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A plasmonic splitter based on slot cavity is proposed and numerically investigated using finite-difference-time-domain (FDTD) methods. The structure consists of the input waveguide, a slot cavity and output waveguides. By varying positions of output waveguides, frequency splitter and power splitter can be achieved in the proposed structure. Flexible output power ratio is feasible through further adjusting the coupling distance and the refractive index of output waveguides.
©2011 Optical Society of America
1. Introduction
Surface plasmon polaritons (SPPs) are waves that propagate along the surface of a conductor due to the interaction between free electrons in the metal and the electromagnetic field in the dielectric. Such waves attenuate exponentially in the direction perpendicular to the interface [1]. So far, various devices based on SPPs have been numerically investigated or experimentally demonstrated, including optical switches, modulators, mirrors, Mach-Zehnder interferometers, filters, sensors, Bragg reflectors, wavelength demultiplexing structures and so on [2–11]. However, one essential problem needs to be solved is that how to guarantee the generated SPPs travel in the desired direction and be splitted with a certain proportion [12]. Controlling the magnitude and the direction of the SPP in nano-scaled structure is essential to nano-photonic related applications (photonic integration, micro-fabrication, smart antennas, etc.).
Several groups have proposed different approaches to control and split the plasmonic waves: (i) By adding different surface nanostructures on both sides of the nanoslit, Gan et al. [13–15] proposed devices capable of confining and guiding light waves of different wavelengths propagating along opposite directions in near-infrared and terahertz domain. (ii) Directional control and splitting of SPP waves has been demonstrated based on asymmetrical metallic gratings with subwavelength apertures [16–18]. (iii) Unidirectional excitation of SPPs has been demonstrated utilizing interferences between two subwavelength nanoslits with different effective refractive indexes [19-20]. (iv) Several different T- and Y-shaped splitters have been proposed [21–23].
The structures used for controlling the SPP intensity and the excitation direction described above can be classified in three categories: (i) the first is associated with two different wavelengths and asymmetrical gratings; (ii) the second is based on SPPs interferences using a single wavelength on one or multiple nano-slit structures; (iii) the third is special geometrically shaped splitters. It is worthy to note that most of these structures can be only used as frequency splitters. In addition, the transmitted light is confined at the output surface instead of being coupled to output waveguides; therefore sometimes such structures are not suitable for integrated photonic circuits for signal interconnection. On the other hand and more important, power splitters of a single wavelength (frequency), instead of frequency splitters are highly desired for photonic integrations.
In this paper, we propose a novel structure, different from above, which can achieve not only the frequency splitter but also the power splitter by varying positions of output waveguides. Notably, a flexible output power splitting ratio is feasible through further adjusting the coupling distance and the refractive index of the material embedded in output waveguides. Different types of power splitters (i.e. 1x2, 1x3, 1x4, etc.) with various splitting ratios are illustrated. Due to its subwavelength size, simple configuration and easy to manipulate, such device can be readily fabricated and deployed into plasmonic integrated circuits.
2. Device structure and theoretical model
As shown in Fig. 1 , a typical metal-insulator-metal (MIM) based plasmonic splitter is composed of the input waveguide, a slot cavity and output waveguides. The length of the cavity is L, and distance of the output waveguides apart from the center of the cavity along the x axis is ΔL. The coupling distance between the slot cavity and the input waveguide is denoted by d. Here parameters of the structure w, L anddare set to be 50 nm, 500 nm and 15 nm through the paper unless specified, respectively. Since widths of the waveguides are much smaller than the incident wavelength, only a single propagation mode TM0 can exist in the structure, whose complex propagation constant β can be obtained as [24]:
Where, k d, m = (β2-εd, m k 0 2)1/2 are propagation constants of the dielectric and metal, respectively. k 0 = 2π/λ 0 is the propagation constant in vacuum. εd and εm is the dielectric constants of metal cladding and dielectric core, respectively. The dielectric in the metal slot is air with the refractive index n=1. The metal is sliver with its frequency-dependent complex relative permittivity characterized by the Drude model.
Fig. 1 Schematic diagram of the typical plasmonic splitter based on slot cavity. L: slot length; w: metal slit width; d, d 1 and d 2: coupling distance.
Here ε ∞=3.7, wp=9.1 eV, γ=0.018 eV, ω is the frequency of the incident light, and the rest optical constants are consistent with experimental ones [25]. The stable standing waves can be exited within the slot cavity only when the following resonance condition is satisfied [26]: Δϕ = β m•2L+ϕ r=2mπ, where ϕ r≡ ϕ 1+ϕ 2, ϕ 1 and ϕ 2 are the phase shifts of the beam reflected at the two ends of the slot cavity. Positive integer m is the order of the resonance mode in the slot cavity. βm is the propagation constant of SPPs corresponding to the resonance mode of the m -th order of the cavity. Thus, the resonance wavelengths can be obtained as:
It can be seen that the peak wavelength λm is proportional to the length of the slot cavity, which well agrees with FDTD simulation results shown in Fig. 2 (using Lumerical FDTD Solution v7.0 software). In this paper, we only consider the first and second resonance mode of the slot cavity (i.e. m = 1 and m = 2). The field inside the cavity is given in Ref [26], which is symmetrical with respect to the vertical axis. According to the temporal coupled mode theory, the transmission T of the system can be obtained form Ref [27].
