How to simulate Metamaterials using lumerical and Some literature Review

HOW TO SIMULATE METAMATERIALS
USING LUMERICAL AND SOME
LITERATURE REVIEW
Presented By: Hossein Babashah

Fields and Waves Basics
■ In rectangular waveguides -->TEmn or TMmn,
– => m is the number of half-wave patterns across the width of the waveguide and n is the number of half-wave
patterns across the height of the waveguide.
– In circular waveguides, circular modes exist and here m is the number of full-wave patterns along the
circumference and n is the number of half-wave patterns along the diameter.[2][3]
■ Modes :
– Transverse electromagnetic (TEM) modes: neither electric nor magnetic field in the direction of propagation.
– Transverse electric (TE) modes: no electric field in the direction of propagation. These are sometimes called H
modes because there is only a magnetic field along the direction of propagation (H is the conventional symbol
for magnetic field).
– Transverse magnetic (TM) modes: no magnetic field in the direction of propagation. These are sometimes
called E modes because there is only an electric field along the direction of propagation.
– Hybrid modes: non-zero electric and magnetic fields in the direction of propagation.

Motivation (Metamaterials)
■ Natural materials exhibit  a small part of EM properties (theory).
■ Researchers  new materials  specific desired properties.
■ EM metamaterials = artificially engineered materials => designed to
– Interact EM waves.
– Control EM waves.
■ "Meta" in Greek means "beyond", or "higher", "alerted", or "changed“ => metamaterials not found in
nature. However, composed of natural materials.
■ Design  engineer the composite "atoms" of the metamaterials from natural materials with different
shapes or structures.
– sub-wavelength, periodic structures.
■ Goal of many metamaterial simulations = design & measure  effective material properties of these
devices.
■ Operation frequency 
– RF
– Microwave (Wire Pairs – Zhou)
– terahertz (THz device – Chen)
– Optics (Chiral materials – Kwon)

Motivation (Photonic metamaterials)
■ Photonic metamaterials
– periodic nanostructures
– metallic elements on a dielectric or semiconducting substrate
– period is shorter than the wavelength of light.
■ Effects of interest
– dielectric response => can be engineered through semiconductor
manufacturing
– structures with an effective negative index of refraction=>negative refraction.
■ =>superlenses (spatial resolution beyond)
– assess split-ring resonators and optical antennas  efficiently capture and
emit optical radiation.

Simulating metamaterials
■ FDTD Solutions  study
– sub-wavelength periodic
– highly-diffractive optical metamaterial
■ Measure Quantities:
■ •Field enhancement at different parts of the structures
■ •Transmission and reflection spectrum
■ •Scattering and absorption cross sections
■ •Chirality and circular dichroism
■ •S parameters (post-processing)
■ •Effective material properties such as the refractive index, impedance permittivity
and permeability. (post-processing)
■ Active metamaterials.(combination of optical solvers )
– For example, DEVICE can be used to simulate the effect of bias-induced carrier
density variations on the refractive index of the metamaterial, and FDTD
Solutions can be used to calculate the corresponding optical response.

Features
■ • Simulate metamaterials at RF, microwave, terahertz (THz) and optical frequencies and provide
simulation results across wide bandwidths in a single calculation for 2D and 3D metamaterials
■ •FDTD Solutions can easily calculate the power reflection, power transmission, field enhancements,
resonant frequencies and associated quality factors, and s-parameters for metamaterials
■ •Flexible post-processing allows for the extraction of bulk/effective material properties like effective
refractive index including the negative index response of metamaterials, effective permittivity and
permeability, circular dichroism, scattering and absorption cross sections
■ •Lumerical’s conformal mesh technology can provide sub-mesh cell accuracy of common materials
used in metamaterials, including perfect electrical conductors (PECs), metals, and other dispersive
materials
■ •Multi-coefficient materials (MCMs) can accurately model dispersive materials across wide wavelength
ranges
■ •Simulate metamaterial microbolometers with FDTD Solutions and the heat transport solver in DEVICE.
■ •Simulate active metamaterials with FDTD Solutions and the charge transport solver in DEVICE.
■ •Built-in parameter sweep and optimization algorithms make it easy to analyze and optimize
parameterized designs

What It contains
Solver Description
FDTD Bulk metamaterials
FDTD Effective parameters - Smith
FDTD Chiral materials - Kwon
FDTD THz - metamaterial
FDTD GHz - wire Pairs
FDTD, DEVICE Active Terahertz Resonator
FDTD All-dielectric zero-index metamaterial
FDTD, DEVICE Metamaterial Absorbers

Bulk metamaterials■ how to set up bulk electric and magnetic properties =>negative index medium over a
range of wavelengths.
■ Material setup
■ FDTD Solutions includes a magnetic and electric Lorentz medium, described
at Permittivity models=>this material model to create=> bulk negative index medium =
both real(ε) and real(μ) are negative at the same wavelength.
■ media relative permittivity and permeability:
■ subscript e and m =>electric and magnetic properties =>example
=>choose these properties:
– εbase = 1 (base material= vacuum=>none)

Plot Lorentz model for permeability &
permittivity
■ visualize eps and mu in "Magnetic Electric Lorentz" material.
– These properties cannot be seen in the Materials Explorer.
– The user simply needs to set the name of the materials and choose a
wavelength range.
■ choose the material
■ base material
■ wavelength range
clear;
matname = "negative index";
basematerial = ""; # set to "" if no base material is used
lambda = linspace(500e-9,1500e-9,1000);
f = c/lambda;
axis = 1; # relevant for anisotropic media only, can be 1,2,3
# the remainer of the script should not need to be modified

Simulation setup
■ a beam at 45 degrees incidence on a 2 micron slab of negative index medium in a background of
air.
■ In addition, we have added a mesh override region over the slab, and set the equivalent index for
the mesh to 2. The reason is that the magnetic electric Lorentz medium is included with FDTD
Solutions but is implemented as a plugin. At mesh time the software will base the target mesh
size for this material on the background material (which defaults to the vacuum if none is
selected). Therefore we may want to use a mesh override region to force a smaller mesh size if we
know that the material will need it. In this case, for safety, we override the mesh with an
equivalent index of 2, which is more than sufficient for the electric and magnetic properties over
the wavelength range of 700 to 800nm.
■ Additionally, since the beam is incident at 45 degrees, which is relatively steep, we increased the
minimum number of layers of PML from 12 to 24 in the Advanced Options of the FDTD simulation
region.
■ Note, the PML default settings are modified to overcome possible diverging simulation, which
need some knowledge on PML.

Results
■ visualize E 'profile’
■ Parameter lambda profiles at different wavelength.
– The profile at approximately 761nm has the lowest reflection and highest transmission, as we would expect from the curve
permittivity data. We can see this result, which clearly shows the unusual refractive properties of a bulk negative index medium.

Step by Step (PML all boundaries)

lambda increases from left to right
Mag E
Ex

In Si doesn’t change with increasing
lambda

EFFECTIVE
PARAMETERS – SMITH
HFSS IS USED IN PAPER

Introduction
■ Goal: magnitude and phase of scattering (S) parameters for a negative index
metamaterial.
■ The metamaterial composed of:
– split ring resonator (SRR)
– wire
– negative refractive index at microwave frequencies.
– D.R. Smith et al.

Simulation setup
■ A cubic unit cell of length 2.5mm=>
– Periodic boundary conditions=> to extend => y and z directions, =>
■ Z is vacume its ok and y is periodicity
– plane wave source operating at 5-20GHz is injected in the x direction.
■
■ The substrate
– 0.25 mm thick
– FR4
■ permittivity of 4.4, loss tangent of 0.02.
■ Also, note that the material fit for FR4 deviates from a straight line as given by the permittivity and loss tangent. This is due to the fact that materials cannot be fit by a
straight line over the whole frequency range. However, this does not noticeably affect the frequency dependence of the S parameters. In addition, a straight line model
for the material properties is not completely accurate since in practice FR4 material properties are frequency dependent.
■ A copper split ring resonator (SRR) and wire are positioned on opposite sides of the substrate.
– width wire is 0.14 mm.
– outer ring length SRR is 2.2 mm and both rings have a linewidth of 0.2 mm.
– The gap in each ring is 0.3 mm, and the gap between the inner and outer rings is 0.15 mm.
– The thickness of the copper is given as 0.017mm in Smith, but since this is much smaller than the wavelength, we use a 2D sheet to represent it.
■ Since in the GHz range most metals act like perfect electrical conductors (PEC), the PEC material model is used for the copper elements.
■ The conformal variant 1 mesh refinement option is used in this example to take full advantage of the conformal meshing technology to accurately represent the ring
widths.
■ In addition, the auto shut off min in the advanced tab of the FDTD region is reduced to 1e-7. This ensures that the fields decay sufficiently at the resonance frequencies
before the simulation automatically shuts off.
■ Relatively coarse mesh settings are used for demonstration purpose due to the properties of PEC. Results with finer mesh are presented in a later section on this page.

