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Re (n eff) 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 ■■■ ■ ■ ■ ■■ ● ● ● ● ● ● 200 300 400 500 600 700 ▲Figure 5. (a) Effective refraction index of even and odd modes versus Wsi in the proposed double-layer waveguide profile, (b) Ex component intensity of the even (left) and odd (right) TE modes at Wsi of 300 nm, 400 nm, and 800 nm. the other is modeled in [21] and given by ● ● nm (×100) ■ ● 800 900 1000 1100 where x =2lc/πlp , and lp is the average attenuation length of the lossy waveguides. From (4), given the loss coefficient of the waveguides, higher maximum transferring optical power can be achieved with shorter coupling. Fig. 5(a) shows the contrast between the effective refraction index of the even and odd modes in the profile of the proposed double-layer waveguides. Fig. 5(b) shows the electric field-intensities, Ex, of the two modes at silicon waveguide widths of 300 nm, 400 nm, and 800 nm. The horizontals in the 90° angles (bottome left) are a scale of 100 nm, and the verticals are a scale of 100 nm. These electric field intensities are obtained using FDTD. Both even and odd modes are transverse electric (TE) modes and are dominant inside the plasmonic-slot waveguide. As the width of the silicon waveguide becomes narrower, the difference between the effective refraction index of the two modes becomes larger, ■ ● WSi (nm) (a) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 WSi = 300 nm 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 WSi = 400 nm nm (×100) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 nm (×100) WSi = 800 nm (b) ■ ● : Re (n even) : Re (n odd) ■ ● 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 nm (×100) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 nm (×100) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 exp(-2x arctan(x p max∝ (4) -1 )) 1+x 2 0.1 nm (×100) S pecial Topic Design of a Silicon-Based High-Speed Plasmonic Modulator Mu Xu, Jiayang Wu, Tao Wang, and Yikai Su leading to a shorter coupling length (Fig. 6). Thus, from (4), a larger fraction of power coupling from one waveguide to another is also achieved. Reducing the width of the silicon waveguide can improve coupling efficiency. However, if the dimensions of the silicon waveguide are too small, the magnetic field is less confined within the core and a larger proportion of Poynting vector leaks into the cladding. Thus, the mode of the optical field is cut off. In waveguide optics, such a process can be quantified as a normalized propagation constant [23]: B = (5) n eff-n clad n core-n clad where n eff is the effective refraction index of the optical mode, and n clad and n core are the refraction indexes of the cladding and core area within the waveguides. If B ≤ 0, the effective refraction index of the particular mode is less than that of the cladding, and the mode is cut off [23]. The B curve for the proposed waveguides at the overlapping area is plotted in Fig. 7. When the width of the silicon waveguide is less than 295 nm, the normalized propagation constant of the TE odd mode is less than zero, and the mode is cut off. Therefore, the proposed couplers use two tapers with widths that gradually vary from 400 nm at the end face to 300 nm at the head face. These tapers reduce the coupling length to the greatest possible extent, and the TE odd mode is not cut off. Figure 6.▶ Coupling length versus Wsi. Re (n eff) 2.4 2.2 2.0 1.8 1.6 1.4 200 ■ ■ ■ LC (μm) 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 Cut-Off Width ■ ■ 300 ■ ■ ■ ■ ■ ■ 400 ■ ■ 200 ■ ■ ■ ■ 500 ■ ■ 300 ▲Figure 7. Effective refraction index and normalized propagation constant of photonic mode versus Wsi. ■ ■ 600 ■ ■ 400 : Re (n eff ) ■ 700 WSi (nm) ■ 500 ■ 600 ■ 800 700 WSi (nm) 900 ■ 800 ■ : Normalized Propogation Constant 1000 900 ■ 1000 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 -0.05 1100 1100 Normalized Propogation Constant B March 2012 Vol.10 No.1 <strong>ZTE</strong> COMMUNICATIONS 37
