Propagation-distance limit for a classical nonlocal optical system

Abstract

We derive closed-form analog quantum-speed-limit (QSL) bounds for highly nonlocal optical beams whose paraxial propagation is mapped to a reversed (inverted) harmonic-oscillator generator. Treating the longitudinal coordinate z as an evolution parameter (propagation distance), we construct the propagator, evaluate the Bures distance, and obtain analytic Mandelstam-Tamm and Margolus-Levitin bounds that fix a propagation distance limit zPDL to reach a prescribed mode distinguishability. This distance-domain constraint is the classical optical analogue of the minimal-orthogonality time in quantum mechanics. We then propose a compact self-defocusing PDL beam shaper that achieves strong transverse mode conversion within millimetre scales. We further show that small variations in refractive index, beam power, or temperature shift zSL with high leverage, enabling SL-based metrology with index sensitivities down to 10-7RIU and temperature resolutions of order 1 mK. The results bridge distance-domain QSL geometry and practical photonic applications.