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Abstract
In this work, we investigate a gold nanoslits array optical transmission filter with dual dielectric cap layers on top of the metal nanoslits. By integrating a low index of refraction dielectric layer between a high index of refraction dielectric cap layer and the gold nanoslits, a narrow spectral linewidth optical filter with a transmission peak far away from the Rayleigh anomaly wavelength is shown. Furthermore, we propose a figure-of-merit as the ratio of the spectral distance between a transmission peak and the Rayleigh anomaly over the spectral linewidth to characterize the performance of gold nanoslits optical filters. It is shown that dual dielectric cap gold nanoslits array optical filters have significantly larger figure-of-merits than that of traditional single dielectric cap gold nanoslits array optical filters.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical spectral filters are one of the most important types of optical devices used for numerous applications such as imaging [1–3], sensing [4,5], and high bandwidth optical communications [6,7], and etc. Traditionally, optical filters are made of multilayer dielectric thin film [8]. Thin film optical filters utilize optical wave interference in the direction of propagation for filtering effect. Thin film optical filter technology works well in the visible and near-infrared spectral range, but it is challenging to make optical filters in the long-wavelength range because long-wavelength thin film filters require thick layers of material depositions. Although the thin film technology can be used make large area filters, making spatially varying optical filters with the thin film technology is difficult. In the past decade, significant efforts have been made for designs and fabrications of subwavelength surface structure optical resonance filters. Surface nanostructure optical filters rely on optical resonance in the lateral directions of a periodic surface structure for selecting the transmission or reflection wavelengths. One type of surface structure optical filter is the guided mode resonance (GMR) filter made of patterned dielectric surface structures [9–15]. Another type of surface nanostructure filter is the localized surface plasmon resonance (LSPR) optical filters made with patterned metal surface structures [16–23]. Guided mode resonance filters rely on the excitation of the guided resonance mode by a surface subwavelength grating. The resonance wavelength of a GMR filter depends on the period of the subwavelength grating and the guided mode index. Guided mode resonance optical filters typically have very narrow spectral linewidth because of the small energy dissipation in the dielectric structure. However, since GMR filters rely on the guided resonance modes, multiple guided modes may result in multiple resonance wavelengths over the spectrum of interest. Also, GMR filters often have high transmittance side lobes around the resonance wavelength. Localized surface plasmon resonance filters rely on the surface plasmon resonance of metal nanohole or nanoslit array structures [18–20,22,23]. At the surface plasmon resonance, the electric field in apertures of nanoholes or nanoslits are strongly enhanced. Therefore, the optical energy can be squeezed through the nanoholes or slits coherently, resulting in a spectral selective optical transmission. Because of high absorption loss in metals, surface plasmon resonance filters have wide spectral linewidth and low transmittance.
Previously, Magnusson’s group reported a metal-dielectric hybrid structure guided mode resonance filter consisting of an aluminum subwavelength grating over an aluminum oxide dielectric film on a glass substrate [24]. The hybrid metal-dielectric structure GMR filter exhibits a 20 nm spectral linewidth. Narrow linewidth metal nanoslits optical filters with a single polymer cap film were also reported recently [25,26]. Although narrow spectral linewidths were achieved in the metal-dielectric nanoslits filters, the peak wavelengths of the filters are close to the Rayleigh anomaly wavelengths. In this work, we propose and investigate a dual dielectric cap layer gold nanoslits optical resonance filter structure. The dual cap gold nanoslits optical filter not only exhibits a narrow spectral linewidth, but also has the transmission peak wavelength far away from the Rayleigh anomaly wavelength.
2. Device structure and simulation results
Fig. 1. (a) Cross section of the single dielectric cap gold nanoslits optical filter structure with the device parameters of period p=1000 nm, nanoslits width w=160 nm, and gold nanoslits thickness t1=40 nm. (b) Calculated transmittance spectra of gold nanoslits array optical filters with a low index of refraction (n =1.45) cap layer of different thicknesses. (c) Calculated transmittance spectra of gold nanoslits array optical filters with a high index of refraction (n =2.74) cap layer of different thicknesses. The low index of refraction cap layer filter has a narrow linewidth transmission peak close the Rayleigh anomaly. The high index of refraction cap layer filter has a wide linewidth transmission peak far from the Rayleigh anomaly.
