Abstract
Characteristics of a multiple-teeth-shaped plasmonic filter are analyzed. As an extension of this structure, an asymmetrical multiple-teeth-shaped structure is proposed and numerically simulated by using the finite difference time domain method with perfectly matched layer absorbing boundary condition. It is found that the asymmetrical structure can realize the function of a narrow-passband filter. The central wavelength of the passband linearly increases with the simultaneous increasing of d 1 and d 2.
©2009 Optical Society of America
1. Introduction
A surface plasmon (SP) is a collective oscillation of the electrons at the interface between a metal and a dielectric. SP gives rise to surface-plasmon-waves, which are propagating electromagnetic waves bound at the metal-dielectric interface [1–4]. A usual dielectric waveguide cannot restrict the spatial localization of optical energy below the λ 0/2n limit, where λ 0 is the free space photon wavelength and n is the refractive index of the waveguide. As opposed to dielectric waveguides, plasmonic waveguides have shown the potential to guide subwavelength optical modes, the so-called surface plasmon polaritons (SPPs), at metal-dielectric interfaces, such as metallic nanowires [5,6] and metallic nanoparticle arrays [7,8]. Recently, several different metal–insulator–metal (MIM) waveguide structures based on SPPs have been numerically and/or experimentally demonstrated, such as U-shaped waveguides [9], splitters [10], Y-shaped combiners [11], multimode-interferometers [12], couplers [13,14] and Mach–Zehnder interferometers [15,16]. To achieve wavelength-filtering characteristics, SPP Bragg reflectors and nanocavities have been proposed [17,18]. Given the perspective of integrating various functional components within several micrometers, people need to decrease the size of a device to meet the demand of high integration. However, most of the filter structures mentioned above have large sizes over several wavelengths with the period number of N > 9 for the grating-like structures. Large size or length also results in relatively high propagation loss. In order to solve these problems, stub structures based on MIM waveguides which can function as wavelength selective filters with a submicron size have been numerically presented [19]. Recently, we have proposed and demonstrated numerically a novel tooth-shaped MIM structure to achieve a plasmonic filter with tens of nanometers in length [20]. Almost all of the structures mentioned above are of broad passband. In many cases such as WDM systems, however, it is required to select specific narrow-band wavelengths.
In this paper, a multiple teeth-shaped structure with a wide bandgap is firstly analyzed, as the extension of the single tooth filtering structure. A narrow-band subwavelength plasmonic waveguide filter with asymmetrical multiple-teeth-shaped structure is proposed, and narrow-passband filter response is achieved. The transmission spectrum as a function of teeth depth and the separation between the closest long tooth and short tooth is respectively discussed.
2. Characteristics of a multiple-teeth-shaped plasmonic filter
We firstly study characteristics of a multiple-teeth-shaped plasmonic filter (shown in Fig. 1(a)) to achieve an ultracompact size with hundreds of nanometers in length and low insertion loss. For the sake of comparison, the waveguide width w and the distance L are fixed to be 50nm and 300nm. Λ and N are the period and the number of rectangular teeth, respectively. wt and wgap stand respectively for teeth width and the width of the gap between any two adjacent teeth, and one has wt + wgap = Λ. In calculation, the insulator in all of the structures is assumed to be air (εin = 1), and the frequency-dependent complex relative permittivity of silver is characterized by the Drude model εm (ω) = ε ∞ - ω 2 p / ω(ω +iγ). Here ωp = 1.38×1016 Hz is the bulk plasma frequency, which represents the natural frequency of the oscillations of free conduction electrons; γ = 2.73×1013 Hz is the damping frequency of the oscillations, ω is the angular frequency of the incident electromagnetic radiation, and ε ∞ stands for the dielectric constant at infinite angular frequency with a value of 3.7 [21].
In the following FDTD simulations, the grid sizes in the x and the z directions are chosen to be5nm×5nm . The fundamental TM mode of the plasmonic waveguide is excited by a dipole source. Two power monitors are, respectively, set at the points of P and Q to detect the incident and the transmission fields for calculating the incident power of Pin and the transmitted power of Pout. The transmittance is defined to be T = Pout / Pin. A typical transmission spectrum of the multiple-teeth-shaped waveguide filter with wt = 50nm, Λ = 150nm, d = 260.5nm and N = 4 is shown in the Fig. 1(b), which is obtained with FDTD method. From Fig. 1(b), one can see that a wide bandgap occurs around λ = 1.55μm with the bandgap width (defined as the difference between the two wavelengths at each of which the transmittance is equal to 1%) of 590nm, and the transmittance of the passband is over 90%.
Fig. 1. (a) Schematic of a multiple-teeth-shaped MIM waveguide structure. (b) The transmission spectrum of the multiple-teeth-shaped waveguide filter with wt = 50nm, Λ = 150nm, d = 260.5nm and N = 4.
