Showing papers in "Journal of The Optical Society of America A-optics Image Science and Vision in 2019"

Quasinormal mode solvers for resonators with dispersive materials

Abstract: Optical resonators are widely used in modern photonics. Their spectral response and temporal dynamics are fundamentally driven by their natural resonances, the so-called quasinormal modes (QNMs), with complex frequencies. For optical resonators made of dispersive materials, the QNM computation requires solving a nonlinear eigenvalue problem. This raises a difficulty that is only scarcely documented in the literature. We review our recent efforts for implementing efficient and accurate QNM solvers for computing and normalizing the QNMs of micro- and nanoresonators made of highly dispersive materials. We benchmark several methods for three geometries, a two-dimensional plasmonic crystal, a two-dimensional metal grating, and a three-dimensional nanopatch antenna on a metal substrate, with the perspective to elaborate standards for the computation of resonance modes.

Refractive index sensing characteristics in a D-shaped photonic quasi-crystal fiber sensor based on surface plasmon resonance.

Abstract: A D-shaped photonic quasi-crystal fiber (PQF) sensor based on surface plasmon resonance is proposed for refractive index (RI) sensing. The influences of the width of the gold film, the diameter of the air holes, and the thickness of the gold film on the sensing performance are analyzed. When the RI of a liquid analyte gradually increases from 1.415 to 1.427, the average sensitivity is calculated as 10,250 nm/RIU, and the maximum sensitivity is up to 34,000 nm/RIU, which realizes the high-sensitivity sensing in the near-infrared band. The D-shaped PQF sensor proposed has great application potential in the detection of biochemical analytes and provides a new way to improve the sensing performance.

Iterative phase retrieval for digital holography: tutorial

Abstract: This paper provides a tutorial of iterative phase retrieval algorithms based on the Gerchberg-Saxton (GS) algorithm applied in digital holography. In addition, a novel GS-based algorithm that allows reconstruction of 3D samples is demonstrated. The GS-based algorithms recover a complex-valued wavefront using wavefront back-and-forth propagation between two planes with constraints superimposed in these two planes. Iterative phase retrieval allows quantitatively correct and twin-image-free reconstructions of object amplitude and phase distributions from its in-line hologram. The present work derives the quantitative criteria on how many holograms are required to reconstruct a complex-valued object distribution, be it a 2D or 3D sample. It is shown that for a sample that can be approximated as a 2D sample, a single-shot in-line hologram is sufficient to reconstruct the absorption and phase distributions of the sample. Previously, the GS-based algorithms have been successfully employed to reconstruct samples that are limited to a 2D plane. However, realistic physical objects always have some finite thickness and therefore are 3D rather than 2D objects. This study demonstrates that 3D samples, including 3D phase objects, can be reconstructed from two or more holograms. It is shown that in principle, two holograms are sufficient to recover the entire wavefront diffracted by a 3D sample distribution. In this method, the reconstruction is performed by applying iterative phase retrieval between the planes where intensity was measured. The recovered complex-valued wavefront is then propagated back to the sample planes, thus reconstructing the 3D distribution of the sample. This method can be applied for 3D samples such as 3D distribution of particles, thick biological samples, and other 3D phase objects. Examples of reconstructions of 3D objects, including phase objects, are provided. Resolution enhancement obtained by iterative extrapolation of holograms is also discussed.

Modified Mach-Zehnder interferometer for determining the high-order topological charge of Laguerre-Gaussian vortex beams

Abstract: This study demonstrates a self-referenced interferometric method to estimate the magnitude and sign of a high-order topological charge (TC) carried by incoming optical vortex beams. The proposed method uses a right-angle prism in a Mach-Zehnder interferometer setup with controlled lateral shift and tilt between the wavefronts of interfering beams. The in-line interference with its conjugate results in a petal-shaped fringe pattern, where the number of petals reveals the magnitude of the TC. When the direction of one of the interfering beams is laterally displaced and rotated to emerge at a small angle for off-axis interference such that the vortices overlap at the output plane, then a fork-like interference pattern with better visibility is obtained, which can be used for estimating the magnitude as well as the sign of the TC. Through numerical simulation and optical experiment, it is shown that the technique is capable of estimating the TC of Laguerre-Gaussian beams even with a nonzero radial index.

