SURFACE plasmon polaritons (SPPs) have the potential to

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1 IEEE TRANSACTIONS ON NANOTECHNOLOGY, VOL. 10, NO. 6, NOVEMBER A Nanoplasmonic High-Pass Wavelength Filter Based on a Metal-Insulator-Metal Circuitous Waveguide Jia Hu Zhu, Qi Jie Wang, Ping Shum, and Xu Guang Huang Abstract A nanoplasmonic high-pass wavelength filter consisting of two straight metal-insulator-metal waveguides sideconnected with a dielectric islet to form a circuitous waveguide is proposed and simulated numerically by using the finite difference time domain method. The simulation demonstrates that the plasmonic filter is characterized as a high-pass wavelength filter in the transmission spectrum. The cutoff wavelength increases with the increase of the length or the decrease of the width of the dielectric islet. Explanation of the high-pass filtering effect is given with a theoretical expression of the cutoff wavelength. Index Terms Integrated optics devices, metal-insulator-metal waveguide, surface plasmons, wavelength filtering. I. INTRODUCTION SURFACE plasmon polaritons (SPPs) have the potential to guide light at deep subwavelength scale [1], [2]. Therefore, the investigation of plasmonic waveguide structures has been paid great attentions, and several different nanoscale plasmonic waveguide structures have been recently proposed, such as metallic nanowires [3], [4] and metallic nanoparticle arrays [5], [6]. Metal-insulator-metal (MIM) waveguide is considered to have unique advantages because of its strong field localization, simplicity, and being convenient for fabrication and integration into optical circuits. A variety of functional plasmonic MIM structures have been designed and fabricated, such as U-shaped waveguides [7], splitters [8], switches [9], [10], Y-shaped combiners [11], couplers [12], M-Z interferometers [13], [14], and filters based on Bragg reflectors or nanocavities [15], [16], side-coupled cavity [17], and teeth structures [18] [20]. However, all of wavelength filters in the literature, either Bragg grating, cavity or teeth structures are almost reflective stop-band or transmitted pass-band filters. Another important Manuscript received November 27, 2010; revised March 16, 2011; accepted March 23, Date of publication April 21, 2011; date of current version November 9, This work was supported by the National Natural Science Foundation of China, Grant No and the start-up grant from Nanyang Technological University (NTU), Singapore, Grant No. M The review of this paper was arranged by Associate Editor Prof. K. Wang. J. H. Zhu and X. G. Huang are with the Key Laboratory of Photonic Information Technology of Guangdong Higher Education Institutes, School of Information and Optoelectronic Science and Engineering, South China Normal University, Guangzhou , China ( huangxg@scnu.edu.cn). Q. J. Wang and P. Shum are with the School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore. Q. J. Wang is also with School Physical and Mathematical Sciences, Nanyang Technological University ( qjwang@ntu.edu.sg). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TNANO Fig. 1. Spectra of the transmission at location Q and the reflection at location P of the filter with w i = 70 nm, w p = 50 nm, and d = 150 nm. The inset: A high-pass filter structure (top view). plasmonic waveguide filter, the so-called high-pass (or shortpass) wavelength filter, which only allows long (or short) wavelengths to pass, has not yet been reported so far. In this letter, a nanoscale plasmonic high-pass wavelength filter is proposed and numerically simulated by using the finite difference time domain (FDTD) method with perfectly matched layer absorbing boundary condition. The dependences of the transmission spectra of the high-pass wavelength filter on the length and the width of the dielectric islet are discussed. The relationship between the cut-off wavelength and the refractive index of the islet is also investigated. II. DEVICE OF A HIGH-PASS WAVELENGTH FILTER STRUCTURE AND SIMULATION RESULTS The structure of the plasmonic high-pass wavelength filter is shown in the inset of Fig. 1. In this new structure, the small metal pillar under the dielectric islet (the red dashed rectangle in the inset) prevents the light directly passing through the straight