  Photon-pair generation must satisfy both the energy conservation and
phase-matching conditions with a specific pump wavelength and dispersion of
nonlinear optical medium, but finding a photon-pair, which has a desired
specific wavelength, generation medium is challenging. Here, we present a
method to create photon pairs that functions efficiently even the pump
wavelength is much larger than the zero GVD wavelength of medium. In this
study, we employ short SMF-28 fibers having ~1310 nm zero GVD wavelength and
C-band pump (1552.52 nm) to generate C-band photon pairs. The measured pair
generation rate and coincidence-to-accidental ratios are comparable to those
from a long dispersion-shifted fiber. Polarization-entangled states are
prepared, and an S value of 2.659 +- 0.094 is achieved from Bell inequality
measurements. Our results indicate that the use of a short SFWM medium yields
adequate photon-pair generation rates regardless of its dispersion properties
in almost any material at any pump wavelength.
