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Compact optical interconnects require efficient lasers and modulators compatible with silicon. Ab initio modeling of Ge 1-xCx (x=0.78%) using density functional theory with HSE06 hybrid functionals predicts a splitting of the conduction band at Γ and a strongly direct bandgap, consistent with band anticrossing. Photoreflectance of Ge 0.998C0.002 shows a bandgap reduction supporting these results. Growth of Ge 0.998C0.002 using tetrakis(germyl)methane as the C source shows no signs of C-C bonds, C clusters, or extended defects, suggesting highly substitutional incorporation of C. Optical gain and modulation are predicted to rival III-V materials due to a larger electron population in the direct valley, reduced intervalley scattering, suppressed Auger recombination, and increased overlap integral for a stronger fundamental optical transition. [ABSTRACT FROM AUTHOR]