgure 6. Transmttance spectra of the alumnum planar subwavelength spectral lght separator array for p-polarzed ncdent lght wth dfferent polar (θ) and azmuthal (φ) angles. (a) The ndvdual transmttance spectra for the aperture par 1 1 n (), 2 2 n (), and 3 3 n (), whle φ s fxed at 0 and θ s changed. The blue, red, orange, and cyan lnes show the ndvdual transmttance spectra of the aperture 1 n (), 2 n (), and 3 n () for θ =0, θ =15, θ =30, and θ =45, respectvely. In each of (), (), and (), there are four separate gray sold lnes concdng almost on top of each other, and they show the ndvdual transmttance spectra of the aperture 1 n (), 2 n (), and 3 n () for θ =0, θ =15, θ =30, and θ =45. (b) Indvdual transmttance spectra for the aperture par 1 1 n (), 2 2 n (), and 3 3 n (), whle θ s fxed at 15 and φ s changed. In each of (), (), and (), the blue, red, orange, and cyan lnes show the ndvdual transmttance spectra for φ = 0, φ = 15, φ = 30, and φ =42, respectvely. The sold lnes correspond to the aperture 1 n (), 2 n (), and 3 n (), and the dotted lnes correspond to the aperture 1 n (), 2 n (), and 3 n (). spectral bands and each band s transmtted through a dfferent aperture par, whch shows that each aperture par behaves as a separate spectral channel for transmsson. For the magng applcatons, these spectral bands can be detected by matchng a dfferent detector wth each aperture par. For ths purpose, subwavelength-sze photodetectors mght be used under each aperture par of our devce, and there have been some works showng subwavelength-sze photodetectors. 58 The physcal areas of the frst (1 1 ), second (2 2 ), and thrd (3 3 ) aperture pars n a sngle perod are 0.1, 0.125, and 0.15 μm 2, respectvely. Ths means that the physcal areas of the frst, second, and thrd aperture pars cover about 3.27%, 4.08%, and 4.9% of a sngle perod, respectvely. However, at resonance, these aperture pars transmt 42.53%, 50.72%, and 57.55% of lght mpngng on a sngle perod. Thus, the apertures funnel and transmt the ncdent lght from an electromagnetc cross-sectonal area that s much larger than ther physcal area. Moreover, snce the electromagnetc cross-sectonal areas of the aperture pars are much larger than the physcal areas of the aperture pars as well as the physcal areas that are separatng the aperture pars, there exsts a very large overlappng regon among the cross-sectonal areas from whch the aperture pars get ther lght, whch sgnfcantly dmnshes the spatal coregstraton errors among dfferent spectral channels. We also note here that the ndvdual transmttance spectra n Fgures 5, 6, and 7 show spectral regons of negatve power flow through the off-resonant apertures near the resonance wave- 532

9 Fgure 7. Transmttance spectra of the alumnum planar subwavelength spectral lght separator array for normally ncdent (θ = 0 ) unpolarzed lght. The blue lne corresponds to the ndvdual transmttance spectrum of the frst aperture par (1 1 ), the green lne corresponds to the ndvdual transmttance spectrum of the second aperture par (2 2 ), and the red lne corresponds to the ndvdual transmttance spectrum of the thrd aperture par (3 3 ). lengths, whch suggests some mnor crosstalk between apertures. Some transmtted power through the resonatng apertures flows back to the nput sde through the off-resonant apertures. We beleve that ths phenomenon agrees wth the prevous observatons of negatve power flow n perodc arrays of compound apertures. 56 However, we also checked the overall transmttance spectra of an entre perod for all the smulated cases n Fgures 5, 6, and 7, and observed that all the values of the overall transmttance spectra are above zero. Ths tells us that even when there s a negatve power flow through the offresonant apertures, the total power flow through the entre structure remans postve, as expected. One should note that the peak transmttance values n Fgure 7 are all above 42% and can almost reach 60%. In comparson, to acheve spectral selectvty, many systems rely on spectral flters, such as spectral flter arrays (SFA), 4,5,19,59 63 where each pxel records only one spectral component of ts nput lght, whch leads to a loss n effcency. An SFA approach where four separate pxels collect three dfferent spectral components, must have effcences less than 25% for at least two spectral components. 17,20,59 Moreover, n a snapshot system composed of spectral flters, each pxel gets ts nput lght from a separate part of a scene, whch necesstates the mplementaton of spatal nterpolaton n postprocessng and leads to artfacts and spatal coregstraton errors between dfferent spectral channels. 4,5,11,45,46,62,63 Our devce, on the other hand, acheves smultaneous decomposton of ncdent lght nto multple spectral components on the same subwavelength-sze pxel area, whch drastcally reduces spatal coregstraton errors and elmnates the need of spatal nterpolaton. We should also note that our devce works better n the spectral ranges where metals have less loss. On the other hand, vsble spectrum, where metals have sgnfcantly large loss, s also a hghly utlzed spectral range n magng applcatons. That s why we have also tested our devce n the vsble wavelength range by scalng the dmensons n our devce, and we have not acheved the spectral separaton effect due to the hgher materal loss. However, we guess that by usng the concept of assemblng several deep-subwavelength resonant structures ( meta-atoms ) formed by dfferent devce desgns and dfferent materals, such as delectrcs, one mght acheve spectral separaton n a subwavelength-sze devce for the vsble spectrum. We thnk that such a devce would be a sgnfcant alternatve to the conventonal color flter arrays for magng applcatons. In summary, we have shown a