Off-axis Parabola Research Articles

Compact laser wakefield acceleration toward high energy with micro-plasma parabola

Laser wakefield acceleration (LWFA) promises compact accelerators toward the high-energy frontier. However, the approach to the 100 GeV milestone faces the obstacle of the long focal length required for optimal acceleration with high-power lasers, which reaches hundreds of meters for 10–100 PW lasers. The long focal length originates from optimal laser intensity required to avoid nonlinear effects and hence large spot size and Rayleigh length. We propose a “telescope” geometry in which a micro-plasma parabola (MPP) is coupled with a short-focal-length off-axis parabola, minimizing the focal length to the meter range for LWFA under optimized conditions driven by lasers beyond 1 PW. Full-dimensional kinetic simulations demonstrate the generation of a 9 GeV electron bunch within only 1 m optical length—only one-tenth of that required with the conventional approach with the same performance. The proposed MPP provides a basis for the construction of compact LWFAs toward single-stage 100 GeV acceleration with 100 PW class lasers.

Second harmonic generation of focused beams on the LFEX laser facility

There is a strong demand for efficient second harmonic generation (SHG) in ultra-intense short-pulse lasers. This paper demonstrates the generation of an unconverted fundamental (1ω)+second harmonics (2ω) mixed laser on the LFEX laser system. The experimental setup utilizes 0.5 mm-thick LBO crystal plates in a focusing beams implemented after an off-axis parabola, the design reduces the size and cost of the SHG system. The LFEX laser beams with four-beams combined energy of 222 J and a pulse duration of 1.5 ps, is successfully converted to 102 J of 2ω light and 100 J of unconverted 1ω light, 20 J is lost through surface reflections, and they are mixed at the focal point. Verification of successful SHG is confirmed through X-ray pinhole imaging and electron spectrometry. This novel technique is not limited to LFEX lasers and holds applicability for various ultra-intense lasers. Consequently, this accomplishment significantly contributes to expanding the capability for high-energy density laser-plasma experiments.

Distortions in focusing laser pulses due to spatio-temporal couplings: an analytic description

Abstract In ultra-short laser pulses, small changes in dispersion properties before the final focusing mirror can lead to severe pulse distortions around the focus and therefore to very different pulse properties at the point of laser–matter interaction, yielding unexpected interaction results. The mapping between far- and near-field laser properties intricately depends on the spatial and angular dispersion properties as well as the focal geometry. For a focused Gaussian laser pulse under the influence of angular, spatial and group-delay dispersion, we derive analytical expressions for its pulse-front tilt, duration and width from a fully analytic expression for its electric field in the time–space domain obtained with scalar diffraction theory. This expression is not only valid in and near the focus but also along the entire propagation distance from the focusing mirror to the focus. Expressions relating angular, spatial and group-delay dispersion before focusing at an off-axis parabola, where they are well measurable, to the respective values in the pulse’s focus are obtained by a ray tracing approach. Together, these formulas are used to show in example setups that the pulse-front tilts of lasers with small initial dispersion can become several tens of degrees larger in the vicinity of the focus while being small directly in the focus. The formulas derived here provide the analytical foundation for observations previously made in numerical experiments. By numerically simulating Gaussian pulse propagation and measuring properties of the pulse at distances several Rayleigh lengths off the focus, we verify the analytic expressions.

Development and suborbital validation of technologies for direct imaging of nearby exoplanetary systems in reflected visible wavelengths

