How to simulate Metamaterials using lumerical and Some literature Review

How to simulate Metamaterials using lumerical and Some literature Review

• 1.
  HOW TO SIMULATEMETAMATERIALS USING LUMERICAL AND SOME LITERATURE REVIEW Presented By: Hossein Babashah
• 2.
  Fields and WavesBasics ■ 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.
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  Motivation (Metamaterials) ■ Naturalmaterials 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)
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  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.
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  Simulating metamaterials ■ FDTDSolutions  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.
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  Features ■ • Simulatemetamaterials 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
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  What It contains SolverDescription 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
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  BULK METAMATERIALS
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  Bulk metamaterials■ howto 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)
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  Plot Lorentz modelfor 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
• 11.
  Simulation setup ■ abeam 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.
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  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.
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  Step by Step(PML all boundaries)
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  lambda increases fromleft to right Mag E Ex
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  In Si doesn’tchange with increasing lambda
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  EFFECTIVE PARAMETERS – SMITH HFSSIS USED IN PAPER
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  Introduction ■ Goal: magnitudeand 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.
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  Simulation setup ■ Acubic 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.
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  Results ■ check ifthe 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
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  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.
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  S-parameter calculation technique ■Just copy s-params ■ Change the values correspondingly – Note polarization for PEC PMC
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  Effective parameters
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  Advanced note: Calculatingthe 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.
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  Test S-parameter phaseoffset
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  EFFECTIVE PARAMETERS - SMITH (SIMULATIONUSING THE EXTRACTED MATERIAL PARAMETERS)
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  About the magneticelectric 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.
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  Simulation using theextracted 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
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  CHIRAL MATERIALS - KWON
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  Introduction An object ora 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.
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  Calculation of thecircular 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:
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  ■ The fielddistributions 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
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  ■ If wenormalize 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.
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  Step by StepSim
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  PARAMETER SWEEP
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  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.
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  NESTED PARAMETER SWEEP https://kb.lumerical.com/en/sweeps_nested_sweeps.html Surface PlasmonResonance 2D
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  THZ DEVICE -CHEN
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  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.
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  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.
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  Paper ■ A greatdeal of research into metamaterials has used microwave radiation; this is in part due to the ease of fabrication of sub-wave- length 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 flex- ibility 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 meta- material switch/modulator operating at THz frequencies. Although the modulation is based on a narrowband metamaterial resonance,
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  Paper ■ these devicescan be engineered to operate at specific frequencies. This would enable, as an example, amplitude modulation of narrow- band 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 subwave- length 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 con- ductivity 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 atmo- sphere. 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) fur- ther 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 elec- trical 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).
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  Paper ■ Without anapplied 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-depend- ent 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 res- onance 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 reso- nances 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 car- riers 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 vari- ous 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 varia- tions 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 reduc- tion 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 perpendic- ular 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 par- allel 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
• 47.
  Paper ■ arises fromsubstrate 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 metamater- ial elements. As expected, only a Drude-like response associated with the wires is observed. Thus without the resonant metamaterial ele- ments 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 struc- tures (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 gen- eration 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 struc- tures 10 —by one order of magnitude on resonance, and operates at room temperature. Higher modulation efficiency for practical appli- cations 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 fre- quency 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 res- onant metamaterials. Finally, consideration of the substrate or embedding environment also offers considerable flexibility in the design of active metamaterial devices at any frequency range.
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  Introduction (FDTD) ■ This metamaterial 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.
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  Symmetric and antisymmetric ■ 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.
• 51.
  Results
• 52.
  Introduction (Device) ■ effect ofbias-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. ■
• 53.
  Setup DEVICE ■ 2D solverfor 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.
• 54.
  ■ 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. ■
• 55.
  Results DEVICE ■ If thesweep 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. ■
• 56.
  FDTD Solutions ■ Openthe 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");
• 57.
  The excitation fromdown does not differ due to the fact that bulk parameters can be obtained hence it does not differ!
• 58.
  WIRE PAIRS -ZHOU
• 59.
  Paper (Abstract) ■ Negativerefraction 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.
• 60.
  Introduction ■ This metamaterial=> negative index of refraction => GHz range. ■ Simulation setup ■ 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.
• 61.
  Results ■ The reflectionspectrum 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)");
• 62.
  ALL-DIELECTRIC ZERO-INDEX METAMATERIAL
• 63.
  Paper (Realization of anall-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.
• 64.
  Bandstructure ■ 2D stackof 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).
• 65.
  ■ The scriptfile 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.
• 67.
  Near zero kamelnist, slide abstract be baed ro nakhondam va dar zemn absorber ha ham hatman barresi kon
• 68.
  PLASMONIC METAMATERIAL ABSORBER
• 69.
  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. ■ Simulation setup ■ 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.
• 70.
  Introduction ■ Both symmetricand 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.
• 71.
  Results ■ For thesetype 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.
• 73.
  My design T2=.5micrometer
• 74.
  TUNABLE GRAPHENE METAMATERIAL ABSORBER
• 75.
  Paper (Abstract) ■ Inthis 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.
• 76.
  Introduction ■ graphene metamaterialabsorber ■ absorption spectrum tuned by  chemical potential applied to the graphene. ■ Simulation setup ■ 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.
• 77.
  ■ 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.
• 78.
  Results ■ The absorptionspectra 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.
• 79.
  Transmission=0 Absorption= 1-Reflection
• 80.
  ■ 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'); ■
• 81.
  Electrical simulation https://kb.lumerical.com/en/other_application_graphene_modulator_electrical.html ■ graphene-basedelectro-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.
• 82.
  ■ CHARGE =>drift-diffusionsolver 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
• 83.
  Electrical model forgraphene 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,
• 84.
  ■ 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.
• 85.
  ■ By comparingthe 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).
• 86.
  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.
• 88.
  My Design1
• 89.
  My Design 2 ■Ef=linspace(0,.5,30); ■ 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),'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");
• 90.
  ■ Ef=linspace(0,.5,30); ■ 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),'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");
• 92.
  Refractive index from1.53 goes to 2.53 It is great
• 93.
  Colnculsion ■ Going tovisible 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
• 94.
  NANOHOLE ARRAY
• 95.
  Introduction ■ T &R spectrum from – nano holes in a metallic film. ■ near field profiles at the surface of the film ■ local field enhancements. ■ Simulation setup ■ 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. ■
• 96.
  Results■ resonances withthe 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.
• 97.
  Gold Material Gold Air(etch)(n=1) n=1.45 Excitation from bottom whichdoes not differ in Optics
• 98.
  CHROMATIC POLARIZERS
• 99.
  Abstract (Paper) ■ Colorfilters 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.
• 100.
  Introduction ■ properties ofchromatic plasmonic polarizers for color filtering and polarimetry. ■ Simulation setup ■ 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)