Supplementary Information for “Optical Activity
Enhanced by Strong Inter-molecular Coupling in
Planar Chiral Metamaterials”
Teun-Teun Kim1, Sang Soon Oh2, Hyun-Sung Park1, Rongkuo Zhao2, Seong-Han
Kim3, Wonjune Choi4, Bumki Min1 and Ortwin Hess2
1
Department of Mechanical Engineering, Korea Advanced Institute of Science and
Technology(KAIST), Daejeon 305-701, Republic of Korea
2
The Blackett Laboratory, Department of Physics, Imperial College London, South
Kensington Campus, London SW7 2AZ, United Kingdom
3
Advanced Photonics Research Institute, GIST, Gwangju, 500-712, Republic of Korea
4
Department of Physics, Korea Advanced Institute of Science and Technology
(KAIST), Daejeon 305-701, Republic of Korea
1
I.
Equivalent RLC model for CDZM
A. Numerical simulation of fields at resonances
B. Derivation of resonance frequencies of CDZM
C. Derivation of effective chirality parameters of CDZM
D. Definition of three regimes of coupling
II.
Intra-molecular coupling in CDZM
A. Single layer double Z metasurface
B. Surface current of cut wires, double cross-wires and CDZM
C. Dependence of effective parameters on geometrical parameters
III. Comparison between numerical simulations and equivalent RLC
model
IV. CDZM at THz frequencies
A. Fabrication process
B. Optical characterization
V.
Electric field profiles for CDZM
VI. Gap width dependent circular dichroism η
A. Two possible loss channels in CDZM
B. High loss dielectric substrate – FR4
2
I.
Equivalent RLC model for CDZM
A. Numerical simulation of fields at resonances
To identify the capacitive and inductive elements in CDZM, we performed the finitedifference time-domain simulations and plotted the electric and magnetic fields at
resonant frequencies. The field distributions for RCP (top in Fig. S1a) and LCP
(bottom in Fig. S1a) waves at resonances are very similar to each other except the
different handedness (rotation direction) of electric or magnetic dipoles around the
axis of propagation, that is, clockwise (anti-clockwise) direction for RCP (LCP)
waves. Therefore, we can describe both the RCP and LCP excitations using an RLC
circuit with the same capacitive and inductive elements.
Figure S1. Snap shots of electric fields at resonant frequencies. (a) z
component of electric field in the middle of dielectric substrate. Outlines of the top
metallic structure are drawn with the solid lines. (b) Cross sectional view of electric
field at the plane denoted by the horizontal dashed line in (a). Metallic structures are
indicated by the six horizontal lines and the direction of the incident waves are
indicated by the arrows.
3
As shown in Fig. S1, electric fields are highly enhanced in several specific locations
of the CDZM. This local field enhancement allows us to identify capacitive and
inductive elements of the CDZM. For example, we can assign a capacitive element,
′
denoted by 𝐶𝑚
, at the side strips of metallic layers since electric fields between the
side strips of top and bottom metallic layers are strong at the resonance frequencies
𝑓1 , 𝑓2 . From the cross-sectional view of electric fields in Fig. S1b, we confirm that
′
the enhancement of the electric fields are due to the capacitive element 𝐶𝑚
. Similarly,
we can assign a capacitive element 𝐶𝑚 at the both ends of the central arms as shown
′
in Fig. S1a. Please note that the two capacitors 𝐶𝑚
and 𝐶𝑚 are activated at both
′
resonance frequencies, but the relative magnitude and sign of electric fields of 𝐶𝑚
and 𝐶𝑚 vary for different resonances. For instance, at the frequency 𝑓1 (𝑓2 ), the 𝐸𝑧
′
′
field at 𝐶𝑚
is stronger (weaker) than the one at 𝐶𝑚 and the 𝐸𝑧 fields at 𝐶𝑚
and
𝐶𝑚 have the same (opposite) signs. The different sign becomes a characteristic of the
two resonances in the Lagrangian description of the CDZM as described below in
Section I.B and I.C
In addition, from the 𝐸𝑦 field plot in Fig. S1b, we can identify the gap capacitance
𝐶𝑔 that induces electric fields between side strips over unit cell boundaries. 𝐶𝑔 is
′
normally weaker than 𝐶𝑚
and 𝐶𝑚 but can be extremely larger and dominant when
the gap width is very small. This will be discussed in Section I.D in more detail.
