Free-standing plasmonic metal-dielectric-metal bandpass filter with high transmission efficiency

Plasmonic spectrum filtering devices based on metallic nanostructures have attracted wide attention due to their good reliability, ease of fabrication, and wideband tunability. However, the presence of thick substrate significantly limits the structure’s longitudinal size for further optoelectronic integration and reduces the devices’ performance. Here we propose and demonstrate an ultra-thin plasmonic bandpass filter based on free-standing periodic metal-dielectric-metal stack geometry working in the near-infrared wavelength range. The coupling between free-space electromagnetic waves and spatially confined plasmonic modes in the designed structure is systematically investigated. As demonstrated in the calculation and experiment, the free-standing plasmonic filters have more than 90% transmission efficiency and superior angular tolerance. The experimental results are in good agreement with the theoretical calculations. These artificial nanostructured filtering devices may find potential applications in the extremely compact device architectures.

. Plasmonic bandpass filter constructed by free-standing MDM stack array. (a) Schematic diagram of the free-standing MDM stack array. The Si 3 N 4 dielectric layer is sandwiched in between Au layers. The periodicity (P) and slit width (L) of the array is 1000 nm and 250 nm. The thickness of Si 3 N 4 dielectric layer and Au layers is 250 nm and 90 nm, respectively. (b) Scanning electron microscopy images of the fabricated device. Scale bar, 4 μm. Inset shows magnified cross-section view. Scale bar, 500 nm. (c) Comparison of calculated transmission spectra for the free-standing structure and the structure with substrate. Calculated transmission diagrams as a function of incident angle and wavelength for (d) the free-standing MDM stack array, (e) the freestanding single layer metallic grating, and (f) the MDM stack array with substrate. spectra of MDM stack array with (solid blue line) and without substrate (solid red line). There are three main differences between two spectra: First, compared to that of the free-standing structure, the wavelength λ R of transmission peak of the substrate structure has an obvious redshift. In other words, to achieve the same transmission peak, array periodicity of substrate structure is smaller than that of free-standing structure, which increases the difficulty of experiment preparation. Second, for substrate structure, there is another small transmission peak in the wavelength range from 1100 nm to 1460 nm as the by-product of structure design, which is resulted from asymmetric coupling from the substrate. Last but not least, compared with the transmission efficiency about 70% from the substrate structure, the free-standing structure has more than 90% transmission efficiency at the peak.
Besides high transmission efficiency, the free-standing MDM stack array also shows a good angular tolerance. Figure 1d presents the angle-resolved transmission spectra for free-standing MDM stack array. When the incident angle increases from 0° to 20°, the transmission peak always keeps high transmission efficiency and the wavelength of transmission peak changes from 1462 nm to 1408 nm. The angular tolerance of transmission peak is defined as the wavelength shift respect to incident angle changes. The smaller angular tolerance is better. Therefore, the angular tolerance of transmission peak is 2.7 nm per degree. As comparisons, here we also calculate the angle-resolved transmission spectra for the free-standing single layer metallic grating structure (Fig. 1e) and the MDM stack array with substrate (Fig. 1f). It can be clearly seen that for the free-standing single layer metallic grating structure, although the transmission efficiency is also high in the incident angle range from 0° to 20°, the angular tolerance of transmission peak is much worse (5.4 nm per degree). For the MDM stack array with substrate, the efficiency of transmission peak is lower and the range of angular tolerance is narrower (about from −5° to 5°) because of asymmetric coupling and the appearance of new transmission dips and peaks from the substrate. Compared to the above two structures, the free-standing MDM stack array has a superior angular tolerance and keeps high transmission efficiency, which is very important for the development of practical devices.
