Wave-optics Simulations Research Articles

Shape optimization design of the offset mirror in FEL-1 beamline at S3FEL

Nowadays, due to the advantages of high peak power, high average power, ultra-short pulse, and fully coherent characteristics, the high-repetition-rate free-electron laser (FEL) is thriving in many countries around the world. The thermal load caused by high-repetition-rate FEL poses a great challenge to the mirror surface shape. Especially in the case of high average power, how to perfectly control the mirror shape to maintain the coherence of the beam has become a difficult problem in beamline design. In addition to multi-segment PZT, when multiple resistive heaters are used to compensate for the mirror shape, the heat flux (or power) generated by each heater must be optimized to obtain sub-nanometer height error. This article establishes MHCKF model for the mirror surface deformation under the combined effect of the mirror initial deformation, the thermal deformation caused by X-rays, and the deformation compensated by multiple heaters. By searching the perturbation term in the mathematical model, the least squares solution of the heat fluxes generated by all heaters can be obtained. This method can not only set multiple constraints on the heat fluxes but also quickly obtain their values when minimizing the mirror shape error. It overcomes the problem of time-consuming optimization processes encountered by traditional finite element analysis software, especially in the context of multi-parameter optimization. This article focuses on the offset mirror in the FEL-1 beamline at S3FEL. Using this method, the optimization of 25 heat fluxes generated by all resistive heaters was accomplished within a few seconds utilizing an ordinary laptop. The results indicate that the height error RMS decreased from 40 nm to 0.009 nm, and the slope error RMS reduced from 192.7nrad to 0.4nrad. Wave-optics simulations show that the wavefront quality has been significantly improved. In addition, some factors affecting mirror shape error, such as the number of heaters, higher repetition rate, film coefficient, and the length of copper tube, were analyzed. The results show that the MHCKF model and optimization algorithm can effectively solve the optimization problem of compensating for the mirror shape with multiple heaters.

Propagation of coherence-OAM matrix of an optical beam in vacuum and turbulence.

Propagation of the coherence-orbital angular momentum (COAM) matrix of partially coherent beams in homogeneous and isotropic turbulence, e.g., atmosphere, is formulated using the extended Huygens-Fresnel principle. It is found that under the effect of turbulence the elements in the COAM matrix will generally be affected by other elements, resulting in certain OAM mode dispersion. We show that if turbulence is homogeneous and isotropic, there exists an analytic "selection rule" for governing such a dispersion mechanism, which states that only the elements having the same index difference, say l - m, may interact with each other, where l and m denote OAM mode indices. Further, we develop a wave-optics simulation method incorporating modal representation of random beams, multi-phase screen method and the coordinate transformation to simulate propagation of the COAM matrix of any partially coherent beam propagating in free space or in turbulent medium. The simulation method is thoroughly discussed. As examples, the propagation characteristics of the most representative COAM matrix elements of circular and elliptical Gaussian Schell-model beams in free space and in turbulent atmosphere are studied, and the selection rule is numerically demonstrated.

Optical Tomography of Polymeric Microsphere Layers Using Confocal Raman Microscopy.

In confocal Raman microscopy, depth profiling is a key application that enables analysis of the structural and chemical composition and size of three-dimensional (3D) transparent objects. However, the precise interpretation of a probed sample's Raman depth profile measurement can be significantly affected by both its size and surrounding objects. This study provides a more comprehensive understanding of the observed optical effects at the interface between polymer spheres and different substrates. Ray- and wave-optical simulations support our results. We derive a correction factor that, depending on the instrumental configuration, allows us to determine the nominal dimensions of the scanned objects more accurately from Raman depth profiles. Our studies support the need for careful consideration when employing depth profiling in confocal Raman microscopy for nondestructive, quantitative tomography of 3D objects.

Branch-point identification using second-moment Shack-Hartmann wavefront sensor statistics.

