microscopic origin of the chiroptical response of optical ... · (or reflection) response to rcp...

SC I ENCE ADVANCES | R E S EARCH ART I C L E

OPT ICS

1Center for Nanoscale Science and Technology, National Institute of Standardsand Technology, Gaithersburg, MD 20899, USA. 2Maryland NanoCenter, Universityof Maryland, College Park, MD 20742, USA. 3Department of Electrical Engineeringand Computer Science, Syracuse University, Syracuse, NY 13244, USA.*Corresponding author: Email: [email protected] (M.S.D.); [email protected] (A.A.)

Davis et al., Sci. Adv. 2019;5 : eaav8262 11 October 2019

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Microscopic origin of the chiroptical responseof optical mediaMatthew S. Davis1,2,3*, Wenqi Zhu1,2, Jay K. Lee3, Henri J. Lezec1, Amit Agrawal1,2*

The potential for enhancing the optical activity of natural chiral media using engineered nanophotonic compo-nents has been central in the quest toward developing next-generation circular-dichroism spectroscopic tech-niques. Through confinement and manipulation of optical fields at the nanoscale, ultrathin optical elementshave enabled a path toward achieving order-of-magnitude enhancements in the chiroptical response. Here,we develop a model framework to describe the underlying physics governing the origin of the chiroptical re-sponse in optical media. The model identifies optical activity to originate from electromagnetic coupling to thehybridized eigenstates of a coupled electron-oscillator system, whereas differential absorption of oppositehandedness light, though resulting in a far-field chiroptical response, is shown to have incorrectly been identi-fied as optical activity. We validate the model predictions using experimental measurements and show them toalso be consistent with observations in the literature. The work provides a generalized framework for the designand study of chiroptical systems.

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INTRODUCTIONChirality is the geometric property of an object being nonsuper-imposable on its mirror image along any symmetry axis and is ubiq-uitous in the natural world. For example, sugars, proteins, anddeoxyribonucleic acids are chiral molecules essential to the func-tioning and continuation of biological processes. The two variantsof a chiral molecule, known as enantiomers, are chemically identicalbut structured in either a left-handed or a right-handed arrange-ment. Biological systems on Earth have evolved to prefer left-handedenantiomers—a property referred to as homochirality (1). A compre-hensive understanding of the evolutionary mechanisms responsiblefor homochirality remains elusive, but investigations are yielding in-sights into the origins of life on Earth (2) and even in the search forextraterrestrial life (3). Many biochemical processes, to function cor-rectly, also require a particular handedness enantiomer. This is ob-served in the metabolism of pharmaceuticals such as thalidomide(4) and penicillamine (5), wherein one enantiomer produces medici-nal effects and the other toxicity. Thus, enantiomer discriminationtechniques such as circular dichroism (CD) spectroscopy are essentialfor minimizing the toxic effects of medications (6, 7), developing ef-fective treatments for diseases (8, 9), and probing the nature of chiralsystems (10). In addition to enantiomer discrimination, CD spectros-copy also provides information on protein secondary structures cru-cial to understanding protein folding (11, 12). This understandingbenefits the development of treatments for several deadly diseases suchasAlzheimer’s, Parkinson’s, and some cancers (13).However, the inher-ently weak CD response from natural molecular systems, coupled withthe limited sensitivity of conventional CD spectroscopic techniques, hasplaced an upper limit on the overall detection sensitivity. In recent years,engineered ultrathin nanoscale optical devices, composed of an array ofmetallic or dielectric nanostructures, have been used to enhance the CDresponse of natural chiral media by several orders in magnitude, sug-

gesting the possibility of next-generation CD spectroscopic techniqueswith substantially improved measurement sensitivities (14, 15). How-ever, the underlying phenomena governing the microscopic origin ofthe chiroptical (CO) response from nano-optical devices are still notwell understood. Here, we present, and experimentally validate, a gen-eralized model that identifies the fundamental origin of optical activityin a chiral medium and unifies the distinct CO phenomenon observedin literature under a single theoretical framework.

CD is a measure of the optical activity in a CO medium and ischaracterized by the differential absorption between right and leftcircularly polarized light (RCP and LCP, respectively). Because chiralmedia exhibit circular birefringence, optical activity can also be char-acterized by the degree of rotation of a linearly polarized light as itpropagates through it—a phenomenon commonly referred to as opticalrotary dispersion (ORD). CD and ORD are both synonymous withoptical activity because they originate from the same quantummechanical phenomenon and are related to each other through theKramers-Kronig transformation (16). We define a generalized far-fieldCO response of an opticalmedium as the differential transmission(or reflection) response to RCP and LCP source fields, quantitativelyexpressed for transmission measurements as CO(w) = TRCP(w) −TLCP(w), where TRCP (TLCP) is the spectral intensity transmissionfor illumination with an RCP (LCP) light. As we demonstrate in thispaper, a far-field CO response does not always correspond to CD andcan originate from other microscopic phenomenon not related tooptical activity. Hence, careful consideration must be given to the in-terpretation of CO measurements (17–19).

We identify three primary CO response types that are experimen-tally characterized and theoretically studied within the framework ofan all-purpose, generalized coupled oscillator model described in thenext section. We demonstrate optical activity to fundamentally orig-inate from the accessibility of RCP and LCP light to the hybridizedenergy-shifted eigenstates of a coupled electron-oscillator system—aresult that is consistent with the predictions of the Born-Kuhnmodel(20). Subtracting the two energy-shifted spectral responses from oneanother, upon illumination with RCP and LCP light, respectively,results in a far-field CO response associated with optical activity,whichwe hereafter refer to as COOA.Differential absorption to oppositehandedness light, not related to optical activity but originating from

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near-field absorption modes in planar chiral media, has also beenshown to produce a far-field CO response, which we refer to as COabs(21, 22). In contrast to COOA, COabs results from a difference in am-plitudes between the transmission (or reflection) spectra without anyassociated spectral shift when subjected to illumination with oppo-site handedness light (23). Last, by using birefringence in an all-di-electric metamaterial acting as a uniaxial or a biaxial medium, astrong far-field CO response has been observed through spatialfiltering of either the RCP or the LCP light (19, 24, 25). This responsetype, referred to here as COaxial, is also not associated with opticalactivity in the underlying optical medium. Because the three responsetypes can be present in a single COmeasurement, we express the totalCO response of optical media as CO=COOA+COabs + COaxial, whereCOOA ≠ COabs ≠ COaxial. Note that these phenomena have beenseparately observed experimentally (20–27), and the former two areanalytically described in previous works (20, 22, 28); however, in-dependent models have been used to describe them without any clearrelation between them. No analytical model has yet successfully de-scribed the various types of CO responses observed in literature undera single comprehensive theoretical framework. The model developedhere provides an analytical foundation for a generalized CO responsefrom an optical medium and suggests easy-to-implement methods foridentifying the presence of, and distinguishing between, the distinctphenomena present in a COmeasurement that may or may not orig-inate from optical activity. The model predictions are experimentallyvalidated using far-field CO measurements on engineered nanoscaleplasmonic devices at optical frequencies and are shown to also beconsistent with observations in the literature.