To investigate the dependence of wavelength position of transmission peak on periodicity P and slit width L, the transmission spectra with different P and L are depicted in Fig. 2. The left column in Fig. 2a and b is calculated from the numerical simulations (see Methods), while the right column shows the experimental results. We can see that the efficiency of transmission peak is more than 90% in the designed free-standing structure. The wavelength of transmission peak exhibits a redshift with the structure periodicity ranging from 800 to 1100 nm with fixed slit width L = 250 nm, and has a blue-shift as slit width L increases from 180 nm to 400 nm with fixed P = 1000 nm. The wavelength position of transmission peak has a good agreement between numerical simulations and experiment. Compare to the calculated transmission spectra, the experimental curves in Fig. 2 have some additional transmission peaks at long wavelength range or short wavelength range, and transmission peaks have wider bandwidth. This is because theoretical curves are calculated under normal incidence. However, in the experiment, a lens with a numerical aperture (NA) of 0.2 is used for focusing the incident light into sample surface, which means that our experiment curves are cumulative data from incident angle range from 0° to 12°. As shown in Fig. 1(d), we can see clearly that when incident angle increases gradually, the additional peaks appear at the long wavelength range or short wavelength range. These peaks would disappear under normal incidence.
In order to better explain the origin of spectrum filtering effect, the normalized magnetic field intensity (color map) and electric displacement (arrow map) in one unit-cell corresponding to the wavelength of 1462 nm under normal incidence are shown in Fig. 3a. The periodicity P and slit width L is 1000 nm and 250 nm, respectively. The magnetic field intensity shows that most of incident energy is localized both within the MDM waveguide layer and the air slit. On one hand, inside the MDM waveguide layer, the antisymmetric waveguide modes is formed along the x direction 30 , which is characterized by maximum magnetic intensity near the edges of top and bottom Au grating. Electric displacement represented by the black arrows in the top and bottom metallic gratings are opposite to each other and forms a loop, which generates a significant magnetic response. So MDM waveguide modes along x direction can be also considered as the magnetic dipole. The excitation of magnetic dipole in the designed structure increases the capacity of angular tolerance 31 . Figure 3b depicts corresponding electromagnetic field distribution at the wavelength 1412 nm with incident angle 15°. Although incident angle increases from 0° to 15°, MDM waveguide mode along the x direction remains nearly the same. However, for the free-standing metallic grating, significant magnetic response cannot be formed (Fig. 2c), which results in poor angular tolerance. On the other hand, the antisymmetric mode in the air slit is formed along the y direction. Compared to that in the MDM waveguide layer, this is a truncated mode. Here, the antisymmetric mode in the air slit is named as the cavity mode to distinguish that of MDM waveguide layer. In addition, this mode in the air slit can be considered as a Fabry-Perot cavity that possesses two mirrors of finite reflection at the end of the slit. Due to the symmetry structure with respect to a vertical mirror, the cavity mode bisects the middle section of slit [32][33][34][35] . The formation of cavity mode in the air slit leads to high transmission. The main difference of above two resonant modes is the direction of propagation, and the interaction of these two modes results in the generation of transmission peak in the free-standing MDM stack array. Figure 3d shows the charge distribution in one unit-cell corresponding to the wavelength of 1462 nm. The charge distribution along x direction of MDM waveguide layer and y direction of air slit is nearly identical, which further verifies the existence of two antisymmetric modes in the structure.
Furthermore, the shift of transmission peak in Fig. 2 can be explained qualitatively by using waveguide mode along the x direction. For the case with fixed air slit width but increasing the stack periodicity, the effective permittivity of the waveguide layer in MDM stack array increases, resulting in a redshift of the transmission wavelength based on three-layer waveguide theory 36 . On the other side, for the case with fixed stack periodicity but increasing air slit width, the effective permittivity of the waveguide layer in MDM stack array decreases, resulting in a blue-shift of the transmission wavelength.