In this paper, an approach for detecting branch points using a Shack-Hartmann wavefront sensor (SHWFS) is introduced. Simulated data are created using Monte Carlo wave-optics simulations of varying turbulence strengths. It is assumed that the presence of a branch point in the SHWFS subaperture lenslet pupils causes appreciable beam spreading in the image plane. Therefore, second-moment statistics are used to quantify beam spread for each subaperture image-plane irradiance pattern. Thresholding is then employed to dictate what degree of beam spreading is sufficient to determine the presence of a branch point. Three different thresholds are imposed: liberal, moderate, and conservative. Furthermore, the collected SHWFS signal is treated as analog, digitized, and digitized with three levels of additive noise: low, moderate, and high. Monte Carlo simulations are conducted for 20 different spherical-wave Rytov numbers (R S W ) ranging from 0.1 to 2.0. It was found that when conservative thresholds were employed, for the analog signal, digitized signal with no noise, and digitized signal with low noise, the percent of detections mostly comprised actual branch points, and false-positive detections were largely minimized. For the liberal thresholding cases, many false-positives were detected for all SHWFS signal types; however, significantly more branch points were also detected. The results presented in this paper are encouraging, and such results will inform efforts to develop branch-point tolerant least-squares reconstructors or use a SHWFS for optical-turbulence characterization in high-R S W environments.

Active-tracking scaling laws using the noise-equivalent angle due to speckle.

It is well known to system engineers that speckle imposes a limitation on active-tracking performance, but scaling laws that quantify this limitation do not currently exist in the peer-reviewed literature. Additionally, existing models lack validation through either simulation or experimentation. With these points in mind, this paper formulates closed-form expressions that accurately predict the noise-equivalent angle due to speckle. The analysis separately treats both well-resolved and unresolved cases for circular and square apertures. When compared with the numerical results from wave-optics simulations, the analytical results show excellent agreement to a track-error limitation of (1/3)λ/D, where λ/D is the aperture diffraction angle. As a result, this paper creates validated scaling laws for system engineers that need to account for active-tracking performance.

Computer Simulation of Multichannel Beam Focusing System in Turbulent Atmosphere

The results of a computer simulation of laser beams focused by a combined multichannel array system in the atmosphere are presented. Beam propagation on atmospheric paths is considered taking into account the influence of turbulence and time-dependent thermal blooming interactions. The increase in the maximum intensity of the focal spot due to the optimization of the initial power density of the emitting aperture is estimated. It is shown that the scaling of the optimal initial power in multichannel arrays preserves the proportional dependence of the maximum intensity in focus with an increase in the number of channels. For wave-optics simulation, custom made software was developed based on the split-step method and modified for parallel algorithms using the functions of the Intel ® Math Kernel Library.

Diffractive Alvarez-Lohmann lenses for correcting aberrations of tunable membrane lenses

Focus-tunable lenses, e.g., liquid filled membrane lenses (MLs), have found increasingly widespread application in optical systems. If a large refractive power range is to be used, the correction of chromatic aberrations is particularly challenging: a group containing a single ML cannot be corrected over the whole refractive power range. In analogy to hybrid achromats for lenses with constant focal lengths, we present the combination of an ML and a diffractive Alvarez-Lohmann-lens (ALL) for the compensation of axial color over a large refractive power range. In contrast to the combination of multiple MLs, this does not increase the axial length of the system significantly. At the same time, the flexible adaption of the phase function of the diffractive ALL can reduce spherical aberration over the whole focal range. Design examples with ray-tracing and wave-optical simulations demonstrate the performance of the resulting hybrid tunable element. Experimental data from fabricated sample lenses provide a proof of principle.

Optical scintillation in a maritime environment.

