Random Phase Plate Research Articles

Random phase plate designed by the genetic algorithm for decoherence in energy homogenization units of a photolithography illumination system

The microlens array (MLA) is used in the flexible pupil shaping module of lithography illumination system for energy balance. However, the coherence of the light source can lead to interference patterns. Most of the decoherence methods are restricted for the pulse laser and the scanning exposure application. To solve this issue, a specific random phase plate (RPP) is designed to eliminate the interference patterns caused by the coherence of the light source. The model of partially coherent light propagation in the MLAs homogeneous system is established based on the mutual intensity theory, and the genetic algorithm is introduced to design a high-performance RPP. The corresponding measurement device is constructed, and the intensity of the image plane light field is measured. Experiment results indicate that the intensity integral non-uniformity is 32.14% in the x-direction and 66.04% in the y-direction without the RPP, and the intensity integral non-uniformity is 22.95% in the x-direction and 19.18% in the y-direction with the RPP, which verifies the feasibility of the proposed method.

Analytical modeling of the spray amplification of a spatially smoothed laser beam

Spatial amplification of the near-forward Brillouin scattering (FSBS) produced by a laser beam smoothed with a random phase plate (RPP) is considered by using a novel technique based on the central limit theorem [C. Ruyer et al., Phys. Rev. E 107, 035208 (2023)]. It is demonstrated that FSBS amplification proceeds over a length much larger than the longitudinal speckle correlation length and, under certain conditions, scales as a square of the average gain coefficient. Analytical expressions for the spatial gain are successfully compared with paraxial electromagnetic simulations, demonstrating that the beamlet correlation through ion-acoustic waves dominates the spatial growth for intense enough laser beams. The scattered wave aperture increases with the gain and can extend beyond the small angle scattering limit. These results open the way for developing reduced modeling of beam spray amplification in radiation hydrodynamics codes.

Backward stimulated Brillouin scattering spatial gain with polarization, spatial, and temporal beam smoothing techniques

A recent study [Ruyer et al., Phys. Rev. E 107, 035208 (2023)] modeling the influence of a random phase plate on the backward stimulated Brillouin scattering growth is here supplemented with the effect of temporal and polarization smoothing. Our analytical predictions are validated by a large number of three dimensional Hera paraxial simulations for various beam smoothing techniques and relevant to most high energy laser facilities. Neglecting all non-linear effects apart from the pump depletion, we then reconstruct the system of differential equations that the backward stimulated Brillouin scattering convective amplification of a smoothed beam propagating in a non-homogeneous plasma satisfies. Its resolution is successfully confronted with our simulation data and prepares the accurate modeling, in a ray tracing scheme, of the effect of laser smoothing techniques on laser plasma instabilities.

Phase flow cytometry with coherent modulation imaging.

Label-free imaging and identification of fast-moving cells is a very challenging task. A kind of phase flow cytometry using coherent modulation imaging was proposed to realize label-free imaging and identification on fast-moving cells with compact optical alignment and high accuracy. Phase image of cells under inspection could be computed qualitatively from their diffraction patterns at the accuracy of about 0.01wavelength and the resolution of about 1.23 μm and the view field of 0.126 mm2 . Since the imaging system was mainly composed by a piece of random phase plate a detector without using commonly adopted reference beam and corresponding complex optical alignment, this method has much compacter optical structure and much higher tolerance capability to environmental instability in comparison with other kinds of phase flow cytometry. Current experimental results prove it could be an efficient optical tool for label-free tumor cell detection. This article is protected by copyright. All rights reserved.

Influence of a random phase plate on the growth of the backward stimulated Brillouin scatter.

We derive the analytical dispersion relation of a high-energy laser beam's backward stimulated Brillouin scattering (BSBS) in a hot plasma, that accounts both for the random phase plate (RPP) induced spatial shaping and its associated phase randomness. Indeed, phase plates are mandatory in large laser facilities where a precise control of the focal spot size is required. While the focal spot size is well controlled, such techniques produce small scale intensity variations that can trigger laser-plasma instabilities such as BSBS. Quantifying the resulting instability variability is shown to be crucial for understanding accurately the backscattering temporal and spatial growth as well as the asymptotic reflectivity. Our model, validated by means of a large number of three-dimensional paraxial simulations and experimental data, offers three quantitative predictions. The first one addresses the temporal exponential growth of the reflectivity by deriving and solving the BSBS RPP dispersion relation. A large statistical variability of the temporal growth rate is shown to be directly related to the phase plate randomness. Then, we predict the portion of the beam's sectionthat is absolutely unstable, thus helping to precisely assess the validity of the vastly used convective analysis. Finally, a simple analytical correction to the plane wave spatial gain is extracted from our theory giving a practical and effective asymptotic reflectivity prediction that includes the impact of phase plates smoothing techniques. Hence, our study sheds light on the long-time studied BSBS, deleterious to many high-energy experimental studies related to the physics of inertial confinement fusion.

Cross-beam energy transfer between spatially smoothed laser beams

The crossing of two spatially smoothed laser beams amounts to the crossings of a large number of speckles. The energy transfer between two of these speckles is mediated by laser induced electron/ion density ripples that act as a Bragg grating. In a weakly Landau-damped plasma, this ion acoustic wave (IAW) may propagate from one crossing region to another, hence perturbing the local electron/ion grating [Oudin et al. Phys. Rev. Lett. 127, 265001 (2021)] even without phase shift between IAWs. In this paper, we investigate how the phase-shifted IAWs generated at the speckle scale interfere and affect the overall energy exchange. To this aim, we perform 2D particle-in-cell simulations with in-phase and out-of-phase Gaussian beams. In the latter situation, which better matches a smoothed laser beam, we find that the destructive interferences between the ion waves significantly reduce the energy exchange compared to the plane wave case. Additional 2D particle-in-cell simulations with random phase plate smoothed laser beams confirm the relevance of this effect in carbon plasma. A second effect is that cross-beam energy transfer (CBET) inhibition persists in strongly damped plasmas when the speckle radius is comparable with the IAW damping distance. There, the reduction in the IAW amplitude is attributed to the smallness of the speckle's envelop. These results are supported by a simple model that analytically estimates the CBET and clearly shows that neglecting the inhomogeneities in the laser intensity would usually lead to an overestimate of the energy exchange.

