1. Introduction

In recent years, there has been wide interest in emerging field of nanoplasmonics. While silicon photonics circuits show promise in overcoming the fundamental speed limits of conventional electronic circuits, they are ultimately limited in size by the diffraction limit. With mode sizes far below the diffraction limit, metal-dielectric nanoplasmonic devices are more capable of competing with conventional electronics in terms of device size, while still retaining the speed advantages of typical photonic devices. The integration of nanoplasmonic devices with Si-based platform system allows for monolithic integration with standard complementary metal-oxide semiconductor (CMOS) technology and gives rise to the possibility of hybrid electronic/plasmonic nanocircuitry [1].

Plasmonic devices, similar to photonic devices, are formed from waveguides, of which there are three main types: coupled nanoparticle chains [2], metal strips (insulator-metal-insulator) [3–5], and gap plasmon waveguides (metal-insulator-metal) [6–8]. The coupled nanoparticle chains have exhibited both propagation lengths and mode sizes on the order of a few hundred nanometers, while the metal strips have shown propagation lengths on the order of millimeters and mode sizes on the order of microns [4], thus offering little advantage over conventional photonic waveguides. Gap plasmon waveguides offer a balance between these two, with mode sizes on the order of a few hundred nanometers and propagation lengths of a few microns [6]. Thus, it is advantageous to exploit device geometries based on gap plasmon waveguides for nanoscale plasmonic circuit integration. Furthermore, gap plasmon waveguides also have the benefit of monolithic integration with a CMOS compatible platform, thus, giving rise to the possibility of having electrical signals travel along the same bus lines as the optical and the plasmonic signals.

One of the major difficulties in a CMOS electronic platform are the vertical connections between device layers and the overlaying of crossed electrical connections, accomplished through the use of vias. Likewise, for advanced nanoplasmonic circuits to play a major role in data processing, signal routing, and computing, they require 3-D integration since device layer stacking increases synchronization and reduces the overall circuit footprint. Small footprints are especially important in plasmonic circuits, which already suffer from relatively high propagation losses caused by metal absorption. However, to date, there has been little work on 3-D integration of plasmonic circuits. This is due to the fact that complications arising from interference between waveguides [9], non-selective signal transfer, low coupling efficiency [10], and signal polarization changes, limit the application of direct 3D surface plasmon signal routing. Thus, the majority of work on integrating plasmonic devices has been focused on planar 2-D integration utilizing laterally coupled plasmonic waveguides [9]. An example of 3-D plasmonic integration has been on vertically coupling gap plasmon waveguides [10], which considered the coupling between vertically stacked gap plasmon waveguides. However, this coupling occurred over micron scale distances, where the relatively long coupling spatial scale was on the order of the propagation length of the waveguides, thus limiting device size. Furthermore, since this coupling method was not frequency-selective for the propagating surface plasmon signal, this scheme does not allow for routing of specific wavelengths between the layers. Wavelength routing is important for wavelength-division multiplexing (WDM) applications and is the backbone of many photonic systems.

In this work, we present a novel nanoplasmonic 3-D coupling platform that can be monolithically integrated with the current Si-based CMOS technology. The layer-to-layer plasmonic signal coupling takes place between vertically stacked nanoplasmonic nanoring resonators. With such a unique design of the 3-D interconnect platform, the inherent constraints imposed on the minimum device size and length are overcome by having the layer-to-layer signal coupling take place over multiple round trips within the resonator. We demonstrate that surface plasmon signal circulation in the nanoplasmoic ring results in high coupling efficiencies of up to 39% between adjacent layers. Furthermore, using nanoplasmonic nanoring resonators as the vertical coupling platform allows for frequency selectivity via the device ports and through varying the radii of the rings, which allows for tailoring the specific frequencies to be transmitted between layers. This unique coupling scheme allows for different device layers to operate at different frequencies without cross-talk. An envisaged application would be stacked independent circuits for parallel processing in a plasmonic analog to coarse WDM in conventional photonic systems.

