A metal-dielectric subwavelength grating structure was investigated for making single-peak narrow linewidth optical reflection filters in the near-infrared region. The subwavelength grating filter structure consists of a one-dimensional periodic array of metal (gold) and dielectric (Al2O3) elements on a dielectric substrate. Optimized reflection filters have a single reflection peak with ~10 nm linewidth in the infrared region over a wide spectral band. Finite-difference time-domain (FDTD) simulations and multipole analysis show that the narrow linewidth reflection is due to the coupling of the Rayleigh anomaly wave to the quadrupole plasmon resonance mode of the subwavelength metal-dielectric grating. Additionally, it was found that the contrast of the indices of refraction of two dielectric materials in the subwavelength structure is critical for realizing optical filter effect.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Optical filters are traditionally made of thin film layer structures. Alternatively, optical filters can also be made of subwavelength grating structures by taking advantage of surface resonance modes such as guided-mode-resonance (GMR) [1–4] and surface plasmon resonance [5–7]. Compared with thin film filters, subwavelength surface structure filters have the advantage of controlling the spatial variation of filters. GMR filters rely on excitation of guided mode resonance along the surface with subwavelength dielectric gratings for achieving narrow linewidth spectral filtering [8–13]. However, GMR filters typically have multiple transmission or reflection peaks over wide spectral ranges. Metal structure plasmonic filters suffer from the same issue. Additionally, plasmonic filters typically have wide spectral linewidths due to strong optical absorption in metals.
In this work, we propose a new metal-dielectric subwavelength grating structure for realizing single-peak narrow band optical reflection filters. The subwavelength grating structure consists of an array of two parallel metal lines separated by two dielectric spacers. The incident light excites the Rayleigh anomaly wave and the Rayleigh anomaly wave couples to the quadrupole resonance mode of the two metal elements in each unit cell. The quadrupole resonance mode is a non-radiative plasmon resonance mode that has higher quality resonance factor compared with the dipole resonance mode, thus contributing to the narrow filter linewidth.
2. Device structure and simulation results
Figure 1(a) illustrates the structure of the subwavelength grating reflection filter. The structure consists of a one-dimensional periodic array of metal and dielectric elements on a dielectric substrate. The metal-dielectric grating structure consists of Au/dielectric-one/Au/dielectric-two in each unit cell with the grating height h. The period of the subwavelength grating Λ is14, 15]. A finite-difference time-domain (FDTD) software (Lumerical Solutions, Inc.) was used for the simulations . The simulation domain was a two-dimensional region with 2 nm mesh resolution. Periodic boundaries were used for normal incidence and Bloch boundaries were used for oblique incidence.
Figure 1(b) shows the calculated reflectance and transmittance spectra of a designed filter which has the structure parameters of Λ = 1100 nm, w1 = 450 nm, w2 = 450 nm, and h = 270 nm. It can be seen that the reflection has a single peak at 1915 nm wavelength over a wide spectral range from 1000 nm to 5000 nm. Considering that the index of refraction of Al2O3 in near infrared region is n = 1.74, the reflection wavelength is close to the Rayleigh anomaly wavelength . The inset in Fig. 1(b) shows that the peak reflectance is 83.5% at 1915 nm wavelength and the full-width at the half-maximum (FWHM) linewidth of the filter is 10 nm.
To investigate how the index of refraction of the dielectric materials affects the reflection spectrum, we calculated the reflectance by independently varying the refractive indices of two dielectric materials. The results are shown in Fig. 2. Figure 2(a) is the 2D plot of reflectance versus the wavelength and the index of refraction of the dielectric-1 while the dielectric-2 is set as the air. The index of refraction of dielectric-1 varies from 1.0 to 3.5. Figure 2(b) is the 2D plot of reflectance versus the wavelength and the index of refraction of the dielectric-2 while the dielectric-1 is Al2O3. It can be seen that the range of the reflection peak wavelength in Fig. 2(a) is larger than that in Fig. 2(b) although the simulated refractive index range of two dielectrics are the same. This is because the change of dielectric-1 also changes the refractive index of the substrate as the two materials are set to the same in calculations. In Fig. 2(a), a quasi-linear redshift of the reflection peak wavelength with the increase of refractive index is observed, which is mainly due to the Rayleigh anomaly caused by subwavelength grating. From Fig. 2(b), it is seen that the reflection peak vanishes when the refractive indices of two dielectric materials are equal. Increase of the index-contrast results in the increase of the linewidth and also increases the peak reflectance. This indicates that the contrast of the refractive indices of two dielectrics is critical for having large reflection peak.
