Tunable band-stop plasmonic waveguide filter with ... - OSA Publishing

Letter

Vol. 41, No. 6 / March 15 2016 / Optics Letters

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Tunable band-stop plasmonic waveguide filter with symmetrical multiple-teeth-shaped structure HONGQING WANG,1,2 JUNBO YANG,2,3,* JINGJING ZHANG,2 JIE HUANG,2 WENJUN WU,2 DINGBO CHEN,2 AND GONGLI XIAO1,4,5 1

School of Information and Communication, Guilin University of Electronic Technology, Guilin, Guangxi 541004, China National University of Defense Technology, Center of Material Science, Changsha 410073, China 3 Peking University, State Key Laboratory on Advanced Optical Communication Systems and Networks, Beijing 100871, China 4 Guangxi Experiment Center of Information Science, Guilin 541004, China 5 e-mail: [email protected] *Corresponding author: [email protected] 2

Received 24 December 2015; revised 10 February 2016; accepted 10 February 2016; posted 11 February 2016 (Doc. ID 256254); published 11 March 2016

A nanometeric plasmonic filter with a symmetrical multiple-teeth-shaped structure is investigated theoretically and numerically. A tunable wide bandgap is achievable by adjusting the depth and number of teeth. This phenomenon can be attributed to the interference superposition of the reflected and transmitted waves from each tooth. Moreover, the effects of varying the number of identical teeth are also discussed. It is found that the bandgap width increases continuously with the increasing number of teeth. The finite difference time domain method is used to simulate and compute the coupling of surface plasmon polariton waves with different structures in this Letter. The plasmonic waveguide filter that we propose here may have meaningful applications in ultra-fine spectrum analysis and high-density nanoplasmonic integration circuits. © 2016 Optical Society of America OCIS codes: (130.3120) Integrated optics devices; (230.7408) Wavelength filtering devices; (240.6680) Surface plasmons. http://dx.doi.org/10.1364/OL.41.001233

Surface plasmon polaritons (SPPs), which are propagating electromagnetic waves at the metal-dielectric interface, have been shown to have great potential in many fields, such as biology, chemistry, and information technology [1–3]. In recent years, many subwavelength optical devices based on SPPs have been achieved because of their ability to overcome the diffraction limit in conventional optics [4,5]. The metalinsulator-metal (MIM) waveguide structure, which can propagate SPPs at the subwavelength scale, is very familiar. Owing to their good light confinement properties, MIM structures have found many applications [6–11]. Plasmonic filters based on MIM waveguide structures, which perfectly solve the problem of the relatively high propagation loss resulting from a large size, have also attracted much attention and been investigated widely. 0146-9592/16/061233-04 Journal © 2016 Optical Society of America

As is well known, the function of plasmonic filters is achieved by the properties of wavelength selection. Recently, different types of plasmonic filters with MIM waveguides were designed, such as demultiplexing filters based on slot cavities [12,13], Bragg reflector filters [14], band-pass plasmonic filters [15,16], and square-ring resonator filters [15,17,18]. Various plasmonic filters based on teeth-shaped structures have also been proposed [8,19–24]. The majority of these have single tooth-shaped [19] or double-sided teeth-shaped [21,22] structures. In addition, nanoplasmonic filters with multiple teeth-shaped structures [22,23] and symmetrical teeth-shaped waveguide couples [24], which realize selectable specific wavelengths, have been investigated. According to [24], a tunable flat stop-band is achieved by adjusting the relative depth of two symmetrical teeth. However, it is found that a projection appears in the bandgap when the depths of two symmetrical teeth are significantly different. Moreover, this phenomenon is not well explained in theory. In this Letter, the reason for the projection, which occurs between the corresponding resonant wavelengths with the two significantly different symmetrical teeth, is analyzed theoretically and numerically. A symmetrical multiple teeth-shaped structure with a tunable wide bandgap is proposed. The transmission spectrum of the SPPs’ mode is calculated by the finitedifference time-domain method with a perfectly matched layer absorbing boundary condition. A dynamic tunable band-stop can be achieved by controlling the number and the depth of teeth. At the same time, the two transmission spectra of the symmetrical multiple-teeth-shaped structure with uniform tooth depths and varying tooth depths are also discussed. Figure 1 shows the schematic of two cascaded symmetrical teeth-shaped plasmonic filters with different depths. The widths of the slit waveguide and teeth-shaped waveguide are all fixed to be w wt 100 nm. The staggered length of two teeth is D 250 nm. d 1 and d 2 are the depths of the teeth on each side of an MIM waveguide. In the following simulations, the fundamental TM mode of the plasmonic waveguide

