Metallic nano-structures for polarization-independent multi-spectral filters
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Cross-shaped-hole arrays (CSHAs) are selected for diminishing the polarization-dependent transmission differences of incident plane waves. We investigate the light transmission spectrum of the CSHAs in a thin gold film over a wide range of features. It is observed that two well-separated and high transmission efficiency peaks could be obtained by designing the parameters in the CSHAs for both p-polarized and s-polarized waves; and a nice transmission band-pass is also observed by specific parameters of a CSHA too. It implicates the possibility to obtain a desired polarization-independent transmission spectrum from the CSHAs by designing their parameters. These findings provide potential applications of the metallic nano-structures in optical filters, optical band-pass, optical imaging, optical sensing, and biosensors.
KeywordsGold Film Electric Field Distribution Transmission Peak Frequency Selective Surface Complex Dielectric Function
extraordinary light transmission
frequency selective surface
finite difference time domain
perfect match layers
surface plasmon polaritons
where εd and εm are the permittivities of the dielectric material and the metal, respectively. For εd = 1 (air as the dielectric) and a negative εm for a metal, it means that the SP wave-vector kSP is larger than the incoming free-space wave-vector k0. Therefore, in order to induce the SPs on a metal surface, it is required to compensate the increased momentum. A few techniques are reported to increase the momentum, such that scattering from a topological defect on the surface, such as a sub-wavelength hole, which provides a convenient way to generate SPs locally ; the prism coupling to enhance the momentum of the incident light [3, 5], and the use of a periodic corrugation in the metal's surface . The surface plasmon resonance is also observed from metal nanocrystal , and from bimetallic interface in Au-Ag core-shell structure nanowires . In this article we will discuss the technique of inducing SP with sub-wavelength-hole array, and specially a polarization-independent cross-shaped-hole array (CSHA) for multi-spectral filters and band-passes.
The mechanism model of the light propagating through these sub-wavelength-hole arrays can be described as three steps below. Firstly, the impinge plane wave is trapped on the metal film as localized surface plasmon (LSP) [9, 10, 11] by the sub-wavelength-holes; secondly, these localized SP polaritons propagate in the sub-wavelength holes; the process of SPs propagating in these sub-wavelength holes is not as simple as pass through them, in fact, partial of SPs are reflected back to the hole at the exit surfaces, due to the refractive index difference of the hole and that of the two surfaces of the metal film, therefore, the two surfaces of the metal can be viewed as two reflectors of the holes, as a result, the sub-wavelength-holes of the metal film form Fabry-Perot like cavities; Finally, light emits from the other side of Fabry-Perot like cavity (or the metal film). It is known that the shape of the sub-wavelength-hole and the periodicity of the array are the most important two elements in controlling the light in these metallic structures . For a rectangular hole array , the transmission efficiency is dependent on the polarization of the incident wave, e.g., it is expected to obtain high transmission efficiency when the polarization is parallel to the short ridge of the hole. In this article, we investigate the optical transmissions as functions of these two elements and the thickness of thin metal films in a CSHA, which is designed to obtain the polarization independent multi-spectral filters and band-passes. As described in the mechanism model above, the transmission spectrum can be managed in a degree by the periodicity and the features of the holes; it shows that it is possible to obtain multi-spectral filters or frequency selective surface (FSS) by manipulate the thickness of the metal film and other parameters of the nano-structures.
Lorentz-Drude model for dielectric function of gold
Parameters of gold dielectric function for simulation
6.2634 × 1021
Polarization-independent multi-spectral filters
A plane wave impinges on the CSHA with an incident angle of θ (shown in Figure 2). The orientation of the incidence plane is located by the azimuthally angle measured from x-axis. When we set θ = 0 and φ = 0, the plane wave is normal to the metal film. Since the optical transmission is greatly dependent on the polarization of the electric field of the plane wave for rectangular hole arrays, the CSHA is introduced to reduce the dependence of the polarization due to its symmetrical structure for both TE and TM waves. In these simulations, the gold dielectric parameters in Table 1 is applied, and the gold film is sitting in the middle of a computing unit cell (see Figure 2b), and the boundary conditions of the unit cell are set as periodically (Bloch-periodic in both x and y directions), two perfect match layers (PMLs) are put at both ends (z direction) in the unit cell, after the PML, a plane wave source is set to illuminate normally to the metal structures (at θ = 0 and φ = 0), and a detectors is placed in front of the PML of the unit cell to measure the transmission spectra by computing the fluxes of these Fourier-transformed electric fields. The thicknesses of the PMLs are dependent on the working wavelength. Therefore, it is important to setup proper thickness of the PMLs to reduce numerical reflection. As mentioned above that the finer the steps the better resolution to be obtained, it is also very important to set a high resolution for the simulations.
