ADVANCED ELECTROMAGNETICS, VOL. 4, NO. 1, JUNE 2015

Nano-Dielectric Resonator Reflectarray/Transmittarray for Terahertz Applications

Hend A. Malhat*, Nermeen A. Eltresy, Saber H. Zainud-Deen, and Kamal H. Awadalla

Faculty of Electronic Eng., Menoufiya University, Egypt *corresponding author, E-mail: [email protected]

Abstract when being excited by an incident light, this is called surface plasmon polariton resonances (SPPRs). The electrical Nanoantennas have been introduced for different properties of these metals are described by the Drude- applications as solar-cell, medical imaging, and fast data Lorentz model which considers both the free electrons communications. The material properties of good contributions and harmonic oscillator SPPRs contributions conducting metals introduce plasmonic behavior at terahertz [8]. frequencies. The electrical properties of different good conducting metals are modelled using the Drude model and The optical properties of the nanoantenna depend on the have been investigated for reflectarray/ transmitarray size, geometry and material. However, only the high ohmic operation. The radiation characteristics of nano-dielectric losses of metals at terahertz frequencies affect the radiation resonator antenna (NDRA) reflectarray at 633 nm have efficiency of nanoantennas [2]. The nanoantenna resonance been investigated. The unit-cell consists of NDR mounted length is not determined by the free space wavelength, but on the metallic supporting plane. A parametric study for the by the SPP wavelength in the metal [2]. The current NDR unit cell dimensions and material has been introduced. distribution on the nanoantenna has a standing wave pattern The NDR unit-cell with silver supporting plane has been similar to that of the RF antennas, but with non-uniform designed and analyzed for reflectarray applications at 633 spacing between subsequent current lobes. Nanoantenna nm. The radiation characteristics of the NDRA arrays introduce a superior , field confinement, transmitarray has been introduced for 633 nm applications. absorption cross-section and flexibility in beam shaping The NDR unit-cell consists of two NDRs mounted on the compared with single nanoantennas. Dielectric resonator top and bottom of the metallic supporting plane. A antennas (DRA) have many attractive features and comparison between the radiation characteristics of 17×17 applications at microwave frequencies [9]. The DRAs have and 21×21 NDRA transmitarray has been introduced. A different shapes as a hemisphere, cylinder, or rectangular compromise between the nano-transmitarray size, and are typically mounted on a metal layer regarded as maximum gain, and operating bandwidth is applied to perfect electric conductor. The DRAs are generally terahertz applications. The finite integral technique is used constructed from low-loss high- dielectric to carry a full wave analysis to design an NDRA materials (up to εr =100). To increase the efficiency of reflectarray and an NDRA transmitarray.. resonant nanoantennas the low-loss high-permittivity dielectric materials available at terahertz frequencies are 1. Introduction used. At terahertz frequencies, the wave penetrates the The radiation characteristics of a conventional radio- metals due to the plasmonic effect and the antenna scaling frequency (RF) antenna have been presented in detail in [1]. property is not valid. The radiation characteristics of the Nanoantenna is a resonant device, which converts the DRA at 633 nm have been investigated in [10]. High-gain electromagnetic wave into a localized energy at terahertz microwave antennas have been used in many applications frequencies [2]. Recently, wide bandwidth nanoantennas such as radar and satellite communications. The parabolic have been introduced for faster information