A sub wavelength localization scheme in optical imaging using conical diffraction

Group velocity of light in internal conical refraction

We calculated the group velocity of light in internal conical refraction in a biaxial crystal as a function of the direction of the electric displacement vector, or the vibration direction, of its carrier wave. Our method represents group velocity through the electromagnetic fields of light, rather than its wave normal or ray direction. The travel time of a light pulse traversing a parallel plate biaxial crystal in internal conical refraction is found to vary as a sinusoidal function of twice the vibration angle of the light wave. Our method distinguishes the four directions of the two optic axes in monoclinic and triclinic crystals. Numerical examples are given for K N b O 3 at the wavelength of 400 nm, and for S n 2 P 2 S 6 at the wavelength of 550 nm.

Polarization-dependent group velocity of light pulses traveling in the optic ray axis directions of a biaxial crystal

We theoretically prove that the group velocity of a light pulse traveling in an optic ray axis direction of a biaxial crystal depends on the polarization state of the light. Our calculation shows that the group index varies as a sinusoidal function of twice the polarization angle of the light pulse. For monoclinic and triclinic crystals, in general the four directions of the two optic ray axes need to be distinguished. Numerical examples show that in KNbO₃ the group velocity varies by 2.7% at 400 nm wavelength, and in Sn₂P₂S₆ it varies by 3.9% at 550 nm wavelength, when the polarization state of the light is changing.

Conical refraction with low-coherence light sources

We report on conical refraction (CR) with low-coherence light sources, such as light-emitting diodes and decoherentized HeNe laser radiation, and demonstrate different CR patterns. In our experiments, a variation of the pinhole sizes from 25 to 100 µm and the distances to pinhole from 50 to 5 cm reduced spatial coherence of radiation that resulted in the disappearance of the dark Poggendorff's ring in the Lloyd's plane. This is attributed to the interference nature of the Lloyd's distribution and found to be in excellent agreement with the paraxial dual-cone model of conical refraction.

Sum-frequency generation with femtosecond conical refraction pulses

In this Letter, we study short-wavelength conical refraction (CR) via sum-frequency generation (SFG) in the femtosecond regime, a previously unaddressed topic. Based on biaxial crystal of KGd(WO₄)₂ whose dispersion of optical-axis orientation is negligible in near-IR, conventional femtosecond lasers at 800 and 1054 nm are transformed into CR beams, respectively. Femtosecond CR beams at 454 nm are generated via SFG with the near-IR CR beams. While the generated sum-frequency ring is typically incomplete, a full-ring distribution can be achieved by adopting Type-II SFG with a large phase mismatch. We find that the femtosecond sum-frequency ring under various phase-matching conditions evolves as typical CR beams.

Quantum correlation enhanced super-resolution localization microscopy enabled by a fibre bundle camera

Despite advances in low-light-level detection, single-photon methods such as photon correlation have rarely been used in the context of imaging. The few demonstrations, for example of subdiffraction-limited imaging utilizing quantum statistics of photons, have remained in the realm of proof-of-principle demonstrations. This is primarily due to a combination of low values of fill factors, quantum efficiencies, frame rates and signal-to-noise characteristic of most available single-photon sensitive imaging detectors. Here we describe an imaging device based on a fibre bundle coupled to single-photon avalanche detectors that combines a large fill factor, a high quantum efficiency, a low noise and scalable architecture. Our device enables localization-based super-resolution microscopy in a non-sparse non-stationary scene, utilizing information on the number of active emitters, as gathered from non-classical photon statistics.

Achromatization of conical diffraction: application to the generation of a polychromatic optical vortex

Vortex beams are plagued by the intrinsic chromaticity of the physical phenomenon used to generate them. To the authors' best knowledge, attempts to generate them in a broad spectral range remain quite scarce and limited in their results. Crystal optics and especially conical diffraction (CD) (or refraction) intrinsically create achromatic vortices. The vortex is created by a wavelength-independent topological charge, embedded directly in the Fresnel equations. However, for biaxial crystals of low crystallographic symmetry, which includes all crystals used practically for CD, the dispersion of the binormal axis creates a chromaticity effect. In this Letter, we propose a new way to compensate this dispersion of the binormal axis of a biaxial crystal in order to generate white-light vortex beams by CD in a 250 nm spectral range, covering almost all the visible range. The advantages of the ability to use CD in a wide spectral range vastly exceed the sole generation of vortex beams.

Variable two-crystal cascade for conical refraction

The cascade conical refraction occurs when a collimated light beam is passed consequently along the optic axes of several biaxial crystals arranged in a series. For commonly used optical arrangements, the general structure of light emerging from such a cascade is rigorously determined by the used crystals, leaving few possibilities for the variations of the established light pattern. A simple modification of a two-crystal arrangement where one of the two crystals is placed beyond the imaging lens is reported. This modification adds an extreme versatility to the effect and allows one to tune continuously the actual cascade parameters. As a result, practically any pattern of two-crystal cascade conical refraction can be obtained for any pair of biaxial crystals.

Polarization tailored novel vector beams based on conical refraction

Coherent vector beams with involved states of polarization (SOP) are widespread in the literature, having applications in laser processing, super-resolution imaging and particle trapping. We report novel vector beams obtained by transforming a Gaussian beam passing through a biaxial crystal, by means of the conical refraction phenomenon. We analyze both experimentally and theoretically the SOP of the different vector beams generated and demonstrate that the SOP of the input beam can be used to control both the shape and the SOP of the transformed beam. We also identify polarization singularities of such beams for the first time and demonstrate their control by the SOP of the input beam.

Laser action along and near the optic axis of a holmium-doped KY(WO₄)₂ crystal

We demonstrate the first (to our knowledge) quasi-three-level conical refraction laser operating at 2 μm, with 1.6 W of output power at 2074 nm, using a holmium-doped KY(WO4)2 crystal. A maximum slope efficiency of 52% has been achieved, along the optic axis with respect to the absorbed pump power. Furthermore, lasing operation around the optic axis has been performed. In this case, a maximum output power of 3 W has been reached, with a slope efficiency better than 70%, which are the best performances ever reported on this material.