2. Device geometry

The basic building block of the 3-D nanoplasmonic circuit architecture is the vertically-stacked nanoring resonators. Strong electromagnetic coupling can be achieved from a nanoring to a vertically-stacked nanoring when the resonant modes are made to satisfy both nanorings’ resonances. The coupling platform presented here is formed of Ag/Si/Ag gap plasmon waveguides. Silver was chosen as the metallic component of the plasmonic waveguides due to its low losses for surface plasmons propagations [11]. Using silicon as the dielectric allows for efficient coupling to conventional silicon photonic devices. In addition, it offers potential for CMOS compatibility with Si electronic components. The input and output waveguides couple to the identical vertically-stacked nanoring resonators to enable the frequency selective signal transfer between device layers. Schematics of the five device platforms under consideration are presented in Fig. 1 . A schematic 2-D representation of the center of the vertically coupled nanoring resonators from perpendicular to the source input direction can be seen in Fig. 1(a). The device layers are formed of silver films of thickness h₁ = 100 nm and square silicon channels of dimensions w₁ = h₁ = 100 nm, forming the gap plasmon waveguides. The input and output waveguides couple to the nanoring resonators through a silver gap of width w₂ = 25 nm. The entire device is submerged in SiO₂, thus actingas both the substrate and the cladding layer. The device layers are seperated by a cladding thickness of h₂ = 100 nm. It should be noted, at this device layer separation, negligible interference in signal propagation of ~5% was caused by the adjacent device layers, except where the waveguides vertically overlapped over lengths greater than the waveguide widths. Most of the devices have a radius, r, of 560 nm, thus leading to device footprint areas of 1.00 μm². The operation of two-level system having parallel input and output waveguides, depicted in Fig. 1(b), was examined with nanorings radii of r = 400, 500, 560, and 600 nm to characterize the affect of the radius on the coupling mechanism. However, the device operation of the two-level system having perpendicular input and output waveguides, depicted in Fig. 1(c), was examined at r = 560 nm. Finally, a three-level system, having the output waveguides opposite to the input waveguide as depicted in Fig. 1(d), above the input waveguide as depicited in Fig. 1(e), and both opposite and above the input waveguide as depicted in Fig. 1(f), were examined at r = 560 nm.

 

Fig. 1 (a) Schematic 2-D representative side view of the vertically coupled nanoring resonators with parallel input and output waveguides and dimensions w₁ = h₁ = h₂ = 100 nm, w₂ = 25 nm, and nanorings with radii, r. (b) Angled-view of the same structure without the Ag and SiO₂ layers. (c) Angled-view of two-level system with perpendicular input and output waveguides. (d,e,f) Angled view of three-level systems with different arrangements of output waveguides. In all of the above devices, the labeled ports are: input (A), throughput (B), drop (C,E), and add (D,F).

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3. Device operation

Finite difference time domain (FDTD) simulations were conducted on the devices presented in Fig. 1 to examine their operation. Optical constants for silver were obtained from [12]. Here, the input optical mode, shown in Fig. 2(a) , was a broadband source centered at 1.42 μm and extends from 1.1 μm to 2.0 μm. This mode had a propagation loss of 0.55 dB/μm at the center wavelength of 1.42 μm, which corresponds to a propagation length of 7.82 μm. The source was injected at the input port, port A in Fig. 1, at a distance of 1.00 μm from the center of the nanorings. The mode is tightly confined within the Si waveguide in the lateral direction by the Ag layer, and extends only 30 nm into the SiO₂ cladding above and below the waveguide. The output spectra, intensity versus wavelength, were measured 1.00 μm from the center of the nanorings at the throughput port, port B shown in Fig. 1, and drop ports, ports C or E shown in Fig. 1, for each level. The results of the simulations are presented in Figs. 2 (b-f) and Fig. 3 .

 

Fig. 2 (a) Normalized intensity input mode for the Ag/Si/Ag gap plasmon waveguide centered at a wavelength of 1.42 μm and measured at a distance of 1 µm from the center of the nanoring at port A. (b-f) Transmission spectra at the throughput port B (blue), and drop port C (red) for the two-level device geometries depicted in Fig. 1. (b) 400 nm, (c) 500 nm, (d) 560 nm, and (e) 600 nm nanorings radii for the two-level system with parallel input and output waveguides as depicted in Fig. 1(b). (f) Two-level system with perpendicular input and output waveguides and r = 560 nm as depicted in Fig. 1(c).

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Fig. 3 Transmission spectra at the throughput port B (blue), and drop ports C (red) and E (green) for the three-level device geometries depicted in Fig. 1. (a) Three-level system with 560 nm nanoring radii as depicted in Fig. 1(d). (b) Three-level system with r = 560 nm as depicted in Fig. 1(e). (c) Three-level system with r = 560 nm as depicted in Fig. 1(f).

