Beam Shaping Elements Research Articles

Differentiable design of freeform diffractive optical elements for beam shaping by representing phase distribution using multi-level B-splines

The generation of a specific laser beam profile on the work surface is key to various laser beam shaping tasks, relying heavily on diffractive optical elements (DOEs). Most beam-shaping DOEs are designed using iterative Fourier transform algorithms (IFTAs), which generally have slow convergence and prone to stagnate at local minima. Moreover, the microreliefs generated by IFTAs tend to be irregular, complicating manufacturing and causing uncontrolled scattering of light. We propose a differentiable DOE design method that applies a phase-smoothness constraint using multi-level B-splines. A multi-scale gradient-descent optimization strategy, naturally linked with the multi-level B-splines, is employed to robustly determine the optimized phase distribution that is fully continuous. This, in turn, can lead to more regular DOE microreliefs, which can simplify the fabrication process and be less sensitive to changes in wavelength and working distance. Furthermore, our method can also design a fully continuous freeform lens, distinguished from most freeform lens design approaches by its foundation in physical optics rather than geometrical optics. Simulation and experimental results of several design tasks demonstrate the effectiveness of the proposed method.

Terahertz reflective imaging systems with improved angle compatibility realized by the designed quasi-scattering screen

Active imaging can provide significantly larger signal margins in the terahertz (THz) spectral region than passive imaging. However, the imaging effect of THz active imaging is severely constrained by the orientation requirement of target reflection, which limits the application scenarios of this technique. In view of the shortcomings of existing THz reflective imaging systems, this paper proposes a new system optimization scheme from the aspect of hardware - a compact quasi-scattering screen (QSS) is proposed and designed as a beam-shaping element to eliminate the need for the best direction of specular reflection to the greatest extent. The corresponding relationship between the divergent Gaussian beam and target light field is directly established by using the equal-energy mapping method in non-imaging optics, which rejects the collimation process of the THz source. By customizing the optimization function in ZEMAX® to automatically optimize the surface of the QSS, the direction of incident light propagation can be adjusted. A non-coaxial reflective THz imaging system using a 0.1 THz continuous wave source demonstrates the ability of the QSS to improve the angle compatibility of the traditional THz reflective imaging system. The results show that the imaging angle compatibility range of the system can be increased to more than 5 times without changing the original imaging optical path and its resolution. In addition, it can also improve the imaging quality of the original imaging optical path for the object with a smooth surface or certain structure.

Freeform surface topology prediction for prescribed illumination via semi-supervised learning.

Despite significant advances in the field of freeform optical design, there still remain various unsolved problems. One of these is the design of smooth, shallow freeform topologies, consisting of multiple convex, concave and saddle shaped regions, in order to generate a prescribed illumination pattern. Such freeform topologies are relevant in the context of glare-free illumination and thin, refractive beam shaping elements. Machine learning techniques already proved to be extremely valuable in solving complex inverse problems in optics and photonics, but their application to freeform optical design is mostly limited to imaging optics. This paper presents a rapid, standalone framework for the prediction of freeform surface topologies that generate a prescribed irradiance distribution, from a predefined light source. The framework employs a 2D convolutional neural network to model the relationship between the prescribed target irradiance and required freeform topology. This network is trained on the loss between the obtained irradiance and input irradiance, using a second network that replaces Monte-Carlo raytracing from source to target. This semi-supervised learning approach proves to be superior compared to a supervised learning approach using ground truth freeform topology/irradiance pairs; a fact that is connected to the observation that multiple freeform topologies can yield similar irradiance patterns. The resulting network is able to rapidly predict smooth freeform topologies that generate arbitrary irradiance patterns, and could serve as an inspiration for applying machine learning to other open problems in freeform illumination design.

An interband cascade laser based heterodyne detector with integrated optical amplifier and local oscillator.

Heterodyne detection based on interband cascade lasers (ICL) has been demonstrated in a wide range of different applications. However, it is still often limited to bulky tabletop systems using individual components such as dual laser setups, beam shaping elements, and discrete detectors. In this work, a versatile integrated ICL platform is investigated for tackling this issue. A RF-optimized, two-section ICL approach is employed, consisting of a short section typically used for efficient modulation of the cavity field and a long gain section. Such a laser is operated in reversed mode, with the entire Fabry-Pérot waveguide utilized as a semiconductor optical amplifier (SOA) and the electrically separated short section as detector. Furthermore, a racetrack cavity is introduced as on-chip single-mode reference generator. The field of the racetrack cavity is coupled into the SOA waveguide via an 800 nm gap. By external injection of a single mode ICL operating at the appropriate wavelength, a heterodyne beating between the on-chip reference and the injected signal can be observed on the integrated detector section of the SOA-detector.