Results
■ check if the transmitted wave can be regarded as plane wave, as required by the
parameter extraction analysis. The intensities of Ey field component from the T
Monitor are shown below at two wavelengths

Effective parameters (S,T,neff)
■ Using the parameter extraction techniques described in the Parameter
extraction page, we will calculate the effective refractive index, and related
properties, for this structure.
■ It can be seen that the Intensity variation in the near field is only on the order to
1e-3, which can be considered as uniform, thus justifies the use of near field point
monitor. The uniformity of the intensity can be further increased if the finer
override mesh is extended.
■ run the script in the S parameters analysis=>figures 3a-3f from Smith et al.

S-parameter calculation technique
■ Just copy s-params
■ Change the values correspondingly
– Note polarization for PEC PMC

Advanced note: Calculating the phase of
the S parameters
■ The S parameter are defined assuming that the incident phase is 0 at the left edge of the
substrate, and the reflected and transmitted phases are measured at the left and right sides of
the substrate respectively.
– source is placed at approximately -4.2mm,
– monitor measuring reflection is at -5mm
– monitor measuring transmission is measured at +5mm.
– =>This results in a phase offset of the measured field compared to the desired result for the
S parameters, however this can be easily corrected as long as the positions of the source,
the substrate and the monitors are known.
■ =>The script makes this phase correction but the user must enter some of the parameters to
define the source position, background index and the position of the substrate.
■ To test both the amplitude and phase, the simulation file s_parameters_test.fsp can be used. in
this file, we simply have a planer substrate with no metallic components so the S parameters can
be easily calculated theoretically. After running this fsp file, the script
file s_parameter_test.lsf can be used to compare the S parameters with the theoretical results. It
will display the following figures.

EFFECTIVE PARAMETERS -
SMITH
(SIMULATION USING THE
EXTRACTED MATERIAL
PARAMETERS)

About the magnetic electric Lorentz model
and the permeability analytical parameters
■ Since the imaginary part of the extracted permittivity is negative, we chose a little
wider absorption of the permeability for the MEL model named "mel".
■ Once the extracted permittivity is imported as the base material (named "bulk") of the
MEL model, the default setting of the material fitting can lead to a good fitting.
However, due to its large imaginary part, the simulation can diverge at late time. To
avoid this, we simply chose the simplest two-coefficient fitting, which neglects the
imaginary part and the anti-resonance of the real part. Even with such simplification,
the result is reasonably good with the original transmission and reflection. Since the
main purpose of this section is to validate the extracted data, we do not pursue highly
agreed results. With careful adjustment, you may get a better agreement with your
own metamaterial design.
■
■ For the magnetic electric Lorentz model, please refer the Material Database section in
the Reference Guide to get more information.

Simulation using the extracted material
parameters
■ Before setting up the simulation file, we need some analytical parameters from
the extracted data in order to use the magnetic electric Lorentz (MEL) model since
it has dispersive and lossy permeability. By some analysis, we can use the
permeability in MEL model, which is relatively easy to have analytical expression,
whereas for the extracted permittivity, we can import it into the material database,
which is used as the base material for the MEL model. Some estimated
parameters for the analytical permeability are listed below:
■ delta_mu = 0.6 (H/m)
■ wm = 6.1e10 (rad Hz)
■ delta_m = 1.43e9 (rad Hz)
■ bulk => 2D Sim.
■ only R and T =>s_using_extracted_parameters.fsp

Introduction
An object or a system is chiral if it is
distinguishable from its mirror image;
■ On this page, we calculate the circular dichroism (CD) of a gammadion shaped
structure, then optimize the structure dimensions to maximize the CD at 1.1um.
■ Circular dichroism (CD) is dichroism involving circularly polarized light, i.e., the differential absorption of left- and right-handed light.[1][2] Left-hand circular
(LHC) and right-hand circular (RHC) polarized light represent two possible spin angular momentum states for a photon, and so circular dichroism is also
referred to as dichroism for spin angular momentum.[3]
■ gammadion shaped periodic structure.
– aluminum layer is sandwiched by silver layers and the excitation of surface
plasmon leads to the enhancement of the circular dichrosim.

Calculation of the circular dichroism for
four-fold symmetrical structure
■ The circular dichroism CD is defined by
where TR and TL is a transmittance when the right- and the left- circularly polarized plane wave is
incident on the device, respectively.
■ To get the transmittance for circularly polarized incidence, we have two alternatives as follows.
■ 1. Use two plane wave sources to generate circularly polarized illumination, as described in
the circular polarization page. In this case, two FDTD simulations will be required to get the CD;
One for right-circular polarization and the other for left-circular polarization. This approach is not
used in the associated example simulation file.
■ 2. Use one plane wave source (as in the example simulation file gammadion_dichrosim.fsp). By
taking advantage of the four-fold rotational symmetry of the structure, the transmittance can be
obtained from a single simulation, as explained below:

■ The field distributions F (E or H) for circular illumination can be obtained from a
single linearly polarized simulation by
■ where FR (FL) is the field distribution for right- (left-) circularly polarized incident
wave, and Fx (Fy) is the field distribution for a x (y) linearly polarized plane wave. If
we assume four-fold rotational symmetry of the structure, the field distribution for
y-polarized plane wave is incident on the structure, Fy, is given by that for x-
polarized incident plane wave, Fx, as
■ where FU_V (u=x, y, z; v=x, y) is the u-component of the field distribution for v-
polarized incident wave.
■ Once we get the field distribution FU (U=R or L) for circularly polarized plane wave
using the relation Eqs.(2) and (3) from one FDTD simulation (simulation for x- or y-
polarized incident wave), the power traveling down in the substrate over a unit cell
is given by

■ If we normalize the power P by incident power using script function "sourcepower",
we obtain transmittance T as
■ The simulation file gammadion_dichrosim.fsp uses a single x-polarized source. The
field distribution on a plane under the gammadion structure (in the substrate) is
recorded in a power monitor named "T", within the analysis group named
"CD". The script in the "Analysis" tab => "Script" tab of this analysis group
calculates the transmittance of circular polarizations following the way mentioned
above (method 2). From the CD analysis object, you can plot the CD vs wavelength
by use of the "visualizer". In the figure below, we can see a peak in the CD around
1.1um.

Parameter sweeps
■ => finding the optimum value
■ find the optimum thickness of an anti-reflection (AR) layer on silicon.
– The optimum thickness is the thickness that gives the minimum reflection at
the wavelength of operation, in this example it is 500 nm.
■ For additional information, see the Optimization and sweeps video.

NESTED
PARAMETER SWEEP
https://kb.lumerical.com/en/sweeps_nested_sweeps.html
Surface Plasmon Resonance 2D

Abstract (Paper)
■ Metamaterials => phenomena that cannot be obtained with natural materials.
■ important => terahertz (1 THz) frequency regime;
– many materials inherently do not respond to THz radiation,
– tools that are necessary to construct devices operating within this range—sources,
lenses, switches, modulators and detectors—largely do not exist.
■ progress has been made in THz generation and detection
– THz quantum cascade lasers.
■ active metamaterial device
– efficient real-time control and manipulation of THz radiation.
– consists of an array of gold electric resonator elements fabricated on a
semiconductor substrate.
– The metamaterial array and substrate together effectively form a Schottky diode,
which enables modulation of THz transmission by 50 percent.

