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Ladder operators for the radial index of the paraxial optical modes in thecylindrical coordinates are calculated. The operators obey the su(1,1) algebracommutation relations. Based on this Lie algebra, we found that coherent modesconstructed as eigenstates of the destruction operator or resulting from theaction of the displacement operator on the fundamental mode are different. Someproperties of these two kinds of radial coherent modes are studied in detail.

Radial coherent and intelligent states of paraxial wave equation