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Metamaterials: Optical Activity Without Chirality
E. Plum, V. A. Fedotov, and N. I. Zheludev
∗
Optoelectronics Research Centre, University of Southampton, SO17 1BJ, UK
(Dated: July 28, 2008)
We report that the classical phenomenon of optical activity, which is traditionally associated
with chirality (helicity) of organic molecules, proteins and inorganic structures, can be observed in
artificial media which exhibit neither volume nor planar chirality (helicity). We have designed a
metamaterial fi lm periodically structured on the subwavelength scale which behaves indistinguish-
ably from chiral three-dimensional media yielding strong circular dichroism and birefringence in
transmission for waves incident at oblique angles.
The phenomenon of optical activity that is the ability
to rotate the polarization state of light is a fundamental
effect of electrodynamics which is traditionally associated
with mirror asymmetry (chirality) of organic molecules.
The effect has enormous importance for analytical chem-
istry, crystallography, molecular bio logy, and the food
industry and is also a signature effect use d to detect life
forms in space missions. The recognition of chirality as
a source negative refraction o f light [1–6] needed for the
creation of a perfect lens [7] inspired intense work in de-
veloping microwave and optical artificial chiral metama-
terials [8–12] and yielded a demonstration of negative
index due to chirality [8, 13]. In this paper we present a
somewhat surprising result that very strong optical ac-
tivity may be se e n in a metamater ial system consisting
of meta-molecules that itself are not chiral. Here chi-
rality is drawn from the mutual o rientation of the wave
propagation direction and the two-dimensional metama-
terial. We demonstrate the optical activity effect using an
artificially created non-chiral planar metamaterial struc-
ture and show that it behaves indistinguishably from chi-
ral three-dimensional molecular sys tems manifesting res-
onant birefringence and dichroism for cir c ularly polarized
electromagnetic waves.
Through the efforts of several generations of re-
searchers optical activity was linked to the three-
dimensional proper ty of molecules known as chirality: a
molecular structure such as a helix for which mirror im-
ages are not co ngruent possesses a sufficient asymmetry
to manifest pola rization rotation (optical activity). The
effect of optical activity is linked to the phenomenon of
circular dichroism, i.e. differential absorbtion for left and
right c ircular polarizations. The recent effort in creat-
ing artificial optically active meta materials that aimed
to achieve strong optical activity was foc used on different
types of arrays of 3D-chiral meta -molecules [8–12, 14–17].
It is significantly less acknowledged that optical activity
can also be seen when oriented non-chiral molecules make
a chiral triad with the wave vector of light. This mecha-
nism of optical activity was first described by Bunn [18]
and detected in liquid crystals [19]. Here we show that
this is a highly significant mechanism of optical activity
in metamaterials that can be seen as essentially planar
structures that possess neither 2D chirality [20, 21] nor
FIG. 1: (Color online) Planar slit metamaterial based on an
array of asymmetrically sp lit rings that manifest optical activ-
ity and circular dichroism at oblique incidence of light. The
direction of asymmetry is represented by a polar vector s (di-
rected from the long to the short arc). O ptical activity is
seen when the metamaterial plane is tilted around x-axis so
the sample normal n is at an angle α 6= 0 with the wave
vector of the incident wave k. Configuration I and II are
the two enantiomeric arrangements showing optical activity
of opposite signs. Configuration III corresponding to normal
incidence shows no optical activity.
3D chirality, and which are much simpler to fabricate
than metamaterials based on arrays of 3D-chiral meta-
molecules.