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We examine the effect changing the radii of the vertically-stacked identical nanoring resonators has on the intensity spectra. Using the two-level system having parallel input and output waveguides as depicted in Fig. 1(b), the effects of changing the radii of the nanorings was investigated first to determine the optimum nanoring radius for the best interlayer coupling. Figure 2 (b-e) illustrates the output intensity spectra for the two-level nanoring resonators as the radii varied from 400 nm to 600 nm. Clearly, altering the radii of the nanorings moves the location of the spectral peaks at the B (throughput) and C (drop) ports. As the radii of the nanorings were reduced, the spectral peaks broadened and thus, their Q factor decreased. However, the longer radii lead to increased propagation losses. The nanoring radius that corresponded to the highest peak intensities spectra for both throughput and drop ports was found to be 560 nm. Here, the Q-factors were found to be 30 for the throughput port at a wavelength of 1.5 μm and 20 at the drop port peak at a wavelength of 1.43 μm. The intensity at the drop port at 1.43 μm was 30% of that of the input intensity. After taking the input and output waveguides propagation losses into account, this corresponds to a coupling efficiency for the two-level system with r = 560 nm at 1.43 μm, of 39%. In comparison, the intensity at the throughput port at 1.5 μm was 49% of the input intensity. For true 3-D integration, it is crucial to have the transmitted signal in the upper layer propagate in an arbitrary direction relative to that of the input signal. For this reason, the effect of changing the output waveguide orienting from parallel to perpendicular to the input waveguide, the device in Fig. 1(b) as opposed to the device in Fig. 1(c), was examined. While the output waveguide cannot be placed directly above the input waveguide, as this would result in undesirable frequency-independent coupling [10], a 560 nm radius 90° bend in the output waveguide after the coupled resonator device would provide access to all propagation direction at the cost of only 11% bending losses at the center wavelength. This change in output waveguide location; however, resulted in a slightly lower intensity at the output ports in the intensity spectra depicted in Fig. 2(f) compared to the parallel output waveguide device. The intensity at the drop port at 1.43 μm and at the throughput port at 1.5 μm were 27% and 42% of the input intensity, respectively. Despite the lower intensities, the Q-factors at these peaks increased to 26 for 1.43 μm at the drop port and 35 for 1.5 μm at the throughput port.

Signal transfer for more than two layers was examined as well through three-level systems having r = 560 nm. Since the signal is often required to by-pass a particular device layer, the effect of multilayer coupling on the transmitted signal must be explored. This method of signal transfer could also be used when the device layers are actually situated farther than 100 nm apart by placing additional coupling nanorings between the device layers. The device shown in Fig. 1(d) is identical to the device shown in Fig. 1(b) except with the addition of a third device layer between the input and output device layers. The addition of the third device layer means more coupling needs to take place, and the effect of this can be seen in the intensity spectra in Fig. 3(a). The effect of adding a third layer acts to load the nanoring resonators and, thus, the spectral location of the output peaks above 1.6 μm shift, while the intensities of the output peaks decrease compared to the two-level system. The intensity at the drop port at 1.43 μm and at the throughput port at 1.5 μm decreased to 17% and 44% of the input intensity, respectively. For the three-level system, the Q-factors were found to be 30 for the throughput port at 1.5 μm and 20 at the drop port peak at 1.43 μm. Changing the location of the output waveguide from the opposite side of the nanorings from the input waveguide to above the input waveguide, Fig. 1(d) to Fig. 1(e), does not cause significant change in the throughput port spectra or the drop port spectra between 1.3 μm and 1.7 μm, while enabling the output waveguide to access a different direction without resorting to bending the waveguide and the accompanying bending losses. The results of the change in output waveguide location can be seen in Fig. 3(b). The addition of a second output waveguide coupled to the nanoring in the middle device layer, as depicted in Fig. 1(f) and results shown in Fig. 3(c), causes ~50% attenuation in the drop port spectra for drop port E without changing the location of the spectra peaks compared to the drop port spectra for the other three-level devices. Below 1.5 μm, the intensity peaks for drop ports C and E occur at the same wavelength for this device, thus allowing for the signal to be transmitted to multiple device layers simultaneously.

4. Conclusion

A series of silicon nanoplasmonic devices were simulated at telecommunication wavelengths, and found to be capable of frequency selective signal transfer between two to three device layers. Coupling efficiencies of a high as 39% were found between the device layers. The frequency selectivity was also found to be tunable through changing the size of the device.