  Spectrally unentangled biphotons with high single-spatiotemporal-mode purity
are highly desirable for many quantum information processing tasks. We generate
biphotons with an inferred heralded-state spectral purity of 99%, the highest
to date without any spectral filtering, by pulsed spontaneous parametric
downconversion in a custom-fabricated periodically-poled KTiOPO$_4$ crystal
under extended Gaussian phase-matching conditions. To efficiently characterize
the joint spectral intensity of the generated biphotons at high spectral
resolution, we employ a commercially available dispersion compensation module
(DCM) with a dispersion equivalent to 100 km of standard optical fiber and with
an insertion loss of only 2.8 dB. Compared with the typical method of using two
temperature-stabilized equal-length fibers that incurs an insertion loss of 20
dB per fiber, the DCM approach achieves high spectral resolution in a much
shorter measurement time. Because the dispersion amount and center wavelengths
of DCMs can be easily customized, spectral characterization in a wide range of
quantum photonic applications should benefit significantly from this technique.