In a similar way, we can also identify inductive elements from calculated magnetic
field plots. Figure S2 clearly shows that there is an inductive element 𝐿𝑚 composed
of the central strips of top and bottom metallic layers.
4
Figure S2. Magnetic fields at resonance frequencies. The inductive elements 𝐿𝑚
at the central strips are dominant at both resonance frequencies.
B. Derivation of resonance frequencies of CDZM
The resonance frequencies 𝑓1 and 𝑓2 of a CDZM can be obtained using an
equivalent RLC model; however, it is challenging to consider all inductive and
capacitive elements and their connections in the CDZM and solve the resulting
coupled equations. Therefore, it is reasonable to simplify the coupled equations by
considering only the dominant elements among various inductors and capacitors of
the CDZM, as is the case for an Ω-particle model [1]. Here, we will use the capacitive
and inductive elements identified in Section I.A to derive analytical expressions for
resonance frequencies of the CDZM.
5
Figure S3. Schematics of an equivalent RLC circuit for CDZM (a) Equivalent RLC
circuit for intra-molecular couplings. C′m is the capacitance of the side strips and Lm
and Cm are the inductance and capacitance of the central strips respectively. The
Solid and dashed lines correspond to the top and bottom metallic layers, respectively.
(b) The inter-molecular couplings between adjacent metamolecules are indicated by
the additional capacitance 𝐶𝑔 . (c) Electric charges induced by an electromagnetic
excitation at the top metallic layer.
By analysing the connections in a CDZM, we can draw an equivalent RLC circuit
′
using the three capacitive elements 𝐶𝑚 , 𝐶𝑚
, 𝐶𝑔 and one inductive element 𝐿𝑚 as
shown in Fig. S3. The equivalent RLC circuit can be regarded as a coupled resonator
system composed of six resonators with two inductive elements and two capacitive
elements. The six resonators can be classified as one of three types of resonators
′
composed of an inductance 𝐿𝑚 and one of 𝐶𝑚 , 𝐶𝑚
, 𝐶𝑔 . To take into account the
6
effect of these couplings, we adopt the Lagrangian formulation for chiral
metamaterials [2]. Then, the total Lagrangian becomes
2
2
Γ = 𝐿𝑚 (𝑄̇1 ± 𝑄̇3 + 𝑄̇1𝑔 ) + 𝐿𝑚 (𝑄̇2 ± 𝑄̇4 + 𝑄̇2𝑔 )
1
1
𝑚
𝑚
1
2
2
− 𝐶 (𝑄12 + 𝑄22 ) − 𝐶 ′ (𝑄32 + 𝑄42 ) − 𝐶 (𝑄1𝑔
+ 𝑄2𝑔
)
𝑔
(S1)
where 𝑄1, 𝑄3 , 𝑄1𝑔 (𝑄2 , 𝑄4 , 𝑄2𝑔 ) are charges accumulated at the capacitance 𝐶𝑚 ,
′
𝐶𝑚
and 𝐶𝑔 , respectively (Fig. S3c). Here, the ± sign corresponds to the lowest two
resonance frequencies of the equivalent RLC circuit.
Subsequently, by putting this into the Euler-Lagrange equation
𝑑
𝜕Γ
𝜕Γ
𝑖
𝑖
( ) − 𝜕𝑄 = 0,
𝑑𝑡 𝜕𝑄̇
𝑖 = 1, 2, 3, 4, 1𝑔, 2𝑔,
(S2)
we have
1
𝐿𝑚 (𝑄̈1 ± 𝑄̈3 + 𝑄̈1𝑔 ) + 𝐶 𝑄1 = 0,
𝑚
1
𝐿𝑚 (𝑄̈1 ± 𝑄̈3 + 𝑄̈1𝑔 ) + 𝐶 ′ 𝑄3 = 0,
(S3a)
(S3b)
𝑚
1
𝐿𝑚 (𝑄̈1 ± 𝑄̈3 + 𝑄̈1𝑔 ) + 𝐶 𝑄1𝑔 = 0.
𝑔
(S3c)
Here, we omit three equations for 𝑄2 , 𝑄4 , 𝑄2𝑔 , since they have identical forms with
(S3) and they are not coupled to these equations.
We assume a solution of the form
𝑄1 = 𝑞1 𝑒 −𝑖𝜔𝑡 , 𝑄3 = 𝑞3 𝑒 −𝑖𝜔𝑡 , 𝑄1𝑔 = 𝑞1𝑔 𝑒 −𝑖𝜔𝑡 , .
