An optical filter, having a maximum transmission of 71% at single mode, with salient out-of-band rejection is designed with a combination of corrugated waveguide and nano-disk resonators. Plasmonic resonances of different bandwidths adjusted at different wavelengths have been achieved by varying the structural parameters (waveguide width, coupling gap, and resonator dimensions). Finally, a combined integrated structure is proposed as an optical filter for exciting multiple modes, which can extend the operating wavelength range (max. 2200 nm). The resonance wavelength and bandwidth of this filter can be adjusted further by tailoring the structural geometry, paving the way for highly efficient and compact optical devices and sensors.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Surface plasmon polaritons (SPPs), having the ability to manipulate light at subwavelength level and conquering the classical diffraction limit have gained significant attention in recent times. This concept proves to be particularly valuable to plethora of applications ranging from optics , data storage , plasmonic sensing [3,4], to solar cells  and biosensors . SPPs are generated along the metal- dielectric interfaces with field components decaying exponentially with distance off the boundary. These electromagnetic waves are generated from the interaction between free electrons in the metal oscillating in resonance with electromagnetic fields in dielectrics . Waveguide structures based on SPPs include metal-insulator-metal (MIM) and insulator-metal-insulator (IMI) structures. Planar SPP IMI (insulator-metal-insulator) waveguides lack the ability to confine light; however, MIM (metal-insulator-metal) waveguides show efficient coupling with considerable propagation length providing possibilities for designing optical devices with smaller size and high degree of confinement [8,9]. For subwavelength confinement, addition of grooves on the waveguide benefits over planar waveguide due to efficient light-momentum coupling. Photonic metallic structures based on SPPs offer framework for the exploration of nano-optical devices such as demultiplexers, switches, sensors, optical amplifiers, modulators, splitters, optical couplers, resonators and filters [10–20].
In recent years, optical filters, based on MIM waveguides, have become one of the most prominent components of machine vision systems, fluorescent microscopy, wavelength division multiplexing (WDM) and telecommunication applications. Among the passband types, the MIM structure filters can be divided into narrow-band band-stop type, narrow-band band-pass type, flat-top band-pass type, and flat-bottom band-stop type categories. For multispectral applications, Liang et al.  proposed free-standing periodic metal-dielectric-metal (MDM) stack geometry that was used to design ultra-thin near-infrared filter with high transmission efficiency. Gao et al.  designed a novel non-porous composite grating array with anomalous transmission to get high-performance plasmonic filter with a narrower line width by using the coupling of different propagation-type SPPs. Plasmonic bandpass filter and band stop filter using MIM waveguide used to realize multifunctionalities was designed in [23–27]. Plasmonic optical filters (PFs) have also been explored using circular and ring shaped nano-resonator [18,28], circular ring cavity (CRC) , CRC with elliptical core , square ring cavity  and hexagonal ring cavity . However, most structures showed inherent multi-mode property and lacked tunability of resonance wavelength. In , hexagonal nano-resonator (HNR) is reported showing resonance transmittance mode at higher wavelength. Despite having better performance, this design suffers from complex nanofabrication process. To realize a simple PF design, while achieving high performance, rectangular nano-resonator (RNR) can be a good candidate. RNR has certain minimum requirements for critical dimension uniformity and corrugated MIM waveguide rather than simple waveguide shows the flexibility to control the cutoff frequency shift providing efficient filtering and de-multiplexing properties.
In this paper, we propose a novel single mode plasmonic filter which is based on corrugated MIM waveguide coupled to RNR. The design has been optimized by varying parameters (length, width and spacing) to control the change of peak wavelength, maximum transmission, and bandwidth of the resonance spectrum. By optimizing structural parameters, the proposed filter is ideal for multispectral filtering applications. A cascaded design, combining simple and corrugated waveguide (CW), both coupled to their respective RNRs, is also explored. The cascaded structure provides dual modes and extended alteration property of resonance wavelengths.