Paper
■ Figure 1 | Experimental design of the active THz metamaterial device. a, Geometry and
dimensions of the THz metamaterial switch/modulator: A 5 36 mm, G 5 2 mm, D 5 10
mm and W 5 4 mm. b, An equivalent circuit of the metamaterial element, where the
dashed variable resistor corresponds to loss due to the substrate free carrier absorption
within the split gap. c, The metamaterial elements are patterned with a period of 50
mm to form a planar array of 5 3 5 mm 2 . These elements are connected together
with metal wires to serve as a metallic (Schottky) gate. A voltage bias applied between
the Schottky and ohmic contacts controls the substrate charge carrier density near the
split gaps, tuning the strength of the resonance. Orientation of the incident THz wave is
indicated and the polarization of the electric field, E, magnetic field, H, and wave vector,
k, are shown. d, Diagram of the substrate and the depletion region near the split gap,
where the grey scale indicates the free charge carrier density. e, Experimental
configuration for THz transmission measurements through a fabricated device. The
black curves show the measured time-domain waveforms of the incident and
transmitted THz pulses when a reverse gate voltage bias of 16 V is applied to the device
and the THz electric field is polarized perpendicular to the connecting wires.

Paper
■ A great deal of research into metamaterials has used microwave radiation; this is in part due to the
ease of fabrication of sub-wavelength structures at these frequencies. Indeed, negative refractive index
media 11,12 composed of negative permittivity 13 (e 1 , 0) and negative permeability 14 (m 1 , 0)
metamaterial elements was first demonstrated at microwave frequencies. This has led to intense
theoretical, computational and experimental studies of exotic phenomena, such as perfect lensing 15
and cloaking 16,17 . Recently, researchers have ventured to create functional metamaterials at near-
infrared and visible frequencies 18–20 . Considerably less work has concentrated on THz frequencies
21,22 . However, the design flexibility associated with metamaterials provides a promising approach,
from a device perspective, towards filling the THz gap. Metamaterials are geometrically scalable, which
translates to oper- ability over many decades of frequency. This engineering tunability is in fact a
distinguishing and advantageous property of these materials. However, for many applications it is
desirable to have real-time tunability. For instance, short-range wireless THz communication or ultrafast
THz interconnects 23,24 require switches and modulators. Current state-of-the-art THz modulators
based on semiconducting structures have the desirable property of being broadband, which is of
relevance to THz interconnects, but are only able to modulate a few per cent 10 and usually require
cryogenic temperatures 25 . Therefore, further improvement of the performance characteristics are
required for practical applications. Here we present an efficient active metamaterial switch/modulator
operating at THz frequencies. Although the modulation is based on a narrowband metamaterial
resonance,

Paper
■ these devices can be engineered to operate at specific frequencies. This would enable, as an example, amplitude modulation of narrowband devices, such as THz
quantum cascade lasers, enabling near- term practical applications. The metamaterial device used in this work is based on a recently presented electric analogue to
split-ring resonators (SRRs) 26 . The geometry and dimensions are shown in Fig. 1a. The element consists of two single SRRs put together on the split gap side. These
two rings provide inductances, L, and the split gap provides a capacitance, C, which are depicted as an equivalent circuit in Fig. 1b. A frequency- dependent dielectric
resonant response results when it is patterned on a suitable substrate to form a planar periodic array of subwavelength structures. The two inductive loops are
oppositely wound and thus any magnetic response is cancelled, resulting in a net electric response. The resistor R models the dissipation in the gold split rings, and
the variable resistor R d (shown dashed) models dissipation due to the substrate free carrier absorption within the split gap 27 . In our device, the metamaterial
elements are electrically connected using conducting wires such that the entire metamaterial array functions as a voltage gate, schematically depicted in Fig. 1c. This
structure has been designed to enable voltage control of the conductivity of the substrate at the split gaps, thereby controlling the THz transmission. The substrate
consists of a 1-mm-thick n-type gallium arsenide (GaAs) layer with a free electron density of n 5 1.9 3 10 16 cm 23 grown on a semi-insulating gallium arsenide (SI-
GaAs) wafer by molecular beam epitaxy (MBE), as detailed in Fig. 1d. The ohmic contact is fabricated by electron-beam deposition of 20 nm of nickel, 20 nm of
germanium, and 150 nm of gold in sequence, followed by rapid thermal annealing at 350 uC for 1 min in a nitrogen atmosphere. Next, the planar electric resonator
array is fabricated using conventional photolithography and electron-beam deposition of a 10-nm-thick adhesion layer of titanium on the GaAs substrate, followed by
200 nm of gold. The metal and n-GaAs form a Schottky junction and the connected metamaterial resonators serve as a metallic gate. Current–voltage (I–V)
measurements confirm the Schottky character of the device (Supplementary Fig. 1). Terahertz time-domain spectroscopy (THz-TDS) 28 was used to characterize the
performance of the metamaterial device, and has been described elsewhere in detail 29 . In our photoconductive THz- TDS experiment, a polyethylene lens focuses
the linearly polarized THz beam onto the metamaterial sample to a diameter of about 3 mm, and a second polyethylene lens recollimates the transmitted THz beam,
which is directed to a photoconductive receiver. The experiments were performed at room temperature in a dry air atmosphere. In THz-TDS, the time-varying electric
field of the impulsive THz radiation is recorded, and the electric field spectral amplitude and phase are directly obtained by performing Fourier analysis.
Measurements of the metamaterial device with respect to a suitable reference, as illustrated in Fig. 1e, allow determination of the complex transmission as a function
of frequency, ~tt(v). Inversion of ~tt(v) further permits model-independent calculation of the frequency- dependent complex permittivity 28 , ~ee(v)~e1 (v)zie2 (v),
where e 1 and e 2 are the real and imaginary portions, respectively. All experiments were performed at normal incidence, with the THz magnetic field lying completely
in-plane. The polarization of the THz electric field was either perpendicular or parallel to the split gaps (and connecting wires). The wires connecting the individual
electric resonators are necessary (as described above) to provide electrical connectivity to the gate. Importantly, these connecting wires have little effect on the
electromagnetic properties of the electric resonators when the THz electric field is normal to the connecting wires. This was confirmed by finite element simulations
using com- mercial software, as shown in Fig. 2a and b. The electric field is strongly concentrated at the split gaps, and there is no significant surface current flowing
along the connecting metal wires between electric resonators at the resonant frequency (,0.72 THz).

