On-axis energy backflow in the focal fields of vector vortex beams with arbitrary initial phase

Area of Science:

• Optics and Photonics
• Electromagnetism
• Light Field Manipulation

Background:

• Energy backflow is a counterintuitive phenomenon observed in the focal region of light beams with singularities.
• Previous studies explored vector vortex beams with both polarization and phase singularities, but the role of initial phase was unclear.

Purpose of the Study:

• To theoretically prove and numerically demonstrate the independence of the longitudinal Poynting vector from the initial phase of light beams.
• To reveal the general conditions for on-axis energy backflow near the focus of light beams with arbitrary initial phases.
• To explore methods for achieving strong longitudinal electric fields on the optical axis.

Main Methods:

• Theoretical analysis of the Poynting vector in the focal plane.
• Numerical simulations to demonstrate energy backflow phenomena.
• Investigation of conditions relating polarization order (l) and phase topological charge (m).

Main Results:

• The longitudinal component of the Poynting vector is independent of the incident light beam's initial phase.
• On-axis energy backflow occurs when polarization order (l) and phase topological charge (m) satisfy l ± m = 2.
• Exceptional cases (l=1, m=±1) allow energy backflow by amplitude modulation; a method for strong longitudinal electric fields is proposed.

Conclusions:

• The initial phase of light beams does not influence on-axis energy backflow.
• A specific relationship between polarization and phase singularities (l ± m = 2) is the key condition for energy backflow.
• These findings provide new tools for controlling light fields and energy flow distributions in optical focal regions.