1. Introduction

Optical networks represent the foundation for large scale digital signal communication. The scalability of these networks revolutionized the next generation integrated on-chip optical communication. Signal interconnects represent the dominant challenge that limits the speed of the digital system. In nanoscale, electronic interconnects which provide connectivity to and from fast transistors, suffer from increased delays and limited scalability. The overall speed of the system is thus limited [1] due to radiation from the wires, cross-talk between the wires, and increase in effective resistance [2]. On the other hand, optical interconnects offer increased speed and bandwidth at minimum power consumption. Ubiquitous miniaturized optical devices and interconnects are proposed owing to their ability to carry 1000 times the capacity of electronic circuits [1–4]. Also, large optical devices have stimulated the need for submicron and nanoscale miniaturized devices. The size mismatch between nanoscale electronic circuits and the diffraction-limited optical devices has limited electronic and optical integration [4, 5].

Sub-wavelength optical devices have been proposed to bridge the gap between the electronic and optical dimensions. A category of devices that can be miniaturized below the diffraction limit are surface plasmon polariton (SPP) devices [1, 3–5]. They are proposed for optical interconnects to replace the copper interconnects. Active SPP structures are proposed to overcome the inherent losses in the plasmonic circuit. The fabrication and integration for these plasmonic devices is done on silicon on insulator (SOI). This led to a new era of integrated optical and electronic devices with excellent characteristics. The routing and datatransfer are done using optical interconnects without affecting the functionality of the electronic circuit [3–5].

The interfaces between electronic and optical components are more challenging for high density of integrated devices. An all-optical signal processing can be exploited to realize a complete optical computation and communication system. The number of optical components placed on a chip is limited by cross talk between the closely placed components [6, 7]. In-plane chips are restricted by the size and the number of components that can be placed. An approach to solve this issue is stacking the optical chips in order to have multiple levels as shown in Fig. 1 . By stacking multiple circuits, highly dense photonic optical circuits with faster processing and wider functionality can be realized.

 

Fig. 1 A 3-D plasmonic chip.

Download Full Size | PDF

Several approaches for realizing 3-D optical chips have been proposed [6–9]. These devices include optical multiplexers, multimode interferometer, splitters, switches and waveguides [6–13]. However, the devices are designed using the conventional Silicon on Insulator (SOI) waveguides. This makes them limited in both band and size and subject to cross talk. Similarly, these devices are very sensitive to wavelength alterations and fabrication [7]. A promising alternative is to exploit plasmonic circuits to provide high density integration with minimal cross talk. However, little work has been done in realizing 3-D chips using plasmonics. The device presented in [14] uses long-range surface plasmon polaritons (LRSPP). This device is long and its operation is limited by its length. In addition, so far 3-D plasmonic chips are limited to the inherent polarization dependence of the surface plasmon polariton waves. Signal manipulation utilizes only one polarization of the input field. The other polarization does not couple to the SPP structures. This is considered a serious draw back that hinders using quadrature functionalities.

Recently, few on-chip plasmonic polarization splitters [15–18] and polarizers [19, 20] were proposed for quantum electrodynamics [21], and for logic gates [22]. These structures dramatically reduce the size of an optical chip. However, all the proposed structures are in-plane, and the splitting is only done at one layer. Also, special care is needed when designing and manufacturing these splitters due to the fine tapering and positioning. The splitting ratio is dimension-dependent which makes it very sensitive to the fabrication process.

In this paper, we propose a novel structure for realizing multilevel plasmonic chips based on the PSW configuration demonstrated in [23]. This structure also acts as a surface plasmon polarization beam splitter. The main functionality of this device is to allow both polarizations of the input field to be manipulated using plasmonic structures by routing each one to a different level. A conventional silicon nano-waveguide is employed as the input waveguide. By controlling the light polarization at nanoscale, on-chip communication will be much faster. Also, optical digital gating functionality can be developed. Moreover, this will introduce a quadrature space that provides multifold of the current capacity. The proposed device helps in realizing 3-D plasmonic chips that are compact and with high integration and density. Two variations of the suggested structure are investigated. In the first one, the two plasmonic waveguides are orthogonal. In the second one, one of the plasmonic waveguides is rotated to allow light propagation in a parallel horizontal plane. These devices are wideband and ultra-compact with realizable dimensions. The Finite difference time domain (FDTD) technique is utilized to verify the operation of the two devices. The polarization splitting capability of these structures can be utilized in linear optics, multiplexers, logic gates [16, 17], or optical interconnect applications.