Paper
■ Without an applied gate bias, the device is not expected to display resonant behaviour associated with the electric resonators because the substrate
free charge carriers short out the capacitive response associated with the gaps. Upon application of a voltage, a resonant transmission should result as
carriers in the substrate are displaced from the gaps. The blue curve in Fig. 2c shows the frequency-dependent transmitted intensity at a reverse gate
bias of 16 V, where the polarization of the incident THz electric field is perpendicular to the connecting wires. Two distinct resonances are observed.
The 0.72 THz resonance is the LC response associated with circulating currents in each metamaterial element, while the resonance at 1.65 THz is due
to in-phase dipolar currents along the 36 mm lengths of the elements 22 . The spectrum is consistent with that from the same structure fabricated on
an SI-GaAs substrate with no free carriers (red curve) and with simulation (black dashed curve), as shown in Fig. 2c. In Fig. 2d the real permittivity e 1
(v) of the THz metamaterial devices is shown as extracted from the experimental data of Fig. 2c assuming a cubic unit cell 26 . The resonances are
strongly dependent on gate bias, as shown in Fig. 3. With zero applied voltage to the gate (black curves), the metamaterial response is very weak and
does not show significant frequency dependence near the 0.72 THz resonance, as the relatively conductive substrate shorts the capacitive split gap
and no LC resonance can be established. An increasing reverse gate bias depletes an increasing fraction of electrons in the n-GaAs layer near the
metallic gate, thus significantly reducing the conductivity of the substrate near the split gaps, thereby restoring the LC resonant response. This is
verified by the experimental results shown in Fig. 3a, as the resonances in the transmission spectra narrow and increase in amplitude with increasing
reverse bias. At a reverse gate bias of 16 V, a 50% relative intensity change of transmission is observed at 0.72 THz, making this device a reasonably
efficient narrowband THz switch/ modulator. We note that the transmitted intensity of the 1.65 THz resonance also decreases with bias. This is
because the substrate carriers screen the dipolar currents and is not associated with shorting of the capacitive gap of the metamaterial elements.
Figure 3b shows the corresponding permittivity e 1 (v) of the metamaterial device at various gate biases. Clearly, e 1 (v) of the device is significantly
modified by the applied gate bias. e 1 (v) increases on the low frequency side of the resonance while at higher frequencies it decreases to less than
unity and even becomes negative. From Fig. 3a, it is evident that at frequencies (,1 THz) between the two resonances, the transmission is significantly
enhanced as a function of reverse gate bias. We have investigated whether this enhancement arises from a reduction of free carrier absorption in the
n-GaAs layer due to depletion. For this purpose, we fabricated a device without the metamaterial array—only the connecting wires remained as the
Schottky contact. With the same polarization of the THz electric field, that is, perpendicular to the connecting wires as indicated by the inset to Fig. 3c,
we measured its THz transmission at various bias voltages. As shown in Fig. 3c for reverse biases of 0 and 16 V, the change of THz transmission is
hardly observable and variations are within the experimental noise. Additionally, we performed measurements of the free carrier absorption in the n-
GaAs layer using an unpatterned sample with SI-GaAs as the reference. The relative intensity change of transmission between samples with carrier
density n 5 1.9 3 10 16 cm 23 and n < 0 is less than 10% at ,1 THz. Furthermore, in our metamaterial device only a small fraction of the n-GaAs layer
is depleted by the reverse gate bias and thus the reduction of free carrier absorption is not nearly enough to account for the change in transmission in
Fig. 3a. The transmission enhancement in this frequency range is dominated by the metamaterial structure and is largest in the vicinity where e 1 (v) <
1. This active metamaterial device was designed such that the LC resonant response occurs with the electric field polarized perpendicular to the
connecting wires. This eliminates the Drude-like response that occurs when the THz electric field is parallel to the array of connecting wires 13 .
Nonetheless, with the electric field applied parallel to the connecting wires, a response that changes with applied bias is still observed, as shown in
Fig. 4a. The small transmitted intensity at low frequencies results from the Drude-like response of the connecting wires. Superimposed on this is a
resonance at 1.25 THz from the metamaterial elements. This resonant response is associated with dipolar currents in the elements analogous to the
higher-lying resonance when the electric field is perpendicular to the connecting wires. As such, the variation in e 1 (v) shown in Fig. 4b

Paper
■ arises from substrate carriers screening the dipolar currents. An applied bias depletes the carriers, thus restoring the dipolar resonant response. Figure
4c shows the response for an array of parallel wires as the Schottky contact to the n-type substrate without the metamaterial elements. As expected,
only a Drude-like response associated with the wires is observed. Thus without the resonant metamaterial elements and their critical dependence
upon substrate properties, it is not possible to modulate the transmission with an applied bias. This further confirms the importance of the
metamaterial elements in creating active THz devices. Substrates typically used to fabricate planar metamaterial structures (for example, Si, GaAs,
Teflon) are insulators and are essentially lossless at THz frequencies. In this case, the metamaterial structure and the substrate can be modelled as an
equivalent LCR resonant circuit as shown in Fig. 1b without the variable resistor R d . However, when the substrate is lossy (in our case this is a result
of doping), the finite resistance at the split gap has to be considered. The equivalent circuit should be modified by attaching a variable resistor in
parallel to the capacitor 27 .
■ In our device, the gate bias changes this resistance by depleting the free charge carriers and modifies the resonance strength. The fact that there are
no significant shifts of the resonance frequencies indicates that the magnitude of the capacitance at the split gap is not strongly affected by the
applied gate bias—rather, the capacitance is shunted. Although the metamaterial structure presented here is a first generation device (that is, no
optimization has been attempted), the performance as a THz modulator already exceeds current state-of- the-art electrical THz modulators—based on
semiconductor structures 10 —by one order of magnitude on resonance, and operates at room temperature. Higher modulation efficiency for practical
applications is expected to be achievable through device optimization, that is, by varying the doping concentration and/or the thickness of the doping
layer. One problem with the current design is that high frequency modulation is not possible. We performed measurements of the THz intensity as a
function of modulation frequency by applying a rectangular a.c. reverse gate bias alternating between 0 and 16 V. The large area (5 3 5 mm 2 ) of the
metamaterial array results in a large overall device capacitance, yielding a maximum modulation frequency of several kilohertz (Supplementary Fig.
2). We anticipate significant increases in the modulation frequency from reducing the total capacitance and resistance of the device by, for example,
pat- terning the n-GaAs regions of the substrate and/or using inter- digitated contacts. This demonstration of an active metamaterial device relied on
electrically connecting the individual metamaterial elements. It is important to emphasize that this does not compromise the resonant LC response of
the elements, and thereby provides additional design flexibility for metamaterials in general. The approach presented here for active THz
metamaterials naturally extends to magnetically resonant metamaterials. Finally, consideration of the substrate or embedding environment also
offers considerable flexibility in the design of active metamaterial devices at any frequency range.

Introduction
(FDTD)
■ This meta material exhibits a negative index of refraction in the THz range.
■ Simulation setup
■ The material properties (plasma resonance and collision frequency) were estimated from gold data in the visible. This should be
a reasonable estimate of the properties in the THz range. The plasma model can be expressed as a simple conductive model in
the low frequency limit (when ω << νc). The PEC (Perfect electrical conductor) material model is appropriate for such situations.
– The gold thickness is meant to be 200 nm, but this would require a very small mesh size for dz. Most likely, the
thickness is not very important, since the gold itself will not support any resonances. Instead, the thickness has been set
to 4 microns with a mesh size of dz = 1 micron. Since the smallest wavelength is about 100 microns, we still have dz <<
lambda and the thickness << lambda. Convergence testing vs gold thickness has not been attempted, but the end result
agrees reasonably well with the results in the paper.
■ Note: a mesh override region has been added to the gold layer to force a 1 micron mesh in this area. For initial simulations, a mesh
size of dx=dy=dz=2 microns will make the simulation much faster.
■ For the GaAs substrate, a simple constant index model was used. It may be possible to account for a free carrier model by
adding a conductivity that depends on bias voltage.
■ In this application exsample section, the other two examples use the conformal variant 1 mesh refinement option. For this
example, the default conformal mesh option is used, since the mesh was set up to line up with the PEC. Due to the fact that the
mesh cells line up exactly with the PEC, there is no benefit to changing the mesh refinement option.

Symmetric and anti symmetric
■ changing from Setting A to Setting B
– will preserve periodicity while reducing the computation time needed by about
4x.
– Again this only applies if the structure and fields are BOTH symmetric and
periodic.

Introduction
(Device)
■ effect of bias-induced carrier density variations on the refractive index of the individual materials and
hence the overall transmission of the metamaterial.
■ unperturbed metamaterial analyzed optically in FDTD
■ analyze electrically using DEVICE.
■ Theory
■ Voltages are applied to the metamaterial via contacts  corresponding carrier densities are calculated
and recorded. The effect of the carrier densities on the refractive index of the GaAs layer is then
calculated.
■ To calculate the effect of the change in the carrier density on the refractive index, an FDTD Solutions
simulation will be run. The np density grid attribute in FDTD Solutions will take the carrier density
information and calculate the corresponding changes in the real and imaginary parts of refractive index
of the material according to the Plasma-Drude formulation. For a more detailed description of this grid
attribute and the formula, please visit the Charge to index conversion.
■

Setup
DEVICE
■ 2D solver for simulation, several y-normal cross sections of the structure are simulated
individually for a full picture of the carrier density profile across the entire metamaterial.
■ A parameter sweep  over the position of the simulation region.
■ The electron density is then collected for each of the cross sections, simulating voltages between
0 and 16 volts for every one of the cross sections.
■ A charge monitor in DEVICE will record the n and p distributions and save them to .mat files for
the corresponding cross sections, which will be imported into the np density grid attribute in FDTD
Solutions.
■ Symmetry boundaries are used and so only the first quarter of the simulation region is included.
– We only create the npdensity objects in that quarter as well.
– The rest of the region is mirrored because of symmetry boundaries.
– Carrier densities are used to calculate the corresponding refractive index of GaAs according
to the Plasma-Drude model explained of Charge to index conversion.

