We studied a novel family of paraxial laser beams forming an overcomplete yet nonorthogonal set of modes. These modes have a singular phase profile and are eigenfunctions of the photon orbital angular momentum. The intensity profile is characterized by a single brilliant ring with the singularity at its center, where the field amplitude vanishes. The complex amplitude is proportional to the degenerate (confluent) hypergeometric function, and therefore we term such beams hypergeometric-Gaussian (HyGG) modes. Unlike the recently introduced hypergeometric modes [Opt. Lett. 32, 742 (2007) ], the HyGG modes carry a finite power and have been generated in this work with a liquid-crystal spatial light modulator. We briefly consider some subfamilies of the HyGG modes as the modified Bessel Gaussian modes, the modified exponential Gaussian modes, and the modified Laguerre–Gaussian modes.

In this work, we investigate the evanescent field sensing mechanism provided by an all-dielectric metasurface supporting bound states in the continuum (BICs). The metasurface is based on a transparent photonic crystal with subwavelength thickness. The BIC electromagnetic field is localized along the direction normal to the photonic crystal nanoscale-thin slab (PhCS) because of a topology-induced confinement, exponentially decaying in the material to detect. On the other hand, it is totally delocalized in the PhCS plane, which favors versatile and multiplexing sensing schemes. Liquids with different refractive indices, ranging from 1.33 to 1.45, are infiltrated in a microfluidic chamber bonded to the sensing dielectric metasurface. We observe an experimental exponential sensitivity leading to differential values as large as 226 nm$/$RIU with excellent FOM. This behavior is explained in terms of the physical superposition of the field with the material under investigation and supported by a thorough numerical analysis. The mechanism is then translated to the case of molecular adsorption where a suitable theoretical engineering of the optical structure points out potential sensitivities as large as 4000 nm$/$RIU.

Photonic bound states in the continuum (BICs), embedded in the spectrum of free-space waves^1,2 with diverging radiative quality factor, are topologically non-trivial dark modes in open-cavity resonators that have enabled important advances in photonics^3,4. However, it is particularly challenging to achieve maximum near-field enhancement, as this requires matching radiative and non-radiative losses. Here we propose the concept of supercritical coupling, drawing inspiration from electromagnetically induced transparency in near-field coupled resonances close to the Friedrich–Wintgen condition². Supercritical coupling occurs when the near-field coupling between dark and bright modes compensates for the negligible direct far-field coupling with the dark mode. This enables a quasi-BIC field to reach maximum enhancement imposed by non-radiative loss, even when the radiative quality factor is divergent. Our experimental design consists of a photonic-crystal nanoslab covered with upconversion nanoparticles. Near-field coupling is finely tuned at the nanostructure edge, in which a coherent upconversion luminescence enhanced by eight orders of magnitude is observed. The emission shows negligible divergence, narrow width at the microscale and controllable directivity through input focusing and polarization. This approach is relevant to various physical processes, with potential applications for light-source development, energy harvesting and photochemical catalysis.

A compact and robust scheme for broadband excitation of whispering gallery mode (WGM) resonances into a microsphere is demonstrated. A polymer microsphere (10 μm) is encapsulated into the capillary of a microstructured optical fiber, in direct contact with the guiding core. Such a configuration allows efficient and reproducible excitation of the in-MOF-microsphere resonator that is characterized by two launch/collection schemes: core input/scattering output, and sphere input/core output. The latter allows an excitation of the microsphere WGMs externally to the fiber. Numerically calculated WGM spectra are in agreement with experiments. $Q$ factors in the range of ${10}^3$ are typically measured.