Hyperspectral imaging in color vision research: tutorial.

Abstract: This tutorial offers an introduction to terrestrial and close-range hyperspectral imaging and some of its uses in human color vision research. The main types of hyperspectral cameras are described together with procedures for image acquisition, postprocessing, and calibration for either radiance or reflectance data. Image transformations are defined for colorimetric representations, color rendering, and cone receptor and postreceptor coding. Several example applications are also presented. These include calculating the color properties of scenes, such as gamut volume and metamerism, and analyzing the utility of color in observer tasks, such as identifying surfaces under illuminant changes. The effects of noise and uncertainty are considered in both image acquisition and color vision applications.

Sampling approach for singular system computation of a radiation operator.

Abstract: The problem of computing the singular system of the radiation operator pertaining to the case of strip currents is dealt with. The associate eigenvalue problem involves a space-variant operator whose kernel is not band-limited. As a consequence, the sampling approach, which has been recently introduced for computing the eigenwavefronts of some band-limited linear space-invariant imaging systems, cannot be used as such. To overcome this drawback, it is shown that the kernel function can be recast as a varying band-limited function. This allows exploiting the pseudo-sampling series theory from which a sampling approximation of the kernel function is derived and eventually used to set the discrete eigenvalue problem. In particular, unlike the classical sampling approach, the sampling points turn out to be non-uniformly distributed. Some numerical examples are used to check the theory. It is shown that the most significant part of the singular system can be very accurately computed by using a number of samples slightly greater than the Shannon number.

Large and extremely low loss: the unique challenges of gravitational wave mirrors

Abstract: This paper describes the making of large mirrors for laser interferometer gravitational wave detectors. These optics, working in the near infrared, are among the best optics ever created and played a crucial role in the first direct detection of gravitational waves from black holes or neutron star fusions.

Dual-slope method for enhanced depth sensitivity in diffuse optical spectroscopy

Abstract: An apparatus for carrying out near-infrared spectroscopy using intensity-modulated near- infrared radiation or pulsed near-infrared radiation includes sources and detectors. For each source, there exists first and second distances. The first distance is a distance between the source and a first detector. The second distance is a distance between the source and the second detector. For each source, the difference between these two distances is the same. Additionally, wherein, for each source, the detector at a shorter distance is the same detector that is at a longer distance for the other source. A processor derives, from signals received by the detectors, a parameter indicative of two matched slopes. This parameter is either phase of the intensity- modulated near-infrared radiation or mean time-of-flight data for the pulsed near-infrared radiation. The processor then provides output data based on an average of the matched slopes. This promotes reduced sensitivity to superficial layers and enhanced sensitivity to deeper portions of a medium that is under investigation.

Hybrid topological evolution of multi-singularity vortex beams: generalized nature for helical-Ince-Gaussian and Hermite-Laguerre-Gaussian modes.

Abstract: A generalized family of scalar structured Gaussian modes including helical-Ince-Gaussian (HIG) and Hermite-Laguerre-Gaussian (HLG) beams is presented with physical insight upon the hybrid topological evolution nature of multi-singularity vortex beams carrying orbital angular momentum. Considering the physical origins of intrinsic coordinates aberration and the Gouy phase shift, a closed-form expression is derived to characterize the general modes in astigmatic optical systems. Moreover, a graphical representation, singularities hybrid evolution nature (SHEN) sphere, is proposed to visualize the topological evolution of the multi-singularity beams, accommodating HLG, HIG, and other typical subfamilies as characteristic curves on the sphere surface. The salient properties of SHEN sphere for describing the precise singularities splitting phenomena, exotic structured light fields, and Gouy phase shift are illustrated with adequate experimental verifications.

Imaging through distributed-volume aberrations using single-shot digital holography.

