Recursive fresnel lens

This research introduces a novel optical framework that extends the Fresnel lens concept into a fractal, golden-ratio-based geometry, capable of producing multi-depth focusing and artificial lensing effects without gravitational or conventional refractive means. The study explores how recursive phase modulation—implemented through fractal scaling guided by the golden ratio—can synthetically reproduce gravitational-like lensing behavior, enabling the perception or capture of distant optical fields within finite physical apertures. Through analytical modeling, Fourier-domain simulations, and numerical comparisons with standard Fresnel lenses, this work quantifies the trade-offs between single-plane focusing efficiency and multi-plane depth continuity. Results demonstrate that although the fractal design sacrifices central peak intensity, it achieves 2–4× greater depth of field, broader axial light distribution, and enhanced potential for synthetic optical magnification. The proposed model bridges classical diffraction optics and meta-surface principles, suggesting pathways toward the next generation of adaptive telescopic systems, computational imaging platforms, and lightfield-based synthetic lensing. The document also outlines future work in meta-lens fabrication, recursion optimization, and machine-tuned phase weighting to improve energy concentration and structural efficiency. This paper forms part of ongoing research toward developing artificial lensing systems—engineered constructs capable of extending the observable optical horizon through geometry, rather than mass or gravity.