To distinguish our hybrid metal-dielectric nanoslits array optical transmission filters from single dielectric cap metal nanoslits optical filters, the transmission curves of the single dielectric cap metal nanoslits optical filters were firstly calculated. Figure 1(a) shows the cross section of the single dielectric cap metal nanoslits optical filter structure which consists of a magnesium fluoride (MgF2) substrate, an array of gold nanoslits with period of p, thickness of t1, and slits width of w, and a homogeneous dielectric cap layer with thickness of t2 on the top. In our simulation, the refractive index of MgF2 was taken to be a constant of 1.38. The electric permittivities of gold were taken from [27]. A finite-difference time-domain (FDTD) software (Lumerical Solutions, Inc.) was used to calculate the transmittance of the structure. The simulation domain was chosen to have periodic boundary conditions in the lateral x-directions. The simulation domain is terminated with a perfect matching layer boundary in the propagation and reflection directions. A plane-wave surface of filter is normally incident to the surface of filter structure with the polarization in the x direction as shown in Fig. 1(a).
Fig. 2. (a) Cross section of dual dielectric cap metal nanoslits optical filter. The optical filter structure is through incorporation of a film layer between the patterned gold and the dielectric layer. The gold gratings have the parameters as listed above, i.e., slits width of 160 nm, thickness of 40 nm, and period of 1000 nm. (b) Simulated transmittance curves from the dual dielectric cap metal nanoslits optical resonance filter for different SiO2 thickness with TiO2 thickness of 300 nm. (c) Spectral linewidth and transmittance as functions of SiO2 thickness. (d) Spectral linewidth and peak wavelength as functions of SiO2 thickness.
A low index of refraction dielectric material (silicon dioxide, SiO2, n=1.45) and high refractive index material (titanium dioxide, TiO2, n=2.74) are chosen as the two dielectric cap layer materials. In the simulations, the gold grating period p is 1000 nm. Slit width w is 160 nm. The gold thickness t1 is 40 nm. Figure 1(b) shows the simulated transmittance spectral curves of the single SiO2 cap layer gold nanoslits optical filters. The SiO2 layer has a thickness of 0, 400, 800, and 1600 nm respectively. When the SiO2 thickness is 0 nm, there is no transmittance peak except for Rayleigh anomaly peak [28]. As the SiO2 thickness is increased until the SiO2 layer can support the fundamental guided mode, a main transmission peak appears. The spectral linewidths of transmission peaks are less than 10 nm. However, the peak wavelengths are close to Rayleigh resonance wavelength. Figure 1(c) shows the simulated transmittance spectral curves from the single TiO2 cap metal nanoslits optical filters. The TiO2 layer has a thickness of 0, 150, 210, and 270 nm respectively. With a high refractive index TiO2 cap layer, the peak transmission wavelength is far away from the Rayleigh wavelength. However, the spectral linewidths are wide. The spectral linewidth is approximately one order of magnitude larger than that of the device with a SiO2 cap layer. Therefore, there is a trade-off between the transmission filter spectral linewidth and the spectral distance from the Rayleigh anomaly wavelength.
Fig. 3. (a) Simulated transmittance curves from the dual dielectric cap metal nanoslits optical filter with different TiO2 thicknesses t3 with a fixed SiO2 thickness t2=240 nm. (b) Spectral linewidth and peak wavelength as functions of TiO2 thickness. (c) Spectral linewidth and transmittance as functions of TiO2 thickness.
Fig. 4. (a) Simulated transmittance versus wavelength from dual dielectric cap metal nanoslits optical filter for different slit widths w. The period p is 1000 nm. Au grating thickness t1 is 40 nm. SiO2 layer thickness t2 is 530 nm. TiO2 layer thickness t3 is 300 nm. (b) Spectral linewidth (black dots), peak transmittance (red diamonds), and peak wavelength (blue triangle dots) as functions of slit width.
