The angular distribution of Stokes and anti-Stokes radiations generated by a laser beam in a filamentary region is calculated. Three cases are discussed: one is the surface radiation which is found to appear if the filament is very thin and long. Secondly, if the first-order Stokes is broadly generated off-axis and the filament is thick, the theory gives volume phase-matching which has been observed as class I radiation. Finally, if the first-order Stokes is strongly directed along the axis and the filament is thin, Raman radiations at angles between those of surface and volume phase-matching conditions are found. They represent class II radiations which have been normally observed in many liquids. Theoretical cone-angles of higher-order Stokes and anti-Stokes show very good agreement with experimental observations by E. Garmire. Some properties of class I and class II radiations are also explained by this theory.
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Kōichi Shimoda (1966) studied this question.