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RESULTSThe generalized coupled oscillator modelWemodel the microscopic CO response of optical media at the mo-lecular unit cell level using two lossy coupled electron oscillators. Thetwo oscillators are assumed to be arbitrarily located and oriented rel-ative to each other, and interacting with an arbitrarily polarized lightat oblique incidence with electric field E

⇀

0eiðk⇀∙r⇀�wtÞ (Fig. 1A), where k

⇀

and w are the wave vector and frequency of the incident light, respec-tively. These coupled oscillators constitute a single molecular unit celldescribed by a pair of fully vectoral second-order coupled differentialequations

∂2t u⇀1þg1∂tu⇀1þ w21u⇀1þz2;1u2û1 ¼ �

em*

ðE⇀0⋅ û1Þû1eiðk⇀⋅r⇀1�wtÞ ð1:1Þ

∂2t u⇀2þg2∂tu⇀2þw22u⇀2þz1;2u1û2 ¼ �

em*

ðE⇀0⋅ û2Þû2eiðk⇀⋅r⇀2�wtÞ ð1:2Þ

Each oscillator u⇀i is characterized by an oscillation amplitude

ui(w, t), resonant frequency wi, damping factor gi, and cross-couplingstrength zi, j(w), representing the electromagnetic interaction betweenthe oscillators, for i, j = 1,2. The oscillator locations are given by r

⇀i ¼

r⇀0 þ dr⇀i, with dr⇀i being the oscillator displacement from the molec-

ular center of mass r⇀0 (Fig. 1, B to D). Furthermore, the electron os-

cillators are described by a charge e and an effective mass m*.Inserting the time harmonic expressionsu

⇀1ðw; tÞ ¼ û1u1e�iwt and

u⇀2ðw; tÞ ¼ û2u2e�iwt into Eqs. 1.1 and 1.2 and using the substitution

Wk ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiw2k � w2 � igkw

pfor k = 1,2 give closed-form solutions for

the two oscillation amplitudes expressed as (section S1)


u1ðwÞ ¼ �em*W22ðE

⇀

0⋅ û1Þeik⇀⋅dr⇀1 � z2;1ðE

⇀

0⋅ û2Þeik⇀⋅ dr⇀2

W21W22 � z1;2z2;1

24

35eik

⇀⋅r⇀0 ð2:1Þ

u2ðwÞ ¼ �em*W21ðE

⇀

0⋅ û2Þeik⇀⋅dr⇀2 � z1;2ðE

⇀

0⋅ û1Þeik⇀⋅ dr⇀1

W21W22 � z1;2z2;1

24

35eik

⇀⋅r⇀0 ð2:2Þ

Using Eqs. 2.1 and 2.2, the medium’s current density responseJ⇀ðw; tÞ to the driving source field can be calculated as (section S2)

J⇀ðw; tÞ ¼ �ie0ww

2p

W21W22 � z1;2z2;1

nW22ðE

⇀

0⋅ û1Þ � z2;1ðE⇀

0⋅ û2Þe�ik⇀⋅ðdr⇀1�dr⇀2Þ

h i

û1 þ W21ðE⇀

0⋅ û2Þ � z1;2ðE⇀

0⋅ û1Þeik⇀⋅ ðdr⇀1�dr⇀2Þ

h iû2oeiðk

⇀⋅r⇀�wtÞ ð3Þ

where wp ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffine2=m*e0

pis the plasma frequency, e0 is the permittiv-

ity of free space, and n is the molecular unit cell density. By rear-ranging Eq. 3, the current density response can be simplified asJ⇀ðw; tÞ ¼ �iwe0cE

⇀

0eiðk⇀∙r⇀�wtÞ; showing J

⇀to be proportional to the

product of the incident source field with a susceptibility tensor ccontaining elements ci, j with i, j = x, y, z. The susceptibility tensorcan be expressed in terms of a modified dielectric tensor D(k, w) anda nonlocality tensor G(k, w) as c(k, w) = D(k, w) + ikG(k, w), wherethe modified dielectric tensor is related to the dielectric tensor asD(k, w) = e(k, w) − Ι (29). The nonlocality tensor has previouslybeen identified as related to the optical activity by the relationsORD = wRe{G}/2c and CD = 2wIm {G}/c, where c is the speed of lightin free space (20). Full expressions for c(k, w) along with derivationsof expressions for D(k, w) and G(k, w) are given in section S3.

Because the relationship between the far- and near-field CO responseis typically approximated asTRCP � TLCPº∣J

⇀RCP∣2 � ∣J⇀LCP∣2, we

express the CO response calculated using the model as CO ¼jJ⇀RCP∣2 � ∣J⇀LCP∣2, where J⇀RCP and J⇀LCP indicate the current den-sity response of the optical medium to RCP and LCP light, respec-tively. Expanding this term results in a concise expression for COgiven as (section S4)

CO=e02w2 ¼ c⇀n � c⇀

�n

� �⋅ E

⇀

0 � E⇀�0

� �ð4Þ

Equation 4 is expressed using the Einstein summation notationsummed over n = x, y, z, where each susceptibility vector c

⇀n contains

elements cn,k for k= x, y, z and is related to the dielectric and nonlocalityvectors by c

⇀n ¼ D⇀n þ ikG

⇀

n (29). Note that the expression for CO isnonzero only if both (i) the incident source field is elliptically or circularlypolarized and (ii) the susceptibility terms are complex, which occurs inthe presence of either damping in the optical medium, g1 or g2 ≠ 0, orspatial separation between the oscillators along the direction of sourcepropagation, k

⇀

∙ðdr⇀1 � dr⇀2Þ≠0 (section S3). Setting the two oscillators’orientation parallel to the x-y plane (q1 = q2 = p/2) and inserting this intoEq. 4 give CO ¼ e02w2½ðD⇀n � D⇀�nÞ þ ikðG

⇀

n � D⇀�n � D⇀n � G⇀�nÞ� ⋅ðE

⇀

0 �E⇀�0Þ. This expression can be rewritten as the sum of two components,

CO = DA = DAD,D + DAG,D, where

DAD;D=e02w2 ¼ D⇀n � D⇀�n

� �⋅ E

⇀

0 � E⇀�0

� �ð5:1Þ

DAG;D=e02w2 ¼ 2ikRe G⇀n � D⇀�n

n o⋅ E

⇀

0 � E⇀�0

� �ð5:2Þ

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Here,DAD,D is determined by the source interactionwith the dielectrictensor andDAG,D is determined by the source interaction with both thenonlocality and dielectric tensors. In the limit where the spatial sepa-ration between the oscillators is much smaller than the wavelength,k⇀

∙ðdr⇀1 � dr⇀2Þ≪ 1, eqs. S12.1 to S12.9 and S13.1 to S13.9 show thatthe dielectric tensor D(k, w) only depends onw, whereas the nonlocalitytensor G(k, w) becomes directly proportional to k̂. This suggests aninteresting dichotomy: The response DAD,D is largely influenced by thesource frequency corresponding to a temporal dispersion in the sys-tem, whereas DAG,D is influenced by the direction of the incident fieldcorresponding to a spatial dispersion in the system. Consistent withthis, we show the dependence of DAD,D on the angular separation be-tween the oscillators in the direction of source electric field rotation andof DAG,D on the separation between oscillators in the direction of thesource propagation.

