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The tunable multi-channel wavelength demultiplexer (WDM) based on metal-insulator-metal plasmonic nanodisk resonators is designed and numerically investigated by utilizing Finite-Difference Time-Domain (FDTD) simulations. It is found that the channel wavelength of WDM is easily tuned by changing the geometrical parameters of the structure and the material filled in the nanodisk resonator. The multi-channel WDM structure consisting of a plasmonic waveguide and several nanodisk resonators increases the transmission up to 70% at telecommunication regime, which is two times higher than the results reported in a recent literature [Opt. Express 18, 11111 (2010)]. Our WDM can find important potential applications in highly integrated optical circuits.
©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 the free electrons of the conductor and electromagnetic field [1]. SPPs have promising application on the devices in highly integrated optical circuits because they overcome the conventional diffraction limit and can manipulate light on sub-wavelength scales [2,3]. Recently, numerous devices based on SPPs such as Mach-Zehnder interferometers [4], Y-shaped combiners [5], couplers [6], and splitters [7], have been investigated theoretically and demonstrated experimentally. The metal-insulator-metal (MIM) structures consist of a dielectric waveguide and two metallic claddings, which strongly confine the incident light in the insulator region [8]. Some devices based on the MIM waveguides have been studied numerically and experimentally, such as the Bragg reflector [9], tooth-shaped plasmonic waveguide filters [10–12], filters based on ring resonators [13] and nanodisk resonator [14], and wavelength selective waveguide [15]. As key factors in the plasmonic filters, optical resonators are crucial structural components of wavelength-selective devices due to their symmetry, simplicity, and ease of fabrication [16].
Filter for wavelength selection has found important applications in optical computing and telecommunication. Based on MIM structures, two types of plasmonic filters, i.e., band-pass and band-stop filters have been proposed in previous work. The former allows light with certain wavelength to pass through the waveguides [10,17] while the latter prohibits certain wavelength from transmitting [18,19]. Both of these two filters are very important in nanoscale optical devices. However, in some devices such as the (WDM) system, the band-pass filter plays very important role. WDM plays an important role in signal processing in optical communications. However, litter attention is paid to design plasmonic WDM so far as we know. Quite recently, Huang et al. had proposed a WDM on the basis of nano-capillary resonators [20].
In this paper, a new kind of tunable multi-channel WDM structures based on the nanodisk resonators are proposed and the transmission properties are investigated numerically. The FDTD results show that the wavelength of each channel is easily tunable by changing the geometrical parameters of the structure (i.e., the radius of resonator and the coupling length) and the refraction index of material in the nanodisk resonator. The multi-channel WDM structures possess high transmission at each channel, which will have potential applications in highly integrated optical circuits and optical computing.
2. Structures and simulations
The inset of Fig. 1 shows the schematic diagram of the filter that consists of two MIM waveguides and a nanodisk resonator in the middle of metallic structure. The width of waveguides t is 50 nm, and the radius of nanodisk resonator r is 410 nm. The coupling length between the waveguide and the nanodisk resonator d is set as 8 nm. The dielectric in the metal slit is air with refractive index n = 1. The metal is assumed as sliver, whose frequency-dependent complex relative permittivity is characterized by the Drude model [18]
Here ε ∞ = 3.7 is the dielectric constant at infinite angular frequency, ω p stands for the bulk plasma frequency and is 9.1 eV, which represents the natural frequency of the oscillations of free conduction electrons, γ represents the damping frequency of the oscillations and is 0.018 eV. ω is the angular frequency of the incident light [21]. The SPPs are excited with inputting a TM-polarized plane wave. The transmission of the structure is defined as T = P tr/P in [18]. P in presents the total incident power, and P tr is transmission power.
Fig. 1 Transmission spectrum of the waveguide with a nanodisk resonator. The inset is schematic diagram of the plasmonic filter.
According to temporal coupled mode theory, the transmission of the band-pass filter structure can be obtained from Ref [22].
Where w is the frequency of the incident light, w 0 is the resonance frequency. τ w is the decay rate of the field in the cavity due to the power escapes through the waveguide and τ i is the decay rate due to the internal loss in the resonator. As presented in Fig. 1, the transmission spectrum shows that the incident light far from w 0 is reflected. There exists a transmitted peak at the resonance frequency. From Eq. (2), when 1/τ i is far less than 1/τ w, the resonance transmission T max = (1/τ w)2/(1/τ w + 1/τ i)2 is close to unity. The transmission is near zero for the modes far from the resonance frequency. The simulation results are in good accordance with the theoretic analysis.3. Transmission properties of nanodisk resonator with different parameters
The FDTD method [23] is utilized to simulate the transmission characteristics with different radii of the nanodisk resonator. In the simulations, the grid sizes in the x and y directions are chosen to be Δx = Δy = 5 nm and Δt = Δx/(2c), c is the velocity of light in vacuum. Figure 2(a) shows the transmission spectra pertinent to different radii of the nanodisk resonator. The transmitted peak has a red-shift with the increase of the radius. Since the internal loss in the resonator cannot be neglected, the peaks do not reach 1.0. The internal loss increases when the radius increases. According to the simulation results, the filtering wavelength can be easily manipulated by adjusting the radius of the nanodisk.