To obtain a narrow spectral linewidth optical filter with a peak wavelength far from the Rayleigh anomaly, we propose a hybrid dielectric-metal nanoslits optical filter by combining a low refractive index dielectric layer and a high refractive index dielectric layer, as shown in Fig. 2(a). This dual dielectric cap metal nanoslits optical filter structure consists of a MgF2 substrate, a periodic array of gold nanoslits with period of p, thickness of t1, and slits width of w, a SiO2 layer of thickness of t2 on the top of gold nanoslits, and a TiO2 high refractive index cap layer with thickness of t3 on the top. Firstly, transmittance spectra of devices with different SiO2 thicknesses and a fixed TiO2 layer of thickness t3=300 nm were calculated. In the simulations, the gold nanoslits period p is 1000 nm, the gold nanoslits layer thickness t1 is 40 nm, and nanoslits width w is160 nm. The results are shown in Fig. 2(b). It can be seen in Fig. 2(b) that when no SiO2 layer exists, the transmittance has a wide linewidth resonance peak and a low Rayleigh anomaly peak in the spectrum. The main transmittance peak linewidth is 83 nm and the peak wavelength is 1979nm. By integrating a SiO2 layer between the gold nanoslits and the TiO2 layer, the spectral linewidth is decreased. Figure 2(c) shows a spectral linewidth and peak transmittance versus the SiO2 layer thickness. As the SiO2 layer thickness is increased, spectral linewidth becomes continuously narrower and the transmittance increases slightly. Figure 2(d) shows peak wavelength versus the SiO2 layer thickness. The peak wavelength blue-shifts slightly with increasing SiO2 layer thickness. Thus, in this dual cap metal nanoslits optical resonance filter structure, the incorporation of a SiO2 layer between the gold nanoslits and the high index TiO2 top cap layer can reduce the optical transmission filter spectral linewidth effectively.
Next, the transmittance curves of the dual dielectric cap optical filter structure with different TiO2 thicknesses t3 were simulated while fixing SiO2 thickness t2=240 nm, in Fig. 3(a). The gold grating arrays have the same parameters as listed above. It is seen that there appears no transmission peak without the TiO2 layer (t3=0) except for Rayleigh anomaly peak, because a 240 nm SiO2 layer is too thin to support a guided mode. As the TiO2 thickness is increased until it can support the fundamental mode, a main transmission peak appears. Figure 3(b) plotted the main peak linewidth and the peak wavelength versus the TiO2 layer thickness. It is seen that the linewidth becomes wider for the TiO2 thickness ranges of 0∼400 nm. More importantly, the peak wavelength red-shifts remarkably from the fairly low side peak. Figure 3(c) shows that as the TiO2 thickness is increased, the spectral transmittance also increases. Thus, in this dual cap metal nanoslits optical filter structure, the use of TiO2 layer can make the peak center wavelength far away from the undesired peak about 1380 nm. In addition, it is pointed that when the TiO2 thickness is 400 nm, a new resonance peak near 1410 nm emerges except the main transmission peak and the Rayleigh anomaly peak, as shown in Fig. 3(b). This emerging peak is due to the excitation of a new guided mode for a 400 nm TiO2 waveguide layer. Thus, the TiO2 thickness must be less than 400 nm, which ensures that just one main transmission peak exists in the whole spectral range.
The nanoslits width affects both the transmittance and the spectral linewidth. Wider slits width allows more transmittance, but makes the spectral linewidth wider. Figure 4(a) shows the simulated transmission spectra from dual cap metal nanoslits optical filters with different nanoslits widths. In simulations, the period of gold grating p was set at 1000 nm. Gold nanoslits thickness t1 is 40 nm. The thickness of SiO2 layer t2 is 530 nm. The thickness of TiO2 cap layer t3 is 300 nm. It is clearly seen that as the slit width is increased, the spectral linewidth and the transmittance also increase and the peak wavelength blue-shifts slightly. This is also shown in Fig. 4(b) where the linewidth and peak transmittance versus the slit width are plotted. Additionally, it is observed that a new side lobe at the right side of the main peak emerges as the nanoslits width is increased. Therefore, choosing small slit width can suppress the side lobe.
