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An analysis and experimental verification of momentum modulation of relativistic electrons by laser light using the inverse Cerenkov effect is presented. As an alternative to the free-electron laser for achieving energy exchange between particles and photons, the inverse Cerenkov effect uses the index of refraction of a gaseous medium to retard the phase velocity of an electromagnetic wave, enabling the electrons to remain in a field of constant phase. The momentum modulation converts to charge-density modulation by allowing the electrons to drift, thus forming electron bunches separated by optical wavelengths. An analysis is presented for the maximum amount of energy exchange, the energy exchange distribution, and the optimum bunching distance. A computer simulation of the interaction process is also given. These results are compared with the observed momentum modulation of a 102 MeV electron beam by a 30 MW Nd:YAG 1.06 μm laser in both hydrogen and methane gases. Initial observation of coherent optical radiation from a 57 MeV electron beam using the same laser system is also presented. Laser-driven particle accelerators and optical klystrons are possible applications of this interaction.