Identify the limits of geometric optics ray tracing by numerically solving the vector Kirchhoff integral

Area of Science:

• Electromagnetism
• Optics
• Wave Scattering

Background:

• Geometric optics provides an approximation for light propagation.
• Accurate computation of electromagnetic near fields is crucial for understanding light behavior.
• Previous theories, like van de Hulst's work on light scattering, provide foundational insights.

Purpose of the Study:

• To investigate the properties of a pencil of light beyond geometric optics approximations.
• To accurately compute the electromagnetic near field of a light pencil using the vector Kirchhoff integral.
• To analyze how beam characteristics (size, shape, direction, medium) influence near-field behavior and energy diffusion.

Main Methods:

• Utilized the vector Kirchhoff integral for electromagnetic near-field computation.
• Investigated pencils of light with varying geometric mean cross-section sizes relative to wavelength.
• Analyzed propagation characteristics and energy diffusion over distances proportional to wavelength squared.

Main Results:

• Electromagnetic near fields within a light pencil are non-uniform and exhibit complex patterns near the beam base.
• Light pencils with a geometric mean cross-section size of the order p times the wavelength can propagate independently up to p^2 times the wavelength.
• Most of the beam energy diffuses out of the beam region at these extended distances.
• Observed convergence of fields towards Fraunhofer diffraction patterns far from the beam base.

Conclusions:

• The vector Kirchhoff integral provides accurate near-field computations for light pencils.
• Light beam propagation and energy diffusion are strongly dependent on the beam's size relative to the wavelength.
• The findings align with classical theories of light scattering and offer a more detailed understanding of near-field electromagnetic phenomena.