## Abstract

We propose three general interference multimode interferometers (MMIs) based on hybrid plasmonic waveguides (HPWs). Among them, the general $2\times 2$ and $4\times 4$ MMIs are designed for a 90° optical hybrid, while the $3\times 3$ MMI is for a 120° optical hybrid. First, by considering the mode interference characteristics inside the multimode HPWs, a compromise between the number of guided modes and the device length is obtained at a determined height of the ${\mathrm{SiO}}_{2}$ interlayer of the HPW. Also, by analyzing the characteristics of multimode propagation in the HPW-MMI, it is found that the optimal positions of self-images would shift from their theoretical ones. In addition, tapered HPW sections are implemented to improve the coupling efficiencies for lights coupled into/out of the multimode section. Therefore, by optimizing the width and length of the multimode section, and especially the position of the input and output single-mode waveguides, the appropriate structure parameters of three HPW-MMIs are obtained, where the footprints of the $2\times 2$, $3\times 3$, and $4\times 4$ HPW-MMIs are only $1.96\times 5.4\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\mathrm{\mu m}}^{2}$, $2.18\times 12.0\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\mathrm{\mu m}}^{2}$, and $2.52\times 11.5\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\mathrm{\mu m}}^{2}$, respectively. The simulation results show that, at the wavelength of 1550 nm, the $2\times 2$ HPW-MMI exhibits a transmission of 75.6%, a maximum transmissions imbalance of 0.55 dB, and a phase error of 3.68°; the $3\times 3$ HPW-MMI exhibits a transmission of 69.2%, a maximum transmissions imbalance of 0.43 dB, and a phase error of 4.66°; and the $4\times 4$ HPW-MMI exhibits a transmission of 68.5%, a maximum transmissions imbalance of 0.91 dB, and a phase error of 4.81°. All these performances meet the standard industry requirements.

© 2019 Optical Society of America

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