Ladder operators for the radial index of the paraxial optical modes in the
cylindrical coordinates are calculated. The operators obey the su(1,1) algebra
commutation relations. Based on this Lie algebra, we found that coherent modes
constructed as eigenstates of the destruction operator or resulting from the
action of the displacement operator on the fundamental mode are different. Some
properties of these two kinds of radial coherent modes are studied in detail.Comment: 3 pages, 3 figure