exchange. reflector and antenna have high gain, narrow Nanoantennas have many applications including solar cells, main lobe and high power capacity, but they suffer some on-chip wireless optical communication and biological disadvantages as high cost, and large volume for the imaging. Different forms of the microwave antennas such as parabolic reflector, and lossy feed networks in a phased dipole, monopole, Yagi-Uda, and bow-tie antenna have been array. combines the advantages of investigated at the terahertz frequencies [3-6] which focus parabolic reflector and phased array and overcomes their on resonant metallic nanostructures. The materials used for disadvantages [11]. The reflectarray antenna consists of a nanoantennas fabrication are generally good conducting primary source illuminating a planar surface composed of an metals such as gold and silver [7]. The resonant structures of array of unit-cells. The phase shift of each unit-cell is good conducting metals show electromagnetic resonances, adjusted to collimate the reflected wave in the desired direction. Reflectarray suffer from feeder blocking effect, so it requires an offset feed to avoid blockage losses, which the angular collision frequency, and is the electron leads to destroying the symmetry of the and plasma angular frequency [8] increases the angle of incidence of some individual elements = (3) [12]. The transmitarray overcomes reflectarray feed where n is the free electron density, m is the electron mass, blocking problem, and both the reflectarray and e e and q is the charge of the electron. Figure 1 shows the transmitarray transform the spherical wave emanating from variation of electric permittivity , and the conductivity , the feeder into a plane wave. Transmitarray is similar to the versus frequency in the terahertz range of gold, copper, reflectarray, but the incident wave is not reflected but passes silver and aluminum. The electrical permittivity and through the antenna structure as it is collimated into a plane conductivity of all metals take an exponential variation with wave on the other side. 9x9 unit-cells elements, nano- reflectarray using single perforated silver sheet at 735 THz frequency. (the permittivity components of  and has been introduced [13]. A detailed analysis of the radiation ) are increased by increasing frequency (negative with characteristics of nano-dielectric resonator antenna single reduced magnitude with higher frequency) while element and the NDRA reflectarray at 633 nm is (the conductivity components with 1 normally dominating investigated in [10]. A circularly polarized graphene at lower frequencies) are decreased in magnitude by transmitarray for terahertz application has been presented in increasing frequency. The skin depth δ(ω) represents how [14]. deep the electromagnetic wave can penetrate the material surface (1/e of its initial value at the surface) [8] In this paper, the electrical material properties of metals at terahertz frequencies have been determined. A parametric study of the NDRA unit-cell for reflectarray at 633 nm has (4) been introduced. The effect of changing the metal material where c is the speed of light. The variation of skin- depth property on the performance of the NDRA unit-cell is versus frequency500 for different metals is shown in Fig.2. At investigated. A 21x21 unit-cell elements NDRA reflectarray 500 data1 474 THz,350 the skin depth is 32 nm for gold, 28 nm for has been designed and analyzed using the finite integral 500 data1data2 copper, 35024.5 nm for silver and 17 nm for aluminum. technique based on the commercial software CST data2data3data1 500200500 microwave studio [15, 16]. A parametric study of an NDRA 350 data3data4data2Gold 200 data1 unit-cell with the silver supporting plane for transmitarray 35050 data4data5data3Copperdata2