Then, this leads to the form
7
(S4)
(−𝜔2 + 𝐿
1
𝑚 𝐶𝑚
) 𝑞1 ∓ 𝜔2 𝑞3 − 𝜔2 𝑞1𝑔 = 0,
−𝜔2 𝑞1 + (∓𝜔2 + 𝐿
1
′
𝑚 𝐶𝑚
) 𝑞3 − 𝜔2 𝑞1𝑔 = 0,
−𝜔2 𝑞1 ∓ 𝜔2 𝑞3 + (−𝜔2 + 𝐿
1
𝑚 𝐶𝑔
) 𝑞1𝑔 = 0.
(S5a)
(S5b)
(S5c)
This can be written in a matrix equation as
−𝜔2 + 𝜔12
( −𝜔2
−𝜔2
where 𝜔12 = 𝐿
1
𝑚 𝐶𝑚
, 𝜔32 = 𝐿
∓ 𝜔2
∓𝜔2 + 𝜔32
∓𝜔2
1
′
𝑚 𝐶𝑚
−𝜔2
𝑞1
0
2
𝑞
−𝜔
3
) ( ) = (0 )
2
𝑞1𝑔
0
−𝜔2 + 𝜔1𝑔
2
, and 𝜔1𝑔
=𝐿
1
𝑚 𝐶𝑔
(S6)
.
The above equation can have solutions only when the determinant of the matrix
becomes 0.
−𝜔2 + 𝜔12
| −𝜔2
−𝜔2
∓ 𝜔2
∓𝜔2 + 𝜔32
∓𝜔2
−𝜔2
−𝜔2 | = 0
2
−𝜔2 + 𝜔1𝑔
(S7)
From this condition, we have two positive resonance frequencies
1
1
𝑓± = 2𝜋 𝜔± = 2𝜋
1
1
1
1
1
√𝜔2 ±𝜔2 +𝜔2
1
3
= 2𝜋
1
′ +𝐶 )
√𝐿𝑚 (𝐶𝑚 ±𝐶𝑚
𝑔
(S8)
1𝑔
where + and – signs corresponds to the first and second resonance frequencies
𝑓1 , 𝑓2 in the main text, respectively.
C. Derivation of effective chirality parameters of CDZM
To derive the effective chirality parameters of the CDZM, we calculate the induced
polarization and magnetization upon electromagnetic wave excitation. For the sake of
convenience, we will use two coordinate systems (𝑥, 𝑦) and (𝑥 ′ , 𝑦 ′ ) as shown in Fig.
S3c. In the primed coordinate system, the incident waves are expressed as
8
𝑬(𝑧, 𝑡) = 𝐸𝑥 ′ (𝑧, 𝑡)𝒙̂′ + 𝐸𝑦 ′ (𝑧, 𝑡)𝒚̂′ = (𝐸𝑥 𝒙̂′ + 𝐸𝑦 ′ 𝒚̂′ )e𝑖(𝑘𝑧−𝜔𝑡)
(S9a)
𝑯(𝑧, 𝑡) = 𝐻𝑥 ′ (𝑧, 𝑡)𝒙̂′ + 𝐻𝑦 ′ (𝑧, 𝑡)𝒚̂′ = (𝐻𝑥 ′ 𝒙̂′ + 𝐻𝑦 ′ 𝒚̂′ )e𝑖(𝑘𝑧−𝜔𝑡)
(S9b)
The field components in the original coordinate systems can be expressed to the ones
in the primed coordinate system as follows:
The equations for the motion of electric charges with this field excitation can be
written as
1
𝐿𝑚 (𝑄̈1 ± 𝑄̈3 − 𝑄̈1𝑔 ) + 𝐶 𝑄1 = −𝛽𝐿𝑚 𝐻̇𝑦 ′ (𝑡)
(S11a)
1
𝐿𝑚 (𝑄̈1 ± 𝑄̈3 − 𝑄̈1𝑔 ) + 𝐶 ′ 𝑄3 = −𝛽𝐿𝑚 𝐻̇𝑦 ′ (𝑡),
(S11b)
1
𝐿𝑚 (𝑄̈1 ± 𝑄̈3 − 𝑄̈1𝑔 ) + 𝐶 𝑄1𝑔 = −𝛽𝐿𝑚 𝐻̇𝑦 ′ (𝑡) .
