Light Modes of Free Space

Abstract A surprisingly large number of known distinct sets of light patterns propagate in free space essentially unchanged. These sets of light patterns (intensity distributions of the electric–magnetic fields) can be divided into two groups: light Waves and light Beams. Wave sets are solutions of the exact Helmholtz equation (HE). Beam sets are solutions of the paraxial HE. The sets of Waves and Beams can be further classified according to the coordinate system to which they belong. All sets are complete and orthogonal such that any square integrable input field can be decomposed into a linear superposition of the set's functions. We classify the patterns, present the solution equations and display sample patterns for each of 4 Wave sets and each of 14 Beam sets.