Primarily through indirect observational techniques, the existence of thousands of exoplanetary systems has been confirmed. However, we still do not have an image of an exoplanetary system in reflected visible light. This is important because planetary systems as old as the solar system (∼5 G yr) have cooled to near equilibrium and are thus no longer as bright as the systems being detected by current infrared coronagraphs. Furthermore, the visible bandpass contains valuable information about aerosols, hazes, and clouds that are unavailable to infrared investigations.Our research group has transitioned key technologies that are necessary for direct imaging of exoplanets and their environments from laboratory to near space using suborbital platforms. Two of our sounding rocket experiments, called Planetary Imaging Concept Testbed Using a Rocket Experiment (PICTURE) and Planet Imaging Coronagraphic Technology Using a Reconfigurable Experimental Base (PICTURE-B), matured a 0.5m diameter Gregorian telescope, a (600nm to 750nm) visible nulling coronagraph (VNC), a 1024 channel deformable mirror (DM) and a fine pointing system.Following up on these rocket experiments, in 2019 we flew a high-altitude balloon called Planetary Imaging Concept Testbed Using a Recoverable Experiment - Coronagraph (PICTURE-C). It carried a telescope employing a 0.6m diameter Off Axis Parabolic (OAP) primary mirror, a vector vortex coronagraph (VVC), a 97-channel low order and a 1024 element high order DM operating in the 540nm to 660nm wavelength range. Like the rocket experiments, the first balloon flight demonstrated a 5 milliarcseconds (mas) fine pointing capability and the space worthiness of the coronagraph.The latest flight of PICTURE-C occurred on September 28 2022. It was designed to obtain the first high contrast (∼10−6) image of a debris disk, a circumstellar ring produced by the sublimation of cometary material and collisions among asteroids, comets and Kuiper-belt analogs, in reflected visible light. The experiment achieved 1 mas root mean square (RMS) fine pointing stability. Even though unanticipated transient vibrations prevented PICTURE-C from attaining its science goals, the conronagraph demonstrated 4×10−6 contrast over 540nm to 660nm (20% bandwidth).

A Submillimeter-Wave FMCW Pulse-Doppler Radar to Characterize the Dynamics of Particle Clouds

This work presents a 340-GHz frequency-modulated continuous-wave (FMCW) pulse-Doppler radar. The radar system is based on a transceiver module with about one milli-Watt output power and more than 30-GHz bandwidth. The front-end optics consists of an off-axis parabola fed by a horn antenna from the transceiver unit, resulting in a collimated radar beam. The digital radar waveform generation allows for coherent and arbitrary FMCW pulse waveforms. The performance in terms of sensitivity and resolution (range/cross-range/velocity) is demonstrated, and the system's ability to detect and map single particles (0.1-10 mm diameter), as well as clouds of particles, at a 5-m distance, is presented. A range resolution of 1 cm and a cross-range resolution of a few centimeters (3-dB beam-width) allow for the characterization of the dynamics of particle clouds with a measurement voxel size of a few cubic centimeters. The monitoring of particle dynamics is of interest in several industrial applications, such as in the manufacturing of pharmaceuticals and the control/analysis of fluidized bed combustion reactors.

Tight-focusing parabolic reflector schemes for petawatt lasers.

A comparative study of three different tight-focusing schemes for high-power lasers is performed numerically. Using the Stratton-Chu formulation, the electromagnetic field in the vicinity of the focus is evaluated for a short-pulse laser beam incident upon an on-axis high numerical aperture parabola (HNAP), an off-axis parabola (OAP), and a transmission parabola (TP). Linearly- and radially-polarized incident beams are considered. It is demonstrated that while all the focusing configurations yield intensities above 1023 W/cm2 for a 1 PW incident beam, the nature of the focused field can be drastically modified. In particular, it is shown that the TP, with its focal point behind the parabola, actually converts an incoming linearly-polarized beam into an m = 2 vector beam. The strengths and weaknesses of each configuration are discussed in the context of future laser-matter interaction experiments. Finally, a generalization of NA calculations up to 4π-illumination is proposed through the solid angle formulation, providing a universal way to compare light cones from any kind of optics.

Fourier convolution-parallel neural network framework with library matching for multi-tool processing decision-making in optical fabrication.

