Wave-optics Simulations Research Articles

Macroscopic wave-optical simulation of dielectric metasurfaces.

We propose a novel method for the wave-optical simulation of diffractive optical elements (DOEs) like metasurfaces or computer-generated holograms (CGHs). Existing techniques mostly rely on the assumption of local periodicity to predict the performance of elements. The utilization of a specially adapted finite-difference beam propagation method (BPM) allows the semi-rigorous simulation of entire DOEs within a reasonable runtime due to linear scaling with the number of grid points. Its applicability is demonstrated by the simulation of a metalens and a polarization-dependent beamsplitter, both based on effective-medium metasurfaces. A comparison shows high conformity to rigorous simulations.

Effect of convergent beam array on reducing scintillation in underwater wireless optical communications with pointing errors

In this paper, we propose the convergent beam array to reduce scintillation induced by oceanic turbulence in underwater wireless optical communications (UWOCs) between misaligned transceivers. In the proposed convergent beam array, the propagation directions of beams are slanted inwards and different from each other. First, we present the convergent beam array system and analyze spatial relationships between the transmitter and the individual beam in beam array systems. Then, in order to simulate beams propagation in UWOCs, we review the power spectrum of refractive index fluctuations in oceanic turbulence and analyze the spatial relationship between the misaligned transceivers in view of pointing errors. Finally, we verify the effectiveness of the proposed convergent beam array on scintillation reduction by multistep wave optics simulation. Simulation results show that convergent beam array is able to decrease scintillation indices effectively in UWOCs with pointing errors.

Variable immersion microscopy with a high numerical aperture.

Three-dimensional (3D) optical microscopy with a high numerical aperture (NA) remains challenging for thick biological specimens owing to aberrations arising from interface refractions. We developed a variable immersion lens (VIL) to passively minimize these aberrations. A VIL is a high-NA concentric meniscus lens and was used in combination with an aberration-corrected high-NA reflecting objective (TORA-FUJI mirror). Wave-optics simulation at a wavelength of 488 nm showed that a VIL microscope enables diffraction-limited 1.2-NA imaging in water (refractive index of 1.34) at a depth of 0.3 mm by minimizing aberrations due to refraction of a sample interface. Another aberration due to the refractive index mismatching between a mounting medium, and an object can also be corrected by the VIL system, because various fluids with different refractive indices can be used as mounting media for the VIL. As a result of correcting the two aberrations at the same time, we experimentally demonstrated that a 6 µm diameter fluorescent bead can be imaged to the true dimensions in 3D.

Wave optical simulation of retinal images in laser safety evaluations.

Lasers with wavelengths in the visible and near infrared region, pose a potential hazard to vision as the radiation can be focused on the retina. The laser safety standard IEC 60825-1:2014 provides limits and evaluation methods to perform a classification for such systems. An important parameter is the retinal spot size which is described by the angular subtense of the apparent source. In laser safety evaluations, the radiation is often described as a Gaussian beam and the image on the retina is calculated using the wave optical propagation through a thin lens. For coherent radiation, this method can be insufficient as the diffraction effects of the pupil aperture influence the retinal image. In this publication, we analyze these effects and propose a general analytical calculation method for the angular subtense. The proposed formula is validated for collimated and divergent Gaussian beams.

Compensated-beacon adaptive optics using least-squares phase reconstruction.

In this paper, we quantify the benefits of compensated-beacon adaptive optics (CBAO) relative to uncompensated-beacon adaptive optics (UBAO) using wave-optics simulations. Throughout, we present results for both the Shack-Hartmann wavefront sensor (SH-WFS) and the digital-holographic wavefront sensor (DH-WFS). Given weak to moderately strong scintillation conditions, the results show that the two noiseless sensors offer similar performance in terms of the peak Strehl ratio when using similar subaperture sampling and least-squares phase reconstruction. Specifically, CBAO leads to an average performance boost of 17% for the SH-WFS and 26% for the DH-WFS relative to UBAO for the turbulence scenarios studied here.