Simulating the filamentation of smoothed laser beams with three-dimensional nonlinear dynamics

In a plasma, the ponderomotive force of an inhomogeneous electromagnetic field expels plasma from regions of high intensity. When a laser propagates through a plasma, this force creates density wells that subsequently modify the index of refraction. The beam refracts and focuses into these wells and may filament. In extreme cases, the laser beam will spray due to increasing angular divergence of the beam. The threshold for ponderomotive self-focusing is well established for isolated laser hotspots or speckles. Here, we define a practical threshold for characterizing the filamentation of thousands of speckles that are found in the focal plane of high-power laser beams spatially smoothed with random phase plates as used at high energy and power laser facilities studying inertial confinement fusion. This threshold is tested against three-dimensional simulations of speckled laser light propagating through plasma. Four metrics are applied to assess filamentation: the fraction of power above five times the average intensity, an effective f-number, the mean-squared perpendicular wavenumber, and the fraction of rarefied density with deviation from the initial density exceeding |δn/n| = 0.1. The speckled beams studied are generated by random phase plates, both with and without additional polarization smoothing, in a parameter regime of relevance to indirect drive experiments. While filamentation has been discussed extensively in the literature, we believe this to be the first published simulation study with three-dimensional nonlinear hydrodynamics that addresses the onset threshold of ponderomotive filamentation and establishes the lengths and time scales necessary to reach a statistical steady state.

Ghost imaging via spectral multiplexing in the broadband terahertz range

A method is proposed for accelerating measurements for ghost imaging reconstruction of objects using spectral multiplexing of speckle patterns formed by broadband terahertz (THz) radiation. The presented method aims at the challenge of a sufficiently large number of measurements, and increases the correlation between reference and reconstructed images. It is experimentally shown that unique speckle patterns for individual frequencies can be formed by broadband THz radiation while propagating through a random phase plate. It is shown by numerical simulation that these speckle patterns can be used to decrease the number of diffusers required by more than one order compared to the integrated method. The possibility of using electro-optical detection in the proposed technique reduces the number of measurements. For example, for the spectral range from 0.2 to 1.2 THz, there is a more than 20-fold decrease in the number of diffusers used.

Fried’s coherence length measurement of dynamic Kolmogorov type turbulence using the autocorrelation function

A new method to find the Fried’s coherence length of a dynamic Kolmogorov type turbulence in a laboratory environment is reported in this paper. This method utilises the autocorrelation function obtained from the quantitative characteristics of a rotating pseudo random phase plate in one of the arms of a Mach–Zehnder interferometer. Theoretical formalism and experimental verification are presented.

Further improvements to iterative off-axis digital holography.

In order to break through the limitation of off-axis holography in the field of measuring rough or strong scattering objects, a new iterative algorithm based on the concept of wavefront-coding was proposed. The reference wave is regarded as a wave modulator and it starts with random guess freed from the result of traditional off-axis holography. The full frequency spectrum could be retrieved iteratively after taking full advantage of the space-bandwidth production of the detector. As one form of coherent diffractive imaging, the theoretical resolution is diffraction limitation. According to the simulations and experiments with random phase plate, when the object fails to be reconstructed by traditional off-axis holography and other iterative off-axis holography algorithm due to the frequency spectrum of object is too wide, the proposed algorithm works well. It could be a general algorithm to prominently improve the capability of off-axis holography to measure rough or strong scattering objects.

Insensitivity of higher order topologically charged Laguerre–Gaussian beams to dynamic turbulence impact

The propagation characteristics of topologically charged Laguerre–Gaussian​ beams through a dynamic (rotating) pseudo random phase plate mimicking atmospheric turbulence, like beam wandering, scintillation etc are measured in laboratory level. Our findings clearly show that the beam wandering and scintillation effects are higher for Laser Gaussian beams compared to topologically charged Laguerre–Gaussian beams. Also, the impact of turbulence reduces considerably when the topological charges of LG beams increase. This may help to use higher order topologically charged Laguerre–Gaussian beams for optical communications in free space.

Phase Retrieval of On-Axis Digital Holography With Modified Coherent Diffraction Imaging

In this paper, a phase retrieval method is proposed to reconstruct the high-quality image free from undesired terms in on-axis digital holography (DH) with modified coherent diffraction imaging (MCDI). A random phase plate (RPP) is applied to generate a modulated diffraction pattern which forms an on-axis digital hologram with a plane reference wave, and a proper iterative algorithm is designed to reconstruct high-quality object information from both on-axis digital hologram and modulated diffraction pattern. Numerical simulations and experiments prove that both modulus and phase distributions can be accurately reconstructed within 100 iterations while the undesired twin image and zero-order diffraction can be effectively removed, thus demonstrating the feasibility of the suggested method.

Crossed beam energy transfer between optically smoothed laser beams in inhomogeneous plasmas.

Crossed beam energy transfer, CBET, in high-intensity laser–plasma interaction is investigated for the case of optically smoothed laser beams. In the two approaches to laser-driