Fast finite difference solver for optical microscopy in deep biological tissue.

Optical scattering poses a significant challenge to high-resolution microscopy within deep tissue. To accurately predict the performance of various microscopy techniques in thick samples, we present a computational model that efficiently solves Maxwell's equation in highly scattering media. This toolkit simulates the deterioration of the laser beam point spread function (PSF) without making a paraxial approximation, enabling accurate modeling of high-numerical-aperture (NA) objective lenses commonly employed in experiments.

OpenSTED: open-source dynamic intensity minimum system for stimulated emission depletion microscopy.

Significance: Stimulated emission depletion (STED) is a powerful super-resolution microscopy technique that can be used for imaging live cells. However, the high STED laser powers can cause significant photobleaching and sample damage in sensitive biological samples. The dynamic intensity minimum (DyMIN) technique turns on the STED laser only in regions of the sample where there is fluorescence signal, thus saving significant sample photobleaching.

Experimental measurement of the geometric phase of non-geodesic circles.

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.

Amplitude structure of optical vortices determines annihilation dynamics.

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.

Hydrodynamics explanation for the splitting of higher-charge optical vortices.

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.

Tilted Poincaré sphere geodesics.

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 of π-converters and Dove prisms.

Hidden Silicon-Vacancy Centers in Diamond.

We characterize a high-density sample of negatively charged silicon-vacancy (SiV^{-}) centers in diamond using collinear optical multidimensional coherent spectroscopy. By comparing the results of complementary signal detection schemes, we identify a hidden population of SiV^{-} centers that is not typically observed in photoluminescence and which exhibits significant spectral inhomogeneity and extended electronic T_{2} times. The phenomenon is likely caused by strain, indicating a potential mechanism for controlling electric coherence in color-center-based quantum devices.

Selective excitation of plasmon resonances with single V-point cylindrical vector beams.

We use a rigorous group theoretical method to identify a class of cylindrical vector beams that can selectively excite the plasmon modes of axially symmetric plasmonic structures. Our choice of the single V-point cylindrical vector beams as the basis to decompose cylindrical beams dramatically simplifies the symmetry analysis in the group theory framework. With numerical simulations, we demonstrate that any plasmon eigenmodes, bright or dark, can be selectively excited individually or jointly.

Observation of the rotational Doppler shift with spatially incoherent light.

The rotational Doppler shift (RDS) is typically measured by illuminating a rotating target with a laser prepared in a simple, known orbital angular momentum (OAM) superposition. We establish theoretically and experimentally that detecting the rotational Doppler shift does not require the incident light to have a well-defined OAM spectrum but instead requires well-defined correlations within the OAM spectrum. We demonstrate measurement of the rotational Doppler shift using spatially incoherent light.

Fast phase cycling in non-collinear optical two-dimensional coherent spectroscopy.

As optical two-dimensional coherent spectroscopy (2DCS) is extended to a broader range of applications, it is critical to improve the detection sensitivity of optical 2DCS. We developed a fast phase-cycling scheme in a non-collinear optical 2DCS implementation by using liquid crystal phase retarders to modulate the phases of two excitation pulses. The background in the signal can be eliminated by combining either two or four interferograms measured with a proper phase configuration.

Detection technique effect on rotational Doppler measurements.

There are two established methods for measuring rotational Doppler shift: (1) heterodyne and (2) fringe. We identify a key distinction, that only the heterodyne method is sensitive to the rotating object's phase, which results in significant differences in the signal-to-noise ratio (SNR) when measuring multiple rotating particles. When used to measure randomly distributed rotating particles, the fringe method produces its strongest SNR when a single particle is present and its SNR tends to zero as the number of particles increases, whereas the heterodyne method's SNR increases proportionally to the number of particles in the beam.

Optical vortex braiding with Bessel beams.

We propose the braiding of optical vortices in a laser beam with more than $ 2\pi $2π rotation by superposing Bessel modes with a plane wave. We experimentally demonstrate this by using a Bessel-Gaussian beam and a coaxial Gaussian, and we present measurements of three complete braids. The amount of braiding is fundamentally limited only by the numerical aperture of the system, and we discuss how braiding can be controlled experimentally for any number of vortices.

A Fiber-Coupled Stimulated Emission Depletion Microscope for Bend-Insensitive Through-Fiber Imaging.

We present results for a new type of fiber-coupled stimulated emission depletion (STED) microscope which uses a single fiber to transport STED and excitation light, as well as collect the fluorescence signal. Our method utilizes two higher-order eigenmodes of polarization maintaining (PM) fiber to generate the doughnut-shaped STED beam. The modes are excited with separate beams that share no temporal coherence, yielding output that is independent of fiber bending.

Absolute phase calibration in phase-modulated multidimensional coherent spectroscopy.