2. Filter design and simulation setup
To design a plasmonic filter, combination of MIM (silver-air-silver) corrugated waveguide and RNR have been used. A two-dimensional geometry of the proposed structure is implemented considering continuous along z axis (see Fig. 1(a)). The TM polarized broadband light having near infrared wavelength range (750 - 2500 nm) is illuminated at input port (IN) (Fig. 1). We chose an inward grating profile for the corrugated waveguide since such slow wave periodic design can strongly couple the surface wave along the interface. For the design, the width of the waveguide, Wg is apodized gradually along the propagation length, l, which is referred to as the gradient corrugated waveguide in this paper. The varying depth of the corrugation on both silver-air interface is designed to increase by 5 nm than that of the previous one till the maximum depth of grating, d, is achieved. The width of the corrugation is defined as the period, S. The output waveguide is the mirror of the input one.
To consider the dispersion properties of the materials firstly the relative permittivity (εd) of air is set to 1. Permittivity of silver is characterized using  six-pole Lorentz-Drude model (LDM) [as in Eq. (1)],
The dielectric air grating couple the electromagnetic excitation to the nano-disk resonator. Light coupling and mode excitation from the rectangular waveguide to rectangular disk strongly depend on the gap width, g. The dimensions (width, Wg, maximum depth of grating d, and period of grating, S) of waveguides are optimized to ensure efficient coupling of SPP modes at the interface of silver and air grating. The performance of the corrugated waveguide based RNR (CWRNR) is numerically analyzed using an in house 2D Finite Difference Time Domain (FDTD) method-based software. Since only the effects of SPP at the metal dielectric interface are being observed here therefore in the 2D model, effect of substrate has not been considered in the simulation domain. It has also significantly reduced computational burden. The transmission efficiency is defined as ,36], as the following,
3. Performance optimization and analysis
To enable this integrated design of waveguide and RNR, firstly a comparative analysis is made among rectangular waveguide, corrugated waveguide and the combined MIM structures of waveguide and RNR, as shown in Fig. 2. With the help of a corrugated structure, we can control the cutoff frequency of the filter , which is not possible using simple waveguide in such a wide range. By changing the geometrical parameters of corrugated waveguide like maximum depth of grating, d and grating period, S, shown in Fig. 2(a) and (b) respectively, we can estimate higher order SP resonance mode of a band pass filter (BPF). From the analysis using these waveguide-based filters, it is apparent that at d = 40 nm, corrugated waveguide offers least noise while suppressing the higher order modes. For simple waveguide, SPs have inherent short lifetime due to the damped electron oscillation effects and create a broadband of resonance spectrum, whereas grating in the corrugated one ensures single mode SP resonance with increased transmission. Having this consideration, later S is varied from 5 nm to 25 nm with maximum d fixed to 40 nm. As in Fig. 2(b), (S) = 15 nm clearly ensures smooth transmission curve at almost same bandwidth. Transmission characteristics of the RNR coupled to corrugated waveguide (CWRNR) is also compared with RNR of same dimensions coupled to a simple waveguide (SWRNR) in Fig. 2(c). The transmission profile for the SWRNR clearly shows dual mode property, whereas the CWRNR has only single mode with 17% increase in transmission at the near infrared wavelength range than SWRNR. Next, we investigate the effect of the gap, g, between corrugated waveguide and RNR, by varying it from 5 nm to 25 nm, with L = 450 nm and W = 400 nm (as in Fig. 2(d)). It is observed that by reducing g, the coupling between the waveguide and RNR gets stronger and transmission increases. When g increases, full width at half maximum (FWHM) corresponding to half of its maximum amplitude is decreased, resulting in a high Q-factor at the expense of a lower transmission.
The transmission spectra at resonance wavelength in plasmonic BPF can also be characterized using the temporal coupled mode theory, and the maximum transmission Tmax, in terms of quality factors can be described as :
The transmission spectra corresponding to variation of W and L is shown in Fig. 3(a) and 4(a) respectively. For a fixed length of resonator (L), variation of W from 200 nm to 450 nm changes the transmission efficiency of CWRNR from 71% to 61% (ER = −1.487 dB to −2.147 dB) (as in Fig. 3(a)). This range of high values were only achievable in previous studies if Drude model is used [30,31,35], which overestimates transmission, whereas in this study, more accurate analysis is presented using LDM. The single mode transmission reported in recent study using LDM  is also significantly lower and lacks bandwidth tuning as compared to our proposed structure. FWHM of the proposed filter can be adjusted from 175 nm to 85 nm (as in Fig. 3(b)) with nearly 5% variation in resonance wavelength from 1111 nm to 1056 nm by changing W. Normalized magnetic field profile |Hz|, at resonance and non-resonance wavelength, 1111 nm and 650 nm is shown in Fig. 3(c) and (d) respectively. When width of the dielectric increases, coupling between charge density oscillations decreases, which results in lower coupling efficiency and narrower bandwidth as in Fig. 5(a), showing normalized electric field |E| at resonance wavelength of 1111 nm with L = W = 450 nm.