Intelligent manufacturing of ultra-precision optical surfaces is urgently desired but rather difficult to achieve due to the complex physical interactions involved. The development of data-oriented neural networks provides a new pathway, but existing networks cannot be adapted for optical fabrication with a high number of feature dimensions and a small specific dataset. In this Letter, for the first time to the best of our knowledge, a novel Fourier convolution-parallel neural network (FCPNN) framework with library matching was proposed to realize multi-tool processing decision-making, including basically all combination processing parameters (tool size and material, slurry type and removal rate). The number of feature dimensions required to achieve supervised learning with a hundred-level dataset is reduced by 3-5 orders of magnitude. Under the guidance of the proposed network model, a 260 mm × 260 mm off-axis parabolic (OAP) fused silica mirror successfully achieved error convergence after a multi-process involving grinding, figuring, and smoothing. The peak valley (PV) of the form error for the OAP fused silica mirror decreased from 15.153λ to 0.42λ and the root mean square (RMS) decreased from 2.944λ to 0.064λ in only 25.34 hours. This network framework has the potential to push the intelligence level of optical manufacturing to a new extreme.

Optical metrology on primary mirror of visible emission line coronagraph on board Aditya-L1 mission

The visible emission line coronagraph (VELC) on board the Aditya-L1 mission is an internally occulted reflective coronagraph. It is capable of simultaneous observations of the solar corona in imaging, spectroscopic, and spectropolarimetric modes very close to the solar limb, to 1.05 R ⊙ (R ⊙ – solar radius). Primary mirror (M1) of the VELC receives the light from both the solar disk and the corona up to 3 R ⊙ . In the VELC, occultation happens at the focus of the M1. Secondary mirror (M2) with a central hole size equal to 1.05 R ⊙ is mounted at the focal plane of M1 and serves the purpose of an internal occulter. To meet the proposed science goals of the payload, M1 surface should be super polished with good imaging characteristics. This results in stringent requirements of the surface figure and microroughness on the mirror surface. M1 is an off-axis parabola, so achieving the demanding requirements is quite challenging. At the same time, testing of M1 after development is crucial for evaluating its performance. This paper provides the details of the optical metrology tests carried out on M1 along with the results obtained and their implications on the performance of the VELC.

Side‐viewing handheld confocal Raman probe coupled with an off‐axis parabolic mirror for superficial epithelial Raman measurements of luminal organs

AbstractWe report on the development of a side‐viewing handheld confocal Raman probe coupled with an off‐axis parabolic (OAP) mirror for superficial epithelial Raman measurements of luminal organs. The OAP mirror realizes an effective numerical aperture of 0.36, a measured Raman excitation spot diameter of 130 μm and a depth of focus of 128 μm, allowing real time Raman spectra acquisition. The OAP mirror tilts the Raman optical path by 90°, making it well suited for superficial epithelium Raman interrogation of luminal organs. In addition, the probe results in no Raman interferences that may arise from transmission optics. The superficial epithelium Raman interrogation capability of the probe developed is validated through a two‐layer tissue phantom experiment. This work suggests the potential of the side‐viewing handheld confocal Raman probe coupled with an OAP mirror for enhancing the diagnosis of epithelial precancer and cancer of luminal organs.

Methodology of designing compact schlieren systems using off-axis parabolic mirrors.

Schlieren imaging is widely adopted in applications where fluid dynamics features are of interest. However, traditional Z-type schlieren systems utilizing on-axis mirrors generally require large system footprints due to the need to use high f-number mirrors. In this context, off-axis parabolic (OAP) mirrors provide an attractive alternative for permitting the use of smaller f-number optics, but well-documented methodologies for designing schlieren systems with OAP mirrors are lacking. The present work outlines a ray-tracing-based workflow applied to the design of a modified Z-type schlieren system utilizing OAP mirrors. The ray-tracing analysis evaluates the defocus and distortion introduced by schlieren optics. The results are used along with system size and illumination efficiency considerations to inform the selection of optimal optical components capable of producing high-quality schlieren images while minimizing the system footprint. As a step-by-step demonstration of the design methodology, an example schlieren system design is presented. The example schlieren design achieved an image resolution of 1.1 lp/mm at 50% contrast, with a 60% reduction in system length compared to traditional Z-type systems with f/8 mirrors; distortion characterizations of the designed schlieren system showed good agreement with ray-tracing predictions, and the distortion can be corrected through image post-processing. The current work provides a systematic approach for the design of compact schlieren systems with OAP mirrors and demonstrates the utility of this underutilized option.