■ Note:
■ 1. When sweeping the simulation positions of x=0um, 3.5um, 9um and 16um, resulting data from
the "Charge" monitor will be recorded in different output .mat files, which is set in the script in
"model";
■ 2. Since no other output is needed, in the "Results" of the sweep, we set the current to output, which
is arbitrary. If you do not set any result, after sweep, you need manually close the sweep dialogue.
■ 3. The sweep of applied voltages is set in the Contact of "emitter".
■ FDTD Solutions
■ transmission -> function of the applied voltage=> parameter sweep in FDTD Solutions.
■ The results of the parameter sweep (the effective mode of each index as a function of voltage) can
then be plotted.
■ The file is set to only sweep voltage points of 1, 29, and 57, corresponding to voltage of 0v, 8v and
16v.
■

Results
DEVICE
■ If the sweep tanysk in DEVICE is run, the location of the simulation region object is
varied from the center to the edge of the structure sweeping over 57 voltage points at
each cross section.
■ For the first position, we can look at the electron density distribution from the visualizer
at zero bias and at a reverse bias of 4 volts:
■ Once the sweep is run, open and run the script analyze_sweep.lsf to extract the electron
density at each positions and export the results to several .ldf files.
■

FDTD Solutions
■ Open the active_thzmaterial.fsp file. In the object tree, right click on the individual ehdensity objects and click import data, to import the .mat files into
the object. Notre that the x span has to be specified according to the cross section of the device. This has already been done in the provided .fsp file so
you can skip this.
■ Run the sweep task in the .fsp file. The sweep will run simulations for all three bias values at a range of frequencies from 0.25 THz to 2.5 THz. Use the
following lines of script to plot the results once the sweep is done:
■ f = pinch(getsweepdata("sweep","f"));
■ T = pinch(getsweepdata("sweep","T"));
■ V = pinch(getsweepdata("sweep","V"));
■ plot(f(1:100,1)*1e-12, T(1:100,1),T(1:100,2),T(1:100,3), "Frequency (THz)", "Transmission");
■ legend("V=0 volts", "V=8 volts", "V=16 volts");

The excitation from down does not
differ due to the fact that bulk
parameters can be obtained hence it
does not differ!

Paper (Abstract)
■ Negative refraction is currently achieved by a combination of artificial “electric
atoms” metallic wires with negative electrical permittivity and artificial “magnetic
atoms” split-ring resonators with negative magnetic permeability . Both and
must be negative at the same frequency, which is not easy to achieve at higher
than THz frequencies. We introduce improved and simplified structures made of
periodic arrays of pairs of short metal wires and continuous wires that offer a
potentially simpler approach to building negative index materials. Using
simulations and microwave experiments, we have investigated the negative index
n properties of short wire-pair structures. We have measured experimentally both
the transmittance and the reflectance properties and found unambiguously that n
0. The same is true for and .Ourresultsshowthatshort wire-pair arrays can be used
very effectively in producing materials with negative refractive indices.

Introduction
■ This metamaterial => negative index of refraction => GHz range.
■ The material properties (plasma resonance and collision frequency) were estimated from copper data in the
visible. This should be a reasonable estimate of the properties in the microwave range.
■ Copper model=>
– Initially, this simulation was quite numerically unstable. This turns out to be due to the fact that the permittivity
is approximately -2.3e4 + 1.6e7 * i. In other words, the properties are completely dominated by the complex
permittivity. To control the instability, the plasma model was replaced by a simple conductive model which can
be obtained by an expansion of the plasma model when the collision resonance frequency is much larger than
the source frequency. Further testing showed that the results were not sensitive to the precise value of the real
permittivity. At the 10-20 GHz frequencies, the imaginary permittivity is so large that the metal behaves like a
perfect electrical conductor. The penetration depth is only lambda/10000, which would never be resolved in
FDTD anyway. It is surprising that in the paper they explicitly say that they use a Drude model, unless they mean
a conductive model which is the limit of the Drude model when w << nu_c. In this simulation, we have used the
PEC (Perfect electrical conductor) material model which is appropriate for such situations.
■ The copper thickness is meant to be 10 um, but this would require a very small mesh size for dz. Most likely the
thickness is not very important since the copper itself will not support any resonances. Convergence testing showed
this to be true. For this reason, the thickness has been set to 20 microns, which is still much smaller than the
wavelength.
■ The mesh size is 100um in the x and y directions and 7.35 microns in the z direction.
– The space between the 2 layers of copper will be important so that the light accumulates the correct phase as it
propagates between the 2 layers.
– The conformal variant 1 mesh refinement option is used in this example to take full advantage of the conformal
meshing technology to accurately represent the spacing between the copper, and the width of the copper.

Results
■ The reflection spectrum does have a bit of a different shape. This is most likely due
to the fact that for the reflection spectrum in Zhou, the source and the receiver
were 7.5 degrees to the normal, whereas in this simulation the source is at normal
incidence and the reflection monitor measures all the reflected power.
###########################################################################
# Scriptfile: negative_index_analysis.lsf
#
# Description: This file plots the normalized transmission and reflection
# as a function of frequency for the simulation negative_index.fsp
# which models the structure described in
# J. Zhou et a., "Negative index materials using
# simple short wire pairs", Physical Review B 73 (2006).
#
#
# Copyright 2007, Lumerical Solutions, Inc.
###########################################################################
# get the frequency, R and T
f = getdata("T","f");
T = transmission("T");
R = -transmission("R");
# plot the results on separate figures, dB scale
plot(f*1e-9,10*log10(T),"frequency (GHz)","Transmission (dB)");
plot(f*1e-9,10*log10(R),"frequency (GHz)","Reflection (dB)");

ALL-DIELECTRIC
ZERO-INDEX
METAMATERIAL

Paper
(Realization of an all-dielectric zero-index
optical metamaterial)■ Metamaterials:
– negative index
– ultrahigh index
– chiral optical properties
– near-zero refractive index
■ NZRI: Light
– no spatial phase change
– extremely large phase velocity,
■ directional emission
■ tunnelling waveguides
■ large-area single-mode device
■ electromagnetic cloaks
■ Optical frequencies, previously NZRI metallic inclusions=>large ohmic loss
■ impedance-matched zero-index metamaterial
– optical frequencies
– purely dielectric constituents.
– stacked silicon-rod unit cells,
– => nearly isotropic low-index response for TM polarized light,=>
■ Angular selectivity of transmission
■ Directive emission from quantum dots placed within the material.

Bandstructure
■ 2D stack of infinitely long silicon rods embedded in a Si02 cladding both of which are assigned
their respective non-dispersive index given in Valentine [1].
■ axial invariance of the ZIM => 2D FDTD simulation =>to obtain the bandstructure.
■ single unit cell  boundaries Bloch periodic boundary conditions with wave vectors kx and ky
specified across them.
■ The dipole cloud is used to excite the ZIM. It consists of a 10 randomly distributed electric dipole
sources which are oriented along the rod's axis to only excite the ZIM's TM modes. The frequency
range of the source is set to 0 to 250THz.
■ A set of randomly distributed time monitors to measure the electric fields,
a bandstructure calculation which apodizes the measured time signal to filter out its beginning
and end, and a FFT, we are able to find the resonances of the ZIM at a particular value of kx
and/or ky. By sweeping over all kx and ky values, we can reconstruct the entire dispersion
diagram (or bandstructure) of the ZIM. This is done in the optimizations and sweeps toolbox which
contains a sweep of kx and ky over the entire brillouin zone (i.e., from the Gamma - X, X - M, and
M - Gamma).