Free space optical propagation affects many application areas, including communication, LIDAR, and directed energy. Optical turbulence causes dynamic changes in the propagated beam that can impact these applications. A primary measure of these effects is the optical scintillation index. In this work, we report on a comparison of experimental measurements of optical scintillation, conducted on a 16 km range across the Chesapeake Bay over a period of three months, to model predictions. Models for turbulence parameters were based on NAVSLaM, a Monin Obhukov similarity theory, and used environmental measurements taken on the range simultaneously with the scintillation measurements. These parameters were then used in two different classes of optical scintillation models: Extended Rytov theory, and wave optic simulation. We show that wave optics simulation matched the data much better than Extended Rytov theory, and that prediction of scintillation using environmental parameters is possible. In addition, we show that optical scintillation over water has different characteristics in stable versus unstable conditions.

Propagation of vortex symmetric Airy beam in the turbulent link

The vortex symmetric Airy beam (VSAB) which couples the autofocusing symmetric Airy beam (SAB) and topological charge can provide new possibilities for the optical carrier of free space optical communication (FSOC). This paper focuses on the performance of VSAB propagating through turbulent link. Based on the wave optics simulation, the model of VSAB propagating in atmospheric turbulence is constructed. By using the model, the evaluation parameters light intensity and aperture averaged scintillation of VSAB are calculated. The influence of different beam parameters on the characteristics of VSAB propagation in turbulent link is investigated. The results show that the VSAB with small decaying factor, small transverse length scales and less topological charge has more advantage in turbulence resistance.

Wide field-of-view x-ray imaging optical system using grazing-incidence mirrors.

A field-curvature-corrected imaging optical system for x-ray microscopy using only grazing-incidence mirrors is proposed. It combines a Wolter type I (WO1) mirror pair, which forms a real image, with field curvature correction (FCC) optics-a convex hyperbolic mirror pair-that form a virtual image; compensation of the field curvatures realizes a wide field-of-view (FOV) and high magnification. Ray-tracing and wave-optics simulations verified the efficacy of the design, for which a FOV width was 111µm-4.7 times larger than that for the uncorrected WO1 design. The addition of FCC optics also produced a 2.3-fold increase in magnification.

Soft X-ray grating monochromators as a source of spatial coherence degradation: A wave-optical approach

We present wave-optical simulations and a coherence analysis of the photon beam transported through a soft X-ray beamline, paying particular attention to a focusing varied line spacing (VLS) plane grating monochromator (PGM). We show that this beamline optical element used in several soft X-ray beamlines at synchrotron sources and free-electron lasers can cause a non-negligible spatial coherence degradation. We demonstrate that the origin of this effect arises from the coupling between spatial and spectral properties of the photon beam generated by the grating. The latter implies that space and frequency dependencies are not separable after such a dispersive element. It is shown which parameters are essential for this effect and how they are linked to each other.

Simulating random optical fields: tutorial.

Numerous applications-including optical communications, directed energy, remote sensing, and optical tweezing-utilize the principles of statistical optics and optical coherence theory. Simulation of these phenomena is, therefore, critical in the design of new technologies for these and other such applications. For this reason, this tutorial describes how to generate random electromagnetic field instances or realizations consistent with a given or desired cross-spectral density matrix for use in wave optics simulations. This tutorial assumes that the reader has knowledge of the fundamental principles of statistical optics and optical coherence theory. An extensive reference list is provided where the necessary background information can be found. We begin this tutorial with a brief summary of the coherent-mode representation and the superposition rule of stochastic electromagnetic fields as these foundational ideas form the basis of all known synthesis techniques. We then present optical field expressions that apply these concepts before discussing proper sampling and discretization. We finally compare and contrast coherent-mode- and superposition-rule-based synthesis approaches, discussing the pros and cons of each. As an example, we simulate the synthesis and propagation of an electromagnetic partially coherent field from the literature. We compare simulated or sample statistics to theory to verify that we have successfully produced the desired field and are capturing its propagation behaviors. All computer programs, including detailed explanations of the source code, are provided with this tutorial. We conclude with a brief summary.

