We present a novel technique for vertical coupling of light guided by nanoscale plasmonic slot waveguides (PSWs). A triangularly-shaped plasmonic slot waveguide rotator is exploited to attain such coupling with a good efficiency over a wide bandwidth. Using this approach, light propagating in a horizontal direction is efficiently coupled to propagate in the vertical direction and vice versa. We also propose a power divider configuration to evenly split a vertically coupled light wave to two horizontal channels. A detailed parametric study of the triangular rotator is demonstrated with multiple configurations analyzed. This structure is suitable for efficient coupling in multilevel nano circuit environment.
© 2013 Optical Society of America
The unrelenting need for faster and more efficient processing with miniaturized components drove electronics into the nanoscale. It is now customary to produce scaled down and ultrafast transistors. Yet, unlike transistors where efficiency improves with miniaturization, copper interconnect efficiency degrades, thus causing delays in the electronic devices . An alternative solution to electronics is using the traditional silicon photonics technology. Silicon photonics are compatible with CMOS electronics and possess 1000 times the data rate present in electronics . However, they are limited in size by the diffraction limit, causing a large size mismatch between silicon photonics and electronics [1, 3]. This size mismatch hinders using the advantages offered by both technologies concurrently.
Surface plasmon polaritons (SPPs) are paving the way for nanoscale optical technology that mitigates size, delay, and radiation limitations . SPPs promise to bridge the gap between electronics and photonics. Plasmonics are not limited in size by the diffraction limit and they enjoy, at the same time, optical data rates [1, 3, 4]. SPPs are realized using metallic/dielectric interfaces, where the metals develop a negative permittivity at optical frequencies. This causes the wave to be guided on the metal/dielectric surface. As a result, the advantages of both electronics and photonics may be combined in the same setting. A number of subwavelength plasmonic devices have been proposed for guiding and localizing electromagnetic energy for a variety of applications. These applications include imaging [4, 5], biosensors , multilevel couplers , photovoltaic , and cancer treatment .
Light control in plasmonic circuits is crucial for the realization of integrated and efficient plasmonic configurations. Controlling and routing of light in-plane is vital for integrating different devices on the same setting. Metal-Insulator-Metal (MIM) waveguides use SPPs confined in a subwavelength dielectric core to permit different nanoscale applications. In-plane light bending utilizing MIM structures has been introduced for efficient wave bending and splitting with minimal losses [10–12]. These techniques provide light bending with little reflections. The optical power is equally divided between orthogonally intersecting MIM waveguides. Using MIM waveguides as a basis for larger two-dimensional structures allows for feedback effects within the structure, hence offering several functionalities at the device level . However with the recent advances in integrating photonic and electronic devices, it is expected that photonic devices may occupy few of the poly-silicon layers at the top of the integrated circuits. These layers will accommodate all the required optical functionalities. The multilevel configuration is also exploited in order to minimize the area of the chip and maintain a small footprint of the hybrid chip. Thus, it is essential to have a good coupling approach between the various layers in the vertical direction. This vertical coupling is challenging using conventional photonics. Significant modal mismatch exists between the coupled waveguides. The propagating wave will not be easily confined within the metallic boundaries as is the case with in-plane structures. Little work has been done in realizing vertical light coupling or routing configurations [14, 15].
In this work, we present a novel out-of-plane light routing configuration for coupling to and from multilayered photonic/plasmonic circuits. The configuration has been briefly introduced in our previous work  with minimal details of its operation. Detailed analysis of this structure will help in optimizing the coupling over a wide band of operation. We study the properties of the device using 3-D FDTD simulations . The proposed configuration is further extended to design a multilayer power splitter with ultra-compact footprint that guides the light to multiple channels.
This paper is organized as follows: The theory of our proposed configuration is introduced in Section 2. In Section 3, we present a thorough parametric study of the plasmonic vertical coupler along with detailed numerical results towards the optimization of the proposed configuration. The stair case realization of the vertical coupler and possible fabrication steps are addressed in Section 4. Section 5 presents an application of the vertical coupling to realize ultra-compact vertical power splitters. Our work is concluded in Section 6.
2. Triangular plasmonic slot waveguide (TPSW)
Ultrafast nano-scale light manipulation ushered the introduction of multilevel optical circuits [14, 15]. In this case the device density is increased due to the utilization of 3-dimensional routing mechanisms. This overcomes the limited number of optical devices that can be integrated on one level of the chip due to cross talk [14, 15]. Clustering these optical chips to multiple levels provides highly dense photonic circuit integration with faster processing and more functionalities.