A fireworks algorithm based Gerchberg–Saxton algorithm for the design of diffractive optical element for beam shaping

In this paper, a fireworks algorithm based Gerchberg–Saxton (GS) algorithm for the design of diffractive optical element is developed, named FW-GS algorithm, in which, the explosion mechanism of the fireworks algorithm is introduced to efficiently find the initial phase, thereby ensuring a superior phase solution for the subsequent GS algorithm. By employing this approach to shape a Gaussian beam into a square beam, the results illustrated the notable improvement of 16.10 % in RMSE and 3.29 % in diffractive efficiency when compared to the traditional GS algorithm, while exhibiting stable optimization performance. Furthermore, the proposed algorithm demonstrated adaptability to various shaping targets, with RMSE improved by about 16 % and diffractive efficiency improved by more than 3 % for shaping to circular, annular, and rectangular beams.

Design of Cascaded Diffractive Optical Elements for Optical Beam Shaping and Image Classification Using a Gradient Method

We present a gradient method for designing cascaded diffractive optical elements (DOEs) consisting of several sequentially located phase DOEs. Using the unitarity property of the operator of light propagation through the cascaded DOE, we obtain explicit expressions for the derivatives of the error functional with respect to the phase functions of the cascaded DOE. We consider the application of the gradient method to the problem of focusing different incident beams to regions with different intensity distributions and to the problem of optical image classification. The presented description of the gradient method treats the problems of designing cascaded DOEs for focusing laser radiation and for image classification within a unified approach reducing the calculation of the derivatives of the error functionals to the same formula. We present examples of the calculation of single and cascaded DOEs for focusing different incident beams to different regions and for classifying handwritten digits, which demonstrate the high performance of the proposed method. The presented results may find application in the design of diffractive neural networks and systems for focusing laser radiation.

Tailoring freeform beam-shaping lenses for edge-emitting lasers

The edge-emitting laser diodes (EELs) are widely used in various applications, however, the strongly asymmetric beam profile along the fast and slow axes gives a big challenge to the beam shaping of EEL. Traditional optical devices mainly focus on adjusting the asymmetric divergence angle of the fast and slow axes of the EEL, and it is difficult to achieve flexible and precise control of the luminous distribution of the EEL due to the limited freedom of the conventional beam-shaping element. In this article, we employ freeform lenses to flexibly reshape EEL beams and develop an approach to tackle the obstacles caused by the strongly asymmetric beam profile by generalizing the Monge–Ampère method to tailor freeform beam-shaping lenses. Three typical but challenging beam-shaping tasks show that both the intensity and wavefront of an EEL beam can be reshaped in a desired manner by using a single compact freeform lens without any symmetric restrictions on the architecture of the beam-shaping system.

Omnidirectional color shift suppression of full-color micro-LED displays with enhanced light extraction efficiency.

The three-primary-color chip array is the most straightforward to realize full-color micro-LED displays. However, the luminous intensity distribution shows high inconsistency between the AlInP-based red micro-LED and GaN-based blue / green micro-LEDs, resulting in the issue of angular color shift with different viewing angles. This Letter analyzes the angular dependence of color difference of conventional three-primary-color micro-LEDs, and proves that the inclined sidewall with homogeneous Ag coating has a limited angular regulation effect for micro-LEDs. Based on this, a patterned conical microstructure array is designed on the micro-LED's bottom layer to effectively eliminate the color shift. This design cannot only regulate the emission of full-color micro-LEDs to perfectly meet Lambert's cosine law without any external beam shaping elements, but also improve the light extraction efficiency of top emission by 16%, 161%, and 228% for red, green, and blue micro-LEDs, respectively. The color shift Δ u ' v ' of the full-color micro-LED display is also kept below 0.02 with the viewing angle ranging from 10° to 90°.

3D-printed facet-attached optical elements for beam shaping in optical phased arrays.