We argue that to manifest optical a c tivity meta-
2
12 mm
140
o
160
o
1mm
15 x 15 mm
2
λ
λλ
λ
x
y
z
FIG. 2: (Color online) A fragment of the planar slit metama-
terial fabricated in 1 mm thick aluminium film photographed
against a light background. The highlighted square section
shows the elementary building block of the two-dimensional
periodic metamaterial. A bar in the lower part of the image
represents the wavelength λ at which the polarization reso-
nance was observed.
molecules of a plana r metamaterial structure may have
a line of mirror symmetry, but shall lack an inversion
center, i.e. they shall posses a p olar direction s (as illus-
trated in Fig. 1). A regular oriented array of such meta-
molecules will not show optical activity at normal inci-
dence. However, the metamaterial will become o ptica lly
active at oblique incidence provided tha t the plane of in-
cidence does not contain the polar direction. Indeed, in
this case the wave vector k, normal to the meta-molecule
plane n and polar vector s constitute a three- dimensional
chiral triad. The enantiomeric configurations of these
vectors corresponding to optical activity of opposite signs
are created by tilting the plane of the structur e in oppo-
site directions with res pect to the incident wave vector
(compare I and II in Fig. 1).
The origin of the effect in such a planar non-chiral
structure may be readily seen by considering a “unit cell”,
which contains a section of tilted metal plate with a sin-
gle split ring slit (Fig. 1). Using the terminology of crys-
tallography, the direction of light propagation will be a
“screw direction” of the unit cell (that is to say it will
have a sense of twist), if several conditions are met [22].
First, the unit cell itself shall not have an inversion cen-
ter. This is as sured by an asymmetry of the ring split.
Second, there should be no reflection symmetry in the
plane perpendicular to the propaga tion direction, which
is provided by oblique incidence. Third, there should be
no inversion or mirror rotation axis along the propagation
direction. This is provided by o blique incidence and the
asymmetric split. And finally there should be no reflec-
tion sy mmetry for any plane containing the propagation
-150
-100
-50
0
50
100
150
3 5 7 9 11 13 15
Frequency (GHz)
Circ. Phase Delay (dB)_
-20
-10
0
10
20
3 5 7 9 11 13 15
Frequency (GHz)
Circ. Dichroism (dB)
case a
case b
case c
case a
case b
case c
Frequency, f (GHz)
Circ. dichroism,
∆
(dB)
Circ. birefringence,
δ
φ
(deg)
case I
case I
case II
case II
case III
case III
FIG. 3: (Color online) (a) Circular dichroism ∆ and (b) cir-
cular birefringence δφ of the planar metamaterial structure
measured for transmitted waves at incidence conditions I, II
(tilt angle α = ±30
◦
) and III (α = 0
◦
) shown in Fig. 1.
direction. This requirement is only fulfilled if the split is
not perpendicular, and therefore vector s is not par allel,
to the incidence plane yz. Therefore, with reference to
Fig. 1, in ca ses I and II the direction of light propagation
is a screw dire c tion and supports optical activity. On the
contrary, case III, i.e. normal incidence, fails the second,
third and forth conditions of the “screw direction” test.
For instance at norma l incidence there is a plane of re-
flection symmetry containing the propagation dir e c tion.
We observed o ptica l activity in a self-standing thin
metal plate perforated with a regular two-dimensional
array of ring slits (Fig. 2). The ring slits are split a sym-
metrically into pairs of arcs of different length separated
by equal gaps. Each split ring has a line of mir ror symme-
try along the x-axis but has no axis of two-fold rotation,
which enables the introduction of a polar vector s that
points in our case towards the short arc (see Fig. 1). The
planar metamaterial is approximately 220 × 220 mm
2
in
size and it has a square unit cell of 15 × 15 mm
2
, which
ensures that the structure does not diffract electromag-
netic radiation at normal incidence for frequencies lower
than 20 GHz. Our measurements were performed in an
3
anechoic chamber in the 3 − 15 GHz range of frequen-
cies us ing br oadband horn antennas (Schwarzbeck BBHA
9120D) equipped w ith lens concentrators and a vector
network analyzer (Agilent E8 364B). We measured losses
and phase delays for circularly po larized electromagnetic
waves transmitted by the metamaterial (see Fig. 3).