waveguide. In the following FDTD simulations, the grid sizes in the x and z directions are set to be 2 nm 2 nm. The fundamental TM mode of the plasmonic waveguide is launched from left to right at the input port (Port1) of the circuitousshape waveguide. Because the width of the MIM plasmonic waveguide is much smaller than the wavelength, only the fundamental transverse magnetic (TM) waveguide mode can propagate. Two power monitors are set at the locations of P and Q to detect the reflected and transmitted powers of P ref and P tr. The transmittance and reflectivity are respectively defined to be T = P tr /P in and R = P ref /P in, where P in is the incident power X/$ IEEE

2 1358 IEEE TRANSACTIONS ON NANOTECHNOLOGY, VOL. 10, NO. 6, NOVEMBER 2011 Fig. 2. Transmission spectra of the filter at various widths w i with the same length d = 150 nm and the same pillar width w p = 50 nm. of the beam. The waveguide width w and the distance L are set to be 50 nm and 100 nm. d and w i are, respectively, the length and the width of the dielectric islet. And the pillar width w p is chosen to be 50 nm. The dielectric constant ε m of silver can be calculated based on Drude-Lorentzian model ε m (ω) =ε ω 2 D ω 2 + iγ D ω 2 m =1 g Lm ω 2 Lm Δε ω 2 ω 2 Lm + i2γ Lmω (1) where ε = , ω D = ev, γ D = ev, Δε = , g L 1 = , ω L 1 = ev, γ L 1 = 0.28 ev, g L 2 = , ω L 2 = ev, and γ L 2 = ev. Equation (1) gives a good description of empirical dielectric constant data for silver within the range of 500 nm 1800 nm [21]. The refractive indices of the dielectrics are all set to be one. Fig. 1 shows the simulation results of the transmission and the reflection spectra of the filter with w i = 70 nm, w p = 50 nm, and d = 150 nm. It can be seen that typical high-pass transmission spectrum occurs at the cutoff wavelength (defined to be the wavelength where the transmittance is equal to 1%) around 820 nm. The transmittance at wavelength around 1800 nm is more than 90%. At short wavelengths less than the cut-off wavelength, the transmittance of the light is nearly zero. It means that the waveguide structure is a typical high-pass wavelength filter. On the contrary, for the reflected beam, the structure acts as a low-pass wavelength filter with very low reflectivity in long wavelengths. Fig. 2 shows transmission spectra of the filter with different widths w i and with the same length of d = 150 nm and the same pillar width of w p = 50 nm. One can see that the cutoff wavelength increases as the width of the islet decreases. And the edge with w i = 60 nm is steeper than that with w i = 80 nm. The smaller w i, the more steep the edge. It is known that effective index n eff of the islet MIM waveguide increases with decreasing its width. Fig. 3 shows transmission spectra of the filter with various lengths d at same widths of w i = 70 nm and w p = 50 nm. Fig. 3. Transmission spectra of the filter at various lengths with the same width of w i = 70 nm and the same pillar width of w p = 50 nm. The inset: The cut-off wavelength as a function of the length with the same width of w i = 70 nm and the same pillar width of w p = 50 nm. Fig. 4. Transmission spectra of the filter at various refractive indices of the islet with d = 150 nm, w i = 70 nm, and w p = 50 nm. The inset: The cut-off wavelength as a function of the refractive index of the islet. The inset of Fig. 3 shows the cutoff wavelength as a function of the length of the islet. The FDTD simulation results reveal that the cutoff wavelength increases linearly with the increase of the length. But the rising edge of the high pass wavelength filter with d = 130 nm is steeper than that with d = 170 nm. The smaller the length is, the steeper the edge is. Therefore, the cutoff wavelength of the waveguide structure can be easily chosen by changing the length d. Fig. 4 shows transmission spectra of the filter at different refractive indices of the islet with the same length of d = 120 nm and the same width of w i = 70 nm and w p = 50 nm, while the inset of Fig. 4 shows the cut-off wavelength as a function of the refractive index of the islet. It can be seen that the cut-off wavelength increases linearly with the increase of the refractive index of the islet, which means one could realize a tunable highpass wavelength filter by changing the refractive index of the islet.