Abstract: This paper explores the use of single-shot digital holography data and a novel algorithm, referred to as multiplane iterative reconstruction (MIR), for imaging through distributed-volume aberrations. Such aberrations result in a linear, shift-varying or “anisoplanatic” physical process, where multiple-look angles give rise to different point spread functions within the field of view of the imaging system. The MIR algorithm jointly computes the maximum a posteriori estimates of the anisoplanatic phase errors and the speckle-free object reflectance from the single-shot digital holography data. Using both simulations and experiments, we show that the MIR algorithm outperforms the leading multiplane image-sharpening algorithm over a wide range of anisoplanatic conditions.

Circular gradient-diameter photonic crystal fiber with large mode area and low bending loss.

Abstract: In this paper, a silica-based sixfold circular gradient-diameter photonic crystal fiber (CGPCF) with five rings is proposed, and the matching conditions of air hole lattices are established considering the gradient and diameter of the air holes. This CGPCF supports endlessly single-mode propagation due to the existence of small air holes near to the fiber core based on the matching rule. Simultaneously, it exhibits an ultralarge effective mode area of 3110 μm2 in the straight case and 1105 μm2 in the bending case with a bending radius of 15 cm at the wavelength of 1550 nm. In addition, within an ultrawide communication wavelength range from 1000 to 2000 nm (from 1350 nm to 2000 nm), the effective mode area in the straight (bending) case still maintains more than 3043 μm2 (981 μm2), and the bending loss maintains an ultralow order of magnitude of 10−4 dB/m at a great degree of bending radius of 15 cm. Moreover, the rotation-symmetric structure of CGPCF can reduce the impact of bending orientation on the optical properties. The proposed CGPCF is highly meaningful for optical fiber communication, high-power laser systems, and optical amplifiers.

Comparative study of multi-look processing for phase map de-noising in digital Fresnel holographic interferometry.

Abstract: This paper presents a comparative study of multi-look approaches for de-noising phase maps from digital holographic interferometry. A database of 160 simulated phase fringe patterns with eight different phase fringe patterns with fringe diversity was computed. For each fringe pattern, 20 realistic noise realizations are generated in order to simulate a multi-look process with 20 inputs. A set of 22 de-noising algorithms was selected and processed for each simulation. Three approaches for multi-look processing are evaluated. Quantitative appraisal is obtained using two metrics. The results show good agreement for algorithm rankings obtained with both metrics. One singular and highly practical result of the study is that a multi-look approach with average looks before noise processing performs better than averaging computed with all de-noised looks. The results also demonstrate that the two-dimensional windowed Fourier transform filtering exhibits the best performance in all cases and that the block-matching 3D (BM3D) algorithm is second in the ranking.

Resolution limits in inverse source problem for strip currents not in Fresnel zone.

Abstract: This paper deals with the classical question of estimating achievable resolution in terms of configuration parameters in inverse source problems. In particular, the study is developed for two-dimensional prototype geometry, where a strip source (magnetic or electric) is to be reconstructed from its radiated field observed over a bounded rectilinear domain parallel to the source. Resolution formulas are well known when the field is collected in the far field or in the Fresnel zone of the source. Here, the plan is to expand those results by removing the geometrical limitations due to the far field or Fresnel approximations. To this end, the involved radiation operators are recast as Fourier-type integral operators upon introducing suitable variable transformations. For magnetic sources, this allows one to find a closed-form approximation of the singular system and hence to estimate achievable resolution, the latter given as the main beam width of the point-spread function. Unfortunately, this does not happen for electric currents. In this case, the radiation operator is inverted by a weighted adjoint inversion method (a back-propagation-like method) that directly allows one to find an analytical expression of the point-spread function and hence of the resolution. The derived resolution formulas are the same for magnetic and electric currents; they clearly point out the role of geometrical parameters and coincide with the one pertaining to the Fresnel zone when the geometry verifies the Fresnel approximation. A few numerical examples are also enclosed to check the theory.

Channel capacity of orbital-angular-momentum-based wireless communication systems with partially coherent elegant Laguerre-Gaussian beams in oceanic turbulence.

