Open Access
Add to BibSonomyAbstract
Using strong couplings of different Fabry–Perot (FP) resonators in metal–insulator–metal waveguides, a compact plasmonic wavelength demultiplexer is numerically demonstrated with high wavelength resolution. In the demultiplexer, it is found that new right–angle resonators emerge with bandwidth narrower than that of the isolated FP resonators. These narrowband right–angle resonators interfere with the broadband FP resonators, resulting in Fano–line shapes in the transmission spectra. Consequently, these sharp and asymmetric Fano–line shapes considerably increase the resolution of wavelength demultiplexing, which is significantly narrower than the full width of the isolated FP resonator.
©2011 Optical Society of America
1. Introduction
Surface plasmon polaritons (SPPs) are electromagnetic waves propagating along metal–dielectric interfaces with tight field confinement, and are regarded as a promising candidate to guide light in subwavelength structures [1–4]. In recent years, various SPP based waveguides have been proposed and demonstrated, such as long–range SPPs [5], channel SPPs [6], dielectric–loaded SPPs [7], and metal–insulator–metal (MIM) [2,3] waveguides. The SPP modes in the MIM waveguide, in particular, can significantly overcome the classical diffraction limit and has acceptable propagation lengths, low bend losses, and convenience for sample fabrication [8–11], so they are quite promising for realizing highly integrated photonic circuits. Based on the MIM waveguide, compact plasmonic devices, such as the nanofocusing structure [12], ring resonator [13], filter [14], and splitter [15] have been designed and demonstrated.
In highly integrated optical communication networks, compact and high–resolution wavelength demultiplexers are one of the key components. Plasmonic 1 × 2 demultiplexers have been investigated numerically by placing rectangular nanocavity resonators inside, or outside, the MIM waveguide in a Y–bent combiner [16]. A MIM waveguide connected with a series of nano–capillary resonators has also been proposed as a wavelength demultiplexer based on the plasmonic nano–capillary resonators [17]. These demultipelxers used the isolated–resonator effect to select wavelength and were designed to avoid the coupling of different resonators. However, these isolated resonators typically exhibit broadband transmission spectra with nearly symmetric Lorentzian–like line shapes. To achieve a high–contrast ratio of wavelength demultiplexing, the separation of wavelengths must be significantly larger than the full width of the resonance of the isolated FP resonator [16,17], which limits the wavelength resolution of the demultiplexer.
In this paper, a MIM waveguide with a baffle is proposed as a Fabry–Perot (FP) resonator and a wavelength selector. Then, a MIM waveguide perpendicularly connected with series of these wavelength selectors is designed as a compact plasmonic wavelength demultiplexer. It is found that new right–angle resonators emerge with narrow bandwidth in the compact demultiplexer. The interference between the new right–angle resonator (narrow band) and the original FP resonator (broad band) results in a Fano–line shape [18,19] in the transmission spectrum. This sharp and asymmetric response line shape considerably increases the resolution of wavelength demultiplexing, which is significantly narrower than the full width of the isolated FP resonator.
2. Isolated FP resonator for wavelength selecting in the MIM waveguide
First, we investigated the characteristics of an isolated FP resonator in the MIM waveguide, as shown schematically in Fig. 1 , consisting of a MIM waveguide perpendicularly connected to another MIM waveguide with a baffle. The baffle can be metals or dielectric with high refractive index. Without the baffle, the power flow of SPPs goes nearly half to channel 1 and half to channel b. With the baffle, SPPs going to the perpendicular MIM waveguide are reflected back and forth off the baffle and the wall of the horizontal MIM waveguide, which is just like an FP resonator (indicated by the red dotted line in Fig. 1). The accumulated phase delay per round trip is
where k spp is the wave vector of SPPs in the MIM waveguide, d is the position of the baffle (as shown in Fig. 1), and θ is the phase shifts brought by the reflection in the FP resonator. According to Eq. (1), constructive or destructive interference should occur when φ FP equals even or odd multiples of π, respectively. When the baffle is thin, a portion of the SPPs in the FP resonator can pass through the baffle, as shown in Fig. 1. At resonance, the field intensity in the FP resonator is the strongest, and thus the output of the channel 1 is the largest. On the contrary, the output of the channel 1 is the smallest at off–resonance. Therefore, the FP resonator can be used to select wavelength based on the resonant condition.
