Vector plane wave spectrum of an arbitrary polarized electromagnetic wave

Area of Science:

• Electromagnetism
• Optics
• Wave Physics

Background:

• The analysis of electromagnetic waves often relies on spectral representations.
• Existing formulas for vector plane wave spectrum (VPWS) can be complex and lack clear physical interpretation.

Purpose of the Study:

• To derive a novel formula for the vector plane wave spectrum (VPWS) of arbitrary polarized electromagnetic waves.
• To enhance the physical interpretability and applicability of VPWS formulas.
• To explore applications in analyzing specific polarized beams and deriving related transforms.

Main Methods:

• Utilizing modal expansions of independent transverse fields.
• Deriving a new VPWS formula composed of TM- and TE-mode plane wave spectra.
• Applying the derived formula to radially and azimuthally polarized beams.
• Deriving vector Fourier-Bessel transform pairs for circularly symmetric waves.

Main Results:

• A new VPWS formula is established, separating amplitude and polarization for each plane wave.
• The new formula offers improved physical meaning and practical convenience over previous methods.
• Demonstrated application to radially and azimuthally polarized beams.
• Derived vector Fourier-Bessel transform pairs for circularly symmetric electromagnetic waves.

Conclusions:

• The developed VPWS formula provides a more intuitive and applicable framework for analyzing electromagnetic waves.
• This method facilitates the study of complex polarized beams and related wave phenomena.
• The findings contribute to a deeper understanding of wave propagation and spectral analysis in electromagnetism.