Establishing the correct phase in multidimensional coherent spectroscopy (MDCS) experiments is critical because the interpretation of quantum pathways is based on the phase of their associated spectral features but is not trivial because the phase introduced by experimental conditions can contaminate the signal. Most phase-modulated MDCS (PM-MDCS) experiments study molecular systems for which the spectra can be phased to produce absorptive lineshapes, but this assumption of absorptive lineshapes can break down in more complicated systems. We present a robust technique for correcting the phase in PM-MDCS experiments and demonstrate accurate spectrum phasing for an anharmonic system.

Quantum Turbulent Structure in Light.

The infinite superpositions of random plane waves are known to be threaded with vortex line singularities which form complicated tangles and obey strict topological rules. We observe that within these structures, a timelike axis appears to emerge with which we can define vortex velocities in a useful way: With both numerical simulations and optical experiments, we show that the statistics of these velocities match those of turbulent quantum fluids such as superfluid helium and atomic Bose-Einstein condensates. These statistics are shown to be independent of system scale.

Characterizing vortex beams from a spatial light modulator with collinear phase-shifting holography.

We demonstrate collinear phase-shifting holography for measuring complex optical modes of twisted light beams with orbital angular momentum (OAM) generated by passing a laser through a spatial light modulator (SLM). This technique measures the mode along the direction of propagation from the SLM and requires no additional optics, so it can be used to aid alignment of the SLM, to efficiently check for the effects of beam wander, and to fully characterize generated beams before use in other experiments. Optimized error analysis and careful SLM alignment allow us to generate and measure OAM with purity as high as 99.

Diagonal slice four-wave mixing: natural separation of coherent broadening mechanisms.

We present an ultrafast coherent spectroscopy data acquisition scheme that samples slices of the time domain used in multidimensional coherent spectroscopy to achieve faster data collection than full spectra. We derive analytical expressions for resonance lineshapes using this technique that completely separate homogeneous and inhomogeneous broadening contributions into separate projected lineshapes for arbitrary inhomogeneous broadening. These lineshape expressions are also valid for slices taken from full multidimensional spectra and allow direct measurement of the parameters contributing to the lineshapes in those spectra as well as our own.

Angular Momentum of Topologically Structured Darkness.

We theoretically analyze and experimentally measure the extrinsic angular momentum contribution of topologically structured darkness found within fractional vortex beams, and show that this structured darkness can be explained by evanescent waves at phase discontinuities in the generating optic. We also demonstrate the first direct measurement of the intrinsic orbital angular momentum of light with both intrinsic and extrinsic angular momentum, and explain why the total orbital angular momenta of fractional vortices do not match the winding number of their generating phases.

Tunable higher-order orbital angular momentum using polarization-maintaining fiber.

For the first time, to the best of our knowledge, light with orbital angular momentum (OAM) of ±2ℏ per photon is produced using commercially available polarization-maintaining fiber with modal purity of 96%. Twist measurements demonstrate that the average orbital angular momentum can be continuously tuned between ±2ℏ. The authors consider beams of non-integer OAM, created using the presented method, as superpositions of integer OAM states.

Simultaneous control of orbital angular momentum and beam profile in two-mode polarization-maintaining fiber.

We report simultaneous control of the orbital angular momentum (OAM) and beam profile of vortex beams generated in two-mode polarization-maintaining optical fiber. Two higher-order eigenmodes of the fiber are combined to form optical vortices. Reduced coherence between the fiber modes decreases the mode purity.

Quantitative measurement of the orbital angular momentum of light with a single, stationary lens.

We show that the average orbital angular momentum (OAM) of twisted light can be measured simply and robustly with a single stationary cylindrical lens and a camera. Theoretical motivation is provided, along with self-consistent optical modeling and experimental results. In contrast to qualitative interference techniques for measuring OAM, we quantitatively measure non-integer average OAM in mode superpositions.

Continuously tunable orbital angular momentum generation using a polarization-maintaining fiber.

We demonstrate the generation of orbital angular momentum (OAM) in a two-mode polarization-maintaining (PM) optical fiber. We combine two linearly polarized modes of PM fiber to generate linearly polarized optical vortex beams with OAM. The average OAM can be finely varied by changing the phase between modes.

Analytical calculation of two-dimensional spectra.

We demonstrate an analytical calculation of two-dimensional (2D) coherent spectra of electronic or vibrational resonances. Starting with the solution to the optical Bloch equations for a two-level system in the 2D time domain, we show that a fully analytical 2D Fourier transform can be performed if the projection-slice and Fourier-shift theorems of Fourier transforms are applied. Results can be fit to experimental 2D coherent spectra of resonances with arbitrary inhomogeneity.

Measurement of the M² beam propagation factor using a focus-tunable liquid lens.

We demonstrate motion-free beam quality M² measurements of stigmatic, simple astigmatic, and general astigmatic (twisted) beams using only a focus-tunable liquid lens and a CCD camera. We extend the variable-focus technique to the characterization of general astigmatic beams by measuring the 10 second-order moments of the power density distribution for the twisted beam produced by passage through multimode optical fiber. Our method measures the same M² values as the traditional variable-distance method for a wide range of laser beam sources, including nearly TEM(00) (M²≈1) and general astigmatic multimode beams (M²≈8).