350200 operating at 633 nm has been proposed. The radiation 50 data5data6data4Silverdata3 200 data7 characteristics of the 21x21 NDRA transmitarray are -10050 data6data5Aluminumdata4 200 determined and compared to a 17x17 NDRA transmitarray.. -100 data7data8data6data5 -25050 -100 data8data7data6 -25050 2. Material properties at Terahertz range Electric model dispersion:Drude -100 data8 data7 -400-250 Electric model dispersion:Drude 0 0.2 0.4 0.6 0.8 data8 1 -100-400

Electric model dispersion:Drude -250 Frequency (THZ)

At terahertz frequencies, the behaviour of conventional dispersion Electrical 0 0.2 0.4 0.6 0.8 1 -400 metals properties behaves in a different way compared to the Electric model dispersion:Drude 0 0.2 Frequency0.4 (THZ)0.6 0.8 1 -250-400 microwave frequencies [7]. In microwave frequency range 0 0.2 Frequency0.4 (THZ)0.6 0.8 1

Electric model dispersion:Drude the electric field inside the conductors is zero, which leads to -400 Frequency (THZ) 500 100 200 300 400 500 600 perfect reflection from the surface of the metal, as the Frequency (THz) conductivity of metal is very high. However, at terahertz Frequency (THZ) 500 (a) Electrical Dispersion frequencies, the assumption of perfect conductor metals is 350 500 17 not valid and the losses cannot be neglected [8]. The 350 x 10 2005003 material properties in the terahertz range can be described by 350 data1Gold a free electron gas moving through a lattice of positive ions. 200 data2Copper 350502 The frequency dependent complex permittivity and the 200 data3Silver electrical conductivity of metal in the terahertz frequency 50 data4Aluminum -1002001 range is described using the Drude model given by [8] 50

-1000 (1) -25050 -100

Electric model dispersion:Drude -250

-1 Reflection coefficient (dB) (2) -400-100

Electric model dispersion:Drude -250100 200 300 400 500 600 0 -250-400-2 85 100Frequency115 130 (THZ)145 160 170

Electric model dispersion:Drude

Electrical conductivity (s/m) 100 200 300 400 500 600 where is the real part of permittivity and is a measure of -400 NDRA raduis (nm) Electric model dispersion:Drude Frequency (THZ) how much energy from an external field is stored in a -400100-3 200 300 400 500 600 material, is the imaginary part of permittivity (loss factor) 100100 200200 Frequency300300 400(THZ)400 500500 600600 and is a measure of how dissipative or lossy a material is to FrequencyFrequency (THZ) (THz) (THZ) (b) Electrical conductivity an external field, is the dielectric constant of vacuum, is the angular frequency of the electromagnetic wave, Figure 1 The variations of complex permittivity and electrical conductivity versus frequency for different types of metals.

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30 4. Design of NDRA reflectarray antenna

25 The unit-cell of nano dielectric resonator reflectarray consists of an NDR made of titanium dioxide (TiO2) with 20 anisotropic frequency independent dielectric relative permittivity of 8.29 in x- and y-axis directions and 6.71 in z-

15 Golddata1 axis direction, and estimated loss tangent of 0.001 [10]. The

Skin (nm) depth Codata2pper NDR has a cylindrical shape with radius R and height hd 10 Silverdata3 placed on a square with thickness h to operate Aluminumdata4 at 474 THz as shown in Fig. 4a. To calculate the required 5 reflection coefficient phase compensation in each unit cell, 100 200 300 400 500 600 the unit cell is put in a waveguide simulator [13]. The FrequencyFrequency (THz) (THZ) Figure 2 The skin depth variation versus frequency for perfect electric and magnetic wall boundary conditions are posted onto the sides of the surrounding waveguide, and

Reflection coefficient (dB) silver, gold, copper and aluminum metals. result in an infinite array. A linearly polarized plane wave 0 was applied as the far-field excitation of the unit cells inside 85 100 115 130 145 160 170 NDRA3. raduisTheory (nm) of Reflectarray/transmitarray Antenna the waveguide simulator and only normal incidence angle is considered. There are several limitations to the infinite array The reflectarray/transmitarray operation can be seen as approach. First, all elements of the reflectarray/ a phased array with spatial feed located at (xf, yf, zf) from the transmitarray are identical; this is not the case in the real array aperture. For the reflectarray/transmitarray located in reflectarray/ transmitarray in which the diameters of the x-y plane the wave is reflected/transmitted from each unit- NDR in each cell element must vary according to the cell at direction ( , ) suffer from additional phase shift required phase compensation. Secondly, the reflectarray/ due to the position of the element in the array ( ) transmitarray itself is not infinite in extent. Finally, only and spacing between the cell element and the feeding horn normal incidence is considered. However, the plane wave as shown in Fig.3. To collimate the reflected/transmitted has an oblique angle on the real array element, but the phase o wave at direction ( , ) each unit-cell requires a variation is nearly the same for incidence angles up to 30 compensation phase [14]. Different metals are used for ground plane as silver, (5) gold, copper, and aluminum. The properties of the ground plane metals are determined using Eq. (1) at 474 THz and where is the wave number, is the distance are listed in Table I. from the feeding horn to each unit cell [12] z R (6)

and is the phase shift due to the location of the unit-cell hd in the array (7) h x x z L (a) 3-D view (b) Side view