Where w0 is the resonance frequency. 1/τw is the decay rate due to the power escape through the waveguide, and 1/τi is the decay rate due to the internal loss in the cavity. At the resonance frequency w0, the cavity mode is excited and the incident light is transmitted. Far from the resonance frequency, the incident mode is completely reflected. From Eq. (4), we can find that the transmission spectra around the resonant modes exhibit Lorentzian profiles. Our simulation results are in good accordance with the theoretic analysis and illustrated later.3. Transmission properties of plasmonic frequency splitter
In order to realize the frequency splitter, the two output ports are deposited at special positions (0 and L/4 apart from the center of the slot cavity along the horizontal axis), where fields of the resonance mode satisfy: Hm(x, t) = 0 (m = 1 and 2 corresponds to x = 0 and L/4, respectively) [26]. Therefore only one resonance mode can be coupled out from the slot cavity at these positions. In the simulation, the FDTD method with perfectly matched layer (PML) absorbing boundary conditions is used, and the grid sizes in x and y directions are chosen to be Δx=Δy=5 nm. The simulation parameters are set as follows: L=400 nm, d 1=d 2=15 nm. The result shown in Fig. 3 demonstrates that two resonance wavelengths can be separated without interfere, which is consistent with the field analysis in Ref [26]. Therefore frequency splitter can be by locating output ports at proper positions. In addition, according to Fig. 2, the splitter wavelength can be easily manipulated by adjusting the length of the slot cavity.
Fig. 3 Transmission spectra of the frequency splitter (d 1=d 2=15 nm, L=400 nm, ΔL=0 and L/4 correspond to Port1 and Port2, respectively.)
4. Transmission properties of 1×2 plasmonic power splitter
Since the field inside the cavity is symmetrical with respect to the vertical axis, it is easy to imagine that the transmission properties should be similar at symmetric positions with the same parameters. In order to realize power splitter, the two output ports are locating at symmetric positions about the vertical central line, intuitively, as shown in Fig. 4(a) . The simulation parameters are set as: L=500 nm, ΔL=L/4, d 1=d 2=15 nm. The results displayed in Figs. 4(b) & (c) prove that transmission properties and field profiles of both ports are almost the same (i.e. 50/50 splitting ratio). Note that the transmission of both ports is ~43%, corresponding to ~15% additional transmission loss passing through the power splitter. Therefore, plasmonic power splitter can be achieved in the proposed structure by locating output ports at proper positions.
Fig. 4 (a) Scheme of the plasmonic power splitter. (b) Transmission spectra of two output ports with d 1=d 2=15 nm, L=500 nm, ΔL=L/4. (c) Contour profiles of field |E x| at wavelength 1500 nm.
Successively, we investigate the influence of coupling distances d 1 and d 2 on the output power ratio (i.e. power splitting ratio) individually. First, we increase d 1 from 10 nm to 30 nm with an increment of 5 nm, while other parameters keep no change. As an example, the transmission spectra and field profile at 1500 nm are displayed in Figs. 5(a) and (b) , respectively. One can found that the transmission properties at two ports become different: the transmitted-peak wavelength at Port 1 exhibits a blue-shift and the peak transmission decreases simultaneously with increased coupling distance, which agrees well with the results in Refs [7, 11, 26]. When d 1 increases, 1/τi keeps almost unchanged, while deceasing 1/τw results in weaker coupling. From Eq. (4), it can be deduced that T max,1 decreases quickly with increased d 1 at the resonance frequency, as can be explained by the result inserted in Fig. 5(c). However, T max,2 is slightly improved with increased d 1, which is attribute to the fact that more power is reflected into the slot cavity by Port 1 and is coupled out from Port 2 by increasing d 1. Thus, the power splitting ratio (PSR) has a curve relationship with d 1 shown in Fig. 5(c) as
Fig. 5 (a) Transmission spectra of power splitter with different coupling distance (L = 500 nm, ΔL=L/4) (b) Contour profiles of field |E x| at wavelength 1500 nm. (c) The peak-wavelength output power ratio versus the coupling distance d 1 and d 2, respectively. Inset: the peak power (transmission) of two ports versus the coupling distance d 1.