The simulation results in Figure 3 are obtained by illuminating a plane wave on a CSHA with a period of 350 nm, length of 300 nm, width of 20 nm, and thickness of 100 nm in a gold film. In these cross-shaped-holes, the open area of the cross-shaped hole is about 2 × 300 × 20 nm2, which is about 1/10 of the area of a unit cell, which is 350 × 350 nm2. The transmission efficiency is about 70% at the center wavelength of 1.25 μm for this CSHA. A range of parameters for the cross-shaped hole (include the length, width, and both of them of the rectangle of the holes) are investigated, the results show that a very similar transmission peak can be obtained by varying these parameters of the CSHAs, though the wavelength center, the band width, and even the magnitude of the transmission peak varies a little bit for the different parameters. These results are consistent with the results that we obtained in the rectangle-hole arrays: the transmission resonance wavelength shifts toward red, at the same time the transmission peak narrows down with same magnitude as the width of the hole decreases; therefore, the width of the rectangular hole is more important on prediction of the transmission peak location; Meanwhile, the length of the rectangular hole plays a more important role on the transmission efficiency and bandwidth. The periodicity of the array as another important parameter is also investigated, the transmission peaks are red shifted from their periodicity, and this result is similar as the transmission peaks' behavior of the rectangle-hole arrays, in other words, for a larger periodicity, a longer wavelength of the transmission peak is observed. Therefore, periodicity of the array and the width of the rectangular hole are two factors in predicting the transmission peak's location.
Since the length of the hole has more effect on the magnitude of the transmission peak, and the width of the hole has more effect on the location of the transmission peak, therefore, in this investigation, we vary the width of the hole from W = 10 nm to W = 50 nm, and keep the length of the hole as a constant (L = 280 nm). The simulation results of the CSHA with same period and lengths but different widths are shown in Figure 5d,e,f. The plots of Figure 5d show that the CSHAs, with a thickness of h = 200 nm, length of L = 330 nm and widths of W = 10 nm, and length of L = 280 nm and widths of W = 20 nm and 50 nm in a periodicity of D = 350 nm, produce two transmission peaks in the spectrum; these two transmission peaks have same magnitude and are well separated for W = 20 nm; The simulations also show that the width of W = 50 nm is a little too wide to produce two well-separated transmission peaks (Figure 5d); however, it can produce a broad band pass transmission peak (Figure 5e) with the thickness of 350 nm; the third and fourth transmission peaks emerge in the thickness of h = 350 nm and h = 500 nm, respectively, for the width of W = 10 nm and 20 nm (Figure 5e,f). In conclusion, it is possible to obtain two well-separated and high transmission peaks by design these parameters in the CSHA (L = 280 nm, W = 10 or 20 nm, D = 350 nm, and h = 250 nm); it is also possible to produce a high efficiency broad band-pass with the CSHA (L = 280 nm, W = 50 nm, D = 350 nm, and h = 350 nm) in a gold film.
Discussion and conclusions
We investigate the process of light propagating in nano-structures of CSHA in gold film, following the localized SPs coupled to light from the hole of the metal film; the SPs experience Fabry-Perot like cavity effect from the metallic structures due to the refractive index at the exits forming reflectors. This Fabry-perot cavity effect in the SPs propagating in the nano-holes can be utilized to produce multi-transmission peaks or broad-band transmission peak. Our simulations show that a CSHA can be a polarization independent multi-spectral filter or a FSS; the increase of the thickness of the metal film leads to multi-modes of light come out from the metallic structures. Two well-separated transmission peaks with same magnitude and a broad band-pass transmission peak are obtained by engineering the parameters of the metallic nano-structures; moreover, these CSHA structures can produce very similar two transmission peaks when the plane wave is illuminating the CSHA with an angle (θ = 0-30). These results indicate that the possibility of the metallic nano-structures in applications of optical communication, optical imaging, optical sensing, and biosensors, etc. The investigations are carried out in the near infrared region. However, our further simulations show that these conclusions also stand in the visible, far infrared, or microwave regions.
Authors would like to thank the support from NSF: HRD-0833184, the support from NASA: NNX09AV07A, along with the MIT MEEP developers.
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