  We demonstrate all-optical temporal integration of arbitrary optical
waveforms with temporal features as short as ~1.9ps. By using a four-port
micro-ring resonator based on CMOS compatible doped glass technology we perform
the 1st- and 2nd-order cumulative time integral of optical signals over a
bandwidth that exceeds 400GHz. This device has applications for a wide range of
ultra-fast data processing and pulse shaping functions as well as in the field
of optical computing for the real-time analysis of differential equations.