Plasmonic waveguides have been recently utilized in the design of subwavelength light guiding and routing. A Plasmonic slot waveguide (PSW) made of silver  on a silicon dioxide substrate is shown in Fig. 1. It has been utilized in on-chip coupling due to its strong confinement of light and low radiation [11, 18]. However, propagation in PSWs is limited to relatively short distances due to the losses that occur as a result of absorption in the metal. The propagation loss for the PSW in Fig. 1 is shown in Fig. 2. This figure shows an exponential decrease in the transmission with increased propagation distances (d) along the waveguide. PSWs allow for only one polarization mode to propagate while completely blocking the other one. It was recently demonstrated in  that using this polarization-dependent nature of PSWs, we can achieve polarization splitting and multilevel coupling capabilities.
A conventional configuration to couple light to and from vertically stacked layers or circuits is through utilizing a direct bend structure (see Fig. 3). This solution is simple but suffers from high reflections and resonant effects. The wideband transmission and reflection are calculated using FDTD (see Fig. 4). The large mismatch introduced by the rectangular section is demonstrated over most of the studied band. This mismatch is a result of modal mismatch between the vertical and horizontal sections which cannot be compensated for by an abrupt transition.
We propose a triangular plasmonic slot waveguide (TPSW) that provides smooth modal conversion to couple the light from a vertical PSW to a horizontal one at minimum losses and reflection. The proposed device, shown in Fig. 5, has the ability to bend light from a horizontal plane to a vertical plane and vice versa. The proposed structure is a silver–air–silver waveguide over a SiO2 substrate. Light is confined to the 50.0 nm slot and guided between the thick metallic layers. The SPP modes in the horizontal and vertical waveguides are calculated numerically .
The typical parameters of the triangular waveguide are the width w = 400.0 nm and height h = 400.0 nm. Those values are chosen with correspondence to the dimensions of the input and output PSWs. However, a parametric study and thorough investigation is provided in Section 3 to determine the optimal dimensions of this triangular rotator.
3. Numerical investigation of the TPSW
To determine the optimal dimensions of the proposed TPSW that would maximize the coupling efficiency, a parametric study is carried out. For an input light from the vertical PSW, we calculate the transmission and reflection introduced at the proposed coupling structure for different parameter values. The normalized amplitude in each waveguide is calculated by determining the power flux through the respective detector, integrating it over the cross section, and normalizing it with respect to the source power.
3.1 Study of the triangular rotator width (w) effect
There are two approaches for changing the width (w) of the triangular interface. In both configurations, the width (w) is changed while keeping the width and height of the vertical and horizontal waveguides fixed at 400.0 nm respectively. The proposed configurations are shown in Fig. 6 where the vertices of the triangular PSW are labeled as 1, 2, and 3. In the first approach, we vary the width (w) of the TPSW by moving the vertical plane containing the vertices 2 and 3 deeper inside the horizontal PSW. The width (w) of the triangular interface is tuned with steps of 100.0 nm to enhance the coupling efficiency. The vertical and horizontal PSWs are 400.0 nm wide with a 50.0 nm slot. The height of the triangular PSW is fixed at h = 400.0 nm. The source is placed 300.0 nm away from the bottom edge of the triangle and the monitor is placed 400.0 nm from the edge of the vertical PSW as shown in Fig. 6. Figure 7 illustrates the transmission efficiency (T) of this configuration. A maximum overall transmission of 70% can be achieved which provides 30% increase over the abrupt coupling. It can be seen that as (w) increases, the transmission efficiency (T) increases over most of the wavelength spectrum until a width of 500.0 nm. The transmission starts to decrease again beyond w = 500.0 nm. It can also be noted from Fig. 7 that the reflections (R) for the different widths (w) are below 15%. We only show the lowest and highest reflection curves in Fig. 7 for clarity purposes.
Another approach for changing the width (w) of the triangular rotator is through altering the width of the triangular PSW using the vertex labeled 1, while keeping the vertical plane containing the vertices 2 and 3 fixed (see Fig. 6). The points 2 and 3 are placed 100.0 nm to the right side of the vertical PSW. The monitor is placed 100.0 nm away from the edge of the TPSW. Maximum transmission is observed for this configuration at a width of w = 500.0 nm over most of the wavelength range as shown in Fig. 8. As (w) increases or decreases from the 500.0 nm value, transmission falls. This demonstrates that the optimal width for the triangle rotator is w = 500.0 nm. It is observed that having the width of the TPSW equal to that of the vertical PSW or 100.0 nm larger provides a simple realization with very good coupling efficiency.
3.2 Study of the triangular height (h) effect
For the same configuration shown in Fig. 6, we conduct a parametric study for different heights (h) of the TPSW. The same dimensions of the PSWs and source locations are used as in Section 3.1. The width of the TPSW is 500.0 nm, and the monitor is placed 100.0 nm away from the edge of the TPSW. In this case, changing the height of the triangular section is accompanied by a similar change in the height of the horizontal PSW. Figure 9 shows the transmission (T) for different heights. It can be seen that as (h) increases, the transmission increases over most of the spectrum. The increase of the height (h) allows for a larger interaction length for modal conversion from the vertical to the horizontal PSW. The reflection is below 12% over most of the band. A maximum of 85% transmission can be achieved with a vanishing reflection for wavelengths above 1.8 μm. In this case, the 15% power losses are attributed to the propagation and radiation losses.