Abstract: For practical wireless communication links, one of the critical challenges is the random fluctuation of turbulence that will impair link performance. Here a transmission model of partially coherent elegant Laguerre-Gaussian (ELG) beams in oceanic turbulence is established. An analytical formula for channel capacity of a partially coherent ELG beam propagating through a turbulent ocean is derived. The effects of oceanic turbulence on the evolution of channel capacity performance are studied quantitatively in a series of numerical simulations. Research results show that decreasing the rate of dissipation of mean-square temperature and ratio of temperature to salinity, as well as increasing the dissipation rate of turbulent kinetic energy per unit mass of fluid of a turbulent ocean can significantly improve communication channel capacity. Furthermore, choosing optimum beam source parameters is favorable to mitigate the influence of oceanic turbulence. Results also show that in the underwater turbulence, the partially coherent ELG beams are more affected by turbulence as compared to the fully coherent ELG beams. These study results may provide potential help in designing the free-space optical vortex communication systems.

Optical radiation force expression for a cylinder exhibiting rotary polarization in plane quasi-standing, standing, or progressive waves.

Abstract: A generalized analytical expression for the radiation force of plane quasi-standing, standing, or progressive electromagnetic (EM) waves is derived for a circular cylinder exhibiting rotary polarization in a TM-polarized incident field. Such a material, allowing rotary polarization, produces cross-polarized waves in the scattered field, which contribute to the radiation force experienced by the cylindrical object as shown here. As an example of a material exhibiting rotary polarization, a perfect electromagnetic conductor (PEMC) nonabsorptive cylinder is chosen to illustrate the analysis. In contrast with perfect electrical conductors (PECs), perfect magnetic conductors (PMCs), or conventional dielectric materials, the radiation force on a PEMC cylinder shows a direct dependency on the expansion coefficients of the cross-polarized waves, which do not exist for PECs, PMCs, or standard dielectrics. Extra new terms contribute to the generalized radiation force series expansions for plane quasi-standing, standing, or progressive waves. Numerical predictions demonstrate the possibility of trapping a circular-shaped cylinder material with rotary polarization in-plane quasi-standing or standing waves. Furthermore, the scattering, extinction, and absorption energy efficiencies for the nonabsorptive PEMC cylinder are computed, which validate the radiation force results from the standpoint of the law of energy conservation applied to EM scattering. The exact analytical radiation force expression for a PEMC cylinder of any arbitrary radius α (i.e., much smaller, comparable, or much larger than the wavelength of the illuminating incident field) in quasi-standing, standing, or progressive waves is also applicable to chiral, plasma, topological insulator, liquid crystal tubular phantom, or any other material exhibiting rotary polarization.

Dual dynamically tunable plasmon-induced transparency in H-type-graphene-based slow-light metamaterial.

Abstract: An H-type-graphene-based slow-light metamaterial is proposed to produce a dual plasmon-induced transparency phenomenon, which can be effectively modulated by Fermi level, carrier mobility of graphene, and the medium environment. The data calculated by coupled mode theory and results of numerical simulation show prominent agreement. In addition, both the simplicity and continuity of the units of graphene-based metamaterial are extraordinary advantages. Furthermore, the slow-light characteristics of the proposed structure show that the group refractive index is as high as 237, which is more competitive than some other slow-light devices.

Doppler fluctuation spectroscopy of intracellular dynamics in living tissue

Abstract: Intracellular dynamics in living tissue are dominated by active transport driven by bioenergetic processes far from thermal equilibrium. Intracellular constituents typically execute persistent walks. In the limit of long mean free paths, the persistent walks are ballistic, exhibiting a "Doppler edge" in light scattering fluctuation spectra. At shorter transport lengths, the fluctuations are described by lifetime-broadened Doppler spectra. Dynamic light scattering from transport in the ballistic, diffusive, or the crossover regimes is derived analytically, including the derivation of autocorrelation functions through a driven damped harmonic oscillator analog for light scattering from persistent walks. The theory is validated through Monte Carlo simulations. Experimental evidence for the Doppler edge in three-dimensional (3D) living tissue is obtained using biodynamic imaging based on low-coherence interferometry and digital holography.

Impact of time-variant turbulence behavior on prediction for adaptive optics systems.