Next, we explore the effect of varying L and found a broad range of shift in resonance wavelength from 750 nm to 1070 nm, while keeping W and g at 350 nm and 10 nm, respectively. It is observed that as L increases, operating wavelength increases with nearly 30% variation in resonance wavelength. Figure 4(a) depicts the transmission spectra and 4(b) shows the FWHM and transmission peak, for a range of L. Maximum transmission of 66% (ER = −1.81 dB) at a wavelength of 1070 nm is obtained when L = 450 nm, which also results in a FWHM value of 100 nm. Increase in L slows down decay rate of intrinsic loss, which ultimately causes Qi to increase and hence transmission increases and slight change in FWHM is observed in Fig. 4(a) for g = 10 nm and W = 350 nm. Normalized magnetic field profile, |Hz|, is verified at resonance wavelength 1070 nm and non-resonance wavelength 650 nm with L = 450 nm and W = 350 nm in Fig. 4(c) and (d) respectively.
Based on the simulation results for the proposed CWRNR filter, the relationship between the geometrical parameters and corresponding resonance wavelength can be formulated into the following equation:
A cascaded structure is proposed in Fig. 6(a) to offer a wider range of frequency selection. Here, a SWRNR and a CWRNR are connected in series. The length, Lmw and width, Wmw of interconnecting waveguide are crucial in controlling the performance of this cascaded device, as shown in Fig. 6(b) and (c). Lmw and Wmw can be optimized to tune mode 1, over a range of wavelengths, from 400-700 nm, while in mode 2 a negligible shift of 20-40 nm is observed. Another efficient way to control the modes is to vary the length to width ratio of the first cavity, L1/W1. Figure 6(d) shows the shifting of mode 1 over 250 nm wavelength range and unlike Fig. 6(b) and (c), the inset shows mode 2 shifting by about 100 nm when L1/W1 ratio changes. The proposed cascaded device can, therefore, be a potential frequency selector in optical communication applications.
Table 1 compares the performance of our proposed design with previously reported filters. Other reported papers shown in the Table 1 used the Drude model, which is less accurate than the LD model  and thus got higher transmission than ours. Applying the Lorentz-Drude model into the proposed design, a transmission efficiency of 71% has been achieved for single mode transmission. This is higher than the transmission efficiencies reported by Khani et al. [33,39] in recent times. Cascaded design also shows its novelty by controlling dual mode property of the filter. Different promising techniques, for example, plasmonic lithography along with multi patterning technique  is now providing high resolution, precision and accuracy with low line edge error (LER) in case of nanopatterning. This leads to a high possibility to realize the performance of the proposed filter considering negligible error.
A highly efficient, and single mode plasmonic filter is proposed based on RNR coupled to a basic MIM corrugated waveguide, having inward apodized grating profile. Light coupling property is numerically analyzed for optimized waveguide dimensions (depth and period of grating), as well as RNR dimensions (length, width and gap of resonator). Numerical FDTD analysis shows single mode transmission having 71% efficiency at resonance peak wavelength of 1111 nm. FWHM varies from 85 nm to 175 nm with change in W, while resonance wavelength changes from 750 nm to 1070 nm when L is varied. A cascaded device, combining SWRNR and CWRNR achieves tuning ability of dual resonance modes by varying Lmw, Wmw, and L1/W1. Finally, we anticipate that, both our proposed single mode and cascaded plasmonic filter may find potential applications in optical devices, integrated photonic circuits and sensors.
The authors thankfully acknowledge the support from Fab Lab DU, at University of Dhaka, for providing the necessary computational resources for this simulation study.
The authors declare no conflicts of interest.
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