Mid-infrared multispectral confocal microscope using off-axis parabolic mirrors to study epiretinal membranes.

Mid-infrared (mid-IR) multispectral microscopy, especially operating at the wavelength of 5-11 µm, is an effective tool for detecting, identifying, and quantifying the structure and composition of biological tissues. Compared with that based on the optical lens, the mid-infrared microscope composed of off-axis parabolic (OAP) mirrors is low cost, simple, and suitable for longer range of wavelength without chromatic aberrations, while keeping the optical transmission efficiency. Here we report a compact and versatile mid-infrared multispectral confocal microscope based on off-axis parabolic mirrors. We also perform numerical calculations based on the vectorial diffraction theory on OAP mirrors and analyze the typical aberrations and misalignment of the OAP-based optical system. Finally, we perform multispectral imaging of the epiretinal membrane of the human eyes with the spectrum selected according to its resonance absorption peak. The system is designed to perform multispectral or even hyperspectral imaging to identify and predict potential disease.

Advantage of a disposable focusing lens in petawatt laser for inertial confinement fusion

The inertial confinement fusion laser facility usually has several hundred large-aperture laser beams. A focusing off-axis parabolic (OAP) mirror combined with a debris shield to focus the petawatt lasers must be placed outside the target chamber for target space limitation. Further increasing the focusing power density of ps-petawatt lasers for large F-number focusing is difficult. However, a disposable lens with a smaller F-number that is used to simultaneously replace the parabolic mirror and debris shield can be placed inside the chamber by an extension pipe. The lens only needs a small target space and can increase the focusing power density of the petawatt laser over 35 times more than an OAP mirror under a 20° solid angle. The nonlinear effect of self-phase modulation may decrease the quality of the spot distribution, but under the correction of a deformable mirror with νcutoff = 0.0625 mm−1, a better focusing spot distribution can be obtained.

Study on Aided Optical Alignment by Programmable Spots Array Generated by Off-Axis Parabolic Phase Based on LCoS-SLM

We present an aided optical alignment method using the liquid crystal on silicon spatial light modulator (LCoS-SLM). An optical system composed of an interferometer and an LCoS-SLM was established to verify the effectiveness of the method. The system was also calibrated to solve the phase modulation nonlinear and nonuniformity problem for better performance of LCoS-SLM as an easily programmable phase compensator. The LCoS-SLM could modulate the phase of incident light precisely to generate an accurate phase desired to achieve a virtual off-axis parabolic phase to generate light spots array. Finally, the 2 × 2 light spots array generated by the optical system was used to verify its potential in optical alignment.

Off-axis parabolas super polished under stress: the case of the Roman Space Telescope coronagraphic instrument mirrors.

Direct imaging of exoplanets requires high contrast imaging techniques that demand tight tolerances on the optical surface error. The Nancy Grace Roman Space Telescope (RST) (previously named WFIRST) aims to perform direct imaging of SuperEarth-like exoplanets through its active coronographic instrument (CGI). Eight off-axis parabola (OAP) mirrors are utilised within the CGI to create a compact instrument and to ensure access to the pupil and focal planes. The surface form error and surface roughness of these relay optics directly impact the quality of the dark hole, and therfore the observable location for exoplanets. A new fabrication process for OAP manufacture via stressed mirror polishing (SMP) is presented in this paper. First, the design of the mirror substrate is investigated to create an innovative thickness distribution capable of producing the OAP geometry with a simple warping harness composed by two micrometer screws. Second, the novel design is implemented on a 60 mm diameter OAP prototype in Zerodur; a description of the fabrication process chain and the characterisation of the optical surface over all spatial frequencies are presented. Results from this first prototype demonstrated that the surface form error deviates from < 1 nm root means square (RMS) from the simulations and with a surface roughness of 2.1 Å Ra.