(xf, yf, zf) Beam direction Figure 4 The detailed structure of the NDR reflectarray unit ( , ) cell. The required compensation phase of the reflection coefficient for each unit-cell is achieved by varying the NDRA radius R. Figure 5 shows the variation of the F reflection coefficient magnitude and phase versus the NDR radius at 474 THz for different ground plane metals. From the losses point of view the gold ground plane has the worst reflection coefficient (i.e. higher losses) variation from -30.4 dB to -2.9 dB, while the Silver ground plane gives the best y reflection coefficient magnitude (i.e. lower losses) varies from -5.8 dB to -1.7 dB for the NDR radius varying from 85 ( ) nm to 170 nm. This is because the conductivity of the gold x material is higher than that of the silver material at 474 THz as appeared in Fig1.b and the penetration in aluminum Figure 3 The detailed structure of the reflectarray/ ground plate is higher than that of silver Fig. 2. transmitarray configuration.

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Table I. The optical properties of the different types of metals at 474 THz [17] Metal (rad/sec) (rad/sec) (nm) Silver -17.46+j 0.56 0.169× -j 5.49× 24.5 Gold -9.27+j 0.95 0.285× -j 3.05× 32 Copper -12.7+j 0.87 0.26× -j 4.04× 28 Aluminum -40+j 15.2 4.5× -j 12.2× 17 360 Gold The phase of the reflection coefficient span of variation is 300 Copper 360o for the silver, 19o for gold, 215o for the copper, and Silver 136o for the aluminum ground plate. The silver material has 240 Aluminum the best performance for the reflectarray unit-cell with 180 reflection coefficient magnitude variation from -5.8 dB to - o 1.7 dB, and phase variation from 0 to 360 . Figure. 6 shows 120 the effect of changing the silver ground plane thickness (h) of the unit cell on the variation of the reflection coefficient 60

Reflection phase (degrees) magnitude and phase. By increasing the ground plane 0 thickness (h), the reflection coefficient magnitude is 85 100 115 130 145 160 170 decreased while the reflection coefficient phase variation is NDRANDR raduisradius (nm) (nm) o increased to achieve 360 . (b) Reflection coefficient phase magnitude

A compromise between the magnitude and phase of the Figure 5 The variations of the reflection coefficient reflection coefficient has been made. A ground plane of magnitude and phase versus the NDR radius at 474 THz for thickness h=200 nm has been chosen for which the the unit cell with different plane materials for h=200 nm, reflection coefficient magnitude varies from -1.7 dB to -5.8 L=350 nm and hd =50 nm. 0 dB and 360 o phase variations. Silver ground plane with thickness h=200 nm has a slower phase variation than -1 h=30nm which introduces a wider operating bandwidth and -2 has a higher reflection coefficient magnitude in the area of -3 -4 interest of the NDR radius changes from R=105 nm to 170 360 nm. The electric field distribution on the unit-cell of the -5 h=20 nm nm NDR reflectarray with silver supporting plane h= 200 nm, hd -6 300 h=30 nm nm =50 nm, and R=130 nm is shown in Fig 7. The incident -7 h=50 nm nm 240 h=70 nm plane wave penetrates the silver supporting plane at a -8 h=70 nm

distance equal to the skin depth and reflects back to the Reflection (dB) magnitude h=100 nm nm -9 180 source direction. The reflection occurs because the thickness h=200 nm nm -10 (h) of the silver supporting plane is much bigger than the 120 85 100 115 130 145 160 170 silver skin depth (about 8.16 ). NDRANDR radius raduis (nm) (nm) 60 Reflection phase (degress) (a) Reflection coefficient magnitude 0 360 0 85 100 115 130 145h=20160 nm 170 -5 NDRA raduis (nm) h=30 nm 300 -10 h=50 nm h=70 nm 240 -15 h=100 nm -20 h=200 nm 180 -25 Gold 120 -30 data1 data2Copper 60