Abstract: For high-contrast imaging systems, the time delay is one of the major limiting factors for the performance of the extreme adaptive optics (AO) sub-system and, in turn, the final contrast. The time delay is due to the finite time needed to measure the incoming disturbance and then apply the correction. By predicting the behavior of the atmospheric disturbance over the time delay we can in principle achieve a better AO performance. Atmospheric turbulence parameters, which determine wavefront phase fluctuations, have time-varying behavior. We present a stochastic model for wind speed and model time-variant atmospheric turbulence effects using varying wind speeds. We test a low-order, data-driven predictor, the linear minimum mean square error predictor, for a near-infrared AO system under varying conditions. Our results show varying wind can have a significant impact on the performance of wavefront prediction, preventing it from reaching optimal performance. The impact depends on the strength of wind fluctuations with the greatest loss in expected performance being for high wind speeds.

As-projective-as-possible bias correction for illumination estimation algorithms

Abstract: Illumination estimation is the key routine in a camera’s onboard auto-white-balance (AWB) function. Illumination estimation algorithms estimate the color of the scene’s illumination from an image in the form of an R, G, B vector in the sensor’s raw-RGB color space. While learning-based methods have demonstrated impressive performance for illumination estimation, cameras still rely on simple statistical-based algorithms that are less accurate but capable of executing quickly on the camera’s hardware. An effective strategy to improve the accuracy of these fast statistical-based algorithms is to apply a post-estimate bias-correction function to transform the estimated R, G, B vector such that it lies closer to the correct solution. Recent work by Finlayson [Interface Focus8, 20180008 (2018)2042-889810.1098/rsfs.2018.0008] showed that a bias-correction function can be formulated as a projective transform because the magnitude of the R, G, B illumination vector does not matter to the AWB procedure. This paper builds on this finding and shows that further improvements can be obtained by using an as-projective-as-possible (APAP) projective transform that locally adapts the projective transform to the input R, G, B vector. We demonstrate the effectiveness of the proposed APAP bias correction on several well-known statistical illumination estimation methods. We also describe a fast lookup method that allows the APAP transform to be performed with only a few lookup operations.

Theory of diffraction of vortex beams from 2D orthogonal periodic structures and Talbot self-healing under vortex beam illumination.

Abstract: This work presents a detailed analytic approach to the diffraction of vortex beams from 2D orthogonal periodic structures. Using the presented formulation, the diffraction of vortex beams from 2D sinusoidal and Ronchi gratings is investigated. For these gratings, the Talbot self-healing effect under vortex beam illumination is examined. In the illumination of a 2D grating with a vortex beam, we refer the Talbot self-healing effect to the filling of the null area of the incident beam under propagation. We show that, for an incident vortex beam having odd value of topological charge, the generated Talbot self-images over the self-healing area are a 2D array of optical vortices, in which each of the individual self-images gets the form of an optical vortex with a topological charge of l=1 regardless of the topological charge of the incident beam. Both the Talbot self-healing effect and generation of the 2D array of optical vortices occur optimally between a definite interval of propagation distance. Using an intuitive approach based on the interference of the diffracted orders of the grating, we determine the self-healing interval. We show that a 2D array of optical vortices can be generated directly in the interference of eight copies of a vortex beam having proper lateral shifts and relative tilts. Easy tuning and energy preservation are two main advantages that the interference-based method has over the above-mentioned diffraction-based method for generating a 2D array of optical vortices. However, setup and implementation of the diffraction-based method are very simple. We believe that both the diffraction-based and interference-based methods for creating vortex beam arrays might find applications in optical tweezers, micromanipulations, and microfluidics.

Freeform lens design for a point source and far-field target.

