Studying and Simulation of a Different Formation of U Shape with T and L shapes of Plasmonic Nanoantennas with Variable Substrates

The optical properties of surface plasmons at the resonant wavelength depend on the geometrical nanostructure of materials, refractive indices, thickness (materials and dielectrics), and shapes of the formation unit cell nanoantennas. In this study, we take different shapes of plasmonic nanoantenna structures with a prototype of single and dual Ushapes as a common part to format a unit cell of nanoantenna by adding T and L-shapes based on a different dielectric such as, a silicon nitride, magnesium fluoride, and aluminium oxide, with gold as a variation of refractive indices. A single U-shape provides a dual spectral resonance at a wavelength range of (500-950) nm. Thus, in these proposed structures, we try to achieve a triple band with the best transmission and field enhancement distributions (electric field intensity and magnetic field intensity), and we design and simulate these fractals by using the 3Dfinite difference time domain method Lumerical program with an incident source between a visible to infrared range. From the results, the triple bands have a wide range of applications in medicine as biosensors and in communication systems (optical modulators).


Introduction
Nanoantenna is a nanoparticle of metallic structures designed to deal with light [1,2]. The principles of working such a device is to improve the energy conversion between the nanoantennas and free radiation field [3]. The operation of the nanoantenna takes place successfully in a range between IR to visible so, it has great development designs [4]. A surface Plasmons (SPs) of metallic that is excited by an incident of light has extraordinary effects that have recently become a study focus [5][6][7]. Currently, nanoantennas are being designed in different shapes and material arrangements [8,9]. The properties of dielectrics have strong effects on LSP (Localized Surface Plasmons), which is important for sensing applications such as optics, biology, and material sciences [10,11] because they depend on localized practical resonances. Thus, it is easy to perform the measurements of (optical parameters) such as absorption, reflection, scattering, and transmission [12][13][14][15].
Over the last few years, different shapes of nanoantenna have been proposed by changing arrangement of the parts to obtain multi resonances in a range of mid IR [16] and improve the reflection for spectrometry [17], such as Bowtie [18], loop [19], and triangular [20] as a basic design. On the other hand, there are complicated structures such as the U-shape [21], and SRR (split ring resonator) [22][23][24]. Several models of nanoantennas plasmonic shave have been designed and fabricated by Altug et al that deposit Au and Ti on SiN membrane layers [25,26], while Mosallaei [27] used silver (Ag) based on Silicon substrate [26]. Also, the U-shape is used with other structures such as the Jerusalem Cross (JC) to present multi resonances as perfect metamaterial absorbers (MA) in the THz region. Zarrabi [28] added the U-shape to the H-shape in order to achieve a triple resonance by using the CST program. The arrays of the U-shaped metallic periodic with SRRs to improve the magnetic resonances of metamaterials are composed of high-quality sensing [29].
In this article, we take a different shape of plasmonic nanoantenna structure with a prototype of a single and dual Ushape as a common part to format a unit cell of nanoantenna by adding T and L-shapes of the gold base on a different dielectric such as , SiN (n=1.98,2,2.16), MgF 2 (n=1.37,1.36) and Al 2 O 3 , (n=1.76) as a variation of the refractive indices. Consequently, in these proposed structures, we attempt to achieve a triple spectral with the best transmission and field enhancement distributions (electric field intensity (E) and magnetic field intensity (H), we design and simulate these fractals by using the 3D-FDTD method Lumerical program with an incident source between the visible -IR range.

Method of Analysis
In this study Figure 1 shows the different shapes of the Symmetric unit cell of the nanoantenna with geometrical parameters (L, H, W, t) representing the length, height, width, and thickness of the metal respectively, including S the distance between the two shapes in the same unit cell. The shapes of the nano structures basically depend on the deposition of a gold (Au) layer with (t=100nm) on a substrate, which is variable like SiN,(n=1.98,2,2.16), MgF 2 ,(n=1.37,1.36)and Al 2 O 3 , (n=1.76), with the dimensions of the unit cell; L=800nm, H=400nm and W=(75-100)nm. Three models of the nano antennas are proposed by using the U-shape added to L, T shapes in a 3D FDTD Lumerical program to design a simulation Plasmonic nanoantenna trying to achieve dual and triple spectral resonance and field enhancement distributions E and H with the best transmission, therefore, we used a multi type of substrate model in order to change the refractive index that effects the surface Plasmon resonance with each a model. We Where ε m, r and ε m,i are real and imaginary parts of the metal's dielectric constant, respectively, ε b is the static term due to the bound charge, and is the damping coefficient [31].  In Figure 3, the field enhancement distributions of E appear strongly with the SiN substrate for all the models in a single U, and a dual L approximate to 0.96 at the center of structure. While the field enhancement distributions of H noticed in the dual U, 4L about 2.62E -3 concentrated on both sides of the structure. On the other hand, with Al 2 O 3; H is concentrated at the center with a value 2.01E -3 . Figure 3: best field distributions of E and H; a and b represent E,H for dual U, dual T. c and d represent E,H for single U, dual L. e and f represent E,H for dual U, 4L.

Conclusion
As a result of the interaction between the incidents light with the surface of the metals, each model demonstrates that dielectric and refractive index and also the thickness of the substrate have an effect on radiation efficiency. High transmission and field enhancements show a distribution that is related to the effect of the positions of the surface plasmons which reveals them to be a good candidate for biosensor applications. These models offer flexibility and a wide range of designing and fabrication structures and optimizing the response of surface Plasmon at visible and near the IR regime. The proposed different shape of models of nanoantenna plasmonic can also support dual and triple response resonances of operations and act as a high transmitted for new devices. Through these results, we can find some methods for new arrangements to enhance plasmonic nanoantennas quality and accuracy.