Reflection coefficient (dB) -35 data3Silver Reflection phase (degress) data4Aluminum -40 0 85 100 115 130 145 160 170 85 100 115 130 145 160 170 NDR radius (nm) NDRANDR raduisradius (nm)(nm) NDRA raduis (nm) (b) Reflection coefficient phase magnitude (a) Reflection coefficient magnitude

Reflection coefficient (dB) Figure 6 The variations of the reflection coefficient magnitude and phase versus the NDR radius of the unit cell 0 85 100 115 130 145 160 170 with silver supporting plane at different plate thickness h, at NDRA raduis (nm) L=350 nm, hd =50 nm.

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maximum gain of 11.1 dB at 474 THz. The E and H-plane ND Sil radiation patterns at 474 THz of the nano-horn and the RA ver NDRA reflectarray with different ground plane thickness h=30, 70 and 200 nm are shown in Fig.9. For the inset variation from -10 o to 10 o, the maximum gain of the NDRA reflectarray is increased by increasing the ground plane thickness and the first level (SLL) is decreased. For h=200 nm the SLL is -15.1 dB and -17.9 dB in E-plane and H-plane respectively, and -23.3 dB in E-plane, and -14.8 h Figure 7 The electric field distribution on the unit-cell with dB in H-plane for nano-horn respectively. The half-power beamwidth (HPBW) of the NDRA reflectarray is 4.7 o in E- silver supporting plane, h=200 nm, L=350 nm, hd =50 nm o o and R=130 nm. plane and 4.5 in H-plane compared to 40.3 in E-plane and 41.3o in H-plane for the nano-. y

30 Lw 30 30 First quadrant 25 h=30data1 nm bw 20

) i 20 a 15 h=70data2 nm 2010 Gain(dB h=200data3 nm aw 510

0

-5 10-20 -10 0 10 20 b 0 Elevation (degrees)

Lh (dBi) Gain F dBi Gain x 0-10 Nano horn (dBi) Gain Lt -20 -10 -30 -180 -120 -60 0 60 120 180 z -20 Elevation (degrees) Lt -180 -120 -60 0 60 120 180 25 350 ElevationElevation (degrees) (degrees) (a) E- Plane (a) 300 30 25 30 20 350 25 h=30 nm 20

) i 15 h=70 nm 300 2010

250 Gain(dB 20 h=200 nm 5 0 250 15 -5

-20 -10 0 10 20 200 10 Elevation (degrees) 15 200 0

Gain dBi Gain

Gain (dBi) Gain 150 150 10 10

100 -10 100 5 5 50 -20 50 -180 -120 -60 0 60 120 180 0 0 Azimuth (degrees) 0 5 10 15 20 25 Elevation (degrees) (b) (b) H- Plane Figure0 8 (a) The detailed structure of the NDRA reflectarray 0 5 10 15 20 25 Figure 9. The gain patterns plot for a 21×21 NDRA with silver supporting plane, (b) The phase shift distribution reflectarray for variable silver supporting plane thickness at on the 21×21 unit-cell elements NDRA reflectarray with 474 THz, L=350 nm, and hd =50 nm. silver supporting plane.

