{"paper":{"title":"Uncertainty relation for focal spots in light beams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"physics.optics","authors_text":"Iwo Bialynicki-Birula, Zofia Bialynicka-Birula","submitted_at":"2013-10-24T11:29:47Z","abstract_excerpt":"Uncertainty relations for light pulses found in [Phys. Rev. A {\\bf 86}, 022118 (2012)] were derived in the three-dimensional case which emphasized the localization in a volume. Here we derive the uncertainty relation for light beams in the two-dimensional plane perpendicular to the direction of the beam propagation which is more interesting for realistic beams. This uncertainty relation connects the area of the focal spot with the spectrum of transverse photon momenta. The shape of the beam that saturates the uncertainty relation is very close to a Gaussian. The directions of the electric and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6570","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}