The slit s tructure has a number of intriguing and useful
properties. Being essentially a perforated sheet of metal,
it is not transparent to electromagnetic radiation apart
from a narrow spectral range around the resonant fre-
quency, at which the wavelength is approximately twice
the length of the slits. Transmission at the resonance
is “extraor dinarily” high and substantially exceeds that
given by the fraction of the area taken by the slits. As
Joule los ses in metals at these frequencies are negligible,
the incident energy is split between reflected and trans-
mitted radiation, and at the resonance re flec tion is low.
Around the resonance frequency and up to one octave
above it the structure does not diffract electromagnetic
radiation: it becomes diffractive for wavelengths shorter
than the pitch of the array. As will be illustrated be-
low the structure shows a strong bell-sha ped resonance
of circular birefringence leading to strong polarization
rotation, while circular dichroism is zero in the r e so-
nance. This very useful feature is in striking contrast
with optical ac tivity in most molecular systems, where
characteristically strong resonant polarization rotation is
accompanied by substantial circular dichroism resulting
in elliptical polarization. Moreover at the optical activ-
ity resonance the system shows no linear birefringence
(anisotropy) and eigenstates are therefore two circular
polarizations with equally modera te losses.
If the structure is considered as a “black b ox” the mea-
surements of losses and phase delays for c ircularly polar-
ized electromagnetic waves provide information on the
circular dichroism and optical activity of the medium in
the “black box”. In practical terms we measured the
complex transmission matrix t
ij
for circularly polarized
waves, where subscripts + and − denote right and le ft
circularly polarized waves correspondingly. Our measure-
ments show that the diago nal elements (t
++
and t
−−
)
are generally not equal indicating that the structure has
true optical activity. The difference between magnitudes
of the dia gonal elements ∆ = |t
++
|
2
− |t
−−
|
2
is a mea-
sure of circular dichroism of the “black box”, while the
corresponding phase difference δφ = arg(t
++
)−arg(t
−−
)
is a measure of its circular birefringence (see Fig. 3). The
off-diagonal elements of the matrix are equal within expe-
riential accuracy, which indicates the expected presence
of some linear anisotropy in the structure but also shows
a complete abs e nce of the asymmetric transmis sion ef-
fect recently discovered in planar chiral structures [21].
Importantly the structure’s gyrotropic properties c annot
by explained by linear anisotropy, which does not con-
tribute to ∆ and δ. Particularly, while linear anisotropy
causes a polarization state dependent modulation of az-
=
+
(a)
(b)
(c)
d
m
(d
)
d
m
k
(e
)
(f
)
d
d
m
m
k
k
FIG. 4: (Color online) Electric and magnetic responses in
an asymmetrically split wire ring. Oscillating currents in the
split ring (a) can be represented as a sum of symmetric (b)
and anti-symmetric (c) currents that correspond to the in-
duced electric dipole in the plane of the ring d (green arrow)
and magnetic dipole perpendicular to the plane m (red ar-
row). For tilted asymmetrically split rings polarization rota-
tion is only absent if the projections of d and m onto th e plane
perpen dicular to the k-vector (correspondingly green and red
dashed arrows) are orthogonal (d). If these projections are
either parallel (e) or anti-parallel (f) , the strongest polariza-
tion rotation occurs, where the optical activity for cases (e)
and (f) has opposite signs.
imuth rota tio n, it has no effect on the material’s average
polarization r otary p ower, which is only determined by δ.
In all cases experiments performed in o pposite directions
of wave propagation show identical results.
The following characteristic features of the effect have
been o bs erved in the experiments: i) no circular bire-
fringence or dichroism is seen at normal incidence to the
metamaterial array (α =0); ii) equal tilt in opposite direc-
tions yields circular dichroism and circular birefringence
of opposite sign. The observed effect has a resonant na-
ture. It is strongest around the resonance between 9 GHz
and 10 GHz, where the average arc length corresponds
to approximately half the wave length.