Abstract: The field of freeform illumination design has surged since the introduction of new fabrication techniques that allow for the production of non-axially symmetric surfaces. Freeform surfaces aim to efficiently control the redistribution of light from a particular source distribution to a target irradiance, but designing such surfaces is a challenging problem in the field of nonimaging optics. Optical design strategies have been developed in both academia and industry. In this paper, we consider the design of a single freeform lens that converts the light from an ideal (zero-etendue) point source into a far-field target. We present a mathematical approach and numerically solve the corresponding generalized Monge–Ampere equation of the optical system. We derive this equation using optimal transport theory and energy conservation. We use a generalized least-squares algorithm that can handle a non-quadratic cost function in the corresponding optimal transport problem. The algorithm first computes the optical map and subsequently constructs the optical surface. We demonstrate that the algorithm can generate a peanut-shaped lens for roadlighting purposes and a highly detailed lens that produces an image on a projection screen in the far field.

Ultraviolet broadband plasmonic absorber with dual visible and near-infrared narrow bands.

Abstract: We propose an ultraviolet broadband plasmonic absorber with dual narrow bands located separately in the visible and near-infrared regions. It employs a three-layer dielectric and metallic film structure based on a ring square nanodisk array. The interaction of surface plasmon resonance with a Fabry-Perot cavity resonance results in perfect absorption. The absorption efficiency is greater than 99.9% at wavelengths of 660 and 919 nm (visible and near-infrared), respectively, under normal incidence. In the ultraviolet region from 240 to 500 nm, absorption efficiency of over 90% can be achieved. The geometric symmetry of the ring square makes the perfect absorber polarization-independent and insensitive to large incident angle. This perfect absorber, which combines broadband and narrowband absorption, can be used as sensors, solar cells, or thermal emitters within one integrated device with further investigations.

Is multiplexed off-axis holography for quantitative phase imaging more spatial bandwidth-efficient than on-axis holography? [Invited].

Abstract: Digital holographic microcopy is a thriving imaging modality that attracts considerable research interest due to its ability not only to create excellent label-free contrast but also to supply valuable physical information regarding the density and dimensions of the sample with nanometer-scale axial sensitivity. Three basic holographic recording geometries currently exist, including on-axis, off-axis, and slightly off-axis holography, each of which enables a variety of architectures in terms of bandwidth use and compression capacity. Specifically, off-axis holography and slightly off-axis holography allow spatial hologram multiplexing, enabling one to compress more information into the same digital hologram. In this paper, we define an efficiency score to analyze the various possible architectures and compare the signal-to-noise ratio and the mean squared error obtained using each of them, thus determining the optimal holographic method.

Average capacity of a UWOC system with partially coherent Gaussian beams propagating in weak oceanic turbulence.

Abstract: The average capacity of a single-input single-output (SISO) underwater wireless optical communication (UWOC) system with partially coherent Gaussian beams in a weak oceanic turbulence regime is investigated. An approximate analytical expression of scintillation index is derived mathematically to characterize the impact of oceanic turbulence on the propagation behavior of the partially coherent Gaussian beams. Then, the path loss caused by absorption and scattering in the ocean is numerically simulated with the Monte Carlo method. With consideration for absorption, scattering, and oceanic turbulence, the combined channel fading model is established, and the average capacity of the UWOC system (defined as the maximum mutual information between the input and output) is examined. Results show that the scintillations are reduced by decreases in propagation distance, the dissipation rate of mean-square temperature, and the ratio of the temperature and salinity contributions to the refractive index spectrum. Scintillations are also decreased by increases in source beam width, degree of partial coherence, and the dissipation rate of turbulent kinetic energy per unit mass of fluid. As a result, the average capacity of the UWOC system is enhanced. Moreover, the average capacity of the UWOC system can be promoted with the availability of channel state information at the receiver. This work will benefit the research and development of UWOC systems.

High-resolution augmented reality 3D display with use of a lenticular lens array holographic optical element

Abstract: An augmented reality (AR) three-dimensional (3D) display based on one-dimensional integral imaging (1DII), by using a lenticular lens array holographic optical element (LLA-HOE), is proposed. The 3D image of the 1DII has higher vertical resolution compared with the image of conventional integral imaging whose resolution is sharply reduced for providing quasi-continuous viewpoints in both the horizontal and vertical directions. The proposed 3D display consists of a projector and an LLA-HOE and is compact. As an image combiner, the LLA-HOE can diffract Bragg-matched light rays that have the same wavelength and incident angle as the original reference wave; it can also function as a lenticular lens array to reconstruct a 3D image but transmit other light rays emitted from the surroundings. In the experiment, an LLA-HOE of 80 mm×80 mm size is recorded, and a combination of a high-resolution 3D virtual image and a real 3D object is presented by the proposed AR 3D display.