Simulation of photon recycling in ultra-thin solar cells

A comprehensive quantum-kinetic simulation framework considering both the optical confinement and the electronic effects of finite size and strong built-in fields is introduced to assess the impact of photon recycling on the photovoltaic performance of ultra-thin absorber solar cells. The radiative recombination accounts for the actual photon density of states that is modified by cavity effects and plasmonic resonances, and via coupling to a quantum transport formalism, the impact of photon recycling is propagated from rigorous wave optical simulation of secondary photogeneration directly into a modification of the current–voltage characteristics of the full photovoltaic device. The self-consistent microscopic treatment of the interacting electronic and optical degrees of freedom in a functional device context elucidates the impact on photovoltaic performance of nanoscale device design in terms of band profiles and contact layers by revealing their effect on the radiative rates and currents. As an example, plasmonic losses related to metallic reflectors are identified in both, emission and re-absorption, and partial mitigation is achieved via dielectric passivation or detaching of the reflector.

Semi-analytic simulation of optical wave propagation through turbulence.

Split-step wave-optical simulations are useful for studying optical propagation through random media like atmospheric turbulence. The standard method involves alternating steps of paraxial vacuum propagation and turbulent phase accumulation. We present a semianalytic approach to evaluating the Fresnel diffraction integral with onephase screen between the source and observation planes and another screen in the observation plane. Specifically, we express the first phase screen's transmittance as a Fourier series, which allows us to bring phase screen effects outside of the Fresnel diffraction integral, thereby reducing the numerical computations. This particular setup is useful for simulating astronomical imaging geometries and two-screen laboratory experiments that emulate real turbulence with phase wheels, spatial light modulators, etc. Further, this is a key building block in more general semianalytic split-step simulations that have an arbitrary number of screens. Compared with the standard angular-spectrum approach using the fast Fourier transform, the semianalytic method provides relaxed sampling constraints and an arbitrary computational grid. Also, when a limited number of observation-plane points is evaluated or when many time steps or random draws are used, the semianalytic method can compute faster than the angular-spectrum method.

Adaptive optics compensation of orbital angular momentum beams using a hybrid input-output algorithm with complementary binary masks.

For orbital angular momentum (OAM) beams, we show that the twin-image problem in the single-intensity-measurement hybrid input-output algorithm (HIOA) severely impairs the phase retrieval performance and propose a very simple method to overcome this problem. First, we introduce the principle of the single-intensity-measurement HIOA together with the underlying reason for the twin-image problem and propose a new scheme of the HIOA using a pair of complementary binary masks (CBMs) to overcome the twin-image problem. To verify the usefulness of the proposed CBM-HIOA in the OAM free-space optical system, a wave-optics simulation is used to produce relatively realistic atmospheric turbulence, and the turbulence-induced distorted phase of the probe Gaussian beam is retrieved to compensate for the phase distortion of OAM beams. The suppression of the bidirectional and stagnant convergence caused by the twin-image problem, the compensation of the turbulence-induced distorted phase of the OAM beams, and the influence of different CBM shapes are studied in detail by numerical simulations. The corresponding numerical results show the feasibility and efficacy of the CBM-HIOA used for the adaptive optics compensation of OAM beams.

Fast algorithm for the simulation of 3D-printed microoptics based on the vector wave propagation method.

In this work, we propose the Fast Polarized Wave Propagation Method (FPWPM), which is an efficient method for vector wave optical simulations of microoptics. The FPWPM is capable of handling comparably large simulation volumes while maintaining quick runtime. This allows for real-world application of this method for the rapid development process of 3D-printed microoptics. By comparison to established routines like the rigorous coupled wave analysis (RCWA) or the Richards-Wolf-Integral, accuracy and superior runtime efficiency of the FPWPM are demonstrated by simulation of interfaces, gratings, and lenses. By considering polarization in simulations, the FPWPM facilitates the analysis of optical elements which employ this property of electromagnetic waves as a feature in their optical design, e.g., diffractive elements, gratings, or optics with high angle of incidence like high numerical aperture lenses.