Fig. 2 (a) Transmission spectra for different radii of the nanodisk resonator with d = 8 nm, t = 50 nm. (b) Transmitted-peak wavelength of the filter versus the radius of the nanodisk.
Successively, we investigate the influence of the material embedded in the resonator on the transmitted-peak wavelength. The radius of the nanocavity is set to be 300 nm. By changing the refractive index, the center wavelength exhibits a red-shift as shown in Fig. 3(a) . As can be seen from Fig. 3(b), it is found that the transmitted-peak wavelength has a nearly linear relationship with the refractive index. Therefore, one can simply manipulate the center wavelength of the filter by fitting the material with appropriate refractive index in the nanodisk resonator.
Fig. 3 (a) Transmission spectra for different refractive index with r = 300 nm, d = 8 nm, and t = 50 nm. (b) Transmitted-peak wavelength of the filter versus refractive index.
Furthermore, we find the coupling length d also affects the transmitted peak of resonant wavelength. The external loss 1/τ w will decrease rapidly when increasing d. However, the internal loss τ i in the cavity will be almost unchanged with the increase of d. Thus, the transmitted-peak will decrease as d increases. As shown in Fig. 4 , the numerical results are in good agreement with the above theoretic analysis. The transmission peaks of the filter can be controlled by changing the coupling length d. Moreover, we find the center wavelength has a slight blue shift.
Fig. 4 (a) Transmission spectra for different coupling length d with r = 360 nm, t = 50 nm, and n = 1.3.(b) Transmitted-peak wavelength versus the coupling length d.
4. Transmission properties of multi-channel WDM
According to the above characteristics of the plasmonic filter based on nanodisk resonators, several multi-channel WDM structures are proposed and investigated. As shown in Fig. 5(a) , three resonators with different parameters are placed near the waveguide. Here, we mark the resonators as cavity I, cavity II, and cavity III. The parameters are set as r 1 = 365 nm, d 1 = 10 nm, n 1 = 1.0, r 2 = 350 nm, d 2 = 8 nm, n 2 = 1.15, r 3 = 350 nm, d 3 = 8 nm, and n 3 = 1.3. The metallic slit width is 50 nm. The power monitors in the three channels are set to record the transmitted power. Figure 5(b) shows the transmission spectra of three channels. The transmitted-peak wavelengths of three channels for cavity I, cavity II, and cavity III are 1376, 1444, and 1550 nm, respectively.
Fig. 5 (a) Schematic diagram of the three-channel WDM. (b) Transmission spectra of the three channels.
We further design a WDM with five output channels. Figure 6(a) shows the geometric structure of the five-channel WDM. We add cavity IV and cavity V into the three-channel WDM. The parameters of new cavities are chosen as r 4 = 300 nm, d 4 = 10 nm, n 4 = 1.0, r 5 = 325 nm, d 5 = 10 nm, and n 5 = 1.0. Figure 6(b) is the transmission spectra of the five channels. The transmitted-peak wavelength for cavity IV and cavity V are 1175 and 1242 nm, respectively. Figures 6(c)-(d) shows the propagation of the field |H z| for incident light with the wavelength of 1444 nm and 1550 nm. It can be seen that the incident lights at 1444 and 1550 nm can pass through cavities II and III, respectively. This is consistent with the transmission spectra shown in Fig. 6(b).
Fig. 6 (a) Schematic diagram of the five-channel WDM. (b) Transmission spectra of the five channels. (c)-(d) Contour profiles of field |H z| at wavelength 1444 nm (Media 1), 1550 nm (Media 2), respectively
Additionally, we remove cavity III and study the transmission properties of the four-channel WDM. The transmission spectra of four channels are plotted in Fig. 7 . It is found that the peak transmission of four channels is less than that of the five-channel WDM. This is due to that cavity III can reflect the band-pass wavelengths of other four cavities. Thus, more power is coupled into the cavities I, II, IV, and V and emitted from the corresponding channels. This is also a main reason that the WDM based on nano-capillary resonators [20] has much lower transmission than ours.
Fig. 7 Transmission spectra of the four-channel WDM without cavity III. The inset is schematic diagram of the four-channel WDM.
Obviously, the research in this work focuses on multiple wavelength responses in the plasmonic devices. Although the nano-capillary resonant technique can achieve multiple wavelength responses [20], its transmission is as low as 30%. Fortunately, the proposed method here overcomes this shortcoming. The transmission in our structure can be up to 70%, besides multiple wavelength responses.
5. Conclusions
In this paper, we have designed a kind of tunable multi-channel WDM structures based on the nanodisk resonators. The transmission properties have been investigated by FDTD simulations. The wavelengths of the channels can be easily manipulated by changing the geometrical parameters and the refractive index of the resonator. It is found that the transmission of each channel can be as high as 70%, rather than about 30% in Ref [20]. The proposed structures can find important applications in highly integrated optical circuits and optical computing.
Acknowledgments
This work was supported by the “Hundreds of Talents Programs” of the Chinese Academy of Sciences and by the National Natural Science Foundation of China under Grants 10874239 and 10604066. Corresponding author (X. Liu). Tel.: + 862988881560; fax: + 862988887603; electronic mail: liuxueming72@yahoo.com and liuxm@opt.ac.cn.
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