Optimal Diffractive Focusing and Single-Photon Parametric Stimulation

Talk

In this talk, I will present two recent and independent results in optical physics. The first concerns the optimal diffractive focusing of vortex beams carrying orbital angular momentum. We formulate the focusing problem as a variational optimization and derive an exact analytical solution for the real-valued radial pupil that maximizes the intensity at a prescribed focal ring. The solution establishes the fundamental focusing limit under the imposed constraints and reveals how the optimal mask combines Fresnel phase matching with the radial structure imposed by the vortex mode. We compare this optimum with conventional diffractive designs and experimentally demonstrate the predicted improvement.
The second part concerns stimulated parametric down-conversion in the weak-seed regime. By measuring higher-order temporal correlations, we identify signatures of seed-induced three-photon correlations and distinguish them from spontaneous emission and accidental coincidences. The results probe parametric stimulation in a regime approaching the few-photon level and provide a direct correlation-based characterization of the process.

I will discuss the main physical results, experimental observations, and possible extensions of each study.

R. Ghobadi, C. Rodriguez, L. Scarfe, M.A. Efremov, M. A., & E. Karimi. arXiv preprint arXiv:2610.10842.
Y. Klein, A. D’Errico, R. Ghobadi, D. Paneru, N. Dehghan, E. Cohen, E. Karimi, Optica, 13(11), 2255-2261 (2026).

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