Extending the Debye–Török theory: modeling and simulation of light focusing through an absorbing interface
Year: 2026
Type: article
Abstract: We develop a unified theoretical and numerical framework for vectorial focusing across a planar interface into a lossy medium. By embedding complex-angle refraction into the Debye–Török integral and enforcing the radiation-branch condition, we derive transmitted-field integrals that explicitly separate phase propagation from absorption-induced attenuation, yielding numerically stable evaluations at high NA. Simulations quantify how increasing loss reshapes the focal field: the Strehl ratio decreases, the axial maximum shifts toward the interface, the effective aperture NA eff narrows, and the longitudinal-field fraction η z decreases, while the lateral main lobe is largely preserved to first order. The framework clarifies energy-flow topology in inhomogeneous waves and provides actionable metrics (Strehl, Δ z , NA eff , η z ) for design and compensation in absorption-dominated settings (e.g., bioimaging, thermoplasmonics, and high-NA patterning). Transparent-limit and convergence checks establish physical consistency and numerical robustness, and the formulation is readily extensible to stratified and anisotropic media.
Source: Optics Express
DOI: 10.1364/oe.582482
Authors: Trang M. Do, Minh N. P. Dang
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,270
OpenAlex ID: W7124441072