The microscopic origin of optical ac tivity of the slit
metamaterial the can be easily understood by consid-
ering the complementary structure, i.e. not the array of
slits, but an array of metal wires in the form of split rings
(see Fig. 4). As with conventional optical activity exhib-
ited by chiral molecules, the effect must result from the
presence of both electric and magnetic responses. Here,
the structural asymmetry of the split rings plays a key
role: as illustrated in Fig. 4(a) a wave polarized along
the split induces unequal oscillating currents in the up-
per and lower arches of the ring. This may be r epresented
as a sum of symmetric and antisymmetric currents that
correspond to the induced electric dipole in the plane o f
the ring and magnetic dipole perpendicular to the ring
(see Fig s. 4(b) and (c)).
4
FIG. 5: (Color online) (a) Dispersions of phase delay φ for
the transmitted left and right circularly polarized waves. The
shaded area indicates the frequency range with almost circular
eigenstates, where the ph ase velocity v
p
and group velocity v
g
for right circular polarization have opposite signs. (b) Trans-
mitted intensity of both left and right circularly polarized
waves. (c) The efficiency of circular polarization conversion,
which is a direct indication of anisotropy (linear birefringence)
of the metamaterial response. The data in all panels corre-
spond to incidence condition I shown in Fig. 1, where the tilt
angle is α = 30
◦
.
Now we sha ll consider non-normal incidence of the
wave on the structure (see Figs. 4(d)-4(f)). Here blue,
red and green arrows represent the wave vector k and in-
duced magnetic m and electric d dipoles of the metama-
terial’s unit cell, while dashed ar rows show projections of
the corresponding dipole moments onto the plane perpen-
dicular to the wave vector. The str uctur e shows optical
activity if the split is not perpendicular to the plane of in-
cidence. Maximum optical activity is observed when the
split is parallel to the plane of incidence, in this case the
wave vector and induced magnetic and electric dipoles
are coplanar. The mutual phase difference between the
electric and magnetic responses and thus the sign of op-
tical activity depends o n the sign of the tilt (compa re
projections of electric and magnetic dipoles in Fig. 4(e)
and 4(f)). Similarly to how it happens in conventional
chiral media, when the wave vector and induced mag-
netic and electric dipoles of the “meta-molec ule” are c o-
planar, the oscillating dipole components perp e ndicula r
to the k-vector create scattered electromagnetic waves
with orthogonal polarizations in the direction of wave
propagation, and therefore the polar ization of the trans-
mitted wave rotates. On the contrary, if the split is per-
pendicular to the plane of incidence, the induced mag -
netic and electric dipoles as well as their projections are
orthogonal and the structure does not show any opti-
cal activity (see Fig. 4(d)): the oscillating magnetic and
electric dipoles emit electromagnetic waves of the s ame
polarization that pro pagate along the direction of the
incident wave. According to Babinet’s principle the slit
metamaterial structure that is complementary to the wire
structure discussed above, will exhibit similar polariza-
tion resonances in the same frequency band.
Intriguingly, in the slit metamaterial, at the resonance
sp e c tral band from about 9 to 10 GHz , phase veloc-
ity (v
p
∼ ω/φ, where ω = 2πf) and g roup velocity
(v
g
∼ dω/dφ) for r ight circular pola rization have o ppo-
site signs indicating the appearance of a backward wave
(see Fig. 5(a)). In accordance with Pendry [1] this is
a necess ary condition or signature of negative re fr ac-
tion in bulk chiral media. Following Pendry negative
refraction should be s een at the resonance fo r one cir-
cular polarization only swapping to the other one in the
enantiomeric form of the medium. In agreement with
this, our experiments show opposite sig ns of group and
phase velocities for right circular polarization at α = 30
◦
and for left circularly polarized waves for the enan-
tiomeric arrangement, at α = −30
◦
. Importantly, linear
anisotropy essentially disappears (here circular conver-
sion t
+−
= t
−+
=
1
2
· (t
xx
− t
yy
) is negligible, as shown
in Fig. 5(c)). Thus the polarization eige nstates are very
close to circular and in the k-vector direction the material
behaves as isotropic optically active medium. Moreover,
in this spectral range losses represented by |t
++
|
2
and
|t
−−
|
2
are relatively small (see Fig. 5(b)). Our re sults in-
dicate that there may be an opportunity to develop novel
negative index media for circular polarization based on
simple a chiral building blocks, where negative refraction
would arise from exceptionally large optical activity.