We start by reviewing the background for the proposed devices in Section 2. The proposed structures are presented in Section 3. The results obtained using the FDTD method are shown in Section 4. Finally, the conclusions are discussed in Section 5.

2. Background

The proposed multilevel devices are based on orthogonal coupling between silicon waveguides and plasmonic slot waveguides (PSW). Utilizing the polarization-dependent nature of the plasmonic slot, we can separate the two different polarizations. Orthogonal orientation between the silicon and plasmonic waveguides not only allows for polarization splitting but has also been proven to provide efficient coupling [23]. This allows for simultaneous efficient coupling to different layers of a 3-D plasmonic chip and polarization splitting.

For the plasmonic slot waveguide shown in Fig. 2 , distinct modes are allowed to propagate [24]. These modes are determined through a numerical solution of reduced Maxwell’s equations in the magnetic field [24]. Figure 3 shows the fundamental TE mode that propagates in the PSW [19]. When the slot is perpendicular to the x-axis (as shown in Fig. 3), the fundamental mode having a dominant E_x and H_y fields propagates. When the slot is perpendicular to the y-axis, the dominant mode has E_y and H_x components. Throughout this paper, we refer to the modes having a dominant E_x and H_y fields as x-polarized (quasi-TE mode), and modes having a dominant E_y and H_x as y-polarized (quasi-TM mode). The PSW demonstrated here is made up of silver with a silicon dioxide substrate [25], using the model presented in Lumerical [26]. The cell size is Δx = Δy = 2.0 nm and Δz = 5.0 nm since the mode of interest is lateral to the z-direction. The PSW is 340.0 x 400.0 µm. Figure 3 demonstrates the mode profile for the x-polarized mode. It is obtained using Lumerical’s mode solver [26]. The mode solver solution is normalized with respect to the maximum field intensity.

 

Fig. 2 A plasmonic slot waveguide with air as the dielectric present in the slot.

Download Full Size | PDF

 

Fig. 3 Cross sectional view of the PSW demonstrating (a) E_x present in a plasmonic slot waveguide and (b) E_z present. The slot width is 50.0 nm.

Download Full Size | PDF

Several approaches for coupling energy into plasmonic waveguides have been suggested. The direct coupling is done by connecting the dielectric waveguide to the plasmonic slot waveguide. Figure 4 illustrates the transmission properties using direct coupling. This figure is created using the same computational information mentioned above, with a detector placed around the slot, 300.0 nm away from the interface. The excitation in the Si waveguide is done by injecting it with a Gaussian-modulated sinusoidal that spans the wavelengths 1.1 µm – 2.5 µm. In Fig. 4, the x-polarized mode, from the input silicon waveguide, is allowed to propagate in the plasmonic waveguide while the y-polarized mode is completely reflected. Themismatch between the silicon waveguide and the PSW reduces the coupling efficiency as evident from Fig. 4.

 

Fig. 4 The transmission plot for the direct coupling method for a slot width = 50.0 nm.

Download Full Size | PDF

It is difficult to separate both the x- and y-polarized modes simultaneously. To separate both polarizations, s-bends or branches [18] are required. This introduces losses and fabrication complexities. The transmission of PSWs also suffers from oscillatory responses, when coupled to and from silicon waveguides [23]. This introduces distortions and reduces the band for efficient operation.

The enhanced performance of right angle coupling between the dielectric waveguide and the PSW was validated in [23]. This right angle coupling provides higher polarization selectivity with minimal coupling losses and enhanced bandwidth. It also provides a wideband modal matching and thus a better coupling efficiency. The modal compatibility between plasmonic and dielectric waveguides is better illustrated through the analysis of the propagation constant (k) [23].

3. The proposed structures for polarization-controlled surface multilevel beam splitter/coupler

Two 3-D polarization-controlled beam splitters are investigated in this work. For the first structure, the light guided by the dielectric waveguide is split using two orthogonal plasmonic slot waveguides. The second structure exploits a rotated plasmonic slot waveguide to couple the signal to a parallel horizontal plane on a different layer. In this section more details are given about the performance of the two devices.