We demonstrate an optical phased-array equipped with a 3D-printed facet-attached element for shaping and deflection of the emitted beam. The beam shaper combines freeform refractive surfaces with total-internal-reflection mirrors and is in-situ printed to edge-emitting waveguide facets using high-resolution multi-photon lithography, thereby ensuring precise alignment with respect to on-chip waveguide structures. In a proof-of-concept experiment, we achieve a grating-lobe free steering range of ±30∘ and a full-width-half-maximum beam divergence of approximately 2∘. The concept opens an attractive alternative to currently used grating structures and is applicable to a wide range of integration platforms.

Ghost projection. II. Beam shaping using realistic spatially random masks

Spatial light modulation is important for many scientific and industrial applications. The spatial light modulator and optical data projector both rely on precisely configurable optical elements to shape a light beam. Here we explore an image-projection approach which does not require a configurable beam-shaping element. We term this approach ghost projection on account of its conceptual relation to computational ghost imaging. Instead of a configurable beam shaping element, the method transversely displaces a single illuminated mask, such as a spatially-random screen, to create specified distributions of radiant exposure. The method has potential applicability to image projection employing a variety of radiation and matter wave fields, such as hard x rays, neutrons, muons, atomic beams and molecular beams. Building on our previous theoretical and computational studies, we here seek to understand the effects, sensitivity, and tolerance of some key experimental limitations of the method. Focusing on the case of hard x rays, we employ experimentally acquired masks to numerically study the deleterious effects of photon shot noise, inaccuracies in random-mask exposure time, and inaccuracies in mask positioning, as well as adapting to spatially non-uniform illumination. Understanding the influence of these factors will assist in optimizing experimental design and work towards achieving ghost projection in practice.

Optimization of FLASH proton beams using a track-repeating algorithm.

Radiation with high dose rate (FLASH) has shown to reduce toxicities to normal tissues around the target and maintain tumor control with the same amount of dose compared to conventional radiation. This phenomenon has been widely studied in electron therapy, which is often used for shallow tumor treatment. Proton therapy is considered a more suitable treatment modality for deep-seated tumors. The feasibility of FLASH proton therapy has recently been demonstrated by a series of pre- and clinical trials. One of the challenges is to efficiently generate wide enough dose distributions in both lateral and longitudinal directions to cover the entire tumor volume. The goal of this paper is to introduce a set of automatic FLASH proton beam optimization algorithms developed recently. To develop a fast and efficient optimizer for the design of a passive scattering proton FLASH radiotherapy delivery at The University of Texas MD Anderson Proton Therapy Center, based on the fast dose calculator (FDC). A track-repeating algorithm, FDC, was validated versus Geant4 simulations and applied to calculate dose distributions in various beamline setups. The design of the components was optimized to deliver homogeneous fields with well-defined diameters between 11.0 and 20.5mm, as well as a spread-out Bragg peak (SOBP) with modulations between 8.5 and 39.0mm. A ridge filter, a high-Z material scatterer, and a collimator with range compensator were inserted in the beam path, and their shapes and sizes were optimized to spread out the Bragg peak, widen the beam, and reduce the penumbra. The optimizer was developed and tested using two proton energies (87.0 and 159.5MeV) in a variety of beamline arrangements. Dose rates of the optimized beams were estimated by scaling their doses to those of unmodified beams. The optimized 87.0-MeV beams, with a distance from the beam pipe window to the phantom surface (window-to-surface distance [WSD]) of 550mm, produced an 8.5-mm-wide SOBP (proximal 90% to distal 90% of the maximum dose); 14.5, 12.0, and 11.0-mm lateral widths at the 50%, 80%, and 90% dose location, respectively; and a 2.5-mm penumbra from 80% to 20% in the lateral profile. The 159.5-MeV beam had an SOBP of 39.0mm and lateral widths of 20.5, 15.0, and 12.5mm at 50%, 80%, and 90% dose location, respectively, when the WSD was 550mm. Wider lateral widths were obtained with increased WSD. The SOBP modulations changed when the ridge filters with different characteristics were inserted. Dose rates on the beam central axis for all optimized beams (other than the 87.0-MeV beam with 2000-mm WSD) were above that needed for the FLASH effect threshold (40Gy/s) except at the very end of the depth dose profile scaling with a dose rate of 1400Gy/s at the Bragg peak in the unmodified beams. The optimizer was able to instantly design the individual beamline components for each of the beamline setups, without the need of time intensive iterative simulations. An efficient system, consisting of an optimizer and an FDC have been developed and validated in a variety of beamline setups, comprising two proton energies, several WSDs, and SOBPs. The set of automatic optimization algorithms produces beam shaping element designs efficiently and with excellent quality.