By further simplification, Eqs. 5.1 and 5.2 can be rewritten as(section S4)

DAD;D ¼ 2e02w2∣E0∣2cosq0ImfD�xxDxy þ D�yxDyyg ð6:1Þ


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DAG;D ¼ 2e02w2∣E0∣2cosq0Re k DxyG�xx � DxxG�xy� �

þhn

DyyG�yx � DyxG�yy

� ��g ð6:2ÞNote that, in the absence of damping,Di;j ¼ D*i;j for i, j = x, y, Eq. 6.1

reduces to DAD,D = 0. Furthermore, for an isotropic medium, thediagonal elements of the dielectric tensor are equal and the oscilla-tor coupling is symmetric (z1,2(w) = z2,1(w)), resulting in Dxx = Dyyand Dxy = Dyx, respectively. Substituting these in Eq. 6.1 results inImfD�xxDxy þ D�yxDyyg ¼ 0, or equivalently DAD,D = 0. Therefore, bothdamping and anisotropy in an optical medium are necessary toachieve a DAD,D type CO response. This conclusion is consistent withprevious observation that absorption plays a critical role in generatinga CO response (22, 23). Moreover, a CO response of the DAD,D typehas also been observed in lossy two-dimensional anisotropic plasmonicmedia (21, 30). We associate DAD,D to the absorption-based CO re-sponse described earlier, COabs, noting again that this type of re-sponse is not related to optical activity. For the second response type,DAG,D, of Eq. 6.2 to be nonzero, a finite coupling between the oscilla-tors is required, z1,2(w) ≠ 0 and z2,1(w) ≠ 0. Note that even for an iso-tropic medium with nonzero symmetric coupling (z1,2(w) = z2,1(w)),nonlocality constants become Gxx = Gyy = 0 and Gxy = −Gyx (sectionS3), resulting in a nonzero DAG,D response. Hence, coupling be-tween oscillators is a necessary condition to achieve a DAG,D typeCO response—a conclusion that is consistent with both the pre-dictions of the Born-Kuhn model (20, 29) and the treatment of bi-isotropic chiral media presented in (31). We associate DAG,D to theCOOA type response described earlier, which is fundamentally re-lated to optical activity.

Further insights into the DAD,D and DAG,D response types can beachieved by expressing them in terms of the fundamental oscillatorparameters of Eqs. 1.1 and 1.2. By inserting expressions for the di-electric (eqs. S12.1 to S12.9) and nonlocality (eqs. S13.1 to S13.9)constants into Eqs. 6.1 and 6.2, and assuming f1 = 90° for simpli-city, DAD,D and DAG,D can be expressed as

DAD;D ¼ kw g2 w2 � w21� �� g1 w2 � w22

� �� sin f2þ

g2z1;2 � g1z2;1� �

cos k⇀

⋅ dr⇀1 � dr⇀2� �h igcos f2 ð7:1Þ

DAG;D ¼ kn

z2;1 w2 � w21

� �þ z1;2 w2 � w22� ��

sin k⇀

⋅ dr⇀1 � dr⇀2� �h iþ

z1;2z2;1sin 2k⇀

⋅ dr⇀1 � dr⇀2� �h i

sin f2ocos f2 ð7:2Þ

where the multiplication factor k is defined as

kðwÞ ¼ 2e02w2w4p∣E0∣2cos q0=

w21 � w2� ��

ig1w�

w22 � w2� �� ig2w� �� z1;2z2;1

2

By allowing the two oscillators to have the same damping coefficient,g1 = g2 = g, and assuming the spatial separation between them to bemuch smaller than the wavelength, k

⇀

∙ðdr⇀1 � dr⇀2Þ≪1, Eqs. 7.1 and7.2 reduce to

C D

BA

Fig. 1. Generalized coupled oscillator model space. (A) Representation of an ar-bitrarily oriented incident plane-wave of wave vector k

⇀ ¼ �kðâxsin q0 cos f0 þâyk sin q0 sin f0 þ âzk cos q0Þ originating from a source placed at infinity. (B) Molec-ular unit cell consisting of two oscillators u

⇀1 and u

⇀2 located at distances dr1 and dr2,

respectively, from the molecular center of mass, O′, which is located at a distance r⇀0

from the origin O. Each oscillator is arbitrarily oriented with respect to the other.(C) Coordinate system with the origin (O′) corresponding to the molecular center ofmass. The oscillator displacement from O′ is given by dr

⇀i ¼ driðâxsin xi cos yi þ

âysin xi sin yi þ âzcos xiÞ for i = 1,2. (D) The origin here corresponds to oscillatorcenter of mass (O″), which is positioned at a distance d r

⇀i from the molecular center

of mass (O′). The orientation of each oscillator is described by the unit vector ûi ¼âxsin qi cos fi þ âysin qi sin fi þ âzcos qi for i = 1,2.

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DAD;D ¼ kwg w22 � w21� �

sin f2 cos f2 þwg z1;2 � z2;1

� �cos f2 ð8:1Þ

DAG;D ¼ k k⇀

⋅ dr⇀1 � dr⇀2� �

z2;1 w2 � w21

� �þ z1;2 w2 � w22� �þ�

2z1;2z2;1sin f2�cos f2 ð8:2Þ

We illustrate the behavior of these two CO response types inEqs. 8.1 and 8.2 by applying them to two Au nanocuboids, actingas oscillators, aligned parallel to the x-y plane (with f1 = 90° andf2 = 45°) excited with a source field normally incident on the struc-ture at angles, q0 = 0° and q0 = 180° (Fig. 2A). We assume the twoAu nanocuboids, separated along the direction of source propagation(z) by a distance dz = d1,z − d2,z = 200 nm and located at d1,y = d2,x =100 nm, to exhibit resonance at wavelengths l1 = 750 nm and l2 =735 nmwith z1,2(w1) = z2,1(w2) = 1.6 × 10

29 s−2. The following values forthe plasma frequency,wp = 1.37 × 10

16 s−1, and damping coefficient, g =g1 = g2 = 1.22 × 10

14 s−1, forAu in the near-infrared region are used (32).DAD,D and DAG,D plotted versus incident wavelength l0 (Fig. 2, B and C)for the two source angles q0 illustrates that the presence of an inversionin the sign of DAD,D as q0 is rotated by 180°, which is consistent with Eq.8.1, where DAD,D(q0 + p) = −DAD,D(q0). Previous observations of inver-sion in the sign of the far-field CO response due to q0 rotation suggestan absence of optical activity in the underlying medium (21, 30), ver-ifying our observations, whereas the lack of sign change in the DAG,Ddue to q0 rotation, where DAG,D(q0 + p) = DAG,D(q0), is indicative of op-tical activity (30). The total response, DA, plotted for q0 = 0° and q0 =180°exhibits an asymmetric spectral line shape due to the competing


contributions from the DAD,D response, which exhibits a single-foldsymmetric line shape, and theDAG,D response, which exhibits a twofoldsymmetric line shape (Fig. 2D), indicating the presence of both COOAand COabs in the total CO response.