Fig. 1 Schematics of the isolated FP resonator in the MIM waveguide with a baffle and the geometrical parameter symbols. The positions of the ports a, b, and 1 are fixed, with L = 1.0 μm.
The wavelength–selecting properties of the isolated FP resonator were numerically investigated using the finite element method with Comsol Multiphysics. We used a 2D simulation, and the eigen-mode source of monochromatic light was injected from the input in Fig. 1. In the simulation, the metal, the baffle, and the insulator were assumed to be silver, silver, and air (ε Air = 1.0), respectively. The width of the MIM waveguide was fixed to h = 50 nm. The wavelength of the incident light is λ = 1000 nm and the permittivity of the silver at this wavelength is ε Ag = –50.7 + 0.57i [10]. It should be stressed that the choice of the incident wavelength is arbitrary, and that the geometry of the FP resonator can always be tuned to match the desired wavelength. Calculations have shown that the effective refractive index and the propagation length of the SPPs in this MIM waveguide are n eff = 1.38 and L SPP = 40.5 μm, respectively (obtained by solving the eigenfunction of the SPP wave vector in the MIM waveguide). The transmittance of SPPs, T 1 (or T b), at Port 1 (or b) is defined as the quotient between the SPP power flows of Port 1 (or b) and Port a [13,14,17]. The power flowers at the ports were obtained by integrating the Poynting vector over the channel cross section. In the simulations, the proposed structure (Fig. 1) is very compact (~μm), which is much smaller than the propagation length (40.5 μm) of SPPs, so the Ohmic loss in the metal can be neglected.
The dependence of the transmittances, T 1 and T b, on the baffle’s position d (corresponding to the length of the FP resonator) for different baffle thicknesses were calculated and are displayed in Fig. 2(a) . Without the baffle, both T 1 and T b are close to 0.5 [the black solid line and the black dash line in Fig. 2 (a)]. This indicates that the power flow of SPPs goes nearly half to channel 1 and half to channel b. With the baffle, T 1 and T b become dependent on the position of the baffle, as indicated by the colored lines in Fig. 2(a). The transmittances are periodic in d, and the period is P≈360 nm, which approximately equals λ spp/2. This verifies the FP resonator model, as discussed above. One important application of the FP resonator is that it can act as a wavelength selector. To obtain a high selecting efficiency, high and low outputs are desired at resonance and off–resonance, respectively. From Fig. 2 (a), we can see that the transmittance of channel 1 increases as the baffle thickness decreases. At the thickness of t = 15 nm, the transmittances are about 0.580 and 0.015 at resonance and off–resonance, respectively. This well satisfies the wavelength–selecting condition above. If the baffle is too thin, the transmittance at off–resonance is not suppressed enough. If the baffle is too thick, the transmittance at resonance is not high enough. So, we chose the proper thickness of t = 15 nm in the following simulations. Typical power flow distributions of the wavelength–selecting phenomenon at λ = 1000 nm are presented in Figs. 2 (b) and (c) for d = 150 nm and d = 350 nm, respectively. It is noted that the power flow goes mainly to channel 1 at resonance [Fig. 2 (b)] and to channel b at off–resonance [Fig. 2 (c)]. This well demonstrates the wavelength–selecting ability of the isolated FP resonator.
Fig. 2 (a) Dependence of the transmittances, T 1 and T b, on the baffle position for different baffle thicknesses: t = 0 nm (without baffles), t = 10 nm, t = 15 nm, and t = 20 nm. (b) and (c) Distributions of the SPP power flow in the air for d = 150 nm and d = 350 nm, respectively.
The wavelength–selecting properties of the isolated FP resonator can also be examined in the frequency domain. The transmittance spectra of the isolated FP resonator were obtained by changing the input wavelength. The permittivity of Ag as a function of wavelength was taken from literature [10] and expanded using the method of interpolation. Figure 3 shows the calculated transmission spectra, T 1 and T b, for three different baffle positions. When the transmittance of channel 1, T 1, reaches the maximum (about 0.5) at resonance, T b is close to zero. Consequently, the isolated FP resonator can be used as a wavelength selector. The full width at half maximum of the transmission spectra is about Δλ FWHM≈90 nm. Moreover, the resonant wavelength can be tuned by changing the length of the FP resonator.
Fig. 3 Transmission spectra, T 1 and T b, for different baffle positions (d = 480 nm, d = 500 nm, and d = 520 nm).
