Up to now, the light coupling schemes of germanium-on-silicon photodetectors (Ge-on-Si PDs) could be divided into three main categories: (1) vertical (or normal-incidence) illumination, which can be from the top or back of the wafer/chip, and waveguide-integrated coupling including (2) butt coupling and (3) evanescent coupling. In evanescent coupling the input waveguide can be positioned on top, at the bottom, or lateral to the absorber. Here, to the best of our knowledge, we propose the first concept of Ge-on-Si PD with double lateral silicon nitride (Si3N4) waveguides, which can serve as a novel waveguide-integrated coupling configuration: double lateral coupling. The Ge-on-Si PD with double lateral Si3N4 waveguides features uniform optical field distribution in the Ge region, which is very beneficial to improving the operation speed for high input power. The proposed Ge-on-Si PD is comprehensively characterized by static and dynamic measurements. The typical internal responsivity is evaluated to be 0.52 A/W at an input power of 25 mW. The equivalent circuit model and theoretical 3 dB opto-electrical (OE) bandwidth investigation of Ge-on-Si PD with lateral coupling are implemented. Based on the small-signal (S21) radio-frequency measurements, under 4 mA photocurrent, a 60 GHz bandwidth operating at -3V bias voltage is demonstrated. When the photocurrent is up to 12 mA, the 3 dB OE bandwidth still has 36 GHz. With 1 mA photocurrent, the 70, 80, 90, and 100 Gbit/s non-return-to-zero (NRZ) and 100, 120, 140, and 150 Gbit/s four-level pulse amplitude modulation clear openings of eye diagrams are experimentally obtained without utilizing any offline digital signal processing at the receiver side. In order to verify the high-power handling performance in high-speed data transmission, we investigate the eye diagram variations with the increase of photocurrents. The clear open electrical eye diagrams of 60 Gbit/s NRZ under 20 mA photocurrent are also obtained. Overall, the proposed lateral Si3N4 waveguide structure is flexibly extendable to a light coupling configuration of PDs, which makes it very attractive for developing high-performance silicon photonic integrated circuits in the future.