# Polymer/Silica Hybrid Waveguide Thermo-Optic VOA Covering O-Band
## 2 Design and Simulation  
The polymer/silica hybrid waveguide consists of a silica buffer layer, a Poly (methylmethacrylate) (PMMA) cladding, and an SU-8 core, whose refractive indices are 1.4456, 1.4769, and 1.5812 at 1310 nm, respectively. With a high thermo-optic (TO) coefficient of 1.86 \(\times\) 10\({}^{-4}\) K\({}^{-1}\), an SU-8 2002 (from Microchem Corporation) core enables low power consumption. Compared with all-polymer devices, silica buffer layer offers an immiscible buffer, reducing the solubility phenomenon problem of waveguide edges due to annealing. Besides, the large thermal conductivity (1.4 W K\({}^{-1}\) m\({}^{-1}\)) of silica improves the speed response. The waveguide dimensions are chosen to be as small as possible while still being reliably producible with fabrication. A square waveguide of 3 \(\times\) 3 \(\upmu\)m\({}^{2}\) is chosen. The effective refractive index is 1.5611 under the fundamental transverse electric (TE) mode. The VOA is simulated through a three-dimensional beam propagation method (3D-BPM). To achieve a large bandwidth, the 3 dB splitter used in MZI should split equally over a large wavelength region. Compared with directional couplers (DC) and Y-branch splitters, MMI offers large optical bandwidth, a compact footprint, and high fabrication tolerance. The loss caused by modal mismatch, between the MMI region and input/output waveguides, can be decreased by taper waveguides. The schematic of the optimized MMI is shown in Figure 1a. Width of the MMI \(W_{mmi}\) is 20 \(\upmu\)m. The gap between output waveguides \(W_{3}\) is 6 \(\upmu\)m. According to self-image theory [29], the length of MMI \(L_{mmi}\) is 250 \(\upmu\)m. With both input and output ports, all three tapers are linear and widen from \(W_{1}\) = 3 \(\upmu\)m to \(W_{2}\) = 4.5 \(\upmu\)m, with the length of \(L_{taper}\) = 6 \(\upmu\)m. An SEM image of the fabricated MMIs with tapered ports is shown in Figure 1b. The field distribution of the optimized MMI is shown, in Figure 1c, to be under 1310 nm. The calculated spectra of the MMI are shown in Figure 1d. The transmissions of two output waveguides are equal, and they are \(-\)3.03 dB at 1310 nm. The excess loss of the MMI is 0.03 dB. The lowest transmission over the O-band is \(-\)3.64 dB.  
The schematic of the MZI-based broadband VOA is shown in Figure 2a. Two MMI-based splitters (combiners) are connected through bend and straight waveguides. The gap between two modulation arms is 50 \(\upmu\)m, which is enlarged from MMI's output tapers \(W_{3}\) through two bend waveguides. The radius of two bend waveguides is 4000 \(\upmu\)m in order to realize a low bend loss. A 2000-\(\upmu\)m-length microheater is fabricated, above a single modulation arm, to tune the VOA. To improve the coupling efficiency, the widths of input and output waveguides are increased from 3 \(\upmu\)m to 16 \(\upmu\)m through the 200-\(\upmu\)m-length linear tapers. We change the temperature of the modulation arm under the microheater to simulate the performance of the VOA. As shown in Figure 2b, the insertion loss (IL) is  
Figure 1: (**a**) The schematic of the optimized MMI; (**b**) SEM image of the fabricated MMI; (**c**) Calculated field distribution along the MMI at 1310 nm; (**d**) Calculated spectra from the two output ports of the MMI.  
0.03 dB, while \(\Delta T\) = 0 K. The minimum transmission, \(-\)38.85 dB, happens while \(\Delta T\) = 1.8 K. The inserts of Figure 2b show the field distributions under temperature changes of 0 and 1.8 K, respectively. Calculated spectra of the VOA, while the temperature change of the modulation arm is 0 K and 1.8 K, are shown in Figure 2c. While the temperature change is 0 K, the insertion loss is 0.03\(\sim\)1.66 dB over the O-band. While the temperature change is 1.8 K, the attenuation is larger than 18.76 dB. The maximum attenuation is 74.42 dB at 1302 nm.