Fig. 5. (a) Simulated transmittance versus wavelength from dual dielectric cap metal nanoslit optical resonance filter for different gold gratings thickness t1. The period p is 1000 nm. SiO2 layer thickness t2 is 530 nm. TiO2 layer thickness t3 is 300 nm. Slit width w is 160 nm. (b) Spectral linewidth (black dots), peak transmittance (red diamonds), and peak wavelength (blue triangle dots) as functions of gold grating thickness.
Fig. 6. (a) Simulated transmission spectrum from dual dielectric cap gold nanoslit array optical filters with different nanoslits periods. The nanoslit width is fixed as 160 nm. Au grating thickness is 40 nm. SiO2 layer thickness is 530 nm. TiO2 layer thickness is 300 nm. (b) Spectral linewidth and peak transmittance as functions of the slit period. (c) Spectral linewidth and peak wavelength as functions of the slit period.
To investigate the dependence of dual cap metal nanoslits optical filter performance on gold nanoslits grating thickness t1, we calculated the transmittance spectral curve by varying gold nanoslits thickness. Figure 5(a) shows the numerically simulated transmission spectrum from dual dielectric cap metal nanoslits optical filters with different gold gratings thicknesses. The period is 1000 nm. SiO2 layer thickness is 530 nm. TiO2 layer thickness is 300 nm. The slit width is 160 nm. It is seen that two side lobes on both sides of main peak appear. Also, as the gold grating thickness is increased, the left-side lobe decreases and the right-side lobe increases. There is a trade-off between two side lobes. Figure 5(b) shows the spectral linewidth (black dots), peak transmittance (red diamonds), and peak wavelength (blue triangle dots) versus the gold grating thickness. It is seen that varying gold nanoslits thickness has no influence on the peak wavelength. The peak transmittance and spectral linewidth slightly decrease slightly as the gold grating thickness is increased
We also investigated the effect of the nanoslits period on the optical resonance of the dual dielectric cap gold nanoslits array optical filter. Figure 6(a) shows the simulated transmission spectra for dual cap optical filter with different gold slits periods p. Slits width w is 160 nm. Au grating thickness t1 is 40 nm. The thickness of SiO2 nanofilm t2 is 530 nm. The thickness of TiO2 cap layer t3 is 300 nm. Figure 6(b) shows the spectral linewidth and peak transmittance versus the slit period. The black dots show that as the slit period is increased, the spectral linewidth also increases. The red diamonds show the transmission strength first increases with increasing the slit period, then decreases for larger slit period. Figure 6(c) shows peak wavelength as a function of slit period. The position of the transmission peak varies linearly with the periodicity of the slits. The results indicate that the selection of the resonance wavelength can be achieved by changing the gold nanoslits period p.