Analogous to the dependence of DAD,D and DAG,D responses onq0, further insight can be achieved by analyzing the dependence ofthe CO response on the azimuth angle f0 (for any q0, except at q0 =0° and 180°, where f0 is undefined). For an identical configurationof Fig. 2A, DAD,D and DAG,D plotted versus incident wavelength l0(Fig. 2, E to G) for two source azimuth angles f0 = 0° and 180° (atq0 = 45°) illustrates the presence of an inversion in the sign of DAG,Dinstead, as f0 is rotated by 180°. This follows from Eqs. 8.1 and 8.2,where DAD,D(f0 + p) = DAD,D(f0) and DAG,D(f0 + p) = −DAG,D(f0),respectively. This inversion in the DAG,D response can be further de-scribed by assuming d1,z = d2,z = 0 nm to make a two-dimensionalstructure wherein the spatial dispersion dependence k

⇀

∙ðdr⇀1 � dr⇀2Þ ofEq. 8.2 simplifies to kd sin q0( sin f0 − cos f0), for the two oscillatorslocated equidistant from the origin (d = d1,y = d2,x), demonstrating thedependence of DAG,D on f0.

In addition to the dependence of the CO response on excitationdirection, q0 and f0, we analyze its dependence on various oscillatorparameters including the angular orientation between the two os-cillators along the x-y plane, by varying angle f2 at f1 = 90°, and thedifference between coupling terms z2,1(w) − z1,2(w), oscillator fre-quencies Dw = w1 − w2, and damping coefficients Dg = g1 − g2. Forthis analysis, we assume the light to be normally incident (q0 = 0°)on the two Au nanocuboids, of lengths l1and l2, that are alignedparallel to the x-y plane with d1,y = l1, d2,x = l2 and placed in a planararrangement with d1,z = d2,z = 0 nm. In such a planar configuration at

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−1.0

−0.5

0.0

0.5

1.0

820735650

B

−1.0

−0.5

0.0

0.5

1.0

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C

−1.0

−0.5

0.0

0.5

1.0

820735650

D

−1.0

−0.5

0.0

0.5

1.0

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E

−1.0820735650

F

−1.0820735650

G

A

−0.5

0.0

0.5

1.0

−0.5

0.0

0.5

1.0

Fig. 2. Dependence of the CO response of nanocuboid bi-oscillator system on source angles q0 and f0. (A) Relative orientation of the incident light of wavevector k

⇀

with respect to the two nanocuboid oscillators. The two oscillators, represented by u⇀1 and u

⇀2, are oriented parallel to the x-y plane (q1 = q2 = p/2) with azimuth

angles f1 = 90° and f2 = 45°, respectively. The nanocuboids are located at d1, z = d2, z = 100 nm with d1, y = d2, x = 100 nm, and for simplicity, d1, x = d2, y = 0 nm wasassumed. The nanocuboid parameters were chosen such that they exhibit resonance at wavelengths of l1 = 750 nm and l2 = 735 nm, with coupling strengths z1,2(w1) =z2,1(w2) = 1.6 × 10

29 s−1. (B) The calculated DAD,D response at source angles q0 = 0° and 180° (note that f0 is undefined at these values of q0) exhibits a onefold symmetricline shape and experiences an inversion in sign when the incident angle is changed from 0° to 180°. a.u., arbitrary units. (C) The corresponding DAG,D response calculatedunder the same conditions exhibits a twofold symmetric line shape and does not experience an inversion in sign for a q0 change from 0° to 180°. (D) The total COresponse DA = DAD,D + DAG,D for the two source angles does not show any symmetry in the spectral line shape due to the presence of competing contributions fromboth DAD,D and DAG,D response types. (E to G) CO response for the oscillator configuration and orientations in (A) calculated at q0 = 45° for two azimuth angles f0 = 0°and 180°. (E) The calculated DAD,D response does not change sign when the incident angle f0 is changed from 0° to 180°. (F) The corresponding DAG,D response, however,exhibits an inversion in sign for a 180° change in the source azimuth. At these source angles, DAD,D exhibits a onefold symmetric line shape, whereas DAG,D is asymmetric.(G) The total CO response DA = DAD,D + DAG,D also exhibits an asymmetric line shape due to the presence of both DAD,D and DAG,D contributions.

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normal incidence, k⇀

∙ðdr⇀1 � dr⇀2Þ ¼ 0, resulting in DAG,D = 0 (Eq. 8.2).Last, by setting the two resonant wavelengths to be l1 = 750 nm andl2 = 735 nm (corresponding to Dw/g = 0.42), and assuming z1,2(w) =z2,1(w), the dependence of DAD,D on f2 exhibits a peak response at f2 =45° (Fig. 3A). Note that this observation that a planar two-dimensionalplasmonic structure can exhibit a COabs type CO response, not relatedto optical activity, is consistent with (30) and is also in agreement withthe findings of Eftekhari and Davis (21). In their work, they also note,without explanation, an experimental finding of a peak CO responseoccurring at f2 = 52° rather than the expected f2 = 45°. A simpleinclusion of a nonzero coupling difference, z2,1 − z1,2, between thetwo oscillators in the model accounts for this behavior wherein byplotting f2 that maximizes the DAD,D response as a function of z2,1 −z1,2 at w = 2.43 × 10

15 s−1 (Fig. 3B), we show that the presence ofasymmetric oscillator coupling causes the maximum peak to oc-cur at values other than f2 = 45°. The DAD,D response can also bemaximized by optimizing the oscillator frequencies, wherein forz1,2 − z2,1 = − 5.2 × 10

28 s−2 corresponding to f2 = 52°, the modelalso predicts a peak DAD,D for Dw/g = 0.74 (Fig. 3C). This includesthe underlying dependence of the multiplication factor k(w) on thedifference between the normalized oscillator frequencies Dw/g (fig.S2). Last, the model predicts a CO response for light normally in-cident on a geometrically achiral system if asymmetric absorption


is present (g1 ≠ g2)—a scenario easily achieved by depositing twodifferent metal types for each of the cuboids (Fig. 3D). Using dis-similar metals to achieve inhomogeneous damping on a geometricallyachiral structure has been shown to exhibit a CO response (33).

Last, we verify the validity of our generalized model by applying itto the structure and excitation conditions studied using the Born-Kuhn model in (20). We assume the two Au nanocuboids in Fig. 2Ato be of equal lengths (l), aligned orthogonal to each other (f1 = 90°and f2 = 0°) with d1,y = d2,x = l/2 and separated by a distance dz alongthe z direction, resulting in w1 = w2 = w and W1 = W2 = W (fig. S3A).Note that, for consistency, the cuboid lengths lwere scaled to shift theresonance wavelengths to l1 = l2 = 1300 nm. Illumination of thestructure at normal incidence, q0 = 0°, under these conditions resultsin DAD,D = 0 (from Eq. 8.1). Also, as expected, due to this lack of COabscontribution, DA = DAG,D plotted versus incident wavelength l0 (fig.S3B) exhibits a twofold symmetric line shape and is consistentwith theresults of (20). Moreover, by applying the geometrical and oscillatorparameters to the configuration of fig. S2A, one could calculate thereduced dielectric and nonlocality tensor elements (section S6). Ap-plying these to Eq. 6.2 and plotting the resulting DAG,D versus l0 resultin the same response (fig. S3B), confirming the predictions of ourgeneralized model as well as its consistency with the Born-Kuhnmodel (20).