Figure 2 shows the central wavelength of the bandgap as a function of teeth depth d at various wt with the same Λ = 150nm and N = 4. The FDTD simulation results reveal that the relationship between the central wavelength of the bandgap and the teeth depth d is a linear function for a given wt. The central wavelength of the bandgap shifts toward long wavelength with the increasing of the teeth depth. It is also found that the role of small number of teeth is just to sharpen and optimize the bandgap of the filter (shown in Fig. 3). Thus, it can be predicted that combing two sets of optimized multiple-teeth-shaped structures with different teeth depths to stagger their passbands or bandgaps may realize a narrow-band filter. It will be tried and proven in the next section.
Fig. 2. The central wavelength of the bandgap as a function of the teeth depth of d at teeth width of 50nm.
Fig. 3. Transmission spectra of multi-teeth filters consisting of different numbers of rectangular teeth with a fixed Λ = 150nm.
3. Device of an asymmetrical multiple-teeth-shaped structure and simulation results
It is straight forward and of basic interest to expand a single set of multiple-teeth structure with same depth to an asymmetrical structure composed of two sets of multiple-teeth with two different teeth depths. The asymmetrical multiple-teeth-shaped structure is shown in Fig. 4(a). The short set has three teeth, and the long set has four. Λ, N 1 and N 2, are the period, the numbers of short rectangular teeth and long teeth, respectively. wgap stands for the width of the gap between any two adjacent teeth in multiple-teeth structure, and one has wt + wgap = Λ. The separation between the 3rd short tooth and 1 st long tooth is ws. The length of L and the waveguide width w are, respectively, fixed to be 150nm and 50nm. In Fig. 4(a) we set d 1 = 148nm, d 2 = 340nm, wt = 50nm, wgap = ws = 84nm. Figure 4(b) shows a typical transmission spectrum of the asymmetrical multiple-teeth-shaped structure using FDTD method.
Fig. 4. (a) Schematic of an asymmetrical multiple-teeth structure consisted of two sets with different teeth depths. (b) The transmission spectrum of the asymmetrical multiple-teeth-shaped waveguide filter with d 1 = 148nm, d 2 = 340nm, wgap = ws = 84nm, N 1 = 3, and N 2 = 4.
One can see the maximum transmittance at the wavelength of 1287nm is nearly 90%, and the full-width at half-maximum (FWHM) is nearly 70nm which is much smaller than the bandgap width of 1300nm. The FWHM of the asymmetrical multiple-teeth-shaped structure is also smaller than our previous coupler-type MIM optical filter [22].
In order to understand the origin of the narrow passband of the structure, the spectra of the transmission of a single-set of short three-teeth structure and a single-set of long four-teeth structure are calculated, and shown in Fig. 5. The parameters of the two structures are respectively equal to the parameters of the short teeth part and the long teeth part of the asymmetrical multiple-teeth-shaped structure (shown in Fig. 4(a)). One can see that the passband (or the bandgap) of the long teeth structure and the bandgap (or the passband) of the short teeth are overlapped from 800nm to 1200nm (or from 1450 to 1800nm), and then the transmittance of the cascade of the two structures is very low within the two regions. Only the overlapping between the right edge of the passband of the long teeth structure and the left edge of the passband of the short teeth is non-zero. This is the reason why the wavelengths around 1300nm have a transmission peak in Fig. 4 (b).
Fig. 5. The transmission spectra of the single-set of multiple-teeth structure with d 1 = 148nm, N 1 = 3 and the single set of multiple-teeth structure with d 2 = 340nm and N 2 = 4, respectively.
Figure 6 shows the central wavelength of the narrow-band as a function of the variation of Δd = Δd 1 = Δd 2, where Δd is the increment of d 1 and d 2. The initial values of d 1 and d 2 are respectively 128nm and 320nm. From the figure one can see that the central wavelength of the narrow-band linearly increases with the simultaneous increasing of d 1 and d 2. Figure 7 shows the dependence of transmittance on separation ws. It can be found the transmittance at the wavelength of 1287nm reaches the peak value when the separation of ws equals the gap of wt. Therefore, one can realize the narrow-band filter function at different required wavelengths by means of properly choosing the parameters of the device, such as the teeth-depth, period or the separation of ws.
Fig. 6. Central wavelength of the narrow-band as a function of the variation Δd = Δd 1 = Δd 2, Δd 1, and Δd 2 are respectively the increments of d 1 and d 2.
Fig. 7. Dependence of transmission characteristic on separation between the 3rd short tooth and the 1st long tooth with d 1 = 148nm, N 1 = 3, d 2 = 340nm, and N 2 = 4, respectively.
4. Conclusion
In conclusion, a narrow-band subwavelength plasmonic waveguide filter with an asymmetrical multiple-teeth structure is proposed. The simulation demonstrates that the device has characteristics of a narrow-band wavelength filter with high transmittance around 90%, and the central wavelength of the narrow-band linearly increases with the simultaneous increasing of d 1 and d 2. The new structure may have applications to ultrahigh nanoscale integrated photonic circuits on flat metallic surfaces.
Acknowledgment
The authors acknowledge the financial support from the Natural Science Foundation of Guangdong Province, China (Grant No. 07117866).
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