Orthogonal Synthesis of Odd and Even Modes

Terahertz Vortex Beam Generation Driven by Orthogonal Synthesis of Odd and Even Modes

Owing to the intrinsic symmetry of the cylindrical coordinate system, an LG mode can be decomposed into odd- and even-symmetric components: an odd solution characterized by a sine azimuthal function and an even solution characterized by a cosine azimuthal function.According to Euler's formula, the complex spiral phase structure can be reconstructed by superposing the real-valued even mode [cos(lθ)] and odd mode [sin(lθ)], while introducing a π/2 phase delay specifically to the odd mode component (i.e., multiplying the odd mode by i).