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Fig. 1. Schematic of the cascaded symmetrical teeth-shaped waveguide structure.

is excited by a plane wave source. The grid sizes in the x and the y directions are set at 5 nm 5 nm. The medium of the insulator is assumed to be air (shaded white), and the metal is made of silver (shaded gray). The dielectric constant of silver is characterized by the Drude model [11]: εm ε∞ − ω2p ∕ωω iγ:

(1)

Here, ε∞ 3.7 is the dielectric constant at the infinite angular frequency, ωp 1.38 × 1016 Hz is the bulk plasma frequency, and γ 2.73 × 1013 Hz is the damping frequency of the oscillations. ω is the angular frequency of the incident electromagnetic radiation. Two power monitors are used at the points P 1 and P 2 to detect the incident and the transmission fields, respectively. The distance between the monitor and the teeth is set to be L 100 nm. The transmittance is defined to be T P 2 ∕P 1 . When the incident light propagates from position P 1 to position P 2 , only the fundamental TM mode is excited in the structure. The response wavelength of an excited SPP can be determined as follows: λm

4neff d ; 2m 1 − πθ

(2)

where λm is the wavelength of the transmission, m is an integer, and θ is the phase shift caused by the reflection on the air-silver interface. Equation (2) reveals that the resonance wavelength λm is linear with the teeth depth d or the effective refractive index neff of the slit waveguide, which is a complex value. In the single MIM waveguide structure, neff can be expressed as β λ λ neff i ; (3) k λMIM 4πLSPP where β is the propagation constant and k 2π∕λ is the freespace wave vector. From Eq. (3), one can see that neff contains two terms: its real part determines the guided wavelength λMIM , while its imaginary part determines the propagation length LSPP of the SPPs. From the teeth-shaped plasmonic waveguide structure, we can see that the effective refractive index neff depends on the teeth width w and the waveguide medium [21]. Figure 2(a) shows the transmission spectrum of two cascaded symmetrical teeth-shaped plasmonic filters with teeth depths d 1 300 nm and d 2 270 nm. It reveals that a flat

Fig. 2. (a) Transmission spectrum of cascaded symmetrical teethshaped structure with teeth depths d 1 300 nm and d 2 270 nm (blue line) and two single symmetrical tooth-shaped structures with d 300 nm (green line) and d 270 nm (red line). The inset shows the transmission spectrum of the cascaded symmetrical teeth-shaped structure at wavelengths ranging from 1250 to 1600 nm. (b) Transmittance as a function of the wavelength for different teeth depths d 2 with d 1 300 nm.

bandgap occurs at the central wavelength λm 1427 nm with a bandgap width of 316 nm. The bandgap width is defined as the difference between the two wavelengths at 1% transmittance. To analyze the reason for this phenomenon, the transmission spectra of two single symmetrical tooth-shaped structures with d 300 nm and d 270 nm are shown in Fig. 2(a). It is found that the two transmission troughs of the single tooth-shaped structures occur around 1356 and 1499 nm. We can see that a bandgap connecting the two transmission troughs is generated, and the bandgap width (from 1269 to 1585 nm) is larger than the difference between the two corresponding resonant wavelengths. This result shows good agreement with the results found in [24]. However, this will generate a problem in that a projection occurs between two transmission troughs when the difference in teeth depth is large. Figure 2(b) shows the transmission spectra with different teeth depths d 2 and widths d 1 300 nm. One can see that there is a very clear projection when d 2 250 nm. The peak value of the projection increases continuously with decreasing d 2 , while the wavelength of the projection peak shifts toward the short wavelength (blue-shift). It can be predicted that the transmission will reach the maximum when the value of d 2 is