Design of Silicon Photonic Structures for Multi-Site, Multi-Spectral Optogenetics in the Deep Brain

Micro- and nanoscale photonic structures and devices play important roles in the development of advanced biophotonic systems, in particular, implantable light sources for optogenetic stimulations. In this paper, we numerically investigate silicon (Si) photonics based microprobes that can achieve multi-site, multi-spectral optical excitation in the deep animal brain. On Si substrates, silicon nitride (Si <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> ) based planar waveguides can deliver visible light in the deep tissue with low losses, and couple to grating emitters diffracting light in targeted brain regions. In our model, we combine near-field wave optic and far-field ray tracing simulations, showing that the designed photonic structures spectrally split blue, green and red photons into different locations in the tissue. Furthermore, by introducing dual grating components, photons at different wavelengths can be spatially separated at different depths. Therefore, these photonic probes can be used to selectively activate or inhibit specific neurons and nuclei, when expressing various corresponding light sensitive opsins. We anticipate that such device strategies can find wide applications in the design of advanced implantable photonic systems for neuroscience and neuroengineering.

Atmospheric Turbulence Study with Deep Machine Learning of Intensity Scintillation Patterns

A new paradigm for machine learning-inspired atmospheric turbulence sensing is developed and applied to predict the atmospheric turbulence refractive index structure parameter using deep neural network (DNN)-based processing of short-exposure laser beam intensity scintillation patterns obtained with both: experimental measurement trials conducted over a 7 km propagation path, and imitation of these trials using wave-optics numerical simulations. The developed DNN model was optimized and evaluated in a set of machine learning experiments. The results obtained demonstrate both good accuracy and high temporal resolution in sensing. The machine learning approach was also employed to challenge the validity of several eminent atmospheric turbulence theoretical models and to evaluate them against the experimentally measured data.

Wavefront Compensation With the Micro Corner-Cube Reflector Array in Modulating Retroreflector Free-Space Optical Channels

In this article, the micro corner-cube reflector array (MCCRA) is considered as the optical retroreflector in the modulating retroreflector (MRR) free-space optical (FSO) channel and its wavefront compensation accompanying with the pseudo phase conjugate optical return wave in the double-pass propagation is investigated by the theoretical analysis and wave-optics (WO) simulation. By WO simulations, we show the impacts of the shape and size of the retroreflector cell, the whole aperture size of the MCCRA, the turbulence condition on the beam spot, the Strehl ratio and the scintillation index of the return wave. Also, we investigate the limitations caused by the phase errors of the MCCRA and the oblique incidence of the optical beam. Finally, the wavefront compensation is demonstrated by the experiments conducted in a laboratory atmospheric chamber.

Research on performance of convex partially coherent flat-topped beams in vertical atmospheric turbulent paths

Previous studies on non-uniformly correlated (NUC) beams mainly focus on beams with Gaussian amplitude profiles. In this paper we research a new class of non-uniformly correlated flat-topped beams, which are called convex partially coherent flat-topped (CPCFT) beams. Using wave optics simulation (WOS), we investigate the propagation properties of such beams in vertical atmospheric turbulent paths in detail and calculated the mean signal-to-noise ratio (SNR) and bit-error rate (BER). It is found that CPCFT beams will self-focus during propagation, resulting in larger on-axis intensity than Gaussian Schell-model (GSM) and PCFT beams, and they also have smaller scintillation in most cases. These properties have made CPCFT beams effective for improving the mean SNR and reducing the mean BER. WOS results show that turbulence induced degradation can be dramatically reduced by using CPCFT beams under certain circumstances.

Fast convolution-based performance estimation method for diffraction-limited source with imperfect X-ray optics.

Although optical element error analysis is always an important part of beamline design for highly coherent synchrotron radiation or free-electron laser sources, the usual wave optics simulation can be very time-consuming, which limits its application at the early stage of the beamline design. In this work, a new theoretical approach has been proposed for quick evaluations of the optical performance degradation due to optical element error. In this way, time-consuming detailed simulations can be applied only when truly necessary. This approach treats the imperfections as perturbations that convolve with the ideal performance. For simplicity, but not by necessity, the Gaussian Schell-model has been used to show the application of this theoretical approach. The influences of the finite aperture size and height error of a focusing mirror are analysed using the proposed theory. The physical explanation of the performance degradation acquired from the presented approach helps to give a better definition of the critical range of error spatial frequencies that most affect the performance of a mirror. An example comparing two mirror surface errors with identical power spectral density functions is given. These two types of mirror surface errors result in very different intensity profiles. The approach presented in this work could help beamline designers specify the error tolerances on general optical elements more accurately.