Independent Light Field Manipulation in Diffraction Orders of Metasurface Holography

AbstractMetasurface holograms are novel optical elements with enormous potential because of the charming electromagnetic features, which can manipulate amplitude, phase, polarization state, and other parameters of light field via an elaborately designed subwavelength nanostructure array. Metagratings are extensively researched for controlling the feature of light in diffraction orders. However, a flexible and simple method is yearned for realizing independent wavefront manipulation in different orders. Here, a metasurface holography that can reconstruct various information in each diffraction order is demonstrated. The physical model is based on Jacobi–Anger expansion and iterative optimization, and both helicity‐dependent and birefringent metasurfaces can work compatibly with this proposed method to achieve arbitrary control of 1D and 2D orders. Specifically, information in 18 channels consisting of diffraction orders and polarization states is encoded in a single metasurface hologram. The approach provides promising and versatile optical elements for beam shaping, holographic display, optical storage, information encryption, etc.

Method for calculating the eikonal function and its application to design of diffractive optical elements for optical beam shaping

We develop a method for calculating the eikonal function (or the phase function) of the light field, ensuring the formation of a prescribed irradiance distribution in the geometrical optics approximation. In the proposed method, the problem being solved is formulated in a semi-discrete form as a problem of the maximization of a concave function. For finding the solution to the latter problem, a gradient method is used, with analytical expressions obtained for the gradient. Using the developed method, we calculate an eikonal function that provides the formation of a “discontinuous” hexagram-shaped irradiance distribution. We demonstrate that the use of the solution obtained in the framework of the geometrical optics as an initial approximation in iterative Fourier transform algorithms allows one to calculate diffractive optical elements having a quasi-regular microrelief.

Hybrid design of diffractive optical elements for optical beam shaping.

Hybrid methods combining the geometrical-optics and diffraction-theory methods enable designing diffractive optical elements (DOEs) with high performance due to the suppression of stray light and speckles and, at the same time, with a regular and fabrication-friendly microrelief. Here, we propose a geometrical-optics method for calculating the eikonal function of the light field providing the generation of a required irradiance distribution. In the method, the problem of calculating the eikonal function is formulated in a semi-discrete form as a problem of maximizing a concave function. For solving the maximization problem, a gradient method is used, with analytical expressions obtained for the gradient. In contrast to geometrical-optics approaches based on solving the Monge-Ampére equation using finite difference methods, the proposed method enables generating irradiance distributions defined on disconnected regions with non-smooth boundaries. As an example, we calculate an eikonal function, which provides the generation of a "discontinuous" irradiance distribution in the form of a hexagram. It is shown that the utilization of the hybrid approach, in which the obtained geometrical-optics solution is used as a starting point in iterative Fourier transform algorithms, enables designing DOEs with a quasi-regular or piecewise-smooth microrelief structure. The calculation results are confirmed by the results of experimental investigations of a DOE generating a hexagram-shaped irradiance distribution.

Squared Focal Intensity Distributions for Applications in Laser Material Processing.

Tailored intensity profiles within the focal spot of the laser beam offer great potential for a well-defined control of the interaction process between laser radiation and material, and thus for improving the processing results. The present paper discusses a novel refractive beam-shaping element that provides different squared intensity distributions converted from the Gaussian output beam of the utilized femtosecond (fs) laser. Using the examples of surface structuring of stainless-steel on the micro- and nano-scale, the suitability of the beam-shaping element for fs-laser material processing with a conventional f-Theta lens is demonstrated. In this context, it was shown that the experimental structuring results are in good agreement with beam profile measurements and numerical simulations of the beam-shaping unit. In addition, the experimental results reveal the improvement of laser processing in terms of a significantly reduced processing time during surface nano-structuring and the possibility to control the ablation geometry during the fabrication of micro-channels.

Generation of structured coherent extreme ultraviolet beams from an MgO crystal.