■ The script file dielectric_zim_band.lsf is used to run all the sweeps and generate the complete dispersion diagram of
the ZIM shown in the above figure. An interesting feature of the dispersion diagram is the frequency in which the two
transverse bands (TM2 and TM4) with linear dispersion intersects a quasi-longitudinal band (TM3). It is at this triple
degeneracy frequency in which the metamaterial exhibits a zero effective index in which both permittivity and
permeability are zero. This can be verified through a retrieval of the bulk effective medium properties of the
metamaterial using a field averaging of the Bloch modes (as detailed in Valentine [1]). Since the dipole cloud will
excite all the resonant modes of the ZIM, the field profiles will consist of a linear combination of each modes. In order
to extract a single mode's field profile (such as the TM4 mode's profile which is used in the field averaging), the
source(s) need to be placed strategically inside the simulation to excite only a single mode and not others. More details
on setting up the simulation can be found in the Bloch Mode Profile page.
■
■ The triple degeneracy response in the dispersion diagram is attributed to exciting the dielectric rod's 1st and 2nd Mie
resonances (the electric monopole and magnetic dipole). To verify this in the simulation, the script finished by turning
off the dipole cloud and turning on a single dipole source located at the center of the simulation. The simulation is run
twice with the orientation and dipole type changed between each simulation in order to excite each resonance
individually. Afterwords, the script generates the electric and magnetic field plots at the triple degeneracy frequency
which are shown below.

Near zero kamel nist, slide abstract be
baed ro nakhondam va dar zemn
absorber ha ham hatman barresi kon

PLASMONIC
METAMATERIAL
ABSORBER

Introduction
■ absorption => plasmonic metamaterial absorber
■ absorption mechanism =>
– by the excitation of localized electromagnetic resonances
– highly dependent on the geometry of the top metal layer
– highly dependent on thickness of the dielectric layer.
■ The plasmonic absorber is composed of a periodic array of subwavelength metal
patches on top of a thin dielectric layer and a highly reflecting thick metal layer.
■ For the optical simulation, we only need to simulate a single unit cell.
■ design parameters of the device can be defined in the 'Setup' tab of the 'model' object
in the object tree.

Introduction
■ Both symmetric and anti-symmetric boundary conditions are used to reduce the
simulation time.
■ The two power monitors, 'R' and 'T', are used to calculate the transmission and
reflection (and therefore, absorption) spectrum of the device.
■ To be consistent with the simulations in reference 1, a Plasma (Drude) material
called 'silver' was added to the material database and assigned to the top and
bottom metal layers and a refractive index of 1.75 was used for the dielectric layer.

Results
■ For these type of metamaterial absorbers, the spectral location of the resonance does
not shift with the angle of incidence when the correct mode is excited. This is a highly
desirable feature for infrared sensing applications as the detected light usually comes
from many different angles.
■ To verify that the desired absorption spectrum is robust for non-normal incident angles,
one can take advantage of the broadband fixed angle source technique (BFAST) to
simulate the absorption spectrum for a range of incident angles.
– The script plasmonic_absorber_angle_sweep.lsf uses BFAST to sweep the
incidence angle for a broadband plane wave source. One can see from the figure
below that the absorption spectrum has little dependence on the illumination
angle, as expected.

TUNABLE
GRAPHENE
METAMATERIAL
ABSORBER

Paper (Abstract)
■ In this paper we present the efficient design of functional thin- film metamaterial
devices with the effective surface conductivity approach.
■ As an example, we demonstrate a graphene based perfect absorber. After
formulating the requirements to the perfect absorber in terms of surface
conductivity we investigate the properties of graphene wire medium and graphene
fishnet metamaterials and demonstrate both narrowband and broadband tunable
absorbers.

Introduction
■ graphene metamaterial absorber
■ absorption spectrum tuned by  chemical potential applied to the graphene.
■ The absorption spectrum of the graphene absorber can be tailed by changing the key geometric
parameters. Below are the two types of structures we will consider: uniform graphene sheet and
graphene fishnet metamaterial.
■ We use a 2D graphene material model based on the surface conductivity of the graphene.
■ For this example, a conductivity scaling of 2 is used for the graphene model to account for the two
layers of graphene sheets used in [1].
■ A 2D rectangle object is used to model the sheet, and there is no need to add a mesh override region
over the graphene to resolve the thin layer.
■ For the fishnet geometry, polygon objects with the refractive index of 1.53 (corresponding to the
background index for dielectric) were used to pattern the 2d graphene sheet.

■ On the 'z min' boundary of the simulation region, a PEC (perfect electrical)
boundary was used to mimic the perfect mirror. A background index of 1.53 was
used.

Results
■ The absorption spectra of the uniform and fishnet structures as a function of the
chemical potential can be obtained by opening each of the simulation file
(graphene_absorber_uniform.fsp and graphene_absorber_fishnet.fsp) and running the
script file (graphene_absorber_ef_sweep.lsf). The key results from the simulation can
be summarized as follows:
■ •The absorption spectrum of the graphene absorber is strongly dependent on the
chemical potential
■ •A broader absorption spectrum can be obtained with the fishnet structure.
Furthermore, this spectrum can be tuned by changing the geometry of the fishnet
metamaterial.
■ If you happen to know the chemical potential of the graphene, you can directly enter
the value in the graphene material model. If not, you can use the charge transport
solver to obtain the chemical potential as a function of applied voltage. Additional
information on how to extract the chemical potential as a function of applied voltage
can be found in the graphene electro-optical modulator example.

Transmission=0
Absorption= 1-Reflection

■ Ef = [0;0.1;0.2;0.5];
■ A = matrix(length(Ef),100);
■ for (i = 1:length(Ef)){
■ switchtolayout;
■ setmaterial("C (graphene) - broadband","chemical potential
(eV)", Ef(i));
■ run;
■ A(i,1:100) = 1-transmission('R');
■ }
■ f = getdata('R','f');
■ plot(f/1e12,A(1,1:100),A(2,1:100),A(3,1:100),A(4,1:100),'f
requency (THz)', 'Absorbance');
■ legend('0 eV','0.1 eV','0.2 eV','0.5 eV');
■

Electrical simulation
https://kb.lumerical.com/en/other_application_graphene_modulator_electrical.html
■ graphene-based electro-optic modulator  modulation byFermi level of the
graphene layers.
■ A gate voltage to graphene sheet =>shifts the Fermi level  modifies its optical
absorption rate=>modulates  optical response of the silicon waveguide.

■ CHARGE =>drift-diffusion solver capable of handling complex geometries.
■ The semi-classical solvereffective-mass, 3D density-of-states (DOS) to model
semiconductor materials. =>challenge for modeling 2D DOS of graphene.
■ By using the electron (and hole) effective mass, me (and mh) and bandgap (or
conduction band minima, Ec) as fitting parameters, we can tailor the 3D DOS used
by CHARGE to mimic the 2D DOS of graphenenot physically accurate=>carrier
density of graphene=>reasonable accuracy

Electrical model for graphene in CHARGE
■ 2D DOS of graphene:
where, vF = 106 m/sec, is the Fermi velocity in graphene and E is the electron energy.
■ 3D DOS of a conventional semiconductor
where, m* is the electron (or hole) effective mass, E is the electron energy, and Ec is
the energy at the bottom of the conduction band.
■ In a semi-classical model, the DOS, g(E) can be used to calculate the carrier density
of a semiconductor. For the zero-bandgap graphene, the 2D electron density
(/cm2) can be calculated as,
where, is the 2D effective DOS, EF is the Fermi level, k is the
Boltzmann constant, T is the temperature, and F1 (η) is the Fermi-Dirac integral of
order 1 with η=EF⁄kT.
■ The 3D DOS can be used in a similar manner to calculate the 3D electron density
(/cm3) of a semiconductor giving,

■ where, F1⁄2 (η) is the Fermi-Dirac integral of order 1/2 with η=(EF-Ec)/kT, EF is the
Fermi level, Ec is the energy at the bottom of the conduction band,
■ is the 3D effective DOS, and m* is the electron effective mass.
■ It is a matter of using a simple scaling factor to resolve the mismatch between
N'c,2d and N'c,3d. Using m* and Ec as fitting parameters along with this scaling
factor, we can compare the electron density of graphene calculated by the 3D DOS
used in DEVICE with the actual electron density calculated by the 2D DOS. Figure 5
below shows that using m*=1.768, and Ec=0.1 eV, the electron density (/m2) of a
1 nm thick (3D) graphene sheet in DEVICE is in good agreement with the analytic
electron density of 2D graphene.