(S11c)
𝑚
𝑚
𝑔
where 𝛽 = 𝜇0 𝑆/𝐿𝑚 and 𝑆 is the cross-sectional area between top and bottom metal
layers. For simplicity, we do not take into account electric field excitations and the
dissipative damping with the electric resistances of the RLC circuits since we are
interested in derivation of the effective chirality parameter from electric polarization
induced by magnetic field excitation. Please note that the electric field terms and the
damping constants (for example, 𝑅/𝐿𝑚 = 𝛾 with a resistance R) can be added to
these equations for complete derivation of all effective parameters including the
effective electric permittivity and magnetic permeability.
This linear equation can be written in a matrix form
−𝜔2 + 𝜔12
( −𝜔2
−𝜔2
∓ 𝜔2
∓𝜔2 + 𝜔32
∓𝜔2
−𝑖𝜔𝛽𝐻𝑦 ′
−𝜔2
𝑞1
2
−𝜔
) ( 𝑞3 ) = (−𝑖𝜔𝛽𝐻𝑦 ′ ),
2
2
𝑞1𝑔
−𝑖𝜔𝛽𝐻𝑦 ′
−𝜔 + 𝜔1𝑔
Then, the solutions are given as
9
(S12)
1 1
1
1
( ∓
− 2 )
𝜔12 𝜔 2 𝜔32 𝜔1𝑔
𝑞1
2
𝜔2 𝜔12 𝜔32 𝜔1𝑔
( 𝑞3 ) =
∆
𝑞1𝑔
1
2 2
𝜔1 𝜔3
−
(
±
1
𝜔12 𝜔32
1
2
𝜔12 𝜔1𝑔
1 1
1
1
2 (𝜔 2 + 2 − 2 )
𝜔3
𝜔1 𝜔1𝑔
1
2
𝜔12 𝜔1𝑔
±
1
2
𝜔32 𝜔1𝑔
−𝑖𝜔𝛽1 𝐻𝑦′
1
2 2
𝜔3 𝜔1𝑔
1
1
1
1
2 (𝜔 2 − 2 ∓ 2 )
𝜔1𝑔
𝜔1 𝜔3 )
( −𝑖𝜔𝛽3 𝐻𝑦′ )
−𝑖𝜔𝛽1𝑔 𝐻𝑦′
(S13)
where the determinant of the 3×3 matrix in (S12) ∆ is
2
∆= 𝜔2 𝜔12 𝜔32 𝜔1𝑔
[
1
1
1
1
−
(
±
+
2
2
2 )]
𝜔2
𝜔1
𝜔3
𝜔1𝑔
2
= 𝜔2 𝜔12 𝜔32 𝜔1𝑔
(
1
1
−
2) .
𝜔 2 𝜔±
By expanding the matrix multiplication, we have
2
𝜔32 𝜔1𝑔
𝑞1
−𝑖𝜔𝛽𝐻𝑦′
2
( 𝑞3 ) =
(𝜔12 𝜔1𝑔
).
∆
𝑞1𝑔
𝜔12 𝜔32
(S14)
The electric polarization components due to the gap capacitance can be expressed
using the charge 𝑞1𝑔 and the effective length between the gap charges 𝑙𝑔 =
𝑁
𝑁
𝑃𝑦 ′ = 𝑞1𝑔 𝑙𝑔 ( ) = −𝑖𝛽𝑙𝑔 ( )
𝑉
𝑉
𝜔
1
1
2
𝜔 2 𝜔1𝑔
( 2 − 2)
𝜔
𝜔±
𝑁
= −𝑖𝛽𝑙𝑔 ( 𝑉 ) 𝜔2
2
𝜔𝜔±
2
2
1𝑔 ( 𝜔± −𝜔 )
𝐻𝑦 ′ ,
1
√2
𝑙 as
𝐻𝑦 ′
(S15)
where N is the number of the resonators in the system and V is the total volume of the
system.
Finally, we have the expressions for chirality parameter in terms of 𝜔 as follows:
𝜔
𝜅 = − 𝜔2±
𝜔± 𝜔
2
2
1𝑔 𝜔± −𝜔
𝑁
𝛽𝑙𝑔 𝑐0 ( 𝑉 ) = −
10
𝛺𝜅 𝜔± 𝜔
2 −𝜔2
𝜔±
(S17)
where the resonant strengths are given as
𝜔
𝑁
𝛺𝜅 = − 𝜔2± 𝛽𝑙𝑔 𝑐0 ( 𝑉 )
(S18)
1𝑔
If we use the definition of the 𝜔± and 𝜔1𝑔 , we obtain
𝛺𝜅 ∝
𝐿𝑚 𝐶𝑔
′ +𝐶 )
√𝐿𝑚 (𝐶𝑚 ±𝐶𝑚
𝑔
.