Short wavelength high-harmonic sources are undergoing intense development for applications in spectroscopy and microscopy. Despite recent progress in peak and average power, spatial control over coherent extreme ultraviolet (XUV) beams remains a formidable challenge due to the lack of suitable optical elements for beam shaping and control. Here we demonstrate a robust and precise approach that structures XUV high-order harmonics in space as they are emitted from a nanostructured MgO crystal. Our demonstration paves the way for bridging the numerous applications of shaped light beams from the visible to the short wavelengths, with potential uses for applications in microscopy and nanoscale machining.

Alignment of electron optical beam shaping elements using a convolutional neural network

A convolutional neural network is used to align an orbital angular momentum sorter in a transmission electron microscope. The method is demonstrated using simulations and experiments. As a result of its accuracy and speed, it offers the possibility of real-time tuning of other electron optical devices and electron beam shaping configurations.

Precision modeling of the IBA Universal Nozzle double scattering mode at the University Proton Therapy Dresden for Monte Carlo simulation

Monte Carlo (MC) simulations are indispensable for many research and advanced clinical questions in proton therapy (PT). However, the necessary site-specific modeling of a double scattering (DS) PT system is extensive and challenging and requires a clear strategy. This work describes a comprehensive method for precise and accurate modeling of a DS nozzle that minimizes additional measurement effort. A detailed model of the IBA universal nozzle is created within the TOPAS simulation framework. This model is subsequently fine-tuned using a step by step procedure to match the same dose profiles used for the commissioning of the treatment planning system. In the proposed bottom-up approach, the geometry of beam-shaping elements is first adjusted to measured quantities and then the beam and model properties are optimized using iterative methods. The resulting dose distributions are validated with a set of independent measurement data to estimate the achieved quality. The resulting simulated dose distributions agree well with the data and show residual range differences of maximum 0.6 mm. The shape of the SOBP plateau regions is accurately reproduced with a spread of the residuals below 1% (i.e., near to the statistical limit) over a large part of the machine settings. The simulated lateral dose profiles, although not directly included in the optimization, match the shape of the validation data better than 0.14 mm. The minimal measurement effort and high-precision proton field modeling make this method attractive, in particular, for retrospective beam modeling needed in clinical outcome or relative biological effectiveness studies after DS treatment.

Translationally Invariant Generation of Annular Beams Using Thin Films

Thin film optical elements exhibiting translational invariance, and thus robustness to optical misalignment, are crucial for rapid development of compact and integrated optical devices. In this letter, we experimentally demonstrate a beam-shaping element that generates an annular beam by spatially filtering the fundamental Gaussian mode of a laser beam. The element comprises of a one-dimensional photonic crystal cavity fabricated using sputtered thin films. The planar architecture and in-plane symmetry of the element render our beam-shaping technique translationally invariant. The generated annular beam is sensitive to the polarization direction and the wavelength of the incident laser beam. Using this property of the annular beam, we show simultaneous generation of concentric annular beams of different wavelengths. Our experimental observations show an excellent agreement with simulation results performed using finite-difference time-domain method. Such a beam-shaping element has applications in areas ranging from microscopy and medicine to semiconductor lithography and manufacturing in microelectronics industry.

Direct micro-structuring of Si(111) surfaces through nanosecond laser Bessel beams

We present here a nanosecond laser ablation of Si(111) wafer with diffraction-free (Bessel-$J_0$) beams. First, the Axicon a conical shaped optical element for beam shaping is characterized with a visible and infrared light sources. Then, ablation profiles are obtained with Bessel beams generated for $\alpha=1^{\circ}$ and $\alpha=20^{\circ}$ base angles, then they are characterized via a Scanning Electron, an Atomic Force and an Optical Interferometric Microscopes. Experimental results compared with theoretical predictions obtained by using Bessel functions. Results show that Bessel beams give possibility of straightforward micro-structuring of Si(111) samples because the only central spot of Bessel beams could damage the surface provided that the laser pulse energy becomes in energy-range we found in our experiments. Moreover, our results clearly indicate that reduced HAZ area due to thermal expansion in ns pulse regime are natural outcome of Bessel beams as opposed to Gauss beams of same spot size. Lastly, nanosecond pulses indicate two-ablation regimes regarding the pulse energy, the quality of structures can be enhanced by using high quality Gauss beams ($M^{2}\approx1$) and the size of fabricated structures can be much reduced by using larger base angle of Axicon (such as $\alpha=40^{\circ}$) in our scheme.