■ By comparing the electron density from the DEVICE model more carefully with the
analytical electron density of 2D graphene, we have identified that the accuracy of
the 3D model can be further improved by using different fitting parameters for
different ranges of Fermi level. We have therefore created two material models for
graphene in DEVICE; 'graphene_1 (Ef <= 0.05 eV)’ models the 2D electron density
of graphene in a 0.1 nm thick 3D graphene sheet when the Fermi level is near or
below Dirac point (EF ≤ 0.05 eV), and ‘graphene_2 (Ef > 0.05 eV)' models the 2D
electron density of graphene in a 0.75 nm thick 3D graphene sheet when the
Fermi level is well above Dirac point (EF > 0.05 eV).

Electrical simulation Setup
■ The attached DEVICE files graphene_electro-optic_modulator_1.ldev and graphene_electro-
optic_modulator_2.ldev contains the modulator geometry which is identical to the setup in the
optical solver. The two files use two different models for graphene to simulate the device in the
appropriate bias ranges. The silicon waveguide is shallow doped with an acceptor concentration
of 1018 /cm3. Two bandstructure monitors ‘band_top’ and ‘band_leftwall’ record the Fermi levels
of the graphene layers on top and on the left wall. The charge monitor ‘charge_wg’ records the
charge variation in the silicon waveguide with respect to gate voltage. Figure 6 shows the cross-
section of the simulation setup in DEVICE on the YZ plane.
■ Once the simulation is run on both DEVICE files, the script
files get_top_Ef_data.lsf and get_leftwall_Ef_data.lsf can be used to read the variation in the
chemical potentials of the graphene sheets on top and on the left wall. Figure 7 plots the
chemical potential of the top graphene sheet as a function of the gate voltage. The DEVICE files
also save the charge profile of the silicon waveguide as a function of gate bias in two Matlab data
files charge_wg_graphene_1.mat and charge_wg_graphene_2.mat which can be incorporated in
the optical simulation.

My Design 2
■ Ef=linspace(0,.5,30);
■ switchtolayout;
■ setmaterial("C (graphene) - broadband","chemical potential (eV)", Ef(i));
■ run;
■ }
■ plot(f/1e12,A(1,1:100),A(2,1:100),A(3,1:100),A(4,1:100),'frequency (THz)', 'Absorbance');
■ legend('0 eV','0.1 eV','0.2 eV','0.5 eV');
■ image(Ef,f/1e12,1-A,"Ef (ev)","Frequency (THz)","Reflection");

■ Ef=linspace(0,.5,30);
■ switchtolayout;
■ setmaterial("C (graphene) - broadband","chemical potential (eV)", Ef(i));
■ run;
■ }
■ plot(f/1e12,A(1,1:100),A(2,1:100),A(3,1:100),A(4,1:100),'frequency (THz)', 'Absorbance');
■ legend('0 eV','0.1 eV','0.2 eV','0.5 eV');
■ image(Ef,f/1e12,1-A,"Ef (ev)","Frequency (THz)","Reflection");

Refractive index from 1.53 goes to 2.53
It is great

Colnculsion
■ Going to visible range may enhance simulation run time but it is good for this SLM
■ The last structure period can vary and make it better
■ IDEA
– We can use two layers and then we add them up all

Introduction
■ T & R spectrum from
– nano holes in a metallic film.
■ near field profiles at the surface of the film
■ local field enhancements.
■ nanoholes of radius 100 nm and pitch 400 nm in a 100 nm thick layer of gold.
■ The gold layer uses the "Au (Gold) - CRC" model included in the default material database.
■ The plane wave source covers a wavelength range of 400 to 750 nm.
■ A single unit cell
– symmetric/anti-symmetric boundary conditions
■ note that symmetric/anti-symmetric boundaries must be consistent with the source polarization.
■ mesh accuracy of 2, and a 10 nm mesh override in the gold,
– typically mesh sizes of 5 nm or less should be used for the final results.
■

Results■ resonances with the strongest at approximately 675nm.
■ transmission normalized to the area of the hole divided by the unit cell area, which makes it easy to see where we have extraordinary transmission.
■ |E|2 at the surface of the gold, on the transmitted and reflected side. We can see that the local near field enhancement is very significant because the
incident field intensity is 1 V/m.
■ The cross section in the x-z plane shown below has the colorbar adjusted to a range of 1 to 10. This makes it possible to easily see the region where
the near field intensity enhancement is at least 10.

Gold Material
Gold
Air(etch)(n=1)
n=1.45
Excitation
from bottom
which does
not differ in
Optics

Abstract (Paper)
■ Color filters used
– color displays
– optical measurement devices,
– imaging devices
■ Conventional color filters=>only one fixed output color.
■ active color filters with controllable color output => more compact and sophisticated color filter-based devices and
applications.
■ interaction of light with metal nanostructures allow us to capture and control light better than ever.
■ fabricate active color filters, based on arrays of metallic optical nanoantennas that are tailored to interact with light at
visible frequencies via excitation of localized surface plasmons.
■ This interaction maps the polarization state of incident white light to visible color. Similarly, it converts unpolarized
white light to chromatically polarized light.
■ applications demonstrated
– active color pixels
– chromatically switchable and invisible tags
– polarization imaging based on these engineered colored metasurfaces.

Introduction
■ properties of chromatic plasmonic polarizers for color filtering and polarimetry.
■ chromatic plasmonic polarizers (CPPs).
■ The polarization angle of the source can be set in the polarization Analysis Group.
– If set to 0 or 90 degrees, the group will automatically use either symmetric or
anti-symmetric boundaries to reduce the simulation volume.
■
■ Two simulations
– polarization information (Fig. 2)
– transmission minimum as a function of CPP horizontal length (Fig. 3)

Results
■ Please modify figre2 and figure3 to be 1 as to run the sweep and 0 not to run the
sweep.
■
■ To improve the results,
– it would be possible to use a smaller mesh size (here we use 5nm over the Al
CPP),
– replace the ITO with a better material model (here we used a dielectric with
n=1.9), and draw the structure in a way that is closer to what has been
fabricated.
– Also, it should be noted that the polarization angle definition was reversed
between figures 2b and 2d of the publication.

A SPATIAL LIGHT
MODULATOR FOR
TERAHERTZ BEAMS

■ multipixel
– 4 * 4 pixel array
– each pixel is an array of subwavelength-sized split-ring resonator elements
fabricated on a semiconductor substrate, and is independently controlled by
applying an external voltage.
– uniform modulation depth of around 40% across all pixels at resonant
frequency
– negligible crosstalk at resonant frequency.
– operate under small voltage levels,
– room temperature
– low power consumption
– high switching speed.

terahertz SLM based on the use of
active terahertz metamaterials.
■ subwavelength-sized split-ring resonator (SRR) on epitaxial n-doped GaAs grown on a semi-
insulating GaAs substrate.
■ control of the metamaterial resonance is by depletion of substrate charge carriers upon
voltage bias which in turn changes the loss at the capacitive split gaps and therefore the
oscillator strength of all of the individual SRR elements within a pixel.
■ device enables an amplitude modulation depth of ~ 3 dB under a relatively small bias voltage
(16 V ) at room temperature.
■ resonant frequency can be tuned by changing the geometry and dimensions of the SRR
elements.
■ Fig.(a). Terahertz amplitude transmission spectra for one of the 16 pixels of the terahertz SLM
without voltage bias (dashed) and with 14 V bias ( solid ) .
■ A large modulation depth is observed at 0.36 THz, the design resonant frequency.
■ A transmission image of the 4 * 4 array at 0.36 THz, with two pixels turned off (biased) , and
the rest turned on (zero bias) .

