Modeling and simulation of light focusing through an absorbing interface based on the Debye– Török–Fedorov–Nakajima framework

Tóm tắt

We develop a unified Debye–Török–Fedorov–Nakajima (DTFN) model for tight focusing across an absorbing interface, extending the Debye–Wolf/Török integrals to complex refractive indices by enforcing the physical branch ℑ(𝑘2𝑧) ≥ 0 and using complex Fresnel coefficients. A Gauss–Legendre implementation achieves fast convergence with flux-preserving apodization. For a glass–to–tissue setting (𝑛1 = 1.51, 𝑛2 = 1.58 + 𝑖 2.9 × 10-3, 𝜆0 = 532 nm, NA = 1.3) the on-axis peak decreases by ∼ 75× and shifts toward the interface by ∼ 0.18 𝜇m, while the lateral width remains nearly diffractionlimited. A new branch-comparison figure shows that enforcing ℑ(𝑘2𝑧) ≥ 0 suppresses non-decaying angular components and stabilizes the axial baseline. The DTFN framework provides a physically rigorous and numerically stable basis for modeling high-NA focusing in weakly absorbing and biomedical media.