In conclusion we have demonstrated strong resonant
optical activity and circular dichroism using a non-chiral
planar metamaterial. We have shown that for artificial
structures chirality arising from the mutual orientation
5
of a non-chiral structure and the incident beam can be
sufficient to lead to an exceptionally str ong gyrotropic
response.
Financial support of the Engineering and Physical Sci-
ences Research Council, UK is acknowledged.
∗
Email: n.i.zheludev@soton.ac.uk; Homepage:www.
nanophotonics.org.uk/niz/
[1] J. B. Pendry, Science 306, 1353 (2004).
[2] S. Tretyakov, A. Sihvola, and L. Jylha, Photonics Nanos-
truct. Fun dam. Appl. 3, 107 (2005).
[3] C. Monzon and D . W. Forester, Phys. Rev. Lett. 95,
123904 (2005).
[4] Y. Jin and S. He, Opt. Express 13, 4974 (2005).
[5] Q. Cheng and T. J. Cui, Phys. Rev. B 73, 113104 (2006).
[6] V. M. Agranovich, Y. N. Gartstein, and A. A. Zakhidov,
Phys. Rev. B 73, 045114 (2006).
[7] J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[8] A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and
N. I. Zheludev, Phys. Rev . Lett. 97, 177401 (2006).
[9] M. D. M. Klein, M. Wegener, and S. Linden, Opt . Lett.
32, 856 (2007).
[10] K. Konishi, T. Sugimoto, B. Bai, Y. Svirko, and
M. Kuwata-Gonokami, Opt. Express 15, 9575 (2007).
[11] E. Plum, V. A. Fedotov, A. S . Schwanecke, N. I. Zhe-
ludev, and Y. Chen, Appl. Phys. Lett. 90, 223113 (2007).
[12] M. Thiel, M. Decker, M. Deubel, M. Wegener, and
S. L. G. von Freymann, Adv. Mat. 19, 207 (2007).
[13] E. Plum, J. Dong, J. Zhou, V. A. Fed otov, T. Koschny,
C. M. Soukoulis, and N. I. Zheludev, arXiv:0806.0823v1
(2008).
[14] I. Tinoco and M. P. Freeman, J. Phys. Chem. 61, 1196
(1957).
[15] D. L. Jaggard and N. Engheta, Electron. Lett. 25, 173
(1989).
[16] F. Mariotte and N. Engheta, Radio Sci. 35, 827 (1995).
[17] M. W. Horn, M. D. Pickett, R. Messier, and
A. Lakhtakia, Nanotech. 15, 303 (2004).
[18] C. W. Bunn, Chemical Crystallography (Oxford Univer-
sity Press, New York , 1945), p. 88.
[19] R. Williams, Phys. Rev. Lett. 21, 342 (1968).
[20] A. Papakostas, A. Potts, D. M. Bagnall, S. I. Prosvirnin,
H. J. Coles, and N. I. Zheludev, Phys. Rev. Lett. 90,
107404 (2003).
[21] V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V.
Rogacheva, Y . Chen, and N. I. Zheludev, Phys. Rev. Lett.
97, 167401 (2006).
[22] I. I. Sirotin and M. P. Shaskolskaya, Crystal physics
(Nauka, Moscow, 1975), in Russian.