Paper
■ 4 * 4 pixels each pixel is a 4 * 4 mm2 array of metamaterial SRRs,
■ The SRR elements have 200 nm gold thickness, 4 micron width,2 micron split gap spacing, 66 micron outer dimension,and 76 micron period such
that the device has a resonant transmission at 0.36 THz upon application of a voltage.
■ Each pixel (consisting of 2500 SRRs) is independently controlled by an external voltage across a 1 *1 mm2 Schottky electric pad and the ohmic
contact.
■ device has low power dissipation, drawing only a few milliamperes of current even when all the pixels are dc-biased at 14 V.
■ We characterize our terahertz SLM in a transmission geometry using a terahertz time-domain spectroscopy system with fiber-coupled photoconductive
antennae for both terahertz generation and detection.
■ The linearly polarized terahertz beam is collimated and directed toward the modulator with the polarization of the terahertz electric field aligned along
the direction across the SRR split gaps.
■ In these experiments, we raster-scan the terahertz receiver across the beam, after it has passed through the modulator. The substrate lens of the
receiver antenna is covered by a metal mask with a 1 mm aperture to improve the spatial resolution of the measurement.
■ At each receiver position, we measure the terahertz waveform using an optical chopper in the terahertz beam and a lock-in amplifier to filter the signal
from the photoconductive antenna.
■ Figure 2 (a) shows the typical transmission spectra for one of the 16 pixels in the “on” and “off” configurations, i.e., under a dc bias voltage of 0 or 14
V, respectively. For all 16 pixels, we observe an amplitude modulation depth between 35% and 50% at the design resonant frequency of 0.36 THz.
Shown in Fig. 2 (b) is the transmission image of the 4 *4 modulator array at 0.36 THz, with two pixels turned off ( biased ) and the rest turned on (
zero bias ).
■ To investigate the amount of crosstalk among the pixels in our terahertz SLM, we remove the optical chopper from the terahertz beam and instead
modulate only certain pixel elements directly by applying a square-wave ac voltage bias, alternating between 0 and 14 V. Using a lock-in amplifier
referenced to this square wave, we detect the terahertz signal at every receiver position of the raster-scan to produce a transmission image ( Fig. 3
inset ) . Signals with the largest amplitudes are concentrated at the two modulated pixels, with only a small amount of crosstalk in the surrounding
pixels. To measure system noise, we perform another raster- scan with all pixels unbiased and unmodulated while the lock-in amplifier is still
referenced to the square wave voltage frequency . From the first data set, for each frequency, we calculate N+C / S, the ratio of the signal power at
the surrounding unmodulated pixels due to both crosstalk C and noise N to the signal power at the modulated pixel S dotted curve in Fig. 3 . We then
calculate N / S, the ratio of the noise power from the second data set to S from the first data set dashed curve . The difference between the two ratios
gives the crosstalk level, independent of the system noise. This procedure is necessary because the crosstalk is so small as to be nearly
indistinguishable from the noise.q

ELECTRICAL BROAD TUNING OF PLASMONIC
COLOR FILTER EMPLOYING AN ASYMMETRIC-
LATTICE NANOHOLE ARRAY OF METASURFACE
CONTROLLED BY POLARIZATION ROTATOR

ABSTRACT
■ Wide range of color change
– nanohole array on metal film =>demonstrated
■ using
– asymmetric-lattice design of nanoholes
– electrically switching polarization rotator.
■ Recentlyvarious color  in a single unit cell
– using
– extraordinary optical transmission (EOT) of nano-patterned structure most important solutions for ultrahigh
integration density in optoelectronic devices.
■ they used the interfacial refractive index or dielectric constant as controlling factors for the color tuning => not capable of
inducing a changeable range of color with different primary color states.
■ To overcome this limitation, in this study,
■ an asymmetric-lattice nanohole array design was integrated with an electrically controlled polarization rotator, employing a
twisted nematic (TN) liquid crystal (LC).
■ rectangular lattice enabled mixed color states as well as precisely designed two different primary colors, by modulating the
polarization of the incident light.
■ The color-tuning shift was greater than 120 nm. Since the surface plasmonic (SP) modes on both side, a top and a bottom
interface, were matched better by the TN-LC layer assembled on the rectangular-lattice nanohole metal layer,
■ transmittance at the resonance peak wavelength was increased by 158% compared to that of the bare nanohole structure.
■ The nanohole-array-on-metal-film simultaneously functions as an electrode, and this advantage, coupled with the low driving
voltage of the TN-LC layer, can open new possibilities in applications to various optoelectronic device concepts.

■ electrically tunable color filter
■ TN-LC is integrated to control the polarization of the incident light.
■ incident white light, (b) a longer and (c) a shorter wavelength => stronger plasmonic
resonance when the polarization of incident light is parallel to the longer and the
shorter periodic nanohole array direction, respectively, in the rectangular-lattice
plasmonic metal surface.

Px
PY
are
Periodic
conditio
n
■ (a) SEM of plasmonic surface with the rectangular-lattice nanohole arrays.
■ (b) Optical photographs and transmission spectra of the square-lattice nanohole array structures, measured for unpolarized incident white light.
■ (c–d) Results of FDTD simulation of the plasmonic resonance field distributions for the asymmetric-lattice nanohole arrays (P x = 325 nm and P y =
225 nm) obtained under an air interface condition, where the incident beam is (c) the x-polarized light ( λ =565 nm) and (d) the y-polarized light ( λ
=419 nm).
■ (e–f) Optical photographs of the rectangular-lattice nanohole arrays prepared with different P x and P y conditions, where the incident conditions are
(e) x-polarized ( φ = 0 o ) and (f) y-polarized ( φ =90 o ).
■ (g) Optical photographs and transmission spectra, measured at two orthogonal incident polarization conditions for the plasmonic metal surface with
the rectangular-lattice nanohole arrays (P x = 325 nm and P y = 225 nm).

■ Figure 6. (a) Optical photographs and
transmission spectra of the square-lattice
nanohole array structures integrated with
the TN-LC layer as an in-cell type device,
obtained for unpolarized incident white
light. (b–c) Optical photographs of the
rectangular-lattice nanohole arrays
prepared with different P x and P y
conditions, which were measured after
integrating the TN-LC layer for (b) the
initial voltage (V a = 0 V) and (c) the
saturated voltage (V a = 5 V) conditions.
(d–f) Voltage- dependent transmission
spectra and their optical photographs, and
the CIE chromaticity diagrams measured
for the TN- LC-integrated rectangular-
lattice nanohole arrays with different
asymmetric periodicity conditions: (d) P x
= 250 nm and P y = 200 nm, (e) P x = 325
nm and P y = 200 nm, and (f) P x = 325
nm and P y = 225 nm.

ELECTRICALLY TUNABLE COLOR FILTER BASED
ON A
POLARIZATION-TAILORED NANO-PHOTONIC
DICHROIC
RESONATOR FEATURING AN ASYMMETRIC
SUBWAVELENGTH GRATING

ITO-FREE, COMPACT, COLOR LIQUID CRYSTAL
DEVICES USING
INTEGRATED STRUCTURAL COLOR FILTERS AND
GRAPHENE ELECTRODES

Abstract
■ LCD dominates display market =>
– largest user of transparent electrode material indium tin oxide (ITO).
■ ITO
– standard transparent electrode
– Limitations
■ increased costs due to the increasing scarcity of indium, brittle- ness, chemical instability
■ non-uniform absorption across the visible spectrum.
■ =>new transparent conductive materials
– Graphene
– metallic nanostructures
– carbon nanotubes
– so on. [ 2–6 ]
■ Among graphene promising material for transparent electrodes due to
– high carrier mobility,
– high transparency
– excellent mechanical flexibility,
– methods for fabricating high-quality, large-area graphene by CVD  replacing ITO as transparent electrodes.
■ Meanwhile, LCD technologies are faced with a popular trend to get thinner, lighter weight, and more energy efficiency.
An effective strategy towards advancing LCD technologies is to integrate multiple functionalities into the each of the
components of the LC system and reduce the number of element layers. Among the several possible uses of
nanotechnology in LCDs, the development of structural color fi lters for display applications is very promising. [ 18,19 ]
For example, besides the essential color fi ltering effect, the top and bottom metal layers of a metal–dielectric–metal
(MDM) Fabry–Perot (F–P) cavity fi lter can be used as electrodes, replacing one layer of ITO in

CIRCUITS WITH LIGHT AT
NANOSCALES: OPTICAL
NANOCIRCUITS INSPIRED BY
METAMATERIALS

CIRCUIT ELEMENTS AT
OPTICAL FREQUENCIES:
NANOINDUCTORS,
NANOCAPACITORS, AND
NANORESISTORS

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