A 21×21 unit cell NDRA reflectarray is simulated. The 3-D of the reflectarray at f=474 Silver ground plane with L=350 nm, h=200 nm, and hd=50 THz of the NDRA reflectarray is shown in Fig.10a. The gain nm is considered as shown in Fig.8a. The phase distribution variations versus frequency for the NDRA reflectarray and of the 21×21 unit cell is calculated using Eq. (7) as shown in 2 the nano-horn are shown in Fig. 10b. The NDRA Fig.8b. The array has total dimensions of 7.35×7.35 μm . A reflectarray has a maximum gain of 25.8 dB at 474 THz linearly polarized pyramidal nano-horn antenna is used to with 1-dB gain variation of 30 THz (from 459 THz to 489 feed the NDRA reflectarray located at (0, 0, 8.133) μm from THz). the array aperture in the horn phase centre. The nano-horn antenna is constructed from gold with Lw=487.5 nm, aperture size a×b of 810 nm ×1275 nm, aw×bw of 412.5 nm ×825 nm, and Lh=470.5 nm. The nano-horn antenna has a

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than that of silver at 474 THz. The skin depth of silver at 474 THz is nearly 24.5 nm, where the transmitarray unit-cell thickness must have approximately twice the skin depth or less to maximize the transmission from the unit-cell. A compromise between the magnitude of the transmission coefficient and phase variation has been made. The electric field distribution on the unit-cell of the NDRA transmitarray with silver supporting plane, h=50 nm, hd =50 nm and R=130 nm is shown in (Fig. 14). The incident plane wave h=30 nm h=70 nm h=200 nm passes to the other side silver supporting plane. The transmission occurs as the thickness of silver supporting (a) The 3-D gain radiation pattern at f=474 THz plane is equal to twice the silver skin depth where the 30 transmission condition is satisfied. z 25 z R

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hd 15 x y h Gain (dB) Gain 1 x Gain dBi Gain 10 horndata1 h=30data2 nm L 5 0.8 h=70data3 nm (a) 3-D view (b) Side view

h=200data4 nm 0.6 Figure 11 The detailed structure of the NDRA 0 445 460 475 490 500 tramsmitarray unit cell. Frequency (THz) Frequency (THZ) 0.4 (b) Gain 0 Figure 10 (a) The 3-D gain radiation pattern at f=474 THz, 0.2 (b) The gain variation versus frequency for a 21 × 21 NDRA -10 reflectarray at different thickness of the 500 silver supporting 0 plane. 450 460 470 480 500490 500 -20 data1 350 500 data2data1 5. Design of NDRA transmitarray350 antenna data3data2 200500 -30 data1 350 data4data3 The NDRA transmitarray unit-cell 200 consists of two Golddata1data2 350 data5data4 NDRA placed on the opposite sides of the supporting50 plane -40 Copperdata2data3 200 data6 50 Silverdata5data3data4 as shown in Fig.11. Each NDRA has radius200 R, height hd and Transmission (dB) magnitude -100 Aluminumdata7data6data4data5 silver supporting plane with thickness h and50 length L. The -50 -100 data8data7 required compensation phase of the transmission50 coefficient 85 100data5data6115 130 145 160 170 -250 NDR radius (nm) for each unit-cell is accomplished by varying-100 the NDR data8data6data7NDRA raduis (nm)

Electric model dispersion:Drude -250 (a) Transmissiondata7data8 coefficient magnitude radius R using the wave guide simulator.-400 -100 Figure 12 shows Electric model dispersion:Drude -2500 0.2 0.4 0.6 0.8data8 1 the variation of the transmission coefficient-400 magnitude and 360 -250 Frequency (THZ) Electric model dispersion:Drude 0 0.2 0.4 0.6 0.8 1 Gold phase versus the NDR radius at 474 THz-400 for L=350 nm, Copper Electric model dispersion:Drude 0 0.2 Frequency0.4 300 (THZ)0.6 0.8 1 h=50 nm, hd =50 nm for different -400 supporting plane Silver 0 0.2 Frequency0.4 0.6(THZ) 0.8 1 materials. The Aluminum supporting plane has the worst Aluminum Frequency240 (THZ) transmission coefficient variation from -26 dB to -17.3 dB, while the silver supporting plane gives the best transmission 180 coefficient magnitude variation from -4 dB to -2.4 dB for the