Characterization of Localized Atmospheric Turbulence Layer Using Laser Light Backscattered off Moving Target

A concept of atmospheric turbulence characterization using laser light backscattered off a moving unresolved target or a moving target with a glint is considered and analyzed through wave-optics numerical simulations. The technique is based on analysis of the autocorrelation function and variance of the power signal measured by the target-in-the-loop atmospheric sensing (TILAS) system composed of a single-mode-fiber-based optical transceiver and the moving target. It is shown that the TILAS received power signal autocorrelation function strongly depends on the turbulence distribution and is weakly sensitive to the turbulence strength, while the signal variance equally depends on these parameters. Assuming the atmospheric turbulence model can be represented by a single spatially localized turbulence layer and the target position and speed are known independently, consecutive analysis of the autocorrelation function and variance of the TILAS signal allows evaluation of both the turbulence layer strength and position along the optical propagation path. It is also demonstrated that the autocorrelation function can potentially be used for the atmospheric turbulence outer scale estimation.

Complex field sensing in strong scintillations with multi-aperture phase contrast techniques

A new class of multi-aperture phase contrast (MAPCO) complex field sensor is introduced and analyzed using wave-optics numerical simulations. The presented analysis of the MAPCO technique demonstrates a potential for high-resolution (256 × 256 pixels) complex field sensing under strong input field intensity scintillations with sub-msec phase retrieval frame rates.

Is the formulation of the Fried parameter accurate in the strong turbulent scattering regime?

The Fried parameter is a fundamental coherence length measure that characterizes the spatial resolution effects of atmospheric turbulence on imaging and beam propagation. Its expression was originally derived with the Rytov approximation and a near-field assumption, which are only strictly valid for weak turbulent scattering. However, the actual range of validity of the Fried parameter formulation remains controversial. Here, wave optic simulations are conducted for modeling the long-exposure point spread function through atmospheric turbulence. The results indicate that analytic expressions for the Fried parameter are accurate throughout the weak to strong turbulent scattering regimes.

Modeling Optical Materials at the Single Scatterer Level: The Transition from Homogeneous to Heterogeneous Materials

AbstractMaterials that contain distinct scatterers, for example, nanoparticles, with sizes exceeding 100 nm scatter light heavily and are heterogeneous. In contrast, the atomic or molecular scatterers in conventional optical materials form a homogeneous distribution on the scale of the wavelength. In this paper, the transition between homogeneous and heterogeneous materials is investigated. To this end, a procedure is introduced that allows for retrieving reliable refractive index values from full wave optical numerical simulations of the underlying multibody scattering problem. Using this procedure, it is shown that the concept of an effective refractive index breaks down on multiple levels as a material transitions out of the homogeneous regime. These findings allow for quantifying how novel dispersion‐engineered nanocomposites for bulk optical applications must be designed and show that Maxwell–Garnett‐type effective medium theories are accurate tools for the design of nanocomposites. The procedure can be readily generalized to other types of scatterers, including atoms and molecules and hence guide the design of different kinds of novel materials.

Fabrication and characterization of deformed microdisk cavities in silicon dioxide with high Q-factor.

We demonstrate the excitation and characterization of whispering gallery modes in a deformed optical microcavity. To fabricate deformed microdisk microresonators we established a fabrication process relying on dry plasma etching tools for many degrees of freedom and a shape-accurate morphology. This approach allowed us to fabricate resonators of different sizes with a controlled sidewall angle and underetching in large quantities with reproducible properties such as a surface roughness RQ≤2nm. The excitation and characterization of these modes were achieved by using a state-of-the-art tapered fiber coupling setup with a narrow linewidth tunable laser source. The conducted measurements in shortegg resonators showed at least two modes within a spectral range of about 237 pm. The highest Q-factors measured were in the range of 105. Wave optical eigenmode and frequency domain simulations were conducted that could partially reproduce the observed behavior and therefore allow us to compare the experimental results.

Single-pass Cr:ZnSe amplifier for broadband infrared undulator radiation.

An amplifier based on a highly-doped chromium zinc-selenide (Cr:ZnSe) crystal is proposed to increase the pulse energy emitted by an electron bunch after it passes through an undulator magnet. The primary motivation is a possible use of the amplified undulator radiation emitted by a beam circulating in a particle accelerator storage ring to increase the particle beam's phase-space density-a technique dubbed optical stochastic cooling (OSC). This paper uses a simple four energy level model to estimate the single-pass gain of Cr:ZnSe and presents numerical calculations combined with wave-optics simulations of undulator radiation to estimate the expected properties of the amplified undulator wave-packet.