3.1 The orthogonal polarization splitter

We first propose a novel multilevel polarization splitter from silicon waveguide to PSW. The proposed structure exploits the orthogonal coupler presented in [23]. This coupler is polarization dependent and allows one polarization only (x-polarized wave) to couple to the PSW. However, slight modification demonstrates that this coupler can couple both polarizations but at different planes. The proposed coupler is shown in Fig. 5 . The input waveguide is a silicon nanowire with dimensions of 340.0 x 400.0 nm fabricated using SOI wafer. The dimensions of the PSW with a 50.0 nm slot are one order of magnitude less than that of the dielectric waveguide. The advantage that PSWs supports only one polarization is exploited in order to setup the device. The principal of operation of this device is to split the two polarizations existing on the dielectric waveguide with each polarization coupling to only one of the two orthogonal PSW waveguides. Both polarizations can be processed at the same time. One polarization is guided horizontally while the other polarization is guided vertically. Each signal is then guided to its respective circuit using sharp bends with maximum efficiency [27]. Each polarization is processed and manipulated in its respective layer. The x-polarized (quasi-TE) mode is responsible for the operation of the horizontal or in-plane layer, while the y-polarized (quasi-TM) is responsible for exciting the stacked layers. This also allows for quadrature modulation.

 

Fig. 5 The proposed orthogonal polarization splitter configuration;(a) 3D view and (b) side view.

Download Full Size | PDF

To illustrate the application of this device, we conduct a dispersion analysis on the proposed 3D configuration using [28]. The dispersion relation is for semi-infinite structures, and this is taken care of in the simulations by terminating the structure with a perfectly matched layer (PML). The dispersion relationship is given by:

$\begin{array}{l}\tan h{k}_{1}a=-\frac{k_2{\epsilon }_1}{k_1{\epsilon }_2},\\ k_1=\sqrt{{\beta }^2-k^2{\epsilon }_1},\\ k_2=\sqrt{{\beta }^2-k^2{\epsilon }_2}.\end{array}$ (1)In Eq. (1) k_{1, 2} are the wave vectors in the dielectric and metal, respectively, and ${\epsilon }_{1\text{,}2}$are the dielectric constants of the dielectric and metal, respectively. β is the effective wave vector and a is half of the slot size. Figure 6 shows that the dielectric propagation constants, k_x and k_y, have a better coordination with the PSW propagation constant, k_spp, than with k_z. This is in agreement with the 2D analysis given in [23].

 

Fig. 6 A wave-vector plot for the proposed 3D orthogonal polarization splitter. The k_x and k_y inside the dielectric waveguide are more closely matched to k_spp than k_z.

Download Full Size | PDF

3.2 The rotated splitter for multilevel coupling

We present a variation of the structure presented in 3.1 to rotate the vertically coupled beam for in-plane light processing. To achieve this goal a polarization rotator is exploited at the top of the polarization splitter. This structure uses a triangular shaped metal in the vertical direction to introduce a discontinuity to the wave. The slope of the triangle forces the wave propagating upwards to move along a path perpendicular to its original propagation. The complete structure is shown in Fig. 7 , where the edge of the triangle is placed 100 nm to the side of the silicon waveguide. This helps in the realization of stacked layer chips. This structure acts as a T- junction at multiple levels where only one polarization is coupled at each of the output ports 1 and 2.

 

Fig. 7 The structure of the rotated polarization splitter that couples each polarization to a different layer.

Download Full Size | PDF

As shown in Fig. 7, this device works by selecting the input polarization. If the input polarization at the silicon waveguide is x-polarized, the light couples to port 2. On the other hand, if the input polarization is y-polarized, the light is coupled to port 1. Thus the light beam can be routed at different horizontal planes by choosing the corresponding polarization. This device, for the first time, allows simultaneous manipulation of the two polarizations using PSW. The main applications of this device include quadrature modulation where each polarization is modulated at a different level. The final beam is combined again using the same device. This device demonstrates more compact and efficient use of the PSW-based applications. It can also be exploited as a selective router that controls the signal route at different layers as shown in Fig. 1.