3 Analysis and discussions
In the dual cap metal-dielectric nanoslits optical filter structure, as shown in Fig. 2(a), the low index of refraction SiO2 layer was placed between the gold nanoslits and the high index TiO2 cap layer. Through coupling of surface plasmon resonance and guided-mode resonance, a narrow linewidth transmission filter with the peak wavelength far from the Rayleigh anomaly can be obtained. Figure 7(a) shows simulated transmittance curves of dual cap gold nanoslits optical filters with different SiO2 layer thicknesses. In the filter structure, the TiO2 layer thickness is 300 nm, nanoslits width is 80 nm, and the gold grating thickness is 40 nm. The period of the nanoslits is 1000 nm. To characterize the performance of metal-dielectric nanoslits optical filters, we define a Figure-of-Merit (FoM) of the nanoslits array filter as
where Δλ1/2 is the full width at the half maximum (FWHM) spectral linewidth, Sd is the spectral distance between the transmission peak wavelength and the Rayleigh anomaly wavelength. A desired nanostructure optical filter should have a large Figure of Merit, i. e., a narrow spectral linewidth with the peak wavelength far away the Rayleigh anomaly. Figure 7(b) shows the spectral linewidth and FoM versus the low index SiO2 layer thickness. As the SiO2 thickness is increased, the peak linewidth becomes narrower and the FoM becomes larger. Table 1 lists the Δλ1/2, Sd, and FoM of the dual dielectric cap optical filters in Fig. 7(a). For comparison, the parameters of single cap optical filters were listed in Table 2. Table 2 lists the results in Figs. 1(b)–1(c). It can be seen that the dual cap metal nanoslits optical filters not only have narrow the linewidths, but also have the transmission peaks far away from the Rayleigh anomaly. It is seen in the Fig. 7(b), the FoM of dual cap metal nanoslits optical filter is 10 times larger than that of single cap nanoslits optical filter in the same wavelength range.Fig. 7. (a) Simulated transmittance curves of dual dielectric cap metal nanoslits optical filters with different SiO2 thicknesses and a fixed TiO2 thickness of 300 nm. The nanoslits width is 80 nm. The gold grating thickness is 40 nm. The slits period is 1000 nm. (b) Spectral linewidth and FoM value versus the SiO2 layer thickness.
To understand why the hybrid metal-dielectric nanoslits optical filters have large FoM values, the electric and magnetic field distributions were calculated at the peak wavelengths of dual dielectric cap metal nanoslits filters with different SiO2 layer thickness. In the structure, TiO2 thickness is 300 nm, the slit width is 80 nm, the gold nanoslits thickness is 40 nm, and the slit period is 1000 nm. The unit cell of the filter structure is included and the black lines indicate the Air/TiO2/SiO2 /Au grating structure/MgF2 substrate. The nanoslit is located in the center of the figure. Firstly, the electromagnetic field distributions of the dual cap optical filter without SiO2 layer (t2 = 0 nm) were calculated at the peak wavelength of 2156 nm, as show in Figs. 8(a)–8(c). Without SiO2 layer, the dual dielectric cap metal nanoslits optical resonance filter structure becomes single dielectric cap optical filter structure. The wide linewidth transmission peak is the coupling between the guide mode resonance and surface plasmon resonance. The refractive index of TiO2 layer (n=2.74) is larger than that of MgF2 (n=1.38), which makes the TiO2 layer act as a waveguide layer. Figures 8(a)–8(b) show the electric field Ex and Ey distributions on the x-y plane at the peak wavelength. It is seen that the electric fields of x- and y-components are mainly located at the interfaces of Air-TiO2 and TiO2-Au. Figure 8(c) shows the magnetic field distributions at the resonance wavelength. It is seen that a strong magnetic field enhancement is confined in TiO2 layer and gold film and is too close to the interface of TiO2-Au. Because the coupled mode profile is close to the gold film, resulting in more electromagnetic energy loss. The peak linewidth is wide. To reduce the peak linewidth, a low refractive index intermediate layer was integrated between the gold nanoslits and TiO2 high refractive index cladding layer. In this dual dielectric cap metal nanoslits optical filter structure, the refractive index of the TiO2 layer is larger than that of the SiO2 layer, which makes the TiO2 layer act as a waveguide layer. Figures 8(d)–8(i) show the calculated electromagnetic field distributions of dual cap optical filters with SiO2 layer (t2 = 150 nm, 300 nm) at their transmittance peak wavelengths. Figures 8(d)–8(e) show the electric field Ex and Ey distributions on the x-y plane of the 150 nm SiO2 intermedia optical filter at the resonance wavelength of 1781.1 nm. It is seen that the electric fields mainly distribute at the interface of Air-TiO2 and TiO2-SiO2. In addition, at the SiO2-Au, the electric field decays exponentially at both sides of the interface and has a largest value at interface, which also means the excitation of evanescent surface plasmon wave and evanescent high-order diffracted waves. At the SiO2-TiO2 interface, there are strong field enhancements, which is due to a strong discontinuity of the electric field [29] in the vertical direction of the boundary. Figure 8(f) shows the magnetic field Hz distribution from the 150 nm SiO2 intermedia optical filter at the resonance wavelength. It shows a predominant magnetic field enhancement distributes in TiO2 dielectric layer, which means the use of SiO2 layer makes the coupled mode profile move away from the metal surface, reducing the electromagnetic energy loss. Figures 8(g)–8(i) show the electric field Ex and Ey distributions on the x-y plane and the magnetic field Hz distribution of the 300 nm SiO2 layer optical filter at the peak wavelength of 1780.7 nm. It is seen that as the SiO2 intermedia thickness is increased, the electromagnetic field enhancement becomes stronger and the electromagnetic field profile is further away from metal surface. This indicates less electromagnetic field energy is located at the gold surface with increasing the SiO2 layer, inducing less the energy loss and narrower peak linewidth.