We also calculated the reflectance of the filter by varying the structure parameters. The widths of two dielectric materials w1 and w2 are set equal in our calculations. Reflection spectra at different metal widths wAu are not shown in this paper because our simulations show that the spectrum of the filter doesn’t change significantly with the change of wAu in the range from 100 nm to 200 nm. Figure 3(a) shows the 2D plot of reflectance versus wavelength for different grating height h. Figure 3(b) shows the reflectance spectra selected from Fig. 3(a). A cut-off reflection wavelength at 1915 nm is seen in Fig. 3(a). The reflection peak occurs in the region of wavelength greater than 1915 nm, which corresponds to the first order Rayleigh anomaly. This is due to the coupling between the localized surface plasmon resonance mode and the evanescent diffraction grating mode. Therefore, the resonance wavelength is longer than the Rayleigh anomaly wavelength [18, 19]. The reflection peak wavelength redshifts when the grating height h increases due to the redshift of LSPR. The linewidth becomes narrower when the peak wavelength is close to the Rayleigh anomaly wavelength. Similar phenomena was also reported previously . The resonance spectrum becomes broader and similar to the broadband LSPR curve with increasing height h . Figures 3(c) and 3(d) show the reflectance spectra with different period Λ. We can see that the reflection peak wavelength is quasi-linearly dependent on Λ and is close to the Rayleigh anomaly wavelength. The reflection filter linewidth decreases as the period Λ increases, and the filter effect vanishes when Λ becomes large. This is because Λ limits the minimum of the coupling wavelength while h is kept as a constant of 270 nm. When the Rayleigh anomaly wavelength becomes longer than LSPR wavelength, the reflection peak disappears. The simulation results indicate that with given materials, a narrow linewidth filter with any peak wavelength can be realized by adjusting the height h and the period Λ of the subwavelength grating structure.
We also investigated the effect of the ratio of the widths of two dielectric materials (Al2O3 and air). Here, we define the ratio of the widths of two dielectrics width as γ = w1/ w2, and set the grating period Λ at 1100 nm as a constant. Figure 4(a) shows the calculated reflection spectra by varying the width ratio γ, where the grating height h is set at 270 nm in the calculations. It can be seen that the peak wavelength stays almost unchanged when γ changes. The reflection peak vanishes gradually when γ becomes too large or too small. Same calculations were carried out for different grating heights. Figures 4(b) to 4(d) show the calculated reflectance versus γ for h equals to 300 nm, 350 nm, and 400 nm, respectively. It can be seen that all reflection peaks are in the wavelength region longer than the Rayleigh anomaly wavelength. The minimum reflection wavelength of the filter is limited by the period, which agrees well with the result in Fig. 3. The peak wavelength strongly depends on the value of γ. The maximum of the peak wavelength occurs around γ = 0.8. It is because Au arrays are arranged in pairs in the unit cell. When γ is large, Al2O3 element will be the environment medium and the volume of Au/Air/Au is small. Smaller γ leads to smaller volume of Au/Al2O3/Au and shorter plasmon resonance wavelength. The maximum peak wavelength is 1917 nm, 1948 nm, 2049 nm, 2174 nm for h = 270 nm, 300 nm, 350 nm, 400 nm, respectively. Indicating the maximum wavelength is limited by grating height.
From Fig. 4, it can be seen that a narrow linewidth filter at peak wavelength of 1915 nm can be realized with any grating height h in the range between 270 nm and 350 nm by varying the width ratio γ of two dielectric materials. Filters of different peak wavelengths can be designed by changing the period Λ and the ratio γ with a fixed grating height h. This property expands the design space of this structure. Figure 4(e) shows that narrow linewidth filters with peak wavelength from 1800 nm to 2300 nm can be designed by adjusting Λ and γ while keeping the same grating height. It shows that spatially varying optical filters can be made on a wafer substrate without varying the height of the subwavelength structure. It is also noticed that the wavelength of the filter is close to the Rayleigh anomaly wavelength. The period Λ of the filter can be calculated from the Rayleigh anomaly condition. If the grating height h is fixed, then adjust the ratio γ to find optimized parameters. If the width ratio γ is fixed, then change the grating height h to narrow the reflection linewidth.
Angular dependence is important to optical filters. At different angles of incidence, we calculated the reflectance spectrum of filters with different grating height h. The simulation results are shown in Fig. 5. It can be seen that with a given period Λ, the angular performance of the reflection filter is highly dependent on the height h. The angular tolerance is less than 0.5° for h = 270 nm and larger than 30° for h = 400 nm. Unlike typical Rayleigh grating, the reflection peak of the filter here doesn’t split under oblique incidence [22, 23]. This indicates that besides the Rayleigh anomaly, the reflection peak should also meet the additional surface plasmon resonance condition. The reflection peak wavelength redshifts as the angle of incidence increases. This is attributed to the increase of Rayleigh anomaly wavelength when the angle of incidence increases.