4. Modeling and simulation results

The FDTD technique is used to simulate the coupling from the Si waveguide to the two orthogonal PSWs. The commercial software, Lumerical FDTD solutions [26], is utilized to simulate and analyze the two suggested structures. The metals used for the PSW are silver and aluminum [25]. The dielectric materials used for the dielectric input waveguide and substrate are silicon and silicon dioxide, respectively [25]. A high order polynomial fitting of measured data is used in dispersive FDTD [26]. The losses in all materials are given by the model used in [26]. The dielectric slot and surrounding medium used are air. For meshing the plasmonic section of the structure, a square cell of Δx = Δy = Δz = 2.5 nm is used. A perfectly matched layer (PML) is utilized to terminate the computational domain. Detectors are placed at the cross section of each PSW at a distance of 200.0 nm away from the splitting junction. These detectors probe the electric fields, magnetic fields, and transmission efficiencies in each arm. The normalized transmission is calculated by determining the power flux through the detector, integrating it over the cross section, and normalizing it with respect to the source power. The answer is then converted into dB using Eq. (2). The absorption in the metal, which is given in Eq. (3), is measured as well:

$\text{Transmission(dB)}=10\log (T),$ (2)

$\text{Absorption(dB)}=10\log (1-T_1-T_2-R),$ (3)where T is the normalized transmission obtained. T₁, T₂ and R are the normalized transmissions in ports 1, 2, and the reflection, respectively. The reflection from the junction is calculated in the same way. The Si waveguide is excited with a Gaussian-modulated sinusoidal that spans the wavelengths 1.0 µm – 2.5 µm. Each of the two dominant modes (x-polarized and y-polarized) is excited separately using the mode solver in [26]. The sources are excited at a distance of 1.5 µm from the splitting junction. The excited x-polarization and y-polarization modes in the dielectric waveguide are shown in Fig. 8 .

 

Fig. 8 The two excitation source modes. x-polarization (a) and y-polarization (b).

Download Full Size | PDF

In this section, we discuss the results obtained for both the orthogonal polarization splitter (Fig. 5), and the rotated polarization splitter (Fig. 7). For the PSW oriented in the y-direction (Fig. 5), the dominant fields are E_y and E_z. The mode profiles in this case are shown in Fig. 9 . While for the PSW oriented in the x-direction, E_x and E_z are the dominant fields, with a modal profile rotated to be in the x–direction as shown in Fig. 10 . For the y-polarized wave, the resulting fields propagate in port 1 with very little transmission to port 2. Figure 9 shows that the most dominant field in port 1 is the E_z field. However, it can be seen that the E_y field intensity has moderate power while propagating along the metal surface. The remaining fields present are very small compared to the dominant ones. Figure 10 shows that the reverse of the y-polarization case occurs at port 2 when the structure is excited using an x-polarized wave at 1.55 µm.

 

Fig. 9 Electric fields intensity plots in port 1 when excited with a y-polarized wave at 1.55 µm.

Download Full Size | PDF

 

Fig. 10 Electric fields intensity plots in port 2 when excited with an x-polarized wave at 1.55 µm.

Download Full Size | PDF

The y- and x-polarized waves are received at port 1 and port 2, respectively. As expected, when the Si waveguide is excited with a y-polarized mode (discontinuity along y-axis), the wave propagates along the PSW oriented in the y-direction (port 1). The transmission is calculated at 1.55 µm in both PSWs. It is found that the y-oriented waveguide has –3.7 dBpower transmission, while the PSW oriented in the x-direction has approximately −17.2 dB. This is illustrated in Fig. 11 . The same procedure is carried out while exciting the Si waveguide with an x-polarized mode (discontinuity along x-axis). A power transmission of −3.87 dB in the x-oriented PSW (port 2) is achieved. A transmission of approximately −15.5 dB is obtained in the y-oriented PSW. The slight difference in the transmission efficiency is attributed to the non-equal dimensions of the Si waveguide. The results are demonstrated in Fig. 12 . The extinction ratios for both ports are shown in Fig. 13 . The extinction ratio is the power in one port compared to the other port for the two different polarizations and is given by:

 

Fig. 11 The transmission efficiency for the orthogonal polarization splitter when excited with a y-polarized mode; (Diamond-Green) is the transmission along port 1, (Circle-Blue) is the transmission efficiency along port 2, (Dotted-Red) is the absorption in the metal, and (Cross-Black) is the reflection from the junction.

