Accelerating Bessel-Coulomb optical beams: planar, spherical and parabolic traveling structured wavefields

Area of Science:

• Physics
• Optics
• Wave Theory

Background:

• Parabolic mirrors have been utilized for centuries in applications like antennas and reflectors.
• Their geometric optics properties, focusing parallel rays to a point, were described by Diocles.
• Existing literature primarily covers stationary wave cases for parabolic mirrors.

Purpose of the Study:

• To present a complete wave theory for parabolic mirrors.
• To demonstrate the creation of paraboloidal traveling wavefields.
• To explore the relationship between paraboloidal, spherical, and planar wavefields.

Main Methods:

• An alternative approach to stationary field analysis was employed.
• The Helmholtz equation was used to model wavefields.
• The study focused on the dynamic, traveling wave scenario.

Main Results:

• The possibility of creating paraboloidal traveling wavefields was demonstrated.
• A connection between these wavefields and spherical/planar wavefields was established.
• The research extends wave theory to dynamic parabolic mirror scenarios.

Conclusions:

• This work provides a comprehensive wave theory for parabolic mirrors.
• The findings open new avenues for understanding wave propagation and reflection.
• The study highlights the versatility of parabolic shapes in wavefield manipulation.