(S19a)
′
When 𝐶𝑔 ≫ 𝐶𝑚 , 𝐶𝑚
, we have
𝛺𝜅 ∝ √𝐶𝑔 .
(S19b)
D. Definition of three regimes of coupling
As stated in the main manuscript, the total capacitance of a single Z element is
composed of three capacitive contributions that are scale differently with the gap
width. For the sake of clarity, the formula for the total capacitance is rewritten here as,
𝐶 = 𝐶𝑖𝑛𝑡𝑒𝑟 + 𝐶𝑖𝑛𝑡𝑟𝑎
2𝑡
2𝑤 0.22
≃ 𝜀0 𝜀𝑟 {1.15 ( 𝑔 ) + 2.80 ( 𝑔 )
} 𝑙𝑒 + 𝐶𝑖𝑛𝑡𝑟𝑎 = 𝐶𝑡 + 𝐶𝑤 + 𝐶𝑖𝑛𝑡𝑟𝑎 ,
(S20)
where 𝜀0 is the vacuum permittivity, 𝜀𝑟 is the relative permittivity of the substrate
material, 𝑡 is the thickness of the strip, 𝑙𝑒 is the effective length of the side strip and
𝑤 is the width of the side strip.
Thus, the resonant frequency 𝑓1 = 2𝜋(𝐿𝐶)−1/2 can be written as,
2𝑡
2𝑤 0.22
𝑓1 = 2𝜋 [𝐿 × {α × (1.15 ( 𝑔 ) + 2.80 ( 𝑔 )
where α = 𝜀0 𝜀𝑟 𝑙𝑒 = 0.0449 pF.
11
−1/2
) + 𝐶𝑖𝑛𝑡𝑟𝑎 }]
,
(S21)
Accordingly, depending on which of the three terms is dominating over the
resonance frequency, three regimes of coupling can be defined for the ranges of gap
width: Uncoupled regime ( 𝐶𝑖𝑛𝑡𝑟𝑎 ≥ 𝐶𝑤 ), weak inter-molecular coupled regime
(𝐶𝑖𝑛𝑡𝑟𝑎 ≤ 𝐶𝑤 and 𝐶𝑡 ≤ 𝐶𝑤 ), and strong inter-molecular coupled regime (𝐶𝑡 ≥ 𝐶𝑤 ).
As shown in Figure S4, in the uncoupled regime (grey shaded area), the resonance
frequencies show negligible shift because the internal capacitance does not depend on
the gap width. In the weak intermolecular coupled regime (blue shaded area), the
second term in the curly bracket of Eq. (S26) is dominating and the resonance
frequency is scaling with a rate of 𝑔−0.11. In the strong inter-molecular coupled
regime (red shaded area), the resonance frequency is scaling with a rate of 𝑔−0.5.
Here, the fitting parameter 𝐿 = 2.19 μH and 𝐶𝑖𝑛𝑡𝑟𝑎 = 0.11 pF.
Figure S4. Simulated resonance frequency 𝒇𝟏 (scatters) and parallel plate
capacitor approximation (lines).
12
II. Intra-molecular coupling in CDZM
A. Single layer double Z metasurface
Figure S5 shows the calculated transmission amplitude and chirality 𝜅 and ellipticity
𝜂 for single layer double Z metasurface with different gap width 𝑔. The chirality of a
single layer chiral metasurface is one order of magnitude smaller than CDZM and one
single resonance is observed in the frequency range of interest. Therefore, it is clearly
shown that strong chirality comes from the double-layering that induces parallel
(antiparallel) current flows along the two (top, bottom) central strips of CDZM.
Figure S5. Optical parameters for single layer double Z metasurface (a)
Calculated transmission spectra of RCP (solid line) and LCP (dashed line) waves
with different gap widths g = 0.1 mm (red) and g = 1.0 mm (blue). Effective
parameters for (b) chirality κ and (c) ellipticity η for different gap widths g = 0.1 mm
and g = 1.0 mm.