Quantum dipole emitters in structured environments: a scattering approach: tutorial

Abstract: We provide a simple semi-classical formalism to describe the coupling between one or several quantum emitters and a structured environment. Describing the emitter by an electric polarizability, and the surrounding medium by a Green function, we show that an intuitive scattering picture allows one to derive a coupling equation from which the eigenfrequencies of the coupled system can be extracted. The model covers a variety of regimes observed in light–matter interaction, including weak and strong coupling, coherent collective interactions, and incoherent energy transfer. It provides a unified description of many processes, showing that different interaction regimes are actually rooted on the same ground. It can also serve as a basis for the development of more refined models in a full quantum electrodynamics framework.

Hermite-Gaussian mode detection via convolution neural networks

Abstract: Hermite–Gaussian (HG) laser modes are a complete set of solutions to the free-space paraxial wave equation in Cartesian coordinates and represent a close approximation to physically realizable laser cavity modes. Additionally, HG modes can be mode-multiplexed to significantly increase the information capacity of optical communication systems due to their orthogonality. Because cavity tuning and optical communication applications benefit from a machine vision determination of HG modes, convolution neural networks were implemented to detect the lowest 21 unique HG modes with an accuracy greater than 99%. As the effectiveness of a CNN is dependent on the diversity of its training data, extensive simulated and experimental data sets were created for training, validation, and testing.

Spatio-angular fluorescence microscopy I. Basic theory.

Abstract: We introduce the basic elements of a spatio-angular theory of fluorescence microscopy, providing a unified framework for analyzing systems that image single fluorescent dipoles and ensembles of overlapping dipoles that label biological molecules. We model an aplanatic microscope imaging an ensemble of fluorescent dipoles as a linear Hilbert-space operator, and we show that the operator takes a particularly convenient form when expressed in a basis of complex exponentials and spherical harmonics-a form we call the dipole spatio-angular transfer function. We discuss the implications of our analysis for all quantitative fluorescence microscopy studies and lay out a path toward a complete theory.

Rigorous multi-slice wave optical simulation of x-ray propagation in inhomogeneous space.

Abstract: The simulation of the propagation of divergent beams using Fourier-based angular spectrum techniques can pose challenges for ensuring correct sampling in the spatial and reciprocal domains. This challenge can be compounded by the presence of diffracting objects, as is often the case. Here, I give details of a method for robustly simulating the propagation of beams with divergent wavefronts in a coordinate system where the wavefronts become planar. I also show how diffracting objects can be simulated, while guaranteeing that correct sampling is maintained. These two advances allow for numerically efficient and accurate simulations of divergent beams propagating through diffracting structures using the multi-slice approximation. The sampling requirements and numerical implementation are discussed in detail, and I have made the computer code freely available.

Performance of underwater quantum key distribution with polarization encoding

Abstract: Underwater quantum key distribution (QKD) has potential applications in absolutely secure underwater communication. However, the performance of underwater QKD is limited by the optical elements, background light, and dark counts of the detector. In this paper, we propose a modified formula for the quantum bit error rate (QBER), which takes into account the effect of detector efficiency on the QBER caused by the background light. Then we calculate the QBER of the polarization encoding BB84 protocol in Jerlov-type seawater by analyzing the effect of the background light and optical components in a more realistic situation. Finally, we further analyze the final key rate and the maximum secure communication distance in three propagation modes, i.e., upward, downward, and horizontal modes. We find that secure QKD can be performed in the clearest Jerlov-type seawater at a distance of hundreds of meters, even in the worst downward propagation mode. Specifically, by optimizing the system parameters, it is possible to securely transmit information with a rate of 67 kbits/s at a distance of 100 m in the seawater channel with an attenuation coefficient of 0.03/m at night. For practical underwater QKD, the performance can also be improved by using decoy states. Our results are useful for long-distance underwater quantum communication.