Construction of freeform mirrors for an off-axis telecentric scanning system through multiple surfaces expansion and mixing

In this paper, a direct design method for an off-axis two-mirror telecentric scanning system with a linear field of view (FOV) is proposed. A single freeform mirror structure is firstly considered, in which the aberration free geometry of the off-axis parabolic (OAP) surface is leveraged to provide the focusing function and build surface contour of the sub-region on the mirror for each FOV. Multiple OAP surfaces for construction of the freeform mirror are located at an OAP base to satisfy the telecentric condition. The imaging distortion of this single freeform mirror structure is analyzed and found unavoidable due to the unsymmetrical geometry of the OAP base. A freeform reflective corrector is supplemented, and it is constructed from multiple plane surfaces located at a curved base to fulfill the f-theta scanning geometry. Thus, a two-mirror structure composed of one freeform primary mirror and one freeform reflective corrector is established. Each plane-OAP surfaces pair corresponds to a specific FOV. These multiple OAP surfaces and multiple plane surfaces are then expanded and mixed respectively, to construct the freeform primary mirror and freeform reflective corrector. An f-theta two-mirror freeform scanning system with ±10.4° linear FOV is designed using the proposed construction method. The design result is diffraction-limited, and a scanning error less than 5 μm and telecentricity angle less than 0.2° are achieved.

Far-field vector-diffraction of off-axis parabolic mirror under oblique incidence**Project supported by the Science Foundation for Youth Scholars of Minjiang University, China (Grant No. Mj9n201602) and the National Science and Technology Major Project of the Ministry of Science and Technology of China.

Based on a full vector-diffraction theory, a detailed theoretical study is carried out, aiming at providing a clear insight into the effects of different focusing and off-axis parabola parameters on far-field vector-diffraction properties of an off-axis parabolic mirror in the presence of misalignments of the incoming beam. The physical origin of these effects is also explored. The results show that the far-field intensity profile is altered by the distortion-, coma-, and astigmatism-like aberrations, which are caused by oblique incidence rather than inherent aberrations for the off-axis configuration. The radius of 90% encircled energy also increases but does not change monotonically with incident beam size increasing, or rather, it first decreases and then increases. The focal shift strongly depends on the effective focal length and oblique incidence angle, but it is almost independent of the beam size, which affects the focusing spot patterns. The intensity distribution produces a higher astigmatic image with off-axis angle increasing. Coma-like aberration starts to become dominant with beam size increasing and results in larger curved propagation trajectory. The incident polarization also affects the intensity distribution. The variation in the Strehl ratio with oblique incidence angle strongly depends on the misalignment direction and beam size as well. In addition, we find that the difference in locus between the catacaustic and the diffraction focus in the meridian is small. But the locus of the sagittal foci is obviously different from the locus of the meridian foci and the catacaustic focus. Moreover, the peak intensity of the sagittal focus is maximum, and the ratio of the peak intensity to that in the meridian plane is approximately 1.5. Understanding these effects is valuable for assessing a practical focused intensity and describing the motion of charged particles under a strong electric field in ultraintense laser–matter interaction.

Off-axis parabolic mirror relay microscope for experiments with ultra-cold matter.

