Engineering the Optical Response of the Novel Plasmonic Binary Nanohole Array

The phenomenon of extraordinary optical transmission (EOT) due to its advantages has been considered by researchers in various applications, and in recent years, many efforts have been made to engineer these structures to get the best possible response for desired applications. In this work, the optical properties of novel binary gold nanohole arrays are investigated theoretically. We engineered the optical response of the system by adjusting the ratio of contribution of surface plasmon polariton (SPP) to localized surface plasmon resonance (LSPR) through the manipulation of the geometrical properties. The changes in the topology of this nanohole array affected the intensity and the wavelength of transmission peaks. The sensitivity of the optical response to the refractive index was also investigated. The designed structure is a good candidate for use as a polarization-independent optical label-free sensor.


Introduction
Different setups and configurations based on different physics introduced to use plasmonic properties of materials for various applications, especially for sensing applications [1,2]. Surface plasmon resonance (SPR)-based systems are one of the most famous plasmonic-based sensors. In these systems, a thin layer of a plasmonic metal like gold or silver is placed on one side of a glass prism, and the other side of the thin layer is in contact with the test medium which is usually a liquid and changes in the location of the resonance peak will be the outcome data to be analyzed [3,4]. Cavity plasmon resonance (CPR)-based systems are another design that uses the coupling of the light to the holes instead of the surface of a flat thin film [5,6]. To obtain the best sensitivity and performance, each of these systems can be tuned by adjusting the topological parameters of the plasmonic part [7,8]. Another fascinating phenomenon that is used to design plasmonic sensors is extraordinary optical transmission (EOT).
The enhanced transmission in a metal film with a subwavelength hole array and its unique geometrical and optical properties was registered by Ebbesen et al. [9] which it was not expected by the Bethe model [19]. The origin of EOT has been explained in the framework of surface plasmon resonance phenomena.
At frequencies lower than the plasma frequency, the electromagnetic field is stored in the collective electron oscillations, raising the possibility for confinement of the incident field to subwavelength volumes. One approach to accomplish this is using a thin metal film. The resulting boundary conditions quantize the plasma oscillations, which cause the creation of surface plasmon polaritons (SPP) [20]. If the dimensions of the thin metal film are further reduced to smaller than the incident wavelength, the retardant effects will be negligible and the electrons throughout the metal oscillate in phase. This phenomenon is known as localized surface plasmon resonance (LSPR) and is usually excited in curved metal objects such as metal nanoparticles and cavities of various topologies, providing the topology of additional momentum to couple directly to incident light [21]. LSPR frequency is dependent on the shape, size, and dielectric constant of metal objects. The LSPR allows the incident light to be highly concentrated and results in an enhancement in the local electromagnetic field. LSPRs and SPPs can co-exist at specific wavelengths such that the coupling between them can contribute to the optimization of the nanohole arrays to get the desired optical response for different applications [22].
Fano resonance is a result of the interference of two different resonances. Thus, Fano-like nature of EOT peaks can be interpreted as a combination of a localized surface plasmon resonance inside single holes and propagating surface plasmon resonance on the surface of the plasmonic thin film [23,24].
The Fano nature of resonances which leads to asymmetric line shape of the EOT peaks has been proved [25]. Fano resonance has been of great interest to researchers for many applications such as color filters [14,26], photonic crystals [27,28], metamaterials [29,30], surface-enhanced Raman spectroscopy (SERS) [25,31,32], and sensors [25,26,33,34] due to its very narrow asymmetric signal shape and its effect on the strong enhancement of the electromagnetic fields.
Therefore, by fitting Fano peaks and finding the Fano parameter of them, more detailed information about the nature of different optical responses for various nanostructure configurations can be achieved.
In addition to works done to investigate the physical roots of this phenomenon, there are also several works [19,[35][36][37] in which attempts were made to manipulate the topology of these systems to achieve the controlled optical responses for different applications.
In this study, we designed and numerically simulated a novel binary nanohole array for extraordinary optical transmission applications. The structure consists of a gold thin film with a binary nanohole array on a glass substrate. We studied the effect of different geometrical parameters on the transmittance spectral characteristics through this binary nanohole array. Besides, we discussed the Fano properties of the main EOT peak as a next step for understanding the physical bases of geometrical parameter changes of nanostructure designed by us on optical response more deeply.