3 ZHU et al.: NANOPLASMONIC HIGH-PASS WAVELENGTH FILTER BASED ON A MIM CIRCUITOUS WAVEGUIDE 1359 Fig. 5. Transmission spectra of the filter with different pillar widths at the same length of d = 150 nm and the same width of w i = 80 nm. Fig. 7. Transmission spectra of port 2 of open three-port structures having different pillar widths at the same w i = 70 nm and w = 50 nm, where w p = 0 means no metal pillar in the three-port structure. The inset: An open three-port splitter structure with metal pillar (top view). Fig. 6. Magnetic field profile of the filter with d = 150 nm, w i = 70 nm, and w p = 50 nm. (a) λ = 700 nm; (b) λ = 1800 nm. Fig. 5 shows transmission spectra of the filter with different pillar widths and at the same length of d = 150 nm and the same width of w i = 80 nm. One can see that the cutoff wavelength increases with a bit higher transmittance as the pillar width increases. Fig. 6(a) and (b) shows the magnetic field profiles of the filter at two wavelengths. An incident monochromatic beam at 700 nm wavelength is completely reflected by the filter with d = 150 nm, w i = 70 nm and w p = 50 nm, while the most of a monochromatic beam at 1800 nm wavelength can transmit through the filter. To understand the working principle of the high-pass wavelength filter, we simulate and compare an open three-port structure with a metal pillar of nonzero w p (shown in the inset of Fig. 7) with an open three-port structure without metal pillar (shown in the inset of Fig. 8 with w p = 0 nm) in their transmission t(λ) and reflection r(λ) characteristics. The small metal pillar can block the light directly passing through the straight waveguide. It can be seen from Fig. 7 that the three-port structures with or without metal pillar act as beam splitters with right-output port 2 and upper-output port 3. However, when pillar width w p increases, the light split into port 2 increase. As pillar width w p is increased to be 50 nm, transmittances t(λ) of port 2 at wavelengths less than 800 nm are below 10%. Therefore, the metal pillar in a three-port structure has the function of long wavelength selection. From the transmission spectrum of a straight MIM waveguide given in Fig. 7, it can be seen that the very high absorption of Ag metal [21] mainly influences transmittances of wavelengths below 500 nm. Therefore, the high-pass characteristic of the proposed structure in wavelengths over 800 nm or more does not result from the very high absorption of Ag metal. Fig. 8 shows transmission t(λ) and s(λ) and reflection r(λ) spectra of different ports of two open three-port structures with and without metal pillar of 50 nm wide. It can be seen that transmittances and reflectance of the two structures are all different due to the barrier function of the metal pillar. In the structure with metal pillar, wavelengths below 800 nm are mostly reflected back to port 1, and wavelengths over 800 nm can transmit into ports 2 and 3 more easily. Therefore, it can be concluded from Figs. 7 and 8 that the metal pillar in a three-port structure has a function of short wavelength blocking. What will happen, when the third ports of the two structures are enclosed? Obviously, the enclosed third port in each of the structures acts as a side-coupled resonant cavity where light beam can propagates forward and backward many times. Fig. 9 shows the transmission spectra of the enclosed-third-port structures with and without metal pillar. One can see that the two

4 1360 IEEE TRANSACTIONS ON NANOTECHNOLOGY, VOL. 10, NO. 6, NOVEMBER 2011 Fig. 8. Transmission or reflection spectra of three-open-port structures with and without metal pillar, with same w = 50 nm and w i = 70 nm. The inset: Top view of a traditional three-port structure without metal pillar. The difference (shown in Figs. 7 and 8) between relatively flat wavelength responses of t(λ), s(λ), and r(λ) in the tooth-shaped structure without metal pillar (shown in the inset of Fig. 9) and high-pass response t(λ) and s(λ) with low-pass response r(λ) in the structure with the metal pillar (shown in the inset of Fig. 1) is