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.
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