| الملخص: | Micro-racetrack resonators have become one of the key components for realizing signal processing, generation, and integration in microwave photonics, owing to their high Q factor, compact footprint, and tunability. However, most of the reported micro-racetrack resonators are confined to the single-mode regime. In this paper, we designed an ultra-compact multimode micro-racetrack resonator (MMRR) based on shape-optimized multimode waveguide bends (MWBs). Cubic spline curves were used to represent the MWB boundary and adjoint methods were utilized for inverse optimization, achieving an effective radius of 8 μm. Asymmetric directional couplers (ADCs) were designed to independently couple three modes into a multimode micro-racetrack, according to phase-matching conditions and transmission analysis. The MMRR was successfully fabricated on a commercial platform using a 193 nm dry lithography process. The device exhibited high loaded Q factors of 2.3 × 10<sup>5</sup>, 4.1 × 10<sup>4</sup>, and 2.9 × 10<sup>4</sup>, and large free spectral ranges (FSRs) of 5.4, 4.7, and 4.2 nm for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>TE</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>TE</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>TE</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> modes, with about a 19 × 55 μm<sup>2</sup> footprint.
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