Download Full Size | PDF

 

Fig. 12 The transmission efficiency for the orthogonal polarization splitter when excited with an x-polarized mode; (Diamond-Green) is the transmission along port 1, (Circle-Blue) is the transmission efficiency along port 2, (Dotted-Red) is the absorption in the metal, and (Cross-Black) is the reflection from the junction.

Download Full Size | PDF

 

Fig. 13 The extinction ratio for the orthogonal polarization splitter calculated for port 1 (Dotted-Red) and for port 2 (Star-Blue).

Download Full Size | PDF

$\text{Extinction}\text{Ratio(dB)}=10\log (\frac{T_{int}}{T_{sub}}),$ (4)where T_int is the transmission in the port of interest and T_sub is the transmission in the other port. Figures 11 and 12 reveal that the absorption increases beyond a wavelength of 1.6 µm. The best band for operating this structure is between 1.4 µm and 1.6 µm. In this band the device enjoys maximum transmission as well as lower reflection and absorption as compared to other frequencies. This demonstrates the broadband feature of this structure.

We repeat the same analysis for the rotated polarization splitter shown in Fig. 7. Figure 14 shows the transmission when the dielectric waveguide is excited with a y-polarized mode. Here, the transmission in port 1 is - 4.7 dB, while that in port 2 is −21.1 dB. This shows that around 75.46% of the vertically propagating wave can be channeled horizontally to port 1. Figure 15 shows a transmission of −4.3 dB to port 2 and −21.7 dB to port 1 when the structure is excited with an x-polarized wave. This shows the excellent splitting and polarization rotation functionality of the device. The extinction ratios for both ports are displayed in Fig. 16 . The functionality of the device, when using aluminum [25] instead of silver, is also presented. Figures 14-16 show that the transmission power using aluminum is around 1 dB less than its counterpart. Also, the extinction ratio for each port using aluminum is closely related to that of the silver. This demonstrates that the structure is more compatible with traditional CMOS technology based on using silicon and aluminum.

 

Fig. 14 The transmission efficiency for the rotated polarization splitter when excited with a y-polarized mode; (Diamond-Green) is the transmission along port 1 for silver, (Circle-Blue) is the transmission efficiency along Port 2 for silver, (X-Red) is the transmission along port 1 for aluminum, and (Star-Black) is the transmission along port 2 for aluminum.

Download Full Size | PDF

 

Fig. 15 The transmission efficiency for the rotated polarization splitter when excited with a x-polarized mode for the polarization rotator; (Diamond-Green) is the transmission along port 1 for silver, (Circle-Blue) is the transmission efficiency along port 2 for silver, (X-Red) is the transmission along port 1 for aluminum, and (Star-Black) is the transmission along port 2 for aluminum.

Download Full Size | PDF

 

Fig. 16 The extinction ratio for the rotated polarization splitter calculated for port 1 (dotted-red) and for port 2 (Star-blue) using silver material. (Cross-Green) and (Diamond-Black) are the extinction ratios for ports 1 and 2, respectively, estimated using aluminum.

Download Full Size | PDF

5. Conclusion

We presented two novel SPP polarization splitters utilizing the orthogonal junction coupling technique. The first structure exploits orthogonal plasmonic slot waveguides while the second one exploits rotated plasmonic waveguides. For the orthogonal splitter, the transmission is more than −3 dB in port 1, when excited with a y-polarized polarization wave, and less than −14 dB in port 2. Also, the transmission results are exchanged when using an x-polarized wave. Similar results are also obtained for the rotated polarization splitter. The rotated splitter is able to guide the vertically propagating wave in a parallel horizontal plane. This provides horizontal propagation on different layers of a 3-D plasmonic circuit. These structures were simulated using 3D FDTD utilizing both silver and aluminum. Our proposed devices may find various applications in integrated circuits that include logic gates, data multiplexing, filtering, and quadrature applications.