S pecial Topic Design of a Silicon-Based High-Speed Plasmonic Modulator Mu Xu, Jiayang Wu, Tao Wang, and Yikai Su Input Input Input Output (a) Output (b) Output (c) Normalized Transmission 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25 0.20 1500 1550 Wavelegngth (nm) 1600 ▲Figure 8. Coupling efficiency for (a) the proposed taper with a width that gradually changes from 400 nm to 300 nm, (b) straight waveguide without taper, and (c) taper with a width that changes sharply from 400 nm to 80 nm. d) Output transmission for the three coupling structures. Three-dimensional simulations of coupling efficiency are performed using FDTD (Fig. 8). Three coupling structures are introduced: 1) the proposed taper with a width that gradually changes from 400 nm to 300 nm (Fig. 8a), 2) a straight waveguide without taper (Fig. 8b), and 3) a taper structure with a width that changes sharply from 400 nm to 80 nm (Fig. 8c). The overlapping longitudes of the first and second coupling structures are tuned nearly to their matched coupling lengths of 1 μm and 1.3 μm, respectively. The third structure has the same overlapping longitude as the first structure. The light fields are coupled into the plasmonic-slot waveguides and propagate for the same distance (1.5 μm) inside the slot. Their transmission curves are measured at the output port and plotted in Fig. 8(d). The resonated peaks on the curves in Fig. 8(d) are caused by the Fabry-Perot effect, which occurs because of the reflection of the end faces. Fig. 8 (a) to (d) shows that the gradually varied taper has better coupling efficiency because it has the largest transmission coefficient at 1450 nm to 1650 nm wavelength. The coupler comprising a straight waveguide has a weaker transmission coefficient because of the longer coupling length, and this leads to a lower maximum fraction of power coupling into the plasmonic-slot waveguide. The coupler with sharply varied taper has the lowest coupling efficiency, which is possibly due to the mode being cut off when the width is below 295 nm. These results show that a gradually varied taper improves mode conversion efficiency by using a short coupling length. The steady-state input and output electric field-intensity distributions of the couplers with gradually varied tapers are shown in Fig. 9(a) to (d). These distributions are calculated using the FDTD method for a wavelength of 1550 nm. The electric-field energy first transfers from the silicon waveguide to the plasmonic-slot waveguide (Fig. 9a and b). Then it is coupled into the silicon waveguide again (Fig. 9c and d), which confirms the feasibility and reliability of 38 <strong>ZTE</strong> COMMUNICATIONS 1450 March 2012 Vol.10 No.1 : Straight Coupler : Gradually Varied Taper : Shaply Varied Taper (d) 1650 the couplers for the proposed phase modulator. 4 Fabrication Feasibility A feasible fabrication process is described in [24]-[26]. First, 100 nm of silicon oxide is deposited on the SOI wafer. The silicon is 240 nm thick, and the buried oxide is 3 mm thick in order to act as hard mask. The pattern is transferred using photoresist and electron-beam lithography. Then, the oxide is etched using reactive ion etching (RIE). After stripping the resist, an inductively coupled plasma (ICP) etcher is used to etch the silicon. The silicon waveguides are 400 nm wide and 220 nm high, and the tapers vary from 400 nm to 300 nm in width. The device is cladded with 50 nm oxide using spin-on-glass. Second, the device window for metal evaporation is opened by a focused ion beam (FIB) on a bilayer photoresist structure over the oxide coating. Then, a 100 nm thick silver film is deposited by electron-beam evaporation. Silver is preferred because it does not oxidize easily and has a relatively small plasmonic loss at a wavelength of 1550 nm. After that, lift-off is performed in acetone to obtain the fi nal metal-slot waveguide. Third, the EO polymer cladding is prepared using AJLS103 cross-linked with a PMMA host, and the refractive index of the polymer is approximately 1.63 at 1550 nm. A spin-coating technique needs to be used, and to achieve a high EO coefficient inside the slot, the polymer should be properly poled before the device is operated. This poling requires a large field intensity (greater than 100 V/ μm) to be applied to the two parallel metal plates as an anode and cathode. 5 Conclusion In this paper, we have proposed a silicon-based 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.1 0.1 0.1 (a) (b) (c) (d) ▲Figure 9. Steady state electric field intensity distributions of (a) the input silicon waveguide, (b) the plasmonic-slot waveguide that overlaps above the input silicon waveguide, (c) the plasmonic-slot waveguide that overlaps above the output silicon waveguides, and (d) the output silicon waveguide. The horizontals in the 90° angle in (a)-(d) are a scale of 200 nm, and the verticals are a scale of 1μm. 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
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