A new optical system is introduced for the imaging of Coulomb crystals held in a cryogenic ion trap where there are space limitations preventing the placement of an objective close to the fluorescing ions. The optical system features an off-axis parabolic (OAP) mirror relay microscope that will serve to acquire images of a lattice of fluorescing ions confined within an ultra-high-vacuum vessel operating at temperatures below 10 K. We report that the OAP mirror relay setup can resolve features smaller than the separation between neighboring ions in Coulomb crystals. The setup presented here consists of two 90-degree OAP mirrors arranged into a relay from which standard microscope optics deliver the image to a camera. This design allows the first element in the imaging setup-an OAP mirror-to be located as close as possible to the ion trap, achieving high resolution without the need for a direct line-of-sight to the trap center or for a view port to be located in close proximity to the ion trap. Such an arrangement would not be possible with a standard microscope objective, which is the approach commonly adopted by the field. OAP mirrors represent a novel solution for delivering polychromatic images with micrometer-scale resolution over extended distances.

Construction method through multiple off-axis parabolic surfaces expansion and mixing to design an easy-aligned freeform spectrometer.

The classic Czerny-Turner spectrometer consists of a plane grating and two spherical mirrors. The optical path geometry adopted for incident and grating dispersed light is off-axis reflection, so the spherical collimating and focusing mirrors introduce coma and astigmatism. The conventional configuration is asymmetrical for coma automatic compensation, but suffers from astigmatism. We substitute the off-axis parabolic (OAP) surfaces for spherical surfaces of the collimating mirror and each sub-region of the focusing mirror, to achieve an aberration free configuration. The multiple OAP surfaces are then expanded and mixed, to construct a freeform surface integrating the collimating and focusing mirrors into a single element. Results show that a 0.1 nm spectral resolution is achieved over a bandwidth of 400 nm centered at 800 nm, in the designed spectrometer comprised of a plane grating and one freeform mirror. The construction method is advantageous to integrated optic design, and the resulting freeform mirror spectrometer is compact, and simplifies manufacture and alignment.

Parametric geometry analysis for circular-aperture off-axis parabolic mirror segment

We investigated the geometrical characteristics of circular-aperture off-axis parabolic (OAP) mirror segments to clarify the meaning of the loosely defined word “center” used in the literature and in documents to describe OAPs. We proposed the elliptical aperture center of an OAP as the definition of the center. The off-axis distance (OAD) is the vertical distance from the reference optical axis to the aperture center. In addition, the OAD can be varied depending on the desired center of a circular aperture to select the part of a parallel beam for focusing. The radius of the circular aperture becomes the minor-axis semidiameter of the elliptical aperture of the OAP. These geometrical parameters were systematically defined, derived, and/or analyzed in the context of optical engineering applications. Based on a set of those fundamental parameters, an intrinsic datum point utilizing the deepest point on the OAP surface was presented. The datum point provides a well-defined reference co-ordinate frame for locating or aligning an OAP within various astronomical telescope designs, instrument manufacturing and assembly processes, and optical system alignment and testing applications.

A divertor scraper observation system for the Wendelstein 7-X stellarator

Two graphite divertor elements called scrapers have been installed on the Wendelstein 7-X stellarator in the throat of the magnetic island divertor. To diagnose one, we have designed, built, calibrated, and installed a new infrared/visible imaging endoscope system to enable detailed observations of the plasma interactions and heat loads at one of the scrapers and the nearby divertor surfaces. The new system uses a shuttered pinhole-protected pair of 90° off-axis 228 mm focal length aluminum parabolic mirrors, and two flat turning metal mirrors, to send light to a sapphire vacuum window 1.6 meters away, beyond which we have co-located telephoto lens-based infrared and visible cameras. The back-to-back off-axis parabolas serve to cancel out most aberrations, enabling the use of off-the-shelf commercial optics outside of the vessel. For the infrared, we use a 3-5 μm 1-megapixel FLIR SC8303HD camera and for the visible, a 5-megapixel CMOS PCO 5.5 edge camera. A short 1-m quartz pickoff fiber is used to send 200-1100 nm light to a compact spectrometer, also located in the same iron shield box as the cameras. The camera field of view covers the 700 mm length of the scraper, and includes locations monitored by thermocouples and Langmuir probes embedded in some of the scraper tiles. Predicted and actual optical test performances of the overall system are compared.