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m

1.0

0.5

0.0850800750700

50

40

−10 −5 0 5 10

1.0

0.5

0.01000900800700

1.0

0.5

0.0850800750700

60

A B

C D

Fig. 3. Dependence of the CO response of nanocuboid bi-oscillator system on oscillator parameters. CO response of the two oscillators, under normal incidenceexcitation (q0 = 0°), oriented parallel to the x-y plane (q1 = q2 = p/2) and arranged in a planar arrangement with d1, z = d2, z = 0 nm and d1, y = d2, x = 100 nm. In thisplanar configuration at normal incidence, DAG, D = 0. (A) Dependence of DA = DAD, D on the angular orientation between the two oscillators in the x-y plane calculated byvarying f2 at f1 = 90°. The oscillators are designed to exhibit resonance at wavelengths of l1 = 750 nm and l2 = 735 nm, and assuming z1,2(w) = z2,1(w), the peak DAD, Dresponse is shown to occur at f2 = 45°. (B) Orientation angle of the second oscillator f2 (at f1 = 90°) at which DAD, D is maximized for a nonzero difference in couplingcoefficients, z1,2 − z2,1, plotted here at w = 2.43 × 10

15 s−1. (C) DAD, D dependence on the normalized difference in resonant frequencies (Dw)/g at z1,2 − z2,1 = − 5.2 ×1028 s−2 corresponding to f2 = 52°. A peak DAD, D response is achieved at (Dw)/g = 0.74. (D) DAD, D dependence at normal incidence on a geometrically achiral system (l1 =l2) for oscillators of the same metal corresponding to g1 = g2 (red line) and of dissimilar metals corresponding to g1 ≠ g2 (blue line).

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Experimental resultsThe model described above provides a comprehensive theoreticalframework to study the origin and characteristics of various CO re-sponse types in both two- and three-dimensional optical media un-der arbitrary excitation conditions. A common performance metricassociated with far-field CO measurements is circular diattenuation(CDA), a normalized form of the CO response expressed as CDA =(TRCP − TLCP)/(TRCP + TLCP). CDA also corresponds to the normal-izedm14 element of theMueller matrix, so it can be directly extractedfrom spectroscopic ellipsometry measurements (34). Note thatMueller matrix spectroscopy also presents an accurate method fordistinguishing between the COOA and COabs contributions in afar-field CO measurement; however, this requires measurement ofbothm14 andm41 elements (17). As shown below, we verify throughmodel calculations that both CDA and DA represent the same opticalphenomenon; hence, for the simplicity of analysis, we present thefollowing experimental measurements and comparisons with modelpredictions in the CDA format. Note that an alternate metric basedon measuring optical chirality flux has recently been proposed as aquantitative far-field observable of themagnitude and handedness ofthe near-field chiral density in a nanostructured optical medium(35). Measured using a technique referred to as chirality flux spec-troscopy, it corresponds to the third Stokes parameter, which is di-rectly related to the degree of circular polarization of the scatteredlight in the far field (36) and carries information of the chiral nearfields. For the purpose of discussion in this article, and its consistencywith existing literature, we limit our analysis to measurements usingthemore prevalentmetric ofCO (or equivalently CDA) obtained fromtraditional CD spectroscopic measurements.

We experimentally characterize three planar cuboid configura-tions (Fig. 4A, left column) by measuring their far-field CDA re-sponse under various excitation conditions and compare them topredictions of the model. Respective expressions for DAD,D and DAG,Din the three configurations, assuming d1,z = d2,z = 0 nm and g1 = g2 = g(Eqs. 8.1 and 8.2), are listed in Fig. 4A (right column). Note that thek⇀

∙ðdr⇀1 � dr⇀2Þ term in these planar configurations simplifies to kdsin q0(sin f0 − cos f0). The devices, consisting of an array of twoAu nanocuboids (thickness t = 40 nm) of varying lengths (l1 andl2) and alignments (varying f2 at f1 = 90°), were fabricated on afused-silica substrate using electron beam lithography and liftoff(see Materials and Methods and section S7). The pitch of the array(p= 375 nm) was chosen to minimize coupling between adjacent bi-oscillator unit cells. The devices were characterized using a spectro-scopic ellipsometer between free-space wavelengths of l0 = 500 and1000 nm under illumination at q0 = 45° for various azimuth angles f0(seeMaterials andMethods). The first device consisted of the two Aunanocuboids arranged orthogonal to each other (f1 = 90° and f2 = 0°)and were designed to be of different lengths (l1 = 120 nm and l2 =100 nm placed at d1,y = d2,x = 100 nm, respectively). Because l1 andl2 determine both the resonant frequencies (w1 and w2) and thecross-coupling strengths (z1,2 and z2,1), setting l1≠ l2 constitutes a gen-eral configuration where both DAD,D and DAG,D type contributions canbe present in a single CDA measurement. The corresponding CDAspectra (Fig. 4B) measured at f0 = 0°, 90°, and 135° (blue plots) andat 180° offset from these angles (red plots) show an inversion in thesign, indicating the response to primarily result from DAG,D. However,note that the CDA measurements at these angles slightly lack thetwofold symmetry in the spectral line shape, a result of a minor DAD,Dcontribution. For f0 = 45° and 225°, the spectra lack the sign inversion,


indicating the response to primarily result from DAD,D, which alsofollows from Fig. 4A, where DAG,D = 0 at these two f0 angles. This re-sult is further validated by fabricating a device consisting of Au nano-cuboids of equal lengths (l1 = l2 = 120 nm),wherein theCDA spectra atf0 = 45° and 225° show noCO response, because both DAG,D = DAD,D =0, confirming the predictions of the model (Fig. 4A). Moreover, bysetting l1 = l2, the twofold symmetry in the CDA line shape at f0 =0° (180°), 90° (270°), and 135° (315°) is recovered, indicating the re-sponse to now only consist ofDAG,D contribution, a signature of opticalactivity (Fig. 4C). Hence, it is possible for a geometrically achiral struc-ture to exhibit optical activity under certain illumination conditions. Itfollows then due to reciprocity that optical activity may be detectableat large scattering angles when a source field is normally incident on aplanar achiral structure. This phenomenonwas recently confirmed byKuntman et al. (37) using a scattering matrix decomposition method.Note that the similarity between the calculated CDA and DA response(plotted under the conditions of Fig. 4B and fig. S5) verifies our as-sumption that they are equivalent measurements and can be used in-terchangeably.

For a device with Au nanocuboids of equal lengths l1 = l2 = 120 nm,aligned parallel to each other (f1 = 90° and f2 = 90°), Eqs. 8.1 and 8.2predict both DAD,D and DAG,D to be zero under illumination at q0 = 45°for any f0. Consistent with these predictions, while the CDA spectrameasured at f0 = 0°(180°) and 90° (270°) show no response, thespectra at f0 = 45°(225°) and 135° (315°) show a pronounced signalof the DAD,D type (no sign inversion for f0 rotation by 180°; Fig. 4D).We attribute this phenomenon to originate from coupling to theoptical resonances (u

⇀ 01 and u

⇀ 02) along the cuboid widths (w1 = w2 =

60 nm), acting as additional orthogonally oriented oscillators in the sys-tem, resulting in a two-dimensional anisotropic optical systemsupporting two orthogonal elliptical eigenmodes (30). A circularly po-larized light at non-normal incidence (q0 ≠ 0° and 180°) projects an el-liptically polarized field along the plane of the device (Fig. 5, A to D, redellipse), which, at certain azimuth angles f0, can access these ellipticaleigenmodes (Fig. 5, A to D, dashed yellow ellipses). At f0 = 0° (180°) orf0 = 90° (270°), both orthogonal eigenmodes are accessed equally, re-sulting in the total CO response to be zero, whereas, at f0 = 45°(225°)and 135° (315°), only one of the two eigenmodes can be excited, result-ing in a strong CDA response. This dependence of peak ∣DAD,D∣ onthe azimuth angle f0 is shown schematically in Fig. 5E. Theseresults are also consistent with Fig. 5F, which follows from Eqs.8.1 and 8.2, wherein incorporation of contributions from these ad-ditional oscillators results in a zero DAG,D response, whereas theDAD,D response is shown to stay proportional to (z1′,2 − z2,1′). Notethat for the CDA calculations in Fig. 4 (B and C), only couplingbetween the oscillators along their long axis (u

⇀1 and u

⇀2) was as-

sumed. The absence of contributions from coupling between theoscillators along their short axis,u

⇀′1 andu

⇀′2, in the calculations could

explain the minor discrepancy between the calculated and experi-mentally measured CDA spectra.