On the contrary, if we change d 2 following the same rule, the relationship is nearly identical, which also verifies that the field inside the cavity is symmetrical with respect to the vertical axis.
Next, we find that the refractive index of the material embedded in output ports (denoted by n 1 and n 2, respectively) also affects on the output power ratio. Here we change n 1 from 1 to 2 with an increment of 0.2, while other parameters keep no change. As an example, the transmission spectra and field profile at 1500 nm are shown in Figs. 6(a) and (b) , respectively. The transmission properties at two ports are different. It can also be found from Fig. 6(c) that there is nearly a linear relationship between the output power ratio and n 1 or n 2.
Fig. 6 (a) Transmission spectra of power splitter with different refractive index material embedded in two ports. (d 1=d 2=15 nm, L=500 nm, ΔL=L/4) (b) Contour profiles of field |E x| at wavelength 1500 nm. (c) The output power ratio versus the refractive index of the material embedded in two ports, respectively.
5. Transmission properties of 1×3 and 1×4 plasmonic power splitter
Since the slot cavity is symmetric along the horizontal axis, the splitter can have more output ports by increasing branches at symmetric positions with respective to the horizontal central line, intuitively. Such functionalities are illustrated in Figs. 7 -10 . The schematic diagrams of 1×3 and 1×4 power splitters is shown in Fig. 7(a) and Fig. 9(a) , respectively. We study transmission performance of the proposed structure under two conditions: (1) with equal coupling distance for each channel; (2) with unequal coupling distance for each channel.
Fig. 7 (a) Scheme of the plasmonic power splitter. (b) Transmission spectra of splitter with equal coupling distance. (d 1=d 2=d 3=15 nm, L=500 nm, ΔL=L/4) (c) Contour profiles of field |E x| at wavelength 1500 nm.
Fig. 10 (a) Transmission spectra of power splitter with unequal coupling distances (d 1=15 nm; d 2=20 nm; d 3=25 nm; d 4=30 nm). (b) Contour profiles of field |E x| at wavelength 1500 nm.
Fig. 9 (a) Scheme of the plasmonic power splitter. (b) Transmission spectra of splitter with equal coupling distances. (d 1=d 2=d 3=d 4=15 nm, L=500 nm, ΔL=L/4) (c) Contour profiles of field |E x| at wavelength 1500 nm.
In the first case, we make the output ports have the same coupling distance of 15 nm. The simulation results shown in Fig. 7(b) and Fig. 9(b) validate that the field inside the cavity is also symmetric with respective to the horizontal axis. All the three or four output ports have almost identical power splitting ratios (~31-33% for the 1×3 power splitter; ~22-23% for the 1×4 power splitter). The contour profiles of the field at wavelength 1500 nm are further displayed in Figs. 7(c) and 9(c).
In the second case, we increase the coupling distance with the step of 5 nm (i.e. 15, 20, 25 etc), with other parameters keep unchanged. It can be seen from Fig. 8(a) and Fig. 10(a) that power splitters with unequal splitting ratios can be achieved by adjusting the coupling distance. In Fig. 8(a), the coupling distances for the three output ports are set to 15 (d 1), 20 (d 2) and 25 nm (d 3), with the corresponding power splitting ratios as 43% (port 1), 23% (port 2) and 12% (port 3), respectively. In Fig. 10(a), the coupling distances for the four output ports are set to 15 (d 1), 20 (d 2), 25 nm (d 3) and 30 nm (d 4), with the corresponding power splitting ratios as 43% (port 1), 23% (port 2), 12% (port 3) and 5% (port 4), respectively. In addition, the contour profiles of the field at wavelength 1500 nm are displayed in Figs. 8(b) and 10(b).
Fig. 8 (a) Transmission spectra of 1×3 power splitter with unequal coupling distances. (d 1=15 nm; d 2=20 nm; d 3=25 nm) (b) Contour profiles of field |E x| at wavelength 1500 nm.
Similarly, splitting ratios can also be adjusted by changing the refractive index of output ports. Therefore, the desired output power ratios can be derived by selecting the appropriate coupler distance or the refractive index of output ports, as illustrated in Fig. 5(c) and Fig. 6(c).
6. Conclusion
In this paper, we proposed a plasmonic splitter based on slot cavity. The splitter properties have been numerically investigated using FDTD methods. The frequency splitter and power splitter can be realized in the proposed structure by locating the output ports at proper positions. More numbers of output ports can be achieved by adding branches at proper positions. More important, by choosing appropriate coupling distance or/and refractive index of the material embedded in output ports, splitters with tunable power splitting ratio can be realized.
Acknowledgements
The work was supported by National Basic Research Program of China (2011CB301800), the Program for New Century Excellent Talents in University (NCET-08-0821), and the State Key Lab of Optical Technologies for Micro-Engineering and Nano-Fabrication of China.
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