Letter zero (single tooth-shaped structures). One can see from the inset of Fig. 2(a) that the projection, which is of negligible peak height, also occurs when the difference of two teeth depths is relatively small. In order to theoretically analyze the origin of the bandgap and the projection, the phase delay in the two cascaded symmetrical teeth-shaped structures is discussed. When the incident light irradiates this structure from the input side, the SPPs’ wave generated by the metal-air interface can divide into two parts, which are the transmitted wave along the slot waveguide and the reflected wave from the two cascaded teeth. This will generate the phase difference between the transmitted SPPs’ wave and the reflected SPPs’ wave, and this phase delay can be expressed by the following equation: 4π n d θ; (4) λ eff where βSPP and neff are, respectively, the propagation constant and the effective refractive index of the SPPs. θ is the phase shift caused by the reflections on the metal-air interface at the end of the teeth. Therefore, for the two cascaded symmetrical teethshaped structure in Fig. 1, the phase differences φ1 and φ2 generated by the first tooth and the second tooth can be derived as follows:

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Fig. 3. (a) Schematic of a staggered three cascaded teeth-shaped structure. (b) Transmission spectrum of the three cascaded teethshaped structure with d 1 300 nm, d 2 260 nm, and d 3 220 nm (blue line), and the two cascaded teeth-shaped structure with d 1 300 nm and d 3 220 nm (red line).

φ 2βSPP d θ

φ1

4π n d θ1 ; λ eff 1 1

(5)

4π n d θ2 : (6) λ eff 2 2 Combining Eqs. (5) and (6), the total phase difference of this structure is φ2

4π n d neff 2 d 2 θ1 θ2 : (7) λ eff 1 1 According to Eq. (7), it is found that the total phase difference depends on the effective refractive index, teeth depth, and phase shift of each of the teeth. In the structure shown in Fig. 1, the widths of the two symmetrical teeth are equal and the entire dielectric medium is assumed to be air. Therefore, the effective refractive indices of both teeth are equal, neff 1 neff 2 . Thus, the values of the phase shift are θ1 θ2 π because of the existence of the half-wave loss. Therefore, Eq. (7) can be simplified to the following form: φtotal φ1 φ2

4π n d d 2 2π: (8) λ eff 1 It can be seen from Eq. (8) that the total phase difference caused by the transmitted SPPs and the reflected SPPs is dependent on the depths of the two teeth, and as we mentioned earlier in this Letter, the depth of the first teeth is fixed to 300 nm. Thus, the phase difference generated by the two teeth of different depths only depends on the second tooth’s depth. Therefore, as is well known, when the difference between d 1 and d 2 is small, there exists a phase difference generated by the superposed waves of each tooth-shaped waveguide, which means that the first tooth and the second tooth are out of phase. The SPPs waves, which are between two transmission troughs, cannot transmit in this structure due to the destructive interference of the superposed waves, which results in a flat bandgap. When d 2 is the decrement, the phase difference decreases and the effect of destructive interference is weaker. φtotal

