Radial coherent and intelligent states of paraxial wave equation
Ebrahim Karimi, and Enrico Santamato
TL;DR
This paper explores the algebraic structure of radial modes in paraxial optics, introducing coherent states based on ladder operators and analyzing their properties to advance understanding of cylindrical optical modes.
Contribution
It derives su(1,1) algebra for radial ladder operators and distinguishes between different types of radial coherent modes, providing new insights into their properties.
Findings
Ladder operators obey su(1,1) algebra
Different radial coherent modes are identified and characterized
Properties of these modes are analyzed in detail
Abstract
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.
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