In addition, it is instructive to study the CO response of a devicewhere the two Au nanocuboids of equal lengths are aligned suchthat f1 = 90° and f2 = 45° in a planar arrangement. Upon illumi-nation of this structure at q0 = 45° for various f0, the measuredCDA response shows neither any clear inversion in sign with180° rotation of f0 nor any apparent symmetry in the spectral lineshape (fig. S6). This is because the various sub-oscillators (u

⇀1, u

⇀2, u

⇀′1,

and u⇀′2) in this system are aligned with respect to each other such

that they can all be intercoupled, resulting in substantial contributions

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B C D

A( )

C D

Fig. 4. Experimental characterization of the CO response of two-dimensional planar Au nanocuboids. (A) Simplified DAD,D and DAG,D relations, calculated from Eqs.8.1 and 8.2, for three planar nanocuboid configurations. Top row: The two oscillators are aligned orthogonal to each other (f1 = 90° and f2 = 0°) and are assumed to be ofdifferent lengths (l1 ≠ l2), corresponding to w1 ≠ w2 and z1,2(w) ≠ z2,1(w). In such a system, it is expected that both DAD,D and DAG,D contributions are present. Middle row:Same as above except with l1 = l2 resulting in w1 = w2 = w0, z1,2 = z2,1. In this configuration, DAD,D contribution is expected to be absent for excitation at any arbitrary angleof incidence. Bottom row: Same as above (l1 = l2) except that the two oscillators are oriented parallel to each other (f1 = 90° and f2 = 90°). Ignoring any optical resonancealong the width of the nanocuboid, the model predicts both DAD,D and DAG,D to be absent, for excitation at any arbitrary angle of incidence. (B to D) Correspondingexperimental CDA measurements for an array of planar Au nanocuboid bi-oscillators, illuminated with free-space light between wavelengths of l0 = 500 and 1000 nm,as a function of incidence angle (varying f0 at a fixed q0 = 45°) for the three configurations shown in (A). Top-down scanning electron microscopy (SEM) images ofunit cells consisting of the two Au nanocuboid oscillators, overlaid with the coordinate system and orientation of the in-plane wave vector of the incident light (k

⇀

∥xy)along the x-y plane, are shown at the top of each column. Scale bar, 120 nm in the SEM images. (B) Experimentally measured (solid lines) and model-calculated (dashedlines) CDA spectra for a sample consisting of Au nanocuboids of unequal lengths (l1 = 120 nm and l2 = 100 nm) oriented orthogonal to each other (f1 = 90° and f2 = 0°) atvarious f0. The spectra at f0 = 0°, 90°, and 135° (blue plots) and at 180° offset from these angles (solid red plots) show an inversion in the sign, which is absent for excitationat f0 = 45° (225°). The CDA model plots were calculated assuming z2,1(w1) = 6.4 × 10

29 s−2 and z1,2(w2) = 8.1 × 1029 s−2 at l1= 750 nm and l2 = 720 nm, respectively. (C)

Equivalent CDA measurements and model calculations for a device with Au nanocuboids of equal lengths (l1 = l2 = 120 nm). As expected, the CDA response is absent fromthis device for excitation at f0 = 45° (225°). Moreover, the response at other f0 angles exhibits a twofold symmetric spectral line shape [absent from measurements in (B)],indicating the CDA to only result from DAG,D contribution. Model parameters used in the calculations are z2,1(w0) = z1,2(w0) = 8.1 × 10

29 s−2 at l1 = l2 = 745 nm. (D) Same as(C) except that the two Au nanocuboids are oriented parallel to each other (f1 = 90° and f2 = 90°). The CDA spectra at f0 = 0° (180°) and 90° (270°) show no response,whereas the spectra at f0 = 45° (225°) and 135° (315°) show a pronounced signal of the DAD,D type (no sign inversion for f0 rotation by 180°). The CDA response at latterangles, though not expected from the model predictions in (A), can be attributed to the coupling to optical resonances along the cuboid widths (w1 = w2 = 60 nm), actingas additional orthogonally oriented oscillators (u

⇀′1 and u

⇀′2) in the system.

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from both DAG,D and DAD,D. This serves as a simple example for a sys-tem where the measured far-field CO response is ambiguous, and itsunderlying origin can be difficult to interpret.

Last, until now, we have applied the model predictions to, andvalidated them against, existing literature and experimental CDAmeasurements on planar metallic nanocuboid oscillators. However,as mentioned earlier, a strong far-field CO response of the COaxialtype has been observed in an all-dielectric metamaterial acting as auniaxial or a biaxial medium, wherein symmetry breaking of theunit cell along the direction of source propagation enables asymmetrictransmission of the two CP components of incident linearly polar-ized light (19, 24, 25). An additional deployment of geometric phasefurther enables independent phase-front manipulation of these twocomponents (24, 38). We demonstrate the generality of the model byapplying it to an all-dielectric optical mediumwith a mirror-symmetrybreaking chiral unit cell that enables asymmetric transmission of thetwo CP components, but without a geometric phase (section S10),and illustrate the conditions under which the Poynting vectors asso-ciated with the LCP and RCP components of a linearly polarized lightnormally incident on an all-dielectric biaxial medium can propagate indifferent directions within the medium. A simple spatial filtering of


either the LCP or the RCP on the exit side can result in a strong COresponse, as shown in (25). Note that such a far-field CO response isnot related to optical activity.

