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The Raman gain coefficients for higher order Hermite-Gaussian modes are derived. The results indicate that the Raman intensity gain coefficient (collimated beam) is relatively insensitive to, while the Raman power gain coefficient (tight focus) is very sensitive to the mode structure of a beam. Thus, for high power lasers in which high gain is attainable with a collimated beam, the conversion efficiency would not be sensitive to the laser mode, while for low power lasers in which high gain is attainable only under focused configuration, the conversion efficiency would be quite sensitive to the laser mode. In addition, the coupling coefficients between modes and their contributions to the gain are discussed.