In the past decade superconducting nanowire single photon detectors (SNSPDs) have gradually become an indispensable part of any demanding quantum optics experiment. Until now, most SNSPDs are coupled to single-mode fibers. SNSPDs coupled to multimode fibers have shown promising efficiencies but are yet to achieve high time resolution. For a number of applications ranging from quantum nano-photonics to bio-optics, high efficiency and high time-resolution are desired at the same time. In this paper, we demonstrate the role of polarization on the efficiency of multi-mode fiber coupled detectors, and show how it can be addressed. We fabricated high performance 20, 25 and 50{mu}m diameter detectors targeted for visible, near infrared, and telecom wavelengths. A custom-built setup was used to simulate realistic experiments with randomized modes in the fiber. We simultaneously achieved system efficiency >80% and time resolution <20 ps and made large detectors that offer outstanding performances.
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