DISCUSSIONIn conclusion, we have developed a comprehensive analytical modelto study the microscopic origin of the CO response in optical media.Closed-form expressions for the various microscopic phenomenagoverning the far-field CO response are shown to provide intuitiveinsights when systematically studied for various sample geometriesand optical excitation conditions. Optical activity, COOA, character-ized in the far field by spectrally shifted transmission (or reflection)curves due to the accessibility of RCP and LCP light to hybridizedeigenmodes, is shown to originate at the microscopic scale whencoupled oscillators are spatially separated along the direction ofsource propagation. Differential absorption, COabs, another CO re-sponse type unrelated to optical activity, is characterized in the farfield by amplitude-shifted transmission (or reflection) curves due tothe presence of distinct near-field absorption modes for RCP andLCP light. COabs is shown to occur when the oscillators, in the presence

A EC

B D

F

Fig. 5. Origin of the CO response from parallel nanocuboid oscillators through coupling along orthogonal oscillator dimensions. (A to D) Top-down SEMimages of the device consisting of an array of Au nanocuboid oscillators oriented parallel to each other. Overlaid are the constitutive elliptical eigenmodes (dashedyellow curves) and the projected in-plane source electric field (E

⇀

∥xy), indicated by a red vector arrow that traces the red elliptical path for a circularly polarized light atnon-normal incidence. Scale bar, 125 nm in the SEM images. (A and B) Orientation of the two eigenmodes relative to the source electric field at f0 = 0° (180°) and90° (270°), illustrating that they can be accessed equally. (C and D) Same as above, except at source azimuths f0 = 45° (225°) and 135° (315°), illustrating that only one ofthe two eigenmodes can be accessed. (E) Dependence of ∣DAD,D∣ on f0 for the parallel nanocuboid oscillator configuration studied here. The orientation of the long-and short-axis oscillators (u

⇀i and u

⇀′i , respectively) corresponding to the length (li) and width (wi) of the two nanocuboids relative to f0 is shown for clarity. (F) Top:

Schematic illustrations of the two coupled oscillator contributions that result in a far-field CO response from parallel nanocuboid oscillators of equal lengths (l1 = l2) andwidths (w1 = w2) upon illumination at q0 = 45° and f0 = 45° (225°) or 135° (315°). Note thatu

⇀1 ¼ u⇀2 and u⇀′1 ¼ u

⇀′2 in this configuration leads to z1,2 = z2,1 as well as z1,2′ = z2,1′

and z2′,1 = z1′,2, resulting in DAD,D response to be doubled (from Eq. 8.1, bottom). However, because of the inversion of the spatial dispersion term k⇀

⋅ðdr⇀1 � dr⇀2Þ of Eq. 8.2,the DAG,D contributions between these two configurations become equal and opposite, canceling each other out.

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of loss, are angularly separated along the direction of source electric fieldrotation. The third CO response type, COaxial, is characterized in the farfield by the spatial separation of RCP and LCP light. COaxial is shown tooccur when the Poynting vectors associated with the characteristic RCPand LCPwaves of a biaxial medium are angularly offset. Both analyticaland experimental methods provided here suggest a simple method foridentifying the presence of, and distinguishing between, these variousCO response types. As engineered chiral opticalmedia become an essen-tial component of advanced technologies such as enhanced CD spec-troscopy, identification of the microscopic behavioral differences inthe far-field optical response has become increasingly crucial. Thegeneralized theoretical framework presented here is expected to aidin the application-specific design and study of engineeredCO systems.

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MATERIALS AND METHODSDevice fabricationThe Au nanocuboid structures were fabricated on 500-mm-thickfused-silica substrates. Polymethyl methacrylate (PMMA) resist(100 nm thick) was spun-coated on the substrates, followed by depo-sition of 20-nmAl film using thermal evaporation as an anti-charginglayer. Electron beam lithography at 100 keV was then used to exposethe nanocuboid patterns. After exposure, the Al layer was removedusing a 60-s bath in a tetramethylammonium hydroxide–based devel-oper followed by a 30-s rinse in deionized water. PMMA was devel-oped for 90 s in methyl isobutyl ketone, followed by a 30-s rinse inisopropyl alcohol. Electron beam evaporation was used to deposit a2-nm-thick Ti adhesion layer, followed by a 40-nm-thick Au film. A12-hour soak in acetone was used for liftoff, revealing the completedcuboid structures on the substrate surface. The fabrication steps areschematically outlined in fig. S4.

Optical characterizationFor experimental characterization, the samples were illuminated fromfree space at wavelengths between l0= 500 and 1000 nm at a fixedangle q0 = 45° for various source azimuth angles f0. The incidentlight was focused on the sample to a spot size (along the long axis)of ≈400 mm, and the incident polarization was controlled using anachromatic wave plate. The CDA spectra were directly measured,using a spectroscopic ellipsometer in reflection mode, by extractingthe m14 element of the Mueller matrix.

SUPPLEMENTARY MATERIALSSupplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/10/eaav8262/DC1Section S1. Generalized coupled oscillator model parameter definitionsSection S2. Current density response calculationSection S3. Homogeneous material parametersSection S4. CO response calculationSection S5. Dependence of the k on the difference between oscillator frequenciesSection S6. CO response for two identical, orthogonally oriented nanocuboids at finite dzSection S7. Device fabricationSection S8. Comparison between calculated CDA and DA spectral responseSection S9. CO response of 45° oriented cuboids of equal lengthsSection S10. Asymmetric transmission CO response of all-dielectric mediaFig. S1. Arrangement of bi-oscillator molecular unit cells in a representative volume ofoptical media.Fig. S2. Dependence of the multiplication factor k on the difference between oscillatorfrequencies.Fig. S3. CO response of orthogonally oriented identical nanocuboids in a three-dimensionalarrangement.


Fig. S4. Nanofabrication process steps.Fig. S5. Comparison between calculated CDA and DA spectral response.Fig. S6. Experimental measurements of the CO response of 45° oriented cuboids ofequal lengths.Fig. S7. Isofrequency surfaces and Poynting vectors for the eigenmodes of a biaxial medium.References (39, 40)

REFERENCES AND NOTES1. D. G. Blackmon, The origin of biological homochirality. Philos. Trans. R. Soc. B 366,

2878–2884 (2011).2. J. M. Dreiling, T. J. Gay, Chirally sensitive electron-induced molecular breakup and the

Vester-Ulbricht hypothesis. Phys. Rev. Lett. 113, 118103 (2014).3. J. C. Aponte, J. E. Elsila, D. P. Glavin, S. N. Milam, S. B. Charnley, J. P. Dworkin, Pathways to

meteoritic glycine and methylamine. ACS Earth Space Chem. 1, 3–13 (2017).4. J. M. Brown, S. G. Davies, Chemical asymmetric synthesis. Nature 342, 631–636 (1989).5. Y. Wang, Q. Han, Q. Zhang, Y. Huang, L. Guo, Y. Fu, Chiral recognition of penicillamine

enantiomers based on a vancomycin membrane electrode. Anal. Methods 5, 5579–5583(2013).

6. D. Leung, E. V. Anslyn, Rapid determination of enantiomeric excess of a-chiralcyclohexanones using circular dichroism spectroscopy. Org. Lett. 13, 2298–2301 (2011).

7. S. W. Smith, Chiral toxicology: It’s the same thing…only different. Toxicol. Sci. 110, 4–30(2009).

8. M. Budău, G. Hancu, A. Rusu, M. Cârcu-Dobrin, D. L. Muntean, Chirality of modernantidepressants: An overview. Adv. Pharm. Bull. 7, 495–500 (2017).

9. D. W. Green, J.-M. Lee, E.-J. Kim, D.-J. Lee, H.-S. Jung, Chiral biomaterials: From moleculardesign to regenerative medicine. Adv. Mater. Interfaces 3, 1500411 (2016).

10. A. K. Visheratina, F. Purcell-Milton, R. Serrano-Garcia, V. A. Kuznetsova, A. O. Orlova,A. V. Fedorov, A. V. Baranov, Y. K. Gun’ko, Chiral recognition of optically activeCoFe2O4magnetic nanoparticles by CdSe/CdS quantum dots stabilised with chiralligands. J. Mater. Chem. C 5, 1692–1698 (2017).

