Propagation-Distance Limit for a Classical Nonlocal Optical System
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911290117586944 |
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| author | Wani, Salman Sajad Shi, Xiaoping Al-Kuwari, Saif- Shabir, Arshid Faizal, Mir |
| author_facet | Wani, Salman Sajad Shi, Xiaoping Al-Kuwari, Saif- Shabir, Arshid Faizal, Mir |
| contents | 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 $z_{\mathrm{PDL}}$ 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 millimeter scales. We further show that small variations in refractive index, beam power, or temperature shift $z_{\mathrm{SL}}$ with high leverage, enabling speed-limit-based metrology with index sensitivities down to $10^{-7}$ RIU and temperature resolutions of order $1$ mK. The results bridge distance-domain QSL geometry and practical photonic applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22085 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Propagation-Distance Limit for a Classical Nonlocal Optical System Wani, Salman Sajad Shi, Xiaoping Al-Kuwari, Saif- Shabir, Arshid Faizal, Mir Quantum Physics 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 $z_{\mathrm{PDL}}$ 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 millimeter scales. We further show that small variations in refractive index, beam power, or temperature shift $z_{\mathrm{SL}}$ with high leverage, enabling speed-limit-based metrology with index sensitivities down to $10^{-7}$ RIU and temperature resolutions of order $1$ mK. The results bridge distance-domain QSL geometry and practical photonic applications. |
| title | Propagation-Distance Limit for a Classical Nonlocal Optical System |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2511.22085 |