the only reason resulting in the spectral T(λ) difference of Fig. 9 between the two structures. Therefore, the high-pass mechanism of the proposed structure can be attributed to the interference between the multi-reflected beam from enclosed port 3 and the directly-split beam of port 2 in combination with the long-wavelength selection of t(λ) and s(λ) of the metal pillar shown in Figs. 7 and 8. Defining 2θ =4πn eff d/λ and θ R to be, respectively, the round-trip phase delay within the enclosed port (or the dielectric islet) and the phase shift caused by the reflection at the end of the dielectric islet. n eff is the real effective index of the islet, which can be solved from the dispersion equation [18]. The total phase difference of the coherent superposition of light in output port 3 is given as follows: φ(λ) =2θ + θ R θ b =4πn eff d eff /λ (3) where d eff = d +(θ R θ b )λ/4πn eff is defined to be the effective length, and the second term in the right side of d eff - definition is the length change resulted from the small penetration depth of the waves into the metal and the phase delay θ b of the waves propagating along the bottom of the islet. The transmittance dip will occur at the phase difference of φ (λ) = (2 m + 1)π (m = 0,1,2,..). If a proper length of the dielectric islet is chosen, for example, d 180 nm for the islet with w i = 70 nm and then n eff = 1.4, the phase difference φ(λ) can be kept within the range of 0 to 2π for any wavelength over 500 nm. Defining the cutoff wavelength of λ c to be Fig. 9. Transmission spectra of the proposed enclosed-third -port structure with metal pillar and a tooth-shaped structure without metal pillar, with same w = 50 nm, d = 150 nm, w p = 50 nm, and w i = 70 nm. The inset: Top view of the tooth-shaped structure. spectra are different. The transmission of the structure without metal pillar (shown in the inset of Fig. 9) has a resonant dip at the wavelength of 800 nm, while the transmission of the structure with metal pillar (shown in the inset of Fig. 1) is of high-pass filtering performance with the cutoff wavelength around 800 nm. The structure without metal pillar has been investigated as the tooth-shaped structure in [18] with the derived formula of transmittance T(λ) in (8) of [18], based on multibeam interference in the side-coupled tooth area. Because the proposed structure with metal pillar has also a side-coupled resonant cavity, its transmission T(λ) can be calculated with the same formula of transmittance T(λ), shown as follows: T (λ) = t 1(λ)+ s 1(λ)s 3 (λ)exp[iφ(λ)] 2 1 r 3 (λ)exp[iφ(λ)] (2) where t i (λ), s i (λ), and r i (λ)(i = 1,2,3) are, respectively, the direct transmission, side transmission, and reflection coefficients of an incident beam from Port i. φ(λ) is the total phase difference given in (3). 4πn eff d eff /λ c = π, or λ c =4n eff d eff. (4) For λ < λ c, the phase difference is φ(λ) >π, the partially destructive interference will happen. Simultaneously, the wavelengths on the left side of the dip are mostly blocked by the metal pillar with small transmittance, according to the above analysis. Therefore, transmission T(λ) of the proposed structure on the left side of the dip (λ < λ c ) will ultimately be close to zero, based on the combination of the side-coupled resonant cavity effect of the dielectric islet and the long wavelength selecting function of the metal pillar. The enclosed structure with metal pillar is a high-pass wavelength filter with the cutoff wavelength of λ c. Equation (4) reveals that the cutoff wavelength of λ c is linear to both the length d and the effective index n eff, which agree with the simulation results in Figs. 3 and 4 as well as Fig. 2, respectively. III. CONCLUSION In conclusion, a nanoscale plasmonic high-pass wavelength filter is proposed. The simulation demonstrates that the new device has characteristics of high-pass filtering in the transmission spectrum and low-pass filtering in the reflective spectrum. The cutoff wavelength increases with the increase of the length of

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