Wave optics simulations of plane-wave propagation in non-Kolmogorov turbulence

We derive limits for wave optics simulations of plane wave propagation in non-Kolmogorov turbulence using the split-step method and thin phase screens. These limits are used to inform two simulation campaigns where the relationship between volume turbulence strength and normalized intensity variance for various non-Kolmogorov power-laws. We find that simulations of smaller power laws are limited turbulence strengths with Rytov numbers of 7 when the simulation side-length sampling rate is 8192. Under these same conditions it is possible to simulate volume turbulence strength out to Rytov numbers of 12 for Kolmogorov power-laws and higher. We show that the peak scintillation and Rytov number where peak scintillation occur increases monotonically with power-law. Also, that if turbulence strength is fixed, the relationship between scintillation index and power-law depends on the operating regime. In weak turbulence the relationship is negative, and it is positive in stronger turbulence. This work also emphasizes the importance of properly scaling turbulence strength with comparing results with different power-laws and the influence and importance of defining inner and outer scales in these simulations.

Study on the X-ray mirror quality specification in advanced light source

The influence of the X-ray mirror errors on the performance of the beamline increases as the X-ray beam’s coherence improves in advanced light sources. The spatial dispersion of the X-ray beam is crucial for spatial resolution and field of view. However, selecting the appropriate merit function for expressing light distribution and identifying its relationship to optical error is very important in beamline design. We develop a high-efficiency wave-optics simulation platform and a deterministic analysis model to address this issue. The simulation experiments evaluated merit functions, including Strehl ratio, root-mean-square spot size, and encircled energy radius. We proved that the encircled energy radius is a good metric of the x-ray beam spatial dispersion, which matches the results of the Church-Takacs theory. In addition, it is found that limiting the contribution of the low frequency (wavelength>110L) error is effective for specifying the requirements of X-ray mirrors.

Hybrid microlens array/grating fabrication based on microfluidic system and its application in the enhancement of spectral resolution

Nowadays, micro-spectrometer has become an important research direction in the field of spectral analysis. The hybrid microlens array (MLA)/gratings element performs both focusing and diffraction duties, and its short focal length allows the optical system to be smaller. In this work, a unique and cost-effective fabrication method for hybrid MLA/grating based on the microfluidic system is described. By this method, the grating line-density, microlens curvature and aperture size of the hybrid MLA/grating can be effectively controlled, so as to bring different diffraction and focusing effects. Finite element simulation is used to describe the principle of the method. The relationship between bulge height and membrane thickness, pressure, hole size was investigated using a profile observation system. Wave optics simulation and diffraction measurements were used to demonstrate the optical properties of this hybrid element. It can be found that the diffracted light is converged at focus points after MLA/grating, and the full width at half maximum (FWHM) is significantly narrowed. The diffraction experimental results are consistent with the simulation results. The MLA/grating structure reduces FWHM of first-order diffracted light by a factor of 7 compared to same type of the planar grating. Therefore, the MLA/grating element can effectively improve the spectral resolution. Due to its small focal length, the MLA/grating has the potential to be used in micro-spectrometers.

Deep-turbulence phase compensation using tiled arrays.

Tiled arrays use modulo-2π phase compensation and coherent beam combination to correct for the effects of deep turbulence. As such, this paper uses wave-optics simulations to compare the closed-loop performance of tiled arrays to a branch-point-tolerant phase reconstructor known as LSPV+7 [Appl. Opt.53, 3821 (2014)10.1364/AO.53.003821]. The wave-optics simulations make use of a point-source beacon and are setup with weak-to-strong scintillation conditions. This setup enables a trade-space exploration in support of a power-in-the-bucket comparison with LSPV+7. In turn, the results show that tiled arrays outperform LSPV+7 when transitioning from weak-to-strong scintillation conditions. These results are both encouraging and informative for those looking to tackle the branch-point problem in adaptive optics.