title: Refraction limit of miniaturized optical systems: a ball-lens example.
abstract: We study experimentally and theoretically the electromagnetic field in amplitude and phase behind ball-lenses across a wide range of diameters, ranging from a millimeter scale down to a micrometer. Based on the observation, we study the transition between the refraction and diffraction regime. The former regime is dominated by observables for which it is sufficient to use a ray-optical picture for an explanation, e.g., a cusp catastrophe and caustics. A wave-optical picture, i.e. Mie theory, is required to explain the features, e.g., photonic nanojets, in the latter regime. The vanishing of the cusp catastrophe and the emergence of the photonic nanojet is here understood as the refraction limit. Three different criteria are used to identify the limit: focal length, spot size, and amount of cross-polarization generated in the scattering process. We identify at a wavelength of 642 nm and while considering ordinary glass as the ball-lens material, a diameter of approximately 10 µm as the refraction limit. With our study, we shed new light on the means necessary to describe micro-optical system. This is useful when designing optical devices for imaging or illumination.
authors.forename: Myun-Sik
authors.initials: MS
authors.lastname: Kim
authors.forename: Toralf
authors.initials: T
authors.lastname: Scharf
authors.forename: Stefan
authors.initials: S
authors.lastname: Mühlig
authors.forename: Martin
authors.initials: M
authors.lastname: Fruhnert
authors.forename: Carsten
authors.initials: C
authors.lastname: Rockstuhl
authors.forename: Roland
authors.initials: R
authors.lastname: Bitterli
authors.forename: Wilfried
authors.initials: W
authors.lastname: Noell
authors.forename: Reinhard
authors.initials: R
authors.lastname: Voelkel
authors.forename: Hans Peter
authors.initials: HP
authors.lastname: Herzig