13
B. Surface current of cut wires, double cross-wires and CDZM
Figure S6 shows the transmission amplitude and the surface current of (a) cut wires,
(b) double cross-wires and (c, d) CDZM with different side metallic strips. Here, gap
width g is fixed at 1.0 mm. This clearly shows how the magnetic resonance and
electric resonance evolve as we change the geometry from cut-wire pairs to CDZM.
As can be seen in Fig. S6, the surface currents for MR and ER are antiparallel and
parallel for cut-wire pairs and double-crosses. However, the surface currents in the
central strips of CDZM cannot be classified clearly as antiparallel and parallel for MR
and ER due to the additional coupling between the top and bottom at the capacitance
′
𝐶𝑚
. This also confirms the fact that CDZM is chiral, literally meaning that it breaks
the mirror symmetry and the oscillating modes along each central arm are not
decoupled to each other under linear polarization excitation.
14
Figure S6.
Surface current
density for
various structures
Calculated
transmission amplitude (left) and surface current density (right) for (a) cut wires, (b)
double cross-wires and (c,d) CDZM with different side metallic strips.
C. Dependence of effective parameters on geometrical parameters
In order to verify an intra-molecular coupling in the CDZM, chirality κ and ellipticity
𝜂 are numerically estimated for samples having different geometrical parameters l and
d. First, the dependency of 𝜅 and 𝜂 on the size l is plotted in Figure S7a. For this
simulation, gap width 𝑔 is fixed at 0.1 mm. In this plot, it is shown that the
resonances are significantly red-shifted as unit cell size increases. It is noteworthy that
while 𝜅𝑓1
increases gradually, 𝜅𝜂=0 does not change significantly as unit cell size
15
increases. Another important parameter is the thickness of the substrate d (i.e. the
inter-planar spacing). In Figure S7b, the dependency of effective parameters κ and 𝜂
with a variation in the thickness of substrate d is plotted. It is shown that κ increases
gradually as d becomes smaller. As briefly discussed in the main manuscript, this
dependence clearly show that the intra-molecular coupling depend on the geometric
parameters of one unit cell. Moreover, 𝜂 decreases as d becomes smaller. This seems
supportive that the ellipticity becomes smaller when the inter-planar coupling
becomes strong. However, in fact the decrease of 𝜂 comes from the reduced
thickness of lossy dielectric resulting in lower loss for both LCP and RCP waves.
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Figure S7. Geometrical parameter dependent optical parameters Effective
parameters chirality 𝜅 and ellipticity 𝜂 as a function of (a) size of CDZM 𝑙 and (b)
thickness of substrate 𝑑 . Here, the gap width 𝑔 is set to 0.1 mm.
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III. Comparison between numerical simulations and equivalent RLC
model
To test the validity of the equivalent RLC model, we compared numerical simulations
with the data fitted by analytical expressions (Eqs. (S17), (S21) and (S19)). In Figure
S8, frequency-dependent chirality parameters, resonant frequencies, and resonant
strengths are plotted as a function of the gap width 𝑔. The fitted data are in excellent
agreement with the simulated ones, which indicates that the physics can be described
well by the equivalent RLC model for all three coupling regimes. Moreover, the red
shift of resonance frequencies and the 𝑔−1/2 dependence of the resonance strength
coefficient can be clearly seen in Figure S8a,b.
Figure S8. Comparison of simulation results with the equivalent RLC model.
Simulated (circles) and fitting (lines) results of (a) chirality parameter 𝜅, (b) resonant
frequencies 𝑓1 and 𝑓2. (c) Fitting result of resonance strength coefficients 𝛺𝜅1 and
𝛺𝜅2 with the gap width g ranging from 10 to 100 μm using adjusted analytical Eqs.
S19a and S19b.
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IV. CDZM at THz frequencies
A. Fabrication process
Fabrication of a terahertz CDZM started with a bare silicon substrate as a sacrificial
wafer, and a polyimide solution (PI-2610, HD MicroSystems) was used for the spacer
material. The polyimide solution was then spin-coated on the bare silicon wafer and
pre-baked at 180°C in a convection oven for 30 min. After the curing, a negative
photoresist (AZnLOF2035, AZ Electronic Materials) was spin-coated and patterned
with conventional photolithography. Metallic patterns were defined by the
evaporation and lift-off process. After spin-coating the spacer layer (2 μm, PI-2610),
the same process was repeated for the second layer, and the CDZM were finally
peeled from the silicon substrate (Fig. S9a).