Narrow-band plasmonic filter based on the free-standing dual-slit MDM stack array. For above designed MDM structure, it is difficult to obtain a narrow transmission peak just by changing structural parameters. To circumvent this problem, here we present a dual-slit MDM stack geometry, as shown in Fig. 4a. This structure can be fabricated by piercing another set of narrow slits all the way through the MDM stack film. Figure 4b shows the oblique view SEM image of the fabricated dual-slit MDM stack array. The periodicity P and slit width L of the MDM array is 1000 nm and 250 nm. The width of second slit W in the middle of MDM stack is 80 nm. Calculated transmission spectrum of the dual-slit structure is depicted in Fig. 4c. The transmission peak has a ~64 nm full width at half maximum (FWHM), which is narrower than ~156 nm FWHM of transmission peak in the single-slit MDM structure. Compared to that of single-slit MDM structure, the efficiency of transmission peak for the dual-slit MDM structure is a little lower but still more than 80%. Figure 4d shows experimentally measured transmission spectrum of the dual-slit structure. The FWHM of transmission peak is ~150 nm, wider than that of the numerical simulations, but narrower than experiment result of single-slit structure (~241 nm) shown in Fig. 2. The difference between numerical simulations and experiment results can be attributed to three reasons: First, the dielectric permittivity of Au and Si 3 N 4 layers used in the numerical simulations has a little different from that in experiment. Second, there are the inevitable roughness of structure surface and imperfect fabrication process. Third, the microscope objective with a non-zero numerical aperture in the experiment measurement brings oblique incidence, widening the line shape of transmission peak and introducing additional transmission peaks. Figure 5a presents transmission spectra under different incident angles in the dual-slit MDM structure. The wavelength position 1454 nm of transmission has a little change and keeps high transmission efficiency in the incident angle ranging from −20° to 20°. It is noteworthy that the transmission peak of dual-slit MDM structure keeps narrow bandwidth. Due to similarity between Fig. 5a and Fig. 1d, we infer that the physical mechanism of transmission peak in the dual-slit structure is nearly identical to that of single-slit structure. The calculated electromagnetic field distribution at the transmission peak shown in Fig. 5b verifies above viewpoint. The electromagnetic field distribution in Fig. 5b is almost identical to that in Fig. 3a. The only difference is that second slit affecting the antisymmetric mode of MDM stack array and decreasing the effective permittivity of the waveguide  Fig. 1(a). Other structure parameters are identical to that in Fig. 1(a)  layer, which is the reason why the wavelength of transmission peak has a small blue-shift in comparison to that of single-slit MDM structure.
Next, we perform the numerical simulations to investigate the relationship between the slit width W and the transmission spectrum, as shown in Fig. 6a. We find that there are two transmission minimum strips in the wavelength range from 1100 to 1900 nm when slit width W is larger than 35 nm. To better illustrate these transmission minimum strips, the results in Fig. 6a are converted into logarithmic scale and shown in Fig. 6b. Clearly, as the slit width W increases, the transmission minimum strip at longer wavelength has an obvious blue-shift while the transmission minimum strip at shorter wavelength doesn't change much, which makes the bandwidth of transmission peak become narrower. Therefore, the appearance and shift of the transmission minimum strip is the reason for narrowing the transmission bandwidth in the dual-slit structure. Furthermore, as shown in theoretical curve of Fig. 2b, as the slit width decreases, bandwidth of transmission peak reduces gradually. Dual-slit MDM structure integrates two sets of single slit structures with different slit width. Compared to that of single-slit MDM structure, dual-slit MDM structure possesses the spectral characteristics of the structure with narrow slit width. Therefore, dual-slit array could provider a narrow bandwidth than the single slit case. This is another reason for narrow bandwidth of transmission peak for dual-slit MDM structure.