Compensation of heat load deformations using adaptive optics for the ALS upgrade: a wave optics study.

A realistic wave optics simulation method has been developed to study how wavefront distortions originating from heat load deformations can be corrected using adaptive X-ray optics. Several planned soft X-ray and tender X-ray insertion-device beamlines in the Advanced Light Source upgrade rely on a common design principle. A flat, first mirror intercepts the white beam; vertical focusing is provided by a variable-line-space monochromator; and horizontal focusing comes from a single, pre-figured, adaptive mirror. A variety of scenarios to cope with thermal distortion in the first mirror are studied by finite-element analysis. The degradation of the intensity distribution at the focal plane is analyzed and the adaptive optics that correct it is modeled. The range of correctable wavefront errors across the operating range of the beamlines is reported in terms of mirror curvature and spatial frequencies. The software developed is a one-dimensional wavefront propagation package made availablein the OASYS suite, an adaptable, customizable and efficient beamline modeling platform.

Focal field analysis of highly multi-mode fiber beams based on modal decomposition

In this work, a numerical modal decomposition approach is applied to model the optical field of laser light after propagating through a highly multi-mode fiber. The algorithm for the decomposition is based on the reconstruction of measured intensity profiles along the laser beam caustic with consideration of intermodal degrees of coherence derived from spectral analysis. To enhance the accuracy of the model, different approaches and strategies are applied and discussed. The presented decomposition into a set of linearly polarized modes enables both the wave-optical simulation of radiation transport by highly multi-mode fibers and, additionally, the analysis of free-space propagation with arbitrarily modified complex amplitude distributions.

Effects of source spatial partial coherence on intensity statistics of optical beams in mono-static turbulent channels.

We investigate, via both experimental measurements and wave-optics computer simulations, the statistical characteristics of the fluctuating intensity, such as the average intensity, the beam wander and the scintillation index, of the Gaussian Schell-model (GSM) beams on passing through double-pass, monostatic turbulence channels with either a retro-reflector (RR) or a flat mirror (FM). Our experimental results reveal that the enhanced backscatter (EBS) gradually weakens as the spatial coherence of the GSM source decreases, and eventually disappears for the sufficiently low source spatial coherence states. The r.m.s beam wander remains practically invariant with the variation of the source coherence width in the range from 0.2 to 6.0 mm both in the case of the RR and the FM, which formed the RR case being much smaller. In addition, it is found that the long-term scintillation index of the untracked beam with the RR is smaller than that with the FM, while the situation is reversed for the short-term scintillation index of the tracked beam. In both cases, the scintillation index decreases as the spatial coherence of the GSM source decreases. The obtained computer simulation results agree reasonably well with the experimental results. In addition, the effects of spatial coherence on statistical characteristics of the GSM beams along a 1 km propagation distance through the double-pass monostatic turbulence are also investigated using wave-optics simulation. We also carry out evaluation and comparison of the intensity probability density functions for the RR and FM cases and for various source coherence states that are of utmost importance for free-space optical communications in retro-reflection modulation regime. In addition, our findings will be beneficial for the development of remote sensing and directed energy laser applications in the presence of air turbulence.

Influence of aberrations and roughness on the chromatic confocal signal based on experiments and wave-optical modeling

This paper addresses the effect and influence of wave optical aberrations and surface roughness on the chromatic confocal signal and resulting measurement errors. Two possible approaches exist for implementing chromatic confocal imaging based on either refraction or diffraction. Both concepts are compared and an expression for the expected chromatic longitudinal aberrations when using a diffractive optical element is derived. Since most chromatic confocal sensors are point sensors, the discussion on wave-optical aberrations is focused on spherical aberrations. Against common belief, the effect of spherical aberrations cannot be eliminated in the calibration process using for instance a piezo mounted mirror. It will be shown in the following that even a diffraction limited system with peak to valley spherical aberration smaller than 0.25 wavelength suffers from measurement errors. Experimental results will be shown to highlight this important issue. In order to develop a deeper understanding of the underlying physics, a wave-optical simulation environment has been realized. This wave-optical model furthermore enables the investigation of the influence of roughness. Herethereto the correct choice of numerical aperture when investigating a rough surface is based on a heuristic approach. Using the wave-optical simulations an explanation for the increased noise when employing a low numerical aperture to examine rough surfaces will be derived. Furthermore, a formula is presented to support the selection of the correct numerical aperture with regards to the roughness parameters of the surface under investigation.