B. Optical characterization
The THz CDZM were characterized by terahertz time domain spectroscopy (THzTDS). Two free-standing extraordinary optical transmission (EOT) polarizers [3], one
in front of and the other after the sample, were used to measure the transmission 𝑇||
with φ = 0° and
𝑇⊥ with φ = 90° (see inset of Fig. S9b). The simulated and
measured transmission amplitudes for 𝑇|| and 𝑇⊥ are shown in Figure S9b and are
in good agreement with each other. Figure S9c shows the ellipticity η for the gap
width 𝑔 = 1.5 μm. The shaded region represents the regime of pure optical activity,
i.e. η ~ 0. In Figure S9d, the chirality κ at η = 0 are plotted as a function of gap width
𝑔. It is clearly shown that the gap width plays a crucial role not only at microwave
frequencies but also in the THz regime.
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Figure S9. CDZM at THz frequencies (a) Optical micrograph of fabricated CDZM
with a unit cell of l = 40 um, d = 2 um, w = 5 um, and different gap width g. (b)
Comparison between simulation and measurement of transmission amplitude for 𝑇+
and 𝑇− in the case of g = 1.5 μm. Two EOT polarizers [3] are employed to measure
the parallel and perpendicular polarization states (inset), respectively. (c) The
ellipticity η in the case of g = 1.5 μm. The shaded region indicates the pure optical
activity region, η = 0. (d) The chirality κ at the η = 0 as a function of g.
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V. Electric field profiles for CDZM
Figure S10 shows the calculated electric field distributions in the unit cells of CDZM
at the frequencies of (a) 𝑓1 , (b) 𝑓η=0 and (c) 𝑓2 with gap width 𝑔 = 1.0 mm and 𝑔
= 0.1. As described in the main manuscript, the electric field is more strongly
concentrated not only at the resonance frequencies but also non-resonance frequencies
as gap width decreased.
Figure S10. Field localization and enhancement in the small gap. Simulated
electric field for CDZM at (a) 𝑓1, (b) 𝑓η=0 and (c) 𝑓2 with gap width (left) 𝑔 = 1.0
mm and (right) 𝑔 = 0.1 mm.
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VI. Gap width dependent circular dichroism η
A. Two possible loss channels in CDZM
Fig. S11 shows comparison of simulated ellipticity spectra between lossy (black line)
and lossless (red line) Teflon substrates, and PEC (black line) and lossy metallic
(copper, blue line) elements with g = 0.1 mm. It is shown that dielectric losses in the
substrate are the main sources of ellipticity in the CDZM.
Figure S11. Two possible loss channels of CDZM. Loss of dielectric substrate is
the main reason for the large ellipticity in the CDZM due to negligible loss in the
metallic element at microwave frequencies.
B. High loss dielectric substrate – FR4
Figure S12 shows the optical parameters for the CDZM patterned on a FR-4 substrate
with a thickness d = 0.4 mm. The dielectric constant of the FR-4 substrate is Re(εr) =
4.0 with a dielectric loss tangent of tan 𝛿 = 0.028. The chiral metamaterial with
different gap width ranging from 0.12 to 5 mm has geometric parameters l = 5.0 mm,
w = 0.8 mm and r = 0.65 mm. In Figure S12a, it is clearly shown that the chirality
parameter 𝜅 at η = 0 also represent gap-dependent behaviour. In Figure S12b, the
ellipticity η is plotted with the gap width 𝑔 ranging from 0.1 mm to 5 mm. As
expected, due to the high loss of the FR-4 material, the ellipticity η of the transmitted
wave is significantly larger than the chiral metasurfaces with Teflon substrate. As the
gap becomes smaller, the ellipticity η decreases at the resonance frequency f1 as well
(Fig. S12c).
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Figure S12. Optical parameters for the CDZM with high-loss substrate FR4. (a)
The simulated (black circled line) and measured (red circle) chirality κ at the
frequencies η = 0 as a function of the gap width g. (b) Simulated ellipticity η as a
function of the gap width g. The black dashed line represents the frequency where
the η = 0. (c) The simulated (black circled line) and measured (red circle) η at the
resonance frequency f1 with the different gap width g.
References
1. R. Zhao, et al., Optics Express 18, 14553, 2010
2. H. Liu, et al., Nature Photonics 3, 157, 2009
3. S. Lee, et al., Nature Materials 11, 936, 2012
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