Fig. 8. The electric field and magnetic distributions of the dual dielectric cap gold slits filters with the SiO2 layer thicknesses of t2=0, 150, 300 nm. (a)-(c) The electric field Ex and Ey distributions on the x-y plane and the magnetic field Hz distribution of the structure without SiO2 layer (t2=0) at the peak wavelength of 2156 nm. (d)-(f) The electric field Ex and Ey distributions and the magnetic field Hz distribution corresponding to SiO2 thickness of 150 nm at the peak wavelength of 1781.1 nm. (g)-(i) The electric field Ex and Ey distributions on the x-y plane and the magnetic field Hz distribution corresponding to SiO2 thickness of 300 nm at the peak transmittance wavelength of 1780.7 nm..
Table 1. Parameters of dual dielectric cap gold nanoslits array optical filters
Table 2. Parameters of single dielectric cap gold nanoslits array optical filters
The explanation for narrow spectral linewidth filter effect is that when a plane electromagnetic wave is incident on the structure, local surface plasmons are excited at the SiO2-gold interface, and are coupled with guided-mode resonance of the structure. Without SiO2 layer, large portion of the electromagnetic energy is in the gold layer, resulting in large energy loss. Therefore, the spectral linewidth is wide. When a SiO2 layer is placed between the gold nanoslits and the top TiO2 cap layer [30,31], a less portion of optical energy exists in the metal layer and the guided mode resonance is dominant, which results in a strong resonance mode and therefore a narrow resonance spectral linewidth. The narrow spectral linewidth is due to the redistribution of the electromagnetic energy caused by the presence of the low refractive index intermediate layers. Since the TiO2 layer has high refractive index and acts as a waveguide layer, the resonance wavelength changes as the TiO2 layer thickness changes to meet the phase matching condition. Thus, the high index of refraction TiO2 cap layer can tune the peak wavelength far away from the Rayleigh anomaly wavelength.
4 Summary
In this work, we investigated a dual dielectric cap layer metal nanoslits optical transmission filter structure. The dual dielectric cap gold nanoslits filter structure has a low refractive index dielectric layer placed between the gold nanoslits array and a high refractive index top cap layer. Simulation results have shown that a narrow spectral linewidth transmission peak far away from the Rayleigh anomaly can be obtained with the dual cap layer metal nanoslits filter structure. We also proposed a figure-of-merit to characterize the performance of the hybrid metal-dielectric nanostructure filter. It is shown that the dual dielectric cap optical filters have significantly large figure-of-merits than that of traditional single cap gold nanoslits array optical filters. It is explained that the spectral linewidth narrowing effect is due to the redistribution of electromagnetic energy caused by the presence of the low refractive index dielectric layer intermediately on top of the gold nanoslits. While the investigation was performed in the near-infrared region, the approach of using dual dielectric cap layers to increase the figure-of-merits is applicable across a wide spectral range by scaling the device parameters.
Funding
National Natural Science Foundation of China (11674062); Fudan -Changguang Basic Research Fund (FC2019-04&06).
Disclosures
The authors declare no conflicts of interest.
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