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In nonlinear spectroscopies, the detected spectrum is determined by the response of the system to the particular excitation pulses, which can vary as excitation energy and pulse duration are tuned. Here, we analytically show that, under reasonable assumptions, the nested integrals that describe the light-matter interaction of the system can be simplified by application of the Fourier convolution and shift theorems, resulting in an expression for the nonlinear spectrum that is a product of the impulsive system response and the interaction laser spectra. The impulsive response can then be obtained by linearly dividing the laser spectrum from the detected signal. We demonstrate our normalization scheme by recovering the impulsive response from two different material systems, highlighting removal of distinct spectral artifacts.

 

We demonstrate entangled-state swapping, within the Hermite–Gaussian (HG) basis of first-order modes, directly from the process of spontaneous parametric downconversion within a nonlinear crystal. The method works by explicitly tailoring the spatial structure of the pump photon such that it resembles the product of the desired entangled spatial modes exiting the crystal. Importantly, the result is an entangled state of balanced HG modes, which may be beneficial in applications that depend on symmetric accumulations of geometric phase through optics or in applications of quantum sensing and imaging with azimuthal sensitivity. Furthermore, the methods are readily adaptable to other spatial mode bases.

 

We present and implement a method for the experimental measurement of geometric phase of non-geodesic (small) circles on any SU(2) parameter space. This phase is measured by subtracting the dynamic phase contribution from the total phase accumulated. Our design does not require theoretical anticipation of this dynamic phase value and the methods are generally applicable to any system accessible to interferometric and projection measurements. Experimental implementations are presented for two settings: (1) the sphere of modes of orbital angular momentum, and (2) the Poincaré sphere of polarizations of Gaussian beams.

 

We numerically compare the null quality for STED microscopy generated by Laguerre-Gaussian beams with orbital angular momentum and donut beams generated by incoherent addition of orthogonal Hermite Gaussian beams when imaging deep biological tissue.

 

We show that annihilation dynamics between oppositely charged optical vortex pairs can be manipulated by the initial size of the vortex cores, consistent with hydrodynamics. When sufficiently close together, vortices with strongly overlapped cores annihilate more quickly than vortices with smaller cores that must wait for diffraction to cause meaningful core overlap. Numerical simulations and experimental measurements for vortices with hyperbolic tangent cores of various initial sizes show that hydrodynamics governs their motion, and reveal distinct phases of vortex recombination; decreasing the core size of an annihilating pair can prevent the annihilation event.

 

We provide the first, to the best of our knowledge, experimental demonstration of a geometric phase generated in association with closed Poincaré sphere trajectories comprising geodesic arcs that do not start, end, or necessarily even include, the north and south poles that represent pure Laguerre–Gaussian modes. Arbitrarily tilted (elliptical) single vortex states are prepared with a spatial light modulator, and Poincaré sphere circuits are driven by beam transit through a series ofπ-converters and Dove prisms.

 

We show that a two-dimensional hydrodynamics model provides a physical explanation for the splitting of higher-charge optical vortices under elliptical deformations. The model is applicable to laser light and quantum fluids alike. The study delineates vortex breakups from vortex unions under different forms of asymmetry in the beam, and it is also applied to explain the motion of intact higher-charge vortices.

 

Imaging sub-diffraction dynamics of neural nanostructures involved in behaviors such as learning and memory in a freely moving animal is not possible with existing techniques. Here, we present a solution in the form of a two-photon (2P), fiber-coupled, stimulated emission depletion microscope and demonstrate its capabilities by acquiring super-resolution imaging of mammalian cells. A polarization-maintaining fiber is used to transport both the 2P excitation light (915 nm) and the donut-shaped depletion beam (592 nm), which is constructed by adding two temporally incoherent and orthogonally polarized Hermite–Gaussian fiber modes. The fiber output is insensitive to bending or temperature changes and is the first demonstration toward deep tissue super-resolution imaging in awake behaving animals. 

The DyMIN method reduces photobleaching, a problem in STED microscopy. Labs implementing custom-built STED microscopes would greatly benefit from DyMIN capabilities. We present an inexpensive, open-source version utilizing an FPGA and multiplexer.