3. New resonator with narrow bandwidth emerging in the plasmonic wavelength demultiplexer
As an application of the wavelength–selecting properties, the above FP resonator can be exploited to construct a compact plasmonic wavelength demultiplexer. Figure 4 shows a typical 1 × 2 demultiplexer structure, consisting of a MIM waveguide perpendicularly connected with two FP resonators with a separation of w. These two FP resonators have different lengths of d 1 = 480 nm and d 2 = 500 nm, corresponding to the resonant wavelengths of λ 1 = 945 nm and λ 2 = 985 nm for the isolated FP resonator, respectively. Here, the difference between these two resonant wavelengths, Δλ = λ 2–λ 1 = 40 nm, is much smaller than the bandwidth of the isolated FP resonator (Δλ FWHM≈90 nm), which implies that these two wavelengths cannot be separated using the traditional isolated–resonator effect. Thus, these two FP resonators will affect each other significantly in this demultiplexer, and the transmittance of each channel should be dependent on the separation, w.
In order to present the coupling effect of these two different FP resonators, the dependence of the transmittances of each channel (T 1, T 2, and T b) on w in the demultiplexer at λ = 985 nm (the resonant wavelength of the second FP resonator) was calculated and is shown in Fig. 5 . It is noted that T 1 and T 2 change with the separation of these two FP resonators significantly, which reveals that there is a strong coupling between these two FP resonators. Moreover, the transmittances exhibit periodic behaviors with a period of P≈360 nm, just the same as that in Fig. 2(a). This vibrating behavior of the transmittances suggests that, in addition to the isolated FP resonators, a new SPP resonator emerges in the demultiplexer.
Fig. 5 Dependence of the transmittances of each channel (T 1, T 2, and T b) on the separation of the two channels, w, in the 1 × 2 demultiplexer for λ = 985 nm.
To clarify the physical picture of the new resonator, we made additional simulations. These simulation results (not shown in this paper) indicate that the value of w for the resonant condition in Fig. 5 are nearly independent on the position and the existence of the baffle in the channel 1, but are linearly dependent on the position of the baffle in the channel 2. This reveals that the new resonator is from the first branch to the baffle in channel 2, as indicated by the red dashed line in Fig. 4. Here, we call it a right–angle resonator. To obtain the resonant property of this new right–angle resonator, we calculated the transmission spectrum of channel 1 without the baffle in channel 1 (schematically illustrated by the inset in Fig. 6 ). Without the resonant effect in channel 1, SPPs from the input go nearly half to channel 1 and half to the other channel at the first branch. Then, the SPPs reflected by the baffle in channel 2 partly go back to the first branch and interfere with the SPPs in channel 1, as shown by the inset in Fig. 6. This will bring a phase difference, Φ = 2k SPP L′ + φ, between these two interfering SPPs, where k SPP is the SPP wave vector; L′ is the length of the red dashed line in the inset in Fig. 6; and φ is the phase shift brought by the reflection off the baffle in channel 2. Thus, the SPP intensity in channel 1 will be affected by the new right–angle resonator. So the transmission spectrum of channel 1 can directly give the resonant behavior of the new right–angle resonator, as shown in Fig. 6. It is found that the bandwidths of these calculated transmission spectra are about Δλ FWHM′≈40 nm, which is much narrower than that of the isolated FP resonator (Δλ FWHM≈90 nm). The reason for the narrower bandwidth is given below. In the proposed structure, the cavity length (~μm) is much smaller than the propagation length of SPPs in this MIM waveguide (~40.5 μm), so the cavity loss is not due to the Ohmic loss (high transmittance of 98% after propagating 1 μm) but mainly determined by the coupling loss from the FP resonator to the input and output waveguides (e.g. reflectance of about 90% at the 15 nm-thick Ag baffle). Thus, the bandwidth is nearly inversely proportional to the cavity length if the coupling loss is a constant for a round rip in the cavity, which is similar to the behaviors of traditional FP cavities. In the manuscript, the length of the original FP resonator is about 500 nm, while the length of the new resonator is about 860 nm, so the bandwidth of the new right-angle resonator is narrower than that of the original FP resonator. Additional simulation shows that if the length of the new right-angle resonator becomes longer, its bandwidth can be further narrowed. For example, when the separation of the two perpendicular channels is w = 720 nm (corresponding to the cavity length of 1220 nm), the bandwidth becomes Δλ FWHM′≈30 nm.
Fig. 6 Transmittance of channel 1 without the baffle in channel 1 for different separations between channel 1 and 2. The inset illustrates the simulation structure.