11. N. J. Greenfield, Using circular dichroism spectra to estimate protein secondary structure.Nat. Protoc. 1, 2876–2890 (2006).

12. B. Ranjbar, P. Gill, Circular dichroism techniques: Biomolecular and nanostructuralanalyses- A review. Chem. Biol. Drug Des. 74, 101–120 (2009).

13. V. Bellotti, M. Stoppini, Protein misfolding diseases. Open Biol. J. 2, 228–234 (2009).14. N. A. Abdulrahman, Z. Fan, T. Tonooka, S. M. Kelly, N. Gadegaard, E. Hendry,

A. O. Govorov, M. Kadodwala, Induced chirality through electromagnetic couplingbetween chiral molecular layers and plasmonic nanostructures. Nano Lett. 12,977–983 (2012).

15. M. L. Nesterov, X. Yin, M. Schäferling, H. Giessen, T. Weiss, The role of plasmon-generatednear fields for enhanced circular dichroism spectroscopy. ACS Photonics 3, 578–583(2016).

16. P. L. Polavarapu, Kramers-Kronig transformation for optical rotary dispersion studies.J. Phys. Chem. A 109, 7013–7023 (2005).

17. O. A. Barriel, “Mueller matrix polarimetry of anisotropic chiral media,” thesis, Universitatde Barcelona (2010).

18. H. Wang, Z. Li, H. Zhang, P. Wang, S. Wen, Giant local circular dichroism within anasymmetric plasmonic nanoparticle trimer. Sci. Rep. 5, 8207 (2015).

19. J. Hu, X. Zhao, Y. Lin, A. Zhu, X. Zhu, P. Guo, B. Cao, C. Wang, All-dielectric metasurfacecircular dichroism waveplate. Sci. Rep. 7, 41893 (2017).

20. X. Yin, M. Schäferling, B. Metzger, H. Giessen, Interpreting chiral nanophotonic spectra:The plasmonic Born-Kuhn model. Nano Lett. 13, 6238–6243 (2013).

21. F. Eftekhari, T. J. Davis, Strong chiral optical response from planar arrays ofsubwavelength metallic structures supporting surface plasmon resonances. Phys. Rev. B86, 075428 (2012).

22. A. F. Najafabadi, T. Pakizeh, Optical absorbing origin of chiroptical activity in planarplasmonic metasurfaces. Sci. Rep. 7, 10251 (2017).

23. A. B. Khanikaev, N. Arju, Z. Fan, D. Purtseladze, F. Lu, J. Lee, P. Sarriugarte, M. Schnell,R. Hillenbrand, M. A. Belkin, G. Shvets, Experimental demonstration of the microscopicorigin of circular dichroism in two-dimensional metamaterials. Nat. Commun. 7, 12045(2016).

24. Z. Ma, Y. Li, Y. Li, Y. Gong, S. A. Maier, M. Hong, All-dielectric planar chiral metasurfacewith gradient geometric phase. Opt. Express 26, 6067–6078 (2018).

25. A. Y. Zhu, W. T. Chen, A. Zaidi, Y.-W. Huang, M. Khorasaninejad, V. Sanjeev, C.-W. Qiu,F. Capasso, Giant intrinsic chiro-optical activity in planar dielectric nanostructures.Light Sci. Appl. 7, 17158 (2018).

26. X. Lan, X. Lu, C. Shen, Y. Ke, W. Ni, Q. Wang, Au nanorod helical superstructures withdesigned chirality. J. Am. Chem. Soc. 137, 457–462 (2015).

27. S. Zu, Y. Bao, Z. Fang, Planar plasmonic chiral nanostructures. Nanoscale 8, 3900–3905(2016).

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28. A. F. Najafabadi, T. Pakizeh, Analytical chiroptics of 2D and 3D nanoantennas. ACSPhotonics 4, 1447–1452 (2017).

29. Y. P. Svirko, N. I. Zheludev, Polarization of Light in Nonlinear Optics (Wiley-VCH, 1998).30. V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, N. I. Zheludev,

Asymmetric propagation of electromagnetic waves through a planar chiral structure.Phys. Rev. Lett. 97, 167401 (2006).

31. M. Schäferling, Chiral Nanophotonics: Chiral Optical Properties of Plasmonic Systems(Springer, 2017).

32. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, H. Giessen, Three-dimensional photonicmetamaterials at optical frequencies. Nat. Mater. 7, 31–37 (2008).

33. P. Banzer, P. Woźniak, U. Mick, I. De Leon, R. W. Boyd, Chiral optical response of planarand symmetric nanotrimers enabled by heteromaterial selection.Nat. Commun. 7, 13117 (2016).

34. R. A. Chipman, Mueller matrices. Polarimetry, in Handbook of Optics, Volume 1:Geometrical and Physical Optics, Polarized Light, Components and Instruments(McGraw-Hill, ed. 3, 2010).

35. L. V. Poulikakos, P. Thureja, A. Stollmann, E. De Leo, D. J. Norris, Chiral light design anddetection inspired by optical antenna theory. Nano Lett. 18, 4633–4640 (2018).

36. J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, ed. 3, 1999).37. M. A. Kuntman, E. Kuntman, J. Sancho-Parramon, O. Arteaga, Light scattering by

coupled oriented dipoles: Decomposition of the scattering matrix. Phys. Rev. B 98, 045410(2018).

38. X. Chen, Z. Tao, C. Chen, C. Wang, L. Wang, H. Jiang, D. Fan, Y. Ekinci, S. Liu, All-dielectricmetasurface-based roll-angle sensor. Sens. Actuators A 279, 509–517 (2018).


39. L. Novotny, B. Hecht, Principles of Nano-Optics (Cambridge Univ. Press, ed. 2, 2012).40. J. A. Kong, Electromagnetic Wave Theory (EMW Publishing, 2005).

AcknowledgmentsFunding: M.S.D., W.Z., and A.A. acknowledge support under the Cooperative ResearchAgreement between the University of Maryland and the National Institute of Standards andTechnology, Center for Nanoscale Science and Technology, award number 70NANB14H209,through the University of Maryland. Author contributions: The experiments were designedand performed by M.S.D., W.Z., and A.A. Simulations were performed by M.S.D. with furtheranalysis by W.Z., J.K.L., H.J.L., and A.A. Device fabrication and characterization were performedby M.S.D. and W.Z. All authors contributed to the interpretation of results and participatedin manuscript preparation. Competing interests: The authors declare that they have nocompeting interests. Data and materials availability: All data needed to evaluate theconclusions in the paper are present in the paper and/or the Supplementary Materials.Additional data related to this paper may be requested from the authors.

Submitted 24 October 2018Accepted 10 September 2019Published 11 October 201910.1126/sciadv.aav8262

Citation: M. S. Davis, W. Zhu, J. K. Lee, H. J. Lezec, A. Agrawal, Microscopic origin of thechiroptical response of optical media. Sci. Adv. 5, eaav8262 (2019).

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Microscopic origin of the chiroptical response of optical mediaMatthew S. Davis, Wenqi Zhu, Jay K. Lee, Henri J. Lezec and Amit Agrawal

DOI: 10.1126/sciadv.aav8262 (10), eaav8262.5Sci Adv

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