3. Theory and analysis
To understand the narrow linewidth filter property, we calculated the electric and magnetic field distributions at the resonance wavelength of 1915 nm and at a none-resonance wavelength of 1850 nm of the filter in Fig. 1(b). As illustrated in Figs. 6(a)-6(d), the unit cell of the filter is included and the white dash line indicates the Air/Au/Al2O3/Au grating structure. A strong electric quadrupole mode resonance occurs at 1915 nm wavelength. And a strong electric dipole resonance is also observed on the top of the grating structure. These resonant modes are excited because the strong field enhancement of localized surface plasmon resonance. The LSPR mode can be analyzed to determine the distributions of electric and magnetic fields inside the structure as well as in the near and far-fields . We use the multipole moment analysis to evaluate the contributions of different moments [24–26]. The multipole electromagnetic moments are the electric dipole (ED) moment p, the magnetic dipole (MD) moment m, and the electric quadrupole (EQ) moment [27, 28] as followingEqs. (2-4), the multipole moments were obtained. Since the incident excitation light is polarized in the x-direction and propagate in the z-direction, the x component of the electric dipole moment px is dominant . The magnetic dipole moment only has y component my and the electric quadrupole (ED) moment is 3x3 tensor which only has two non-zero components of Qxz and Qzx (Qzx = Qxz) in this configuration. Figure 6(e) shows the calculated spectra of MD moment my and EQ moment Qzx at the peak reflection wavelength of 1915 nm. It is noticed that the spectral curves of my and Qzx have similar shapes and both reach to the maximum at the peak reflection wavelength approximately. This is because the structure is one-dimensional grating. The electric quadrupole is solely consisting of two electric dipoles. The configuration of the electric quadrupole (ED) is similar with the circular displacement current configuration of a magnetic dipole. The electric quadrupole resonance mode is a none-radiative mode with small radiation loss. Figure 6(f) shows the calculated electric dipole moment spectrum plotted together with the reflection spectrum. A sharp electric dipole resonance is observed near the reflection peak wavelength. The ED moment is radiative, which contributes to the peak reflection and the filter property. For the grating height h = 270 nm and width ratio γ = 1, the quadruple mode resonance can be excited by LSPR. And the Rayleigh anomaly condition is also satisfied with period Λ = 1100 nm. Therefore the filter has a narrow spectral linewidth.
It was discussed earlier in Fig. 2(b) that the reflection peak vanishes when the contrast of the indices of refraction of dielectric materials disappears as indicated by the white dash line. This can be explained with the electromagnetic field distributions shown in Figs. 6(a) and 6(c). Figure 6(a) shows the distributions of electric field and displacement current at the peak reflection wavelength of 1915 nm. Figure 6(c) shows the distributions of electric field and displacement current at a non-resonance wavelength of 1850 nm. The displacement currents in Al2O3 and air are out of phase at the resonance wavelength. The total ED moment cancels out when the two dielectric materials are same, which results in zero far-field radiation. Therefore, the contrast of the indices of refraction plays a critical role for this type of optical filters.
Previously, optical filters due to the coupling of Rayleigh anomaly to plasmonic dipole mode resonance have been investigated [29, 30]. In this work, the narrow band filter property is attributed to the coupling of Rayleigh anomaly to the high-order quadrupole plasmon resonance mode. Upon normal incidence, Rayleigh anomaly wave excites the quadrupole surface plasmon resonance as the Rayleigh anomaly wave propagates along the substrate surface. The quadrupole plasmon resonance creates an overall dipole resonance in the subwavelength structure due to the contrast of the dielectric constants of the two dielectric materials. As illustrated in Figs. 6 (a) and 6(c), the electric and magnetic fields at the peak reflection wavelength are much stronger than that at the non-resonance, indicating that strong local surface plasmon resonance is excited. Since the quadrupole plasmon resonance system has less radiative energy loss than the dipole plasmon resonance systems, the optical filters based on quadruple plasmon resonance have narrow spectral linewidths.
In summary, we investigated a new type of narrow linewidth optical filters based on a hybrid metal-dielectric subwavelength grating structure. Designed filters have a single reflection peak of narrow linewidth over a wide spectral range in the near-infrared region. The narrow linewidth resonance is due to the coupling of Rayleigh anomaly wave to the quadruple localized surface plasmon resonance mode. The dielectric contrast plays a critical role in forming a high electric dipole component for high reflectance at the peak reflection wavelength. Numerical simulations of filter structures with different geometric parameters show that the reflection peak wavelength can be tuned by varying the ratio of two dielectric materials and the grating period. The choice of two dielectric materials is flexible as long as they have a large contrast of indices of refraction. The investigated narrow linewidth filters can be used for many applications related to optical spectroscopy measurement.
National Science Foundation (award no. 1158862); National Natural Science Foundation of China (award no.11674062).
The work was conducted while Z. Wang was a visiting Ph.D. student at the University of Alabama in Huntsville. Z. Wang and R. Zhang acknowledge the support from the China Scholarship Council (201606100168 and 201606100277).
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