4. High wavelength resolution of the plasmonic demultiplexs based on Fano interference
Next, we investigated the wavelength–selecting properties of the above 1 × 2 demultiplexer in the frequency domain. The transmission spectra of each channel (T 1, T 2, and T b) in the demultiplexer with d 1 = 480 nm and d 2 = 500 nm were calculated and are displayed in Fig. 7 (a) . Here, w is chosen to be 360 nm, which is the separation where T 1 reaches its minimum value and T 2 is nearly largest at λ = 985 nm, as shown in Fig. 5. This ensures that the wavelength of λ = 985 nm is efficiently selected by channel 2. Since a new right–angle resonator emerges in the demultiplexer, the transmittance spectrum of each channel displays a sharp and asymmetric response line shape [the red and blue lines in Fig. 7(a)]. These line shapes exhibit the typical Fano profile [18–20] and are considerably different from the line shapes of the isolated FP resonator. It is well known that Fano profiles are typical spectral features arising from the coupling of a discrete state (or a narrow band) with a continuum (or a broad band) [18–20]. In the current case, the resonant spectrum of the isolated FP resonator is broadband (Δλ FWHM≈90 nm), and the resonant spectrum of the new right-angle resonator is narrowband [the dashed line in Fig. 7(b), Δλ FWHM′≈40 nm]. Moreover, the resonant wavelength in the new right–angle resonator (λ new = 978 nm) is just between the resonant wavelengths of the isolated FP resonators with d = 480 nm (λ 1 = 945 nm) and d = 500 nm (λ 2 = 985 nm), as shown in Fig. 7(b). Therefore, the interference of the isolated FP resonator (broad band) with the new right–angle resonator (narrow band) can result in the inverse Fano profiles [18–20] [the red and blue lines in Fig. 7 (a)] in the transmittances of the channel 1 and 2 in the demultiplexer.
Fig. 7 (a) Dependence of the transmittances, T 1, T 2, and T b, on the incident wavelength in the 1 × 2 demultiplexer. (b) Transmittance of channel 1 without the baffle in channel 1 (dash line) and transmittances of the isolated FP resonator with d = 480 nm and d = 500 nm.
These sharp and asymmetric Fano–line shapes in Fig. 7 (a) have important applications because they considerably increase the resolution of wavelength selecting. As a result, two wavelengths with a separation of 30 nm, which is significantly narrower than the full width of the resonance of the isolated FP resonator (Δλ FWHM≈90 nm), can be split and selected by different channels efficiently [Fig. 7(a), SPPs of λ = 950 nm go to channel 1, and SPPs of λ = 980 nm go to channel 2]. While, based on the traditional isolated–resonator effect, two wavelengths with a separation smaller than Δλ FWHM could not be split efficiently. In fact, the separation of wavelengths usually has to be quite larger than Δλ FWHM in order to achieve a high contrast ratio of wavelength demultiplexing [16,17]. By carefully adjusting the geometrical parameters of the compact plasmonic demultiplexer, the demultiplexing resolution can be even higher. This can be realized by adjusting the length of the two FP resonators to make the separation of their resonant wavelengths become smaller. For example, we realize a demultiplexing resolution of 18 nm by changing the length of the FP resonator in channel 1 from d 1 = 480 nm to d 1 = 485 nm, as shown in Fig. 8 .
Fig. 8 Dependence of the transmittances, T 1, T 2, and T b, on the incident wavelength in the 1 × 2 demultiplexer. d 1 = 485 nm, d 2 = 500 nm, and w = 360 nm.
This principle based on the Fano interference can also be exploited to design the 1 × N demultiplexer. As an example, Fig. 9 displays the transmission spectra of each channel (T 1, T 2, T 3, and T b) in a typical 1 × 3 demultiplexer (d 1 = 480 nm, d 2 = 500 nm, d 3 = 520 nm, and the distances between every two channels are w 12 = 360 nm and w 23 = 380 nm, respectively). Again, we observe Fano–line shapes for T 1 and T 3. The wavelengths of λ = 950 nm, λ = 980 nm, and λ = 1020 nm are efficiently split and selected by channel 1, 2, and 3, respectively. Corresponding distributions of the SPP power flow in the 1 × 3 plasmonic wavelength demultiplexer are shown in Figs. 9 (b), (c), and (d). The demultiplexing resolution is also much smaller than the full width at half maximum of the transmission spectra in the isolated FP resonators due to the Fano interference.
