  We demonstrate pulsed polarization-entangled photons generated from a
periodically poled $\mathrm{KTiOPO_4}$ (PPKTP) crystal in a Sagnac
interferometer configuration at telecom wavelength. Since the
group-velocity-matching (GVM) condition is satisfied, the intrinsic spectral
purity of the photons is much higher than in the previous scheme at around 800
nm wavelength. The combination of a Sagnac interferometer and the GVM-PPKTP
crystal makes our entangled source compact, stable, highly entangled,
spectrally pure and ultra-bright. The photons were detected by two
superconducting nanowire single photon detectors (SNSPDs) with detection
efficiencies of 70% and 68% at dark counts of less than 1 kcps. We achieved
fidelities of 0.981 $\pm$ 0.0002 for $\left| {\psi ^ -} \right\rangle$ and
0.980 $\pm$ 0.001 for $\left| {\psi ^ +} \right\rangle$ respectively. This
GVM-PPKTP-Sagnac scheme is directly applicable to quantum communication
experiments at telecom wavelength, especially in free space.
