Mode coupling enhancement from dielectric to plasmonic waveguides

Abstract. Efficient dielectric–plasmonic interconnect is significant in the design of future electronic–photonic integrated circuits that deal with large data transfer. We propose three designs and analysis of small-footprint couplers that are located at the interface between dielectric and plasmonic waveguides. To the best of our knowledge, our proposed couplers outperform all the works reported in the literature in several aspects including size and coupling efficiency (CE). Our results indicate that the optimum dimensions of the proposed couplers are determined based on whether the coupler is located in the metal side or dielectric side, or the coupler extends equally in both types of materials. The proposed couplers work over a broad frequency range achieving a CE above 88% at the optical communications wavelength 1550 nm. In addition, our results indicate that the CE can be further increased to above 93% by increasing the width of the dielectric waveguide before it is connected to the coupler. Moreover, our proposed designs provide a considerable alignment tolerance, which is needed when aligning the dielectric waveguide to the metal–dielectric–metal waveguide. Our proposed couplers have an impact on the design and miniaturization of nanoscale all-optical devices.


Introduction
Metal-dielectric-metal (MDM) waveguides confine light in a subwavelength-sized dielectric region, which is needed for the future of on-chip electronic-photonic integrated circuits. 1,2 The propagation losses in the MDM waveguides are high due to their large metallic losses, which have prevented using them to propagate light over long distances. On the other hand, the conventional dielectric waveguides have very low propagation losses and are used to propagate light over long distances. To use the MDM waveguides in the fabrication of plasmonic devices, such as splitters, 3 Mach-Zehnder interferometers, 4 reflectors, 5 wavelength demultiplexers, 6 circulators, 7 filters, 8 and all-optical switching, 9 integrating both dielectric and plasmonic waveguides on the same chip is needed. Consequently, an efficient coupler between those two kinds of waveguides is needed, in which the dielectric waveguides are used for transmission of light into and out of the MDM waveguides. Several different coupling methods have been proposed to achieve mode matching between those two types of waveguides: some designed a coupler and placed it inside the metal side, 3,10,11 others placed it inside the dielectric side, 12,13 and some others placed it inside both sides. [14][15][16] Aligning the dielectric waveguide to the MDM waveguide is challenging as demonstrated in Refs. 12 and 17-19, in which considerable alignment tolerance is needed.
In this research work, we propose three designs of ultracompact couplers to increase the coupling efficiency (CE) from a 300-nm-wide silicon waveguide into a 40-nm silver-air-silver plasmonic waveguide. In our previous work, 3 we achieved a CE of 88% by incorporating an ultrashort rectangular air-gap at the interface between dielectric and MDM plasmonic *Address all correspondence to Rami A. Wahsheh, E-mail: r.wahsheh@psut.edu.jo waveguides. The width of the air-gap-coupler (AGC) matched that of the dielectric waveguide and was located inside the metal region. Herein, we show a different approach other than that followed in our previous work to design three types of couplers. Our proposed three AGCs are all located at the interface between the dielectric and MDM plasmonic waveguides: AGC #1 is located inside the metal region [as shown in Fig. 1(a)], AGC #2 is located inside the dielectric region [as shown in Fig. 1(b)], and AGC #3 extends equally inside both types of materials [as shown in Fig. 1(c)].
The proposed couplers were designed using the two-dimensional finite-difference timedomain method with a uniform mesh size of 1 nm to accurately capture the field changes at the interface between the dielectric and MDM waveguides. In all simulations, the fundamental mode was excited in the dielectric waveguide, and the CE was measured close to the interface with the plasmonic waveguide. The CE is defined as the ratio of the transmitted light power into the MDM waveguide to that launched into the dielectric waveguide. All numerical simulations were done at the optical communications wavelength 1550 nm taking into account the propagation losses in the MDM waveguides.
Herein, we present the design steps and numerical results for our proposed AGCs. The remainder of this research work is organized as follows. In Sec. 2, we explain the design procedures and results. Also, we show how the proposed designs increase the fabrication tolerance, which is needed when aligning the dielectric waveguide to the plasmonic waveguide. In Sec. 3, we compare the spectrum results of each proposed design. In Sec. 4, we provide a conclusion.