In order to examine the improvement introduced by the TPSW solely, we keep the horizontal PSW height fixed at HW = 400.0 nm next to the uppermost corner of the TPSW as shown in Fig. 10. Figure 11 displays the results of changing (h) on the transmission. As (h) increases, (T) increases over most of the domain up to h = 600.0 nm. By comparing Fig. 9 and Fig. 11, we notice that the transmission for h = 600.0 nm is similar in both cases, even though, the horizontal PSW is fixed in the latter case. This shows that most of the vertically propagating wave bends in the upper section of the TPSW.
For the case of h = 600.0 nm, as evident from Fig. 9 and Fig. 11, the transmission is larger when increasing (h) and Hw together (≈80%) as compared to the case of a constant Hw = 400.0 nm (≈71%). From Fig. 11, the transmission in the case of h = 500.0 nm reaches a maximum of ≈74%. Thus, having a TPSW height (h) similar to that of the straight PSW or 100.0 nm higher produces the optimal transmission.
In order to examine the scalability of our findings, we conducted other simulations using 200.0 nm wide PSWs. The width of the TPSW is fixed at w = 300 nm. The height (h) is varied from 200.0 nm to 300.0 nm, while keeping the straight PSW fixed at 200.0 nm at the uppermost corner of the TPSW. Figure 12 shows that h = 300.0 nm produces higher transmission than the 200.0 nm case. More than 70% transmission (T) is achieved over most of the domain and the reflections (R) are below 4%. This is consistent with our previous finding that the optimal (h) is 100.0 nm higher than HW for the case of a 400.0 nm high PSW.
3.3 TPSW Normalized calculations
To compare the losses introduced by the TPSW, we normalize the transmission with respect to the transmission of a straight PSW with a similar length. For our calculations, we assume that most of the wave propagates along the middle of the PSW and the TPSW, and divide the transmission by that of a straight PSW with the same length. The normalized results are shown for varying widths (w) of the TPSW in Fig. 13. It can be noticed that the TPSW achieves a transmission of at least 50% of that of the straight PSW over most of the band. Figure 13 also demonstrates that the value w = 500.0 nm achieves the minimum average coupling losses over the entire bandwidth.
4. The stair case TPSW configuration and possible fabrication steps
One possible realization of the proposed TPSW is through a stair case approximation (see Fig. 14), which simplifies the fabrication process. This realization provides similar coupling efficiency to that of the continuous triangular case. There are 8 rectangular sections, with each section being 50.0 nm high. The width of the lower section is 500.0 nm. The width decreases by steps of 75.0 nm for each upper section. The highest section is 20.0 nm wide. In Fig. 15, the transmission of the stair case assembly is compared to that of the TPSW and a rectangular rotator with the same dimensions. We notice that the transmission of the stair case section is similar to that of the TPSW over most of the spectrum. Having more rectangle sections in the stair case configuration would result in a transmission efficiency closer to that of the TPSW.
The fabrication of the triangular coupler can be done using an isotropic etch on the (111) silicon plane. The silicon can then be covered by 200.0 nm thick metal to assure similar functionality to the pure metal structure. The stair case can be prepared by successive etching of the silicon. Once the stair feature is achieved, the silicon can be covered by metal to ensure plasmonic functionality.
5. Vertical light power splitter/combiner
In this section we introduce a direct application to the proposed triangular rotator. A power splitter that splits a vertically propagating wave equally to a horizontal plane is demonstrated. This configuration uses two symmetric triangle rotators so that the wave is divided equally in the two opposite horizontal waveguides.
The configuration is shown in Fig. 16. This design causes the vertically propagating wave to split so that different light manipulations can be performed at different sections. Half of the wave is guided to the right (monitor 1) while the other half is guided to the left (monitor 2). Figure 17 displays the transmission (T) for the power splitter at both monitors 1 and 2. It can be seen that when (h2) varies from 0 nm – 400.0 nm the transmission in the ports decreases. It is noted that the reflection (R) is very low for h2 = 0 nm and 160.0 nm (below 8% over most of the band). It reaches its highest value for h2 = 400.0 nm which corresponds to the case of a rectangular junction.
We propose a triangular plasmonic waveguide that works as an efficient out-of-plane coupler. Vertical to horizontal light coupling and vice versa is achieved using this triangular rotator. We demonstrated various configurations of the device and how different parameters affect the operation of the structure. We also proposed a power splitter using the TPSW. This splitter divides the power of a vertically propagating wave equally in two horizontal arms. It can be used for multi-level couplers or for light bending and splitting from one circuit plane to another with minimum losses. The fabrication of this device is under investigation.
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