NDR radius variation from 85 nm to 170 nm. The phase of 120 the transmission coefficient variation is 240o for gold, 300o o o

for the copper, 350 for the silver and 180 for the Transmission phase (dB) 60 Aluminum supporting plate. The silver material has the best performance for the transmitarray unit-cell with 0 85 100 115 130 145 160 170 transmission coefficient magnitude variation from -4 dB to - NDR radius (nm) o NDRA raduis (nm) 2.4 dB and phase variation from 0 to 350 . The variation of (b) Transmission coefficient phase magnitude the transmission coefficient magnitude and phase versus the NDRA radius for different silver supporting plane thickness Figure 12 The variations of the transmission coefficient of the unit-cell is shown in Fig.13. By increasing the magnitude and phase of the NDR transmitarray unit cell supporting plane thickness the transmission coefficient with different supporting plane materials for h=50 nm, magnitude is decreased. The skin depth of gold is greater L=350 nm and hd=50 nm.

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0 -15.9 dB in H-plane. The HPBW of the transmitarray is 5.1 o in E-plane and 4.8 o in H-plane. The 3-D radiation patterns of the transmitarrays at f=474 THz are shown in Fig.17a. -5 The nano DRA transmitarray gain variation versus frequency is shown in Fig. 17b. The max gain is 23.9 dBi for 17×17 transmitarray and 27.5 dBi for 21×21 transmitarray -10 and 11.2 dBi for nano horn antenna. The 1-dB band width is 55 THz (from 451.5 THz to 496.5 THz) for 17×17 0 transmitarray and 40 THz (from 460 THz to 500 THz) for -15 h=50 nm data1 21×21 transmitarray. The E-plane and H-plane gain patterns h=60data2 nm -5 for the 21×21 NDRA transmitarray at different frequencies Transmission (dB) magnitude h=70data3 nm -20 are shown in Fig.18. 85 100 115 130 145 160 170 -10 NDRANDR radiusraduis (nm)(nm) (a) Transmission coefficient magnitude y -15 360

Transmission (dB) magnitude -20 300 85 100 115 130 145 160 170 NDRA raduis (nm) 240

180 x

120 z h=50 nm 60 h=60 nm h=70 nm (a)

Transmission phase (degrees)

0 z 85 100 115 130 145 160 170 NDRANDR raduis radius (nm) (nm) b. Transmi ssion coefficient phase

Figure 13 The variations of the transmission coefficient magnitude and phase versus the NDR radius with silver supporting plane thickness L=350 nm, hd =50 nm.

ND Silver ND RA RA x (b)

18 350 18 350

16 16 300 300 14 14 250 250 12 Figure 14 The electric field distribution12 on the NDR 200200 transmitarray unit-cell with silver supporti10 ng plane h=50 10

8 8 nm, L=350 nm, hd =50 nm and R=130 nm. 150150

6 6 100 100 4 A design of 17×17 unit-cells and a 21×21 unit-cells of 4

50 the NDRA transmitarray at 474 THz are2 investigated. The 50 2

element spacing between the unit cells0 is 350 nm, and 0 0 2 4 6 8 10 12 14 16 18 0 0 supporting plane thickness h=50 nm, h =50 nm. The 0 2 4 6 8 (c10) 12 14 16 18 d feeding horn is located at a distance F=8.133 μm in the Figure 15 (a) The detailed structure of the NDRA normal direction of the array plane. The E and H-plane transmitarray with silver supporting plane, (b) side view, (c) radiation patterns at 474 THz for the17×17 and the 21×21 The phase shift distribution of the NDRA transmitarray with NDRA Transmitarrays, and the horn antenna are shown in the silver supporting plane. Fig. 16. For the17×17 NDRA transmitarray, the SLL is - 18.2 dB in E plane and -14.4 dB in H-plane respectively. The HPBW is 6.3o in E-plane and 5.8o in H-plane. For the 21×21 transmitarray, the SLL for is -18.2 dB in E plane and