Air-Gap-Coupler Design and Analysis
Our proposed AGCs are all located at the interface between the dielectric and MDM plasmonic waveguides. In the simulations, the dimensions of the couplers (i.e., length and width) were changed and the corresponding CE was measured at 10 nm away from the AGC boundary. The length of the coupler, L C , was changed in steps of 5 nm from 5 to 50 nm. For each step of L C , the width of the coupler, W C , was changed from 0 to 400 nm (as shown in Fig. 2), where 0 means direct connection of the two types of waveguides. We found that the CE for AGC #1 was above 89% that occurred at L C1−Ag ¼ 15 nm and W C1−Ag ¼ 260 nm [as shown in Fig. 2(a)]. Whereas the CE for AGC #2 was about 88% that occurred at L C2−Si ¼ 20 nm and W C2−Si ¼ 210 nm [as shown in Fig. 2(b)] and that for AGC #3 was about 89% that occurred at L C3−Both ¼ 20 nm and W C3−Both ¼ 240 nm [as shown in Fig. 2(c)]. Light couples into the AGC before it is funneled into the MDM waveguide. Without using the AGC, the CE was about 68% in which there was a large mode-size mismatch between the size of the mode in the dielectric waveguide and that in the MDM waveguide. In our proposed designs, using the AGC increased the CE to above 88% by reducing the mode-size mismatch between the two waveguides and by reducing the transverse leakage at the interface between the dielectric and MDM waveguides. Moreover, we found that the CE of all three proposed designs that are shown in Fig. 1 can be further increased by gradual increase of the width of the dielectric waveguide, W Si , over a length L Si before it is connected to the AGC (see Fig. 3). In the simulations, the corresponding CE was measured at 10 nm away from the AGC boundary taking into account the propagation losses in the tapered-dielectric waveguides. We found that, for AGC #1, the CE increased from 89% to above 93% when the width of the dielectric waveguide was expanded to W Si−C1 ¼ 380 nm over a length of L Si−C1 ¼ 330 nm [as shown in Fig. 4(a)]. Whereas for AGC #2, the CE increased from 88% to above 93% when the width of the dielectric waveguide was expanded to W Si−C2 ¼ 380 nm over a length of L Si−C2 ¼ 340 nm [as shown in Fig. 4(b)], and for AGC #3, the CE increased from 89% to above 93% when the width of the dielectric waveguide was expanded to W Si−C3 ¼ 380 nm over a length of L Si−C3 ¼ 330 nm [as shown in Fig. 4(c)]. The gradual increase of the width of the dielectric waveguide acted as a fine-tuning-mode matching that enabled more light to couple into the AGC and consequently resulted in increasing the CE into the MDM waveguide.
We also found that our proposed couplers provide a considerable fabrication tolerance when aligning the dielectric waveguide to the MDM waveguide. To show that, the misalignment between the center of the dielectric waveguide and that of the MDM waveguide was changed as a function of the misalignment distance, d (see Fig. 5). In the simulations, the AGC was kept connected to the MDM waveguide for all designs as if the focused ion beam (FIB) was used to define both the MDM waveguide and AGC. Figure 6 shows the CE as a function of the misalignment distance d for all the proposed AGCs. We increased d until there was no overlap between the two waveguides. We found that the CE decreased for all types of couplers as d was increased. For example, when d ¼ 100 nm, the CE was above 40% for all proposed couplers compared to about 8% without using the AGC (i.e., butt coupling). From the results shown in Fig. 6, the misalignment tolerance was much higher when using the AGC and maximum CE occurs when the center of the AGC was aligned to that of the dielectric waveguide.

Spectrum Analysis
All our proposed AGCs operate at a broad frequency range. To show that, we varied the wavelength of the light source from 900 to 2300 nm and measured the corresponding CE at each wavelength. The spectrum of the proposed couplers that are shown in Figs. 1 and 3 are all shown in Fig. 7. For comparison, we also added the spectrum of the butt coupling of the two waveguides. Using the AGCs broadens the spectrum range around the communications wavelength of 1550 nm for all the proposed couplers compared to that without using the AGC. As shown in Fig. 7, the spectrum of AGC #2 without Si width expansion has better CE than the other couplers when the wavelength is <1370 nm, whereas the spectrum of AGC #1 with Si width expansion has better CE than the other couplers when the wavelength is >1370 nm. The coupler that has very close results to the best coupler before and after the 1370 nm is AGC #3 that extends equally in both types of waveguides. Based on these results and since we do not have high precision fabrication techniques, using AGC #3 is our best choice especially when using the FIB to define both the AGC and the MDM waveguides. It is almost impossible to fabricate AGC #1 inside the metal region that exactly starts at the interface with the dielectric waveguide without having part of the coupler in the dielectric waveguide. The same scenario can be said about fabricating AGC #2. Our only choice is to fabricate AGC #3 that extends into both types of waveguides. Figure 2(c) shows that the CE is >50% when the coupler's width, W C3−Both is between 30 and 400 nm for any coupler's length, L C3−Both is between 5 and 50 nm. This means that as long as there is an overlap between AGC #3 and the two types of waveguides, light couples from the dielectric waveguide into the plasmonic waveguide, which can be achieved using the FIB. To fabricate AGC #3 on a 250-nm silicon-on-insulator wafer, the height of the dielectric and plasmonic waveguides should match that of the silicon layer (i.e., 250 nm). First, the dielectric waveguides are defined followed by depositing metal in the required areas. After that, the AGC and MDM waveguides are defined using the FIB. A platinum layer of a thickness of 7 to 10 nm is deposited on top of the metal layer before defining the AGC and MDM waveguides. The platinum layer is deposited to assist in getting a rectangular shape slot waveguide (i.e., the top of the slot waveguide has the same width as that of its bottom).

Conclusions
We proposed and optimized highly efficient couplers between a 300-nm-wide Si waveguide and 40-nm-wide silver-air-silver plasmonic waveguide. The proposed three types of AGCs resulted in a CE above 88% compared to 68% without using the AGCs (i.e., butt coupling). Further increase of the CE (above 93%) was possible by increasing the width of the dielectric waveguide before it was connected to our proposed couplers. Moreover, the spectrum of all the proposed AGCs operates at a broad frequency range and provides large fabrication tolerance when aligning the dielectric and plasmonic MDM waveguides.