Simulation Method
In this paper, the numerical analysis of light interaction with the proposed nanohole array has been carried out using the 3D finite difference time domain (FDTD) approach.
FDTD is one of the most used methods to solve Maxwell's time-dependent equations numerically, particularly when obtaining an analytical solution is extremely hard or even impossible [26]. We used MEEP which is an opensource FDTD package to do our numerical simulations [38].
Normal incidence zero-οrder transmission spectra were simulated. In our geometry, the light first passes through the array of metal holes and then glass.
The refractive indexes were set equal to 1.0 for air and 1.49 for substrate (glass from albite or PMMA). The periodic boundary conditions have been applied in x-and y-directions in a unit cell of the nanohole array. This lets us obtain the optical response of the entire system in a much shorter time scale. The transmission monitor is located above the surface at a distance of 0.25 µm. The light source is positioned inside the glass layer which is emitting EM waves to the nanohole layer with a P-polarization. Putting electromagnetic source inside the glass substrate is a common method [39]; this is done to ensure that the light is coupled and to prevent the light from scattering. Gold permittivity data is given from the CRC dataset [40]. Meshing steps in different directions are dx = 0.003 μm , dy = 0.003 μm , and dz = 0.02 μm . In the z-direction of the incident plane wave propagation, perfectly matched layers (PML) were utilized. The dimension of the unit cell is 0.4μm × 0.4μm × 0.6μm.

Results and Discussion
Here, we investigate the evolution of plasmonic properties of binary nanohole array using transmittance spectra. The metal nanostructure consists of two holes in different sizes with large and smaller diameters ( D1 and D2 , respectively) in the unit cell which is schematically shown in Fig. 1.
The diameter of the larger hole is fixed. The diameter of the smaller holes is variated and calculated as D2 = × D1 where is a real number between 0 and 1. The periodic length of the hole array is shown with L and equals the minimum distance of the origin of two same neighbors (either large or small) holes. The simplest unit cell is denoted in Fig. 1 with the unit cell parameter W being the distance between large and small holes, measured along the x-axis. Constant parameters are defined as large hole diameter 1 = 100nm , L = 400nm , thickness H = 200nm , and h = 200nm (see Fig. 1). The gold film thickness is chosen optimal and equal to 200nm based on previous works [41][42][43].
The effects of other structural parameters on the optical response of the binary nanohole array are presented in the separated sections. In the first two sections, the effect of the and W on the transmission spectrum of a p-polarized light has been discussed. In the next, the effect of asymmetry on the transmission spectra of different polarizations states of illuminated light has been analyzed. And finally, as an example of applications of such a system, we studied its sensing properties by varying different geometrical parameters.

I. Effect of hole size on optical transmission
The optical transmission spectrum of the binary nanohole array for different values of α is shown in Fig. 2a. For = 0 , the most amplitude asymmetric peak is located at 446THz ; also, there is a wide peak, which has a lower amplitude. As increases, the width of the EOT peak decreases, so that for α 0, 0.3, 0.6, and 0.9, the full width at half maximum (FWHM) respectively is equal to 51, 48, 55, and 91 nm, which means better resolution in the case of using nanohole array as a refractive index sensitive sensor. But also, we have a decrease in transmission value, so that for those α values, transmission is 0.49, 0.48, 0.44, and 23 (a.u.), respectively. Therefore, geometric characteristics should be selected in such a way that the intensity   and width of the peak be in a balance that does not impair the detector's ability. The formation of multipolarity in the dip frequency is visible to all cases in Fig. 2b, which confirms the hypothesis that LSPR leads to scattering or absorption resulting in transmission dips [44]. These kinds of dips imply an asymmetry in the shape of EOT peaks. The asymmetry in the shape of the curve is a characteristic of the Fano peaks. According to Fig. 2a, with an increase in , the amplitude of the Fano peak is decreased, whereas for = 1 , it has disappeared. Also, the plot shows that the Fano transmission peak shifts toward blue as decreases. This blue shift can be explained by the effect of increasing air volume, which is caused by increasing the α, because with a bigger α, we will have bigger diameter for the hole [45,46].
The asymmetric line shape of a Fano peak can be described by the well-known Fano formula [47]: where A and F are constant factors; 0 and Γ are resonance frequency and linewidth, respectively; and q is the Fano parameter which accounts for lineshape asymmetry. The Q factor is usually used as a dimensionless parameter to characterize the damping strength of the metamaterial and/or plasmonic structures. For a metamaterial system with large damping, resonance will not be able to adequately withstand the energy lost through radiative and non-radiative paths, which will cause the resonance linewidth to be greatly widened and vice versa. Therefore, the Q factor helps determine how much energy is lost or confined in the structure, which can be further improved to optimize the performance of plasmonic structures [48]. We fitted Fano peaks of simulated transmission spectra with the mentioned Fano formula to obtain q parameter for them. Comparison of simulated spectra with analytical Eq. (2) is presented in Fig. 3 for = 0.3 and W = 200nm . If we ignore = 0 , for other values of , as increases, q gets larger which means the asymmetry of the resonance line shape is increased.

