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We report the characterization of optical coupling efficiency and the absorption coefficient of fiber-coupled superconducting nanowire single photon detector with an optical cavity, which limit the system detection efficiency. The small lenses were applied to compact fiber-coupled package and the efficient optical coupling higher than 95% were confirmed experimentally. The absorption coefficient was also verified and reached to \sim60% at 1550 nm wavelength and optimum polarized condition. The system detection efficiencies at 1550, 1310 and 810 nm were 28, 40 and 3%, respectively, which are related to the absorptance dependencies on wavelengths. [ABSTRACT FROM AUTHOR]