In order to investigate the physical origin of the generation of transmission minimum strips, the calculated magnetic field intensity (color map) and electric displacement (arrow map) with slit width W = 80 nm are given in Figs. 6c and 6d, respectively, corresponding to the transmission minimum wavelengths D 1 and D 2 shown in Fig. 6b. At the transmission minimum wavelength D 1 , we can see that the magnetic field is mainly localized on the upper surface of the metallic grating which is attributed to the excitation of SP on the upper surface induced by grating structure. The SP excitation condition of the metallic grating is defined as 37,38 where λ is the incident light wavelength, n is diffraction order, θ is the incident angle, P is the grating periodicity, and ε d and ε m stand for the permittivity of dielectric and metal. On the upper surface of structure, there is a wave crest for magnetic field distribution in one unite cell, corresponding to 1st order of SP mode (n = 1 in Eq. 1). However, the existence of additional slit makes the localized electromagnetic field on the upper surface of structure leak into MDM waveguide layer, which results in the excitation of 2nd order SP mode on the upper surface of bottom Au grating, where there are two wave crests for magnetic field distribution in one unite cell. The SP modes propagating along the two upper surfaces of the Au grating eventually reflects the incident light in the backward direction, which reduces the transmission close to zero. At the transmission minimum wavelength D 2 , we can see that strong magnetic fields are localized in MDM waveguide layer and electric displacement forms a loop, which means that antisymmetric waveguide mode is formed along the x direction in the MDM waveguide layer. Different from the single-slit MDM structure shown in Fig. 3a, here the SP modes inside the MDM structure induced by the second slit would interfere with the cavity mode. At the transmission minimum wavelength D 2 , the destructive interference occurs at the slit exit and so that significantly suppresses the optical transmission.

Conclusions
High performance and ultracompact size are two important features for the next generation photonic components. In the previous reports [23][24][25][26] , the existence of structure substrate not only degrades device's performance, but also remains the longitudinal thickness of device in the range of a few hundreds of micrometers, which significantly limits device's integration. Here, our designed plasmonic device has a longitudinal thickness a few hundreds of nanometers, 2-3 orders of magnitude thinner than that of reported filters, which is very attractive for the design of ultracompact integrated optoelectronics system.
In summary, we propose and experimentally demonstrate a new type of ultra-thin plasmonic bandpass filter based on the free-standing MDM stack array. Compared with conventional plasmonic devices, this filter has higher transmission efficiency and better angular tolerance. Moreover, the bandwidth of transmission peak can be further tuned by introducing the dual-slit geometry. Due to its good spectral filtering performance, the proposed device is a potential candidate for developing a high performance photonic platform for near-infrared spectral imaging system. The design principle can also be easily expanded to other wavelength ranges for multispectral applications.

Methods
Numerical simulations. The simulations are performed by using a commercial software (FDTD solutions, Lumerical Solutions) based on FDTD algorithm to obtain the transmission spectra, magnetic field distribution and electric displacement distribution of the free-standing MDM stack array. At the normal incidence, the periodic boundary conditions are applied in x direction and perfectly matched layers are used in z direction. However, the bloch boundary conditions need to be applied in x direction under condition of oblique incidence. The grid size in the x and y direction is 1 × 1 nm, respectively, in order to satisfy the integer number of grid in simulation region. The dielectric permittivity of bulk gold in the near-infrared region is from Johnson and Christy 39 , and the refractive index of the Si 3 N 4 waveguide layer is 2. All the sizes are set according to the measured ones from the SEM images.
The preparation and measurement of free-standing MDM stack array. Structures are fabricated on a commercially available 250-nm-thick Si 3 N 4 membrane with a 3 × 3 mm window opened in the silicon layer. A 3-nm Ti film and a 90-nm Au film are e-beam evaporated sequentially onto the front and back sides, respectively. The deposition rate for Ti and Au is R Ti ≈ 0.016 nm s −1 and R Au ≈ 0.02 nm s −1 , respectively. Then, subwavelength gratings are fabricated by FIB milling using a dual-beam (FIB/SEM) system (Ga + ions, 24 pA beam current, 30 k eV beam energy). To prevent the Au from water in the air, we store the samples in a nitrogen gas holder before measurement. All transmission spectra are measured by using a commercial microspectrometer (PV20/30 from CRAIC Technologies). A lens with a numerical aperture about 0.2 is used for focusing the incident light onto the sample surface. Transmission light is collected using a 20× microscope objective with a numerical aperture of 0.45. Measurement area is set to an area of roughly 13 × 13 μm 2 .