Fig. 9 (a) Transmission spectra (T 1, T 2, T 3, and T b) in the 1 × 3 demultiplexer. Distributions of the SPP power flow in the air in the demultiplexer at different incident wavelengths (b) λ = 950 nm, (c) λ = 980 nm, and (d) λ = 1020 nm.
5. Conclusion
A MIM waveguide with a baffle was proposed as a FP resonator and a wavelength selector. Based on the strong coupling of different resonators in MIM waveguides, a compact and high–resolution plasmonic wavelength demultipelxer was demonstrated numerically. In the demultiplexer, new right–angle resonators emerge with narrow bandwidths. The interference between the new right–angle resonator (narrow band) and the original FP resonator (broad band) results in Fano–line shapes in the transmission spectra. These sharp and asymmetric response line shapes considerably increase the resolution of wavelength selecting (Δλ≈30 nm), which is significantly narrower than the full width of the isolated resonator (Δλ FWHM≈90 nm). While, based on the traditional isolated–resonator effect, two wavelengths with a separation smaller than Δλ FWHM cannot be split efficiently. The mechanism based on Fano interference may provide a novel possibility for designing ultracompact and highly wavelength–resolved components in optical communication and computing, especially in wavelength-division-multiplex and all–optical switching systems.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant Nos. 10804004, 10821062 and 90921008) and the National Basic Research Program of China (Grant Nos. 2007CB307001 and 2009CB930504).
References and links
1. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer–Verlag, 1988).
2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]
3. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010). [CrossRef]
4. T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61(5), 44 (2008). [CrossRef]
5. D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47(26), 1927–1930 (1981). [CrossRef]
6. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006). [CrossRef] [PubMed]
7. T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon–polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007). [CrossRef]
8. G. Veronis and S. Fan, “Bends and splitters in metal–dielectric–metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87(13), 131102 (2005). [CrossRef]
9. P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal–insulator–metal waveguides,” Nat. Photonics 3(5), 283–286 (2009). [CrossRef]
10. R. J. Walters, R. V. A. van Loon, I. Brunets, J. Schmitz, and A. Polman, “A silicon-based electrical source of surface plasmon polaritons,” Nat. Mater. 9(1), 21–25 (2010). [CrossRef]
11. E. Verhagen, J. A. Dionne, L. K. Kuipers, H. A. Atwater, and A. Polman, “Near-field visualization of strongly confined surface plasmon polaritons in metal–insulator–metal waveguides,” Nano Lett. 8(9), 2925–2929 (2008). [CrossRef] [PubMed]
12. A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105(11), 116804 (2010). [CrossRef] [PubMed]
13. T. B. Wang, X. W. Wen, C. P. Yin, and H. Z. Wang, “The transmission characteristics of surface plasmon polaritons in ring resonator,” Opt. Express 17(26), 24096–24101 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-26-24096. [CrossRef]
14. X. S. Lin and X. G. Huang, “Tooth-shaped plasmonic waveguide filters with nanometeric sizes,” Opt. Lett. 33(23), 2874–2876 (2008). [CrossRef] [PubMed]
15. A. A. Reiserer, J. S. Huang, B. Hecht, and T. Brixner, “Subwavelength broadband splitters and switches for femtosecond plasmonic signals,” Opt. Express 18(11), 11810–11820 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=oe-18-11-11810. [CrossRef] [PubMed]
16. A. Noual, A. Akjouj, Y. Pennec, J.-N. Gillet, and B. Djafari-Rouhani, “Modeling of two-dimensional nanoscale Y-bent plasmonic waveguides with cavities for demultiplexing of the telecommunication wavelengths,” N. J. Phys. 11(10), 103020 (2009). [CrossRef]
17. J. Tao, X. G. Huang, and J. H. Zhu, “A wavelength demultiplexing structure based on metal–dielectric–metal plasmonic nano-capillary resonators,” Opt. Express 18(11), 11111–11116 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=oe-18-11-11111. [CrossRef] [PubMed]
18. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961). [CrossRef]
19. G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, N. Del Fatti, F. Vallée, and P.-F. Brevet, “Fano profiles induced by near-field coupling in heterogeneous dimers of gold and silver nanoparticles,” Phys. Rev. Lett. 101(19), 197401 (2008). [CrossRef] [PubMed]
20. S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80(6), 908 (2002). [CrossRef]
