  We observe a strong polarization dependent optical loss of in-plane light
propagation in silicon waveguide due to the presence of graphene. Both
transverse-electric (TE) and transverse-magnetic (TM) modes are efficiently (~3
dB) coupled to the graphene on suspended membrane waveguides using an apodized
focusing subwavelength grating. The TE mode has 7.7 dB less excess optical loss
than the TM mode at 1.5 {\mu}m for a 150 {\mu}m long waveguide in good
agreement with a theoretical model. All-optical modulation of light is
demonstrated. There is also a large thermally induced change in waveguide
effective index because of optical absorption in graphene.