At the same time, a projection, which occurs between two corresponding resonant wavelengths, will become larger with decreasing d 2 . This implies that a part of the SPP waves can transmit this structure. In this case, the structure of two cascaded symmetrical teeth-shaped waveguides cannot realize a filtering function, owing to the unflat bandgap. Based on the analysis above, a band-stop filter with three cascaded symmetrical teeth-shaped structure is designed as shown in Fig. 3(a). In this structure, the widths of the slot and teeth are equal to those shown in Fig. 1. The staggered lengths D are set to be 200 nm. Figure 3(b) shows the transmission spectrum of this structure with d 1 300 nm, d 2 260 nm, and d 3 220 nm. This figure reveals that a flat and wide bandgap (blue line) in the range of wavelength from 1015 to 1585 nm is achieved. For the sake of comparison, the transmission spectra of the two cascaded teeth-shaped structures with d 1 300 nm and d 2 220 nm are also calculated, as shown in Fig. 3(b). It can be seen from Fig. 3(b) that when the depths of two symmetrical teeth-shaped structures are set as d 1 300 nm and d 2 220 nm, a projection occurs between the corresponding resonant wavelengths of λ1 1120 nm and λ2 1499 nm. The bandgap width of the three cascaded teeth-shaped structure is larger than the difference between the two resonant wavelengths of the double cascaded symmetrical teeth-shaped structure. This phenomenon is the same as that discussed in the introduction of this Letter. In order to illustrate the dependence of the bandgap on the teeth number N, Fig. 4 shows the transmittance as a function of the wavelength for various N . During the simulation, the teeth depths of multiple-teeth-shaped structures decrease linearly with a step of 30 nm and the maximum value is 300 nm. Therefore, the two teeth of d 1 300 nm and d 2 270 nm are discussed when N 2, while when N 4, the four teeth of d 1 300 nm, d 2 270 nm, d 3 240 nm, and d 4 210 nm are investigated. One can see from Fig. 4 that the bandgap shifts to a shorter wavelength and hardly moves to the right with an increase of N . This phenomenon is consistent with our assumption. The pass-band transmittances of each structure also exceed 85%. According to these results, we can obtain the bandgap of the random center wavelength in principle, and its width can be tuned by adjusting the depth and the number of teeth. In all the discussions above, our research is focused on teethshaped structures at different depths. N identical teeth with

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Letter resonant wavelengths that was introduced in [24]. Additionally, a tunable plasmonic waveguide filter with a symmetrical multiple teeth-shaped structure is proposed. This filter, which has a purely nanometeric structure, can realize an ultrawide, tunable bandgap by adjusting the depth and the number of teeth. Our results may be useful for optical communications and optical information processing, such as optical interconnect networks, optical computing, fiber to the home, wavelength division multiplexing/dense wavelength division multiplexing, and on-chip optoelectronic modules.

Fig. 4. Transmission spectrum for staggered teeth-shaped structure with different teeth numbers N .

Funding. National Natural Science Foundation of China (NSFC) (60907003, 61465004); Foundation of NUDT (JC13-02-13); Natural Science Foundation of Hunan Province (13JJ3001); Program for New Century Excellent Talents in University (NCET-12-0142); Guangxi Natural Science Foundation of China (2013GXNSFAA019338); Innovation Project of GUET Graduate Education (YJCXS201514). REFERENCES 1. 2. 3. 4. 5. 6.

Fig. 5. (a) Schematic of N identical cascaded teeth-shaped structure. (b) Transmittance as a function of the wavelength for different teeth numbers with N identical cascaded teeth-shaped structures.

a periodic arrangement are also investigated, as shown in Fig. 5(a). Figure 5(b) shows the transmission spectrum of this structure. All the teeth depths d are fixed at 300 nm. N is the number of teeth. Figure 5(b) shows that when N ≥ 2, a bandgap will be generated, and the bandgap width increases continuously with the increasing teeth number N, but the rate of increase is decreasing. The pass-band transmittance decreases with increasing N , which can be attributed to the propagation loss of the SPP wave due to the absorption by the metal. We can also find from Fig. 5(b) that all the bandgaps (N ≥ 2) are divergent to the two sides of the transmission trough, which is generated by the single tooth structure (N 1). We define the left bandgap and the right bandgap of the transmission trough as bL and bR , respectively. It can be seen that bL is larger than bR when N > 2. This result is determined by the different metal losses, which depend on the wavelength. In summary, we have theoretically and numerically analyzed the reason for the projection between the two corresponding

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