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30 30 30 30 data1Horn 25 F=460f=460 THz THZ 17×17data2 25 25 20 25 f=474 THz 21×21data3 F=474 THZ 20 f=500 THz 20 15 20 F=500 THZ

15 10 15 15

Gain (dBi) Gain 5 10 10 10 0

Gain(dBi) 5

Gain (dBi) Gain Gain (dBi) Gain 5 -5 5 0 0 -10 0 -90 -60 -30 0 30 60 90 -5 Elevation (degrees) -5 -5 -10 -10 -10 -90 -60 -30 0 30 60 90 -90 -90-60 -60-30 -30 0 0 30 30 60 60 90 90 Elevation (degrees) Elevation (degrees) Elevation (degrees) ElevationElevation (degrees) (degrees) (a) E- Plane (a) E- Plane 30 Horn 30 25 17×17 f=460 THz 21×21 25 f=474 THz 20 f=500 THz 20 15 15 10 10

Gain (dBi) Gain 5 Gain(dBi) 5 0 0 -5 -5 -10 -10 -90 -60 -30 0 30 60 90 -90 -60 -30 0 30 60 90 ElevationAzimuth (degrees)(degrees) ElevationAzimuth (degrees) (degrees) (b) H- Plane (b) H- Plane Figure 16 The gain patterns for 21×21 NDRA transmitarray Figure 18 The gain radiation patterns for a 21×21 NDRA with silver supporting plane at 474 THz. h=50 nm, L=350 transmitarray with silver supporting plane at different nm, and h =50 nm. d frequencies. 6. Conclusion The use of NDR in the design of nano-reflectarray and nano- transmitarray for terahertz application at 633 nm is introduced. The reflectarray unit cell consists of a cylindrical NDR on a square ground plane of a good conductor. A parametric study for the unit cell dimensions optimization has been introduced. The gold ground plane has got the (a) worst reflection coefficient (higher losses), while the silver 30 ground plane gives the best reflection coefficient magnitude. Silver ground plane with thickness of 200 nm has been 25 chosen for reflection coefficient magnitude varies from -1.7 o 20 dB to -5.8 dB and 360 phase variation. The silver ground plane with thickness 200 nm introduces slower phase 15 variation and hence wider bandwidth. The NDRA reflectarray consists of 21×21 unit cells with a silver ground

Gain (dB) Gain Gain dBi Gain 10 30 plane of L=350 nm, h=200 nm, and hd=50 nm is simulated Horn using the full-wave simulator. The maximum gain of the 25 5 17×17Transmitarray NDRA reflectarray is increased by increasing the ground 17data321×21 20 0 plane thickness and the SLL is decreased. The NDRA 445 460 475 490 500 reflectarray introduces a maximum gain of 25.8 dB at 474 Frequency(THZ) 15 Frequency (THz) THz with 1-dB gain variation bandwidth of 30 THz. The (b)

Gain (dB) Gain NDRA transmitarray unit-cell consists of two NDRA placed 10 Figure 17 (a) The 3-D gain radiation pattern at f=474 THz. on both sides of the supporting plane, has been designed and 5 (b) The gain variation versus frequency for 17×17 and a analyzed. The Aluminum ground plane has the worst 21×21 NDRA transmitarray with silver supporting plane. transmission coefficient variation from -26 dB to -17.3 dB. 0 445 460 475 490 500 Frequency(THZ) 43

The silver as a supporting plane material has shown the best metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in characteristics when compared with gold, copper, and the infrared and far infrared,” APPLIED OPTICS ,vol.22, no. aluminum. Comparison between transmitarray with 17×17 7, pp.1099-11201, April 1983. unit-cells and of 21×21 unit-cells at 474 THz have been introduced. The maximum gain is 23.9 dB for the 17×17 transmitarray and 27.5 dB for the 21×21 transmitarray while 11.2 dB for the feeding nano horn antenna.

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