II. Effect of W
In this section, we investigated the influence of changing the distance between the holes along the y-axis ( W parameter) and fixed α parameter with a value equal to 0.7 on transmission spectra of our binary nanohole array structure. The presented binary nanohole array structure is periodical; therefore, the value range for parameter W is changed from 0 to just half of the structure period L.
Transformation in transmission spectral characteristics for different values of parameter W is shown in Fig. 4b. The EOT peak with a spectral position around 418THz has its maximum intensity for W = 0 . With this W parameter value for nanostructure from Fig. 1, its morphology transformed into two holes located in a single column along the x-axis. For W = 120nm , the main Fano transmission peak shifted to high frequencies (blue shift) with decreasing its amplitude. As a result, the new peaks with low intensity at 454, 496, and 537 THz are observed. Further increasing of W leads to distribution in the middle of gold layer for peaks and dips, at four different configurations with different W values including W = 0 , 0.60 , 120, and 180 while is fixed and equals 0.7 for all the configurations. For W = 0 and 0.60, the electric fields inside two holes are coupled so that we can define them as a single hole with an effective radius that is why there is only one reliable peak in the transmission spectrum. For W = 120 and 180 , the electric field inside two different holes is independent which leads to the formation of different resonance modes, resulting in more peaks that can be useful in surface-enhanced Raman spectroscopy (SERS) applications [49]. The other two parameters that can be discussed are the depth of the holes and the period of the structure.
In this regard, two articles by Chao et al. [50,51], which are consistent with our calculations, show that by increasing the depth of the hole, in other words, increasing the thickness of the thin layer in which the holes are located, we will have a red shift and FWHM of the peak will increase. In contrast, as the system period increases, the transmission peak undergoes a blue shift and the FWHM decreases.

III. Polarization dependence
The use of polarization of light is an emerging research field that has progressed significantly in recent years within the biomedical field [52][53][54][55]. In this section, we are investigating the response of our proposed design to the changes in the polarization of incident light.
Here we have found that the position of spectral peaks is almost nonsensitive for different polarization states when symmetrical nanostructure with W = L∕2 is considered. The other values of the W parameter led to the asymmetry of nanostructure and the influence of different polarization states on the transmission spectrum is observed. The polarization features of transmission spectra for binary   For different polarization states with the component of electrical field oscillated along the x-axis for incidence light, the transmission spectra with main Fano-like peak The FWHM of the Fano peak reduces due to the continuous increase of the polarization angle from 0 to 90°. The shifts in transmission spectra caused by different polarization angles of incident light are negligible for sensory application.

IV. Refractive index sensitivity
One of the most important applications of nanohole arrays is sensing. The performance of a sensor can be evaluated by the figure of merit (FOM) which is the ratio of refractive index sensitivity to FWHM , where the sensitivity itself is defined as S = Δ ∕Δn . For four different morphologies of binary nanohole array structure, the sensitivity was simulated. Figure 6 shows the sensitivity and shift of EOT peaks for four morphologies of nanostructure for the detection of different medium with refractive index = 1 − 1.5 RIU . The transmission spectra for the combination of morphology parameters = 0 and = 0.7 and W = 0 are shown in Fig. 6a, b, and the determined refractive index sensitivity for both cases is 43, and the average FOM values equal to 0.8053 and 0.3561, respectively. Increasing of W parameter influences the gradual decrease of the main transmission peak intensity. This result is a perspective for sensors based on amplitude measuring. The new Fano-like peaks for = 0.7 and W = 100nm with a spectral position near 490THz and average FOM equal to 0.5338 were determined (Fig. 6c). For = 0.7 and W = 200nm , the amplitude of the transmission peaks has reached its lowest value in comparison with the three previous combinations of morphology parameters.
The largest average FOM among all structural configurations equals to 0.8185 due to the regular shape of EOT peak obtained (Fig. 6d).
The high refractive index sensitivity of these nanostructures makes them suitable for use in chemical and biological sensing for gaseous and liquid mediums.

Conclusions
Novel binary nanohole array structure with tunable optical parameters was developed and analyzed in detail. The main peak in transmission spectra is identified with Fanolike nature resonance. The tunability of transmission spectra is carried out by the variation of nanohole's surface density. These spectral transformations occur under changing the ratio of the contribution of localized surface plasmon resonance excited in single holes and non-localized surface plasmon resonance excited on the up/down flat surfaces. The increasing of structural parameters, such as the and W , leads to Fano parameter increases in range values from q = 0.12 to 0.35 for different , as well as from q = 0.10 to 0.32 for different values of W (for the case when = 0.7 ) was shown. Thus, simulation results demonstrate the blue wavelength shift in the Fano-like transmission spectra associated with the increasing of or W parameters.
The application possibility of developing the structure for optical sensors has been shown for various configurations of the morphology. The sensitivity for changing of detection medium is calculated. The unique morphology configuration combines with properties of Fano-like resonance of nanohole arrays which are a perspective for plasmonic optical sensors and nanoelectromechanical systems.
Author Contribution Mahdi Javidnasab provided the idea of designing binary-shaped nanohole array. Mahdi Javidnasab, Saeid Khesali Azadi, and Majid Ahmadpouri Legha did the calculations and data representations. Dr. Hamid Naghshara helped to explain the physics behind the optical response of the proposed structure.

Availability of Data and Material
The data created by the simulations during the current study are available from the corresponding author on reasonable request.

Code Availability
The simulation codes written for the current study are available from the corresponding author on reasonable request.

Declarations
Ethics Approval Not applicable.

Competing Interests
The authors declare no competing interests.