three-dmensonal, planar, ultrathn, subwavelength spectral lght separator that allows the smultaneous decomposton of ncdent lght nto ts spectral components. The devce operates by utlzng multple metaatoms, each supportng a strong, localzed resonance. The meta-atoms are based on subwavelength apertures n a metallc flm of deep-subwavelength thckness. The devce s very photon effcent, whch s of great mportance n multspectral magng applcatons. As a specfc example of our devce, we have desgned an solated metallc structure wth three dfferent rectangular aperture pars, where each aperture par s composed of two perpendcularly orented, same-sze apertures; and we have shown that each aperture par effectvely transmts lght n a dfferent spectral range. In our devce, electromagnetc felds are concentrated n a dfferent aperture par n each resonance wavelength. Addtonally, spatal coregstraton errors between dfferent spectral channels are qute reduced snce the areas from whch the resonant aperture pars collect ther lght sgnfcantly overlap. We have shown that our devce can operate as a sngle, non-perodc devce snce t acheves spectral separaton of lght wthout relyng on any mechansm that depends on perodcty; that beng sad, we have also demonstrated that our devce can operate also n an array confguraton composed of subwavelength-sze unt cells. Furthermore, we have shown that achevng spectral separaton s robust and ndependent of lght polarzaton for a very large range of angle of ncdence whle usng aperture pars as detected elements. As a result of all these features, our devce suggests a photon-effcent alternatve to absorptve spectral flter arrays n multspectral magng applcatons. Fnally, we have demonstrated that our devce also smultaneously separates dfferent lnear polarzaton components of lght, and collects ther power n dfferent apertures of aperture pars. Ths mght be useful n applcatons that requre selectng lght wth a partcular lnear polarzaton, or partcular electromagnetc feld components, n addton to a partcular frequency. METHODS To smulate the devces shown n Fgures 1 and 4, we use the fnte-dfference frequency-doman (FDFD) method Unlke tme-doman methods, such as the fnte-dfference tme-doman method, the FDFD method allows us to use expermentally measured delectrc constants for dspersve materals such as alumnum 47 wthout approxmaton. To smulate an nfnte space n whch the operaton of a sngle solated (.e., nonperodc) devce shown n Fgure 1 s examned, the fnte smulaton doman s surrounded n all dmensons (sx boundary surfaces) by stretched-coordnate perfectly matched layers (SC-PMLs). 49,50 To smulate the perodc devce shown n Fgure 4, SC-PMLs are appled only for the top and bottom boundares of the smulaton doman, and the Bloch boundary condtons are appled at the four remanng sdes of the doman. 64,65 In both cases, the 533

10 smulaton doman szes are chosen such that there are enough dstances between SC-PMLs and the apertures. For the sngle solated devce shown n Fgure 1, we calculate the ndvdual transmsson cross secton spectra of each aperture and the overall transmsson cross secton spectra of the entre devce. To calculate the ndvdual transmsson cross secton of each aperture, we frst locally measure the transmtted power flux through each aperture on a rectangular observaton area at the ext of the aperture. The sze of each observaton area s chosen such that the measured power flux through t corresponds to the transmtted power flux through the correspondng aperture only. Then, the ndvdual transmsson cross secton of each aperture s obtaned by normalzng the transmtted power flux through each aperture wth respect to the power flux densty of the ncdent lght. To calculate the overall transmsson cross secton of the entre devce, we measure the transmtted power flux through the entre structure, and normalze t wth respect to the power flux densty of the ncdent lght. Then, to obtan Fgure 2, we also perform these calculatons for another smulaton case where the devce materal s PEC, and all the other parameters are the same as the devce shown n Fgure 1. For the perodc devce shown n Fgure 4, we calculate the ndvdual transmttance spectra of each aperture. The ndvdual transmttance of an aperture s calculated based on the locally measured power flux transmtted through that aperture only. To calculate the ndvdual transmttance of each aperture, we frst locally measure the transmtted power flux through each ndvdual aperture on a rectangular observaton area at the ext of each aperture. The sze of each observaton area s chosen such that the measured power flux through t corresponds to the transmtted power flux through the correspondng aperture only. Then, the ndvdual transmttance of each aperture s obtaned by normalzng the transmtted power flux through each aperture wth respect to the ncdent power flux mpngng on the entre devce n a sngle perod. AUTHOR INFORMATION Correspondng Authors *E-mal: buyukalp@stanford.edu. *E-mal: pcatryss@stanford.edu. *E-mal: shanhu@stanford.edu. ORCID Yasn Buyukalp: X Peter B. Catrysse: Present Address Department of Mathematcs, Massachusetts Insttute of Technology, Cambrdge, Massachusetts 02139, U.S.A. Notes The authors declare no competng fnancal nterest. ACKNOWLEDGMENTS Ths work was supported n part by Samsung Electroncs. REFERENCES (1) Bao, J.; Bawend, M. G. A Collodal Quantum Dot Spectrometer. Nature 2015, 523, (2) Reddng, B.; Lew, S. F.; Sarma, R.; Cao, H. Compact Spectrometer Based on a Dsordered Photonc Chp. Nat. Photoncs 2013, 7, (3) Yang, T.; Xu, C.; Ho, H.; Zhu, Y.; Hong, X.; Wang, Q.; Chen, Y.; L, X.; Zhou, X.; Y, M.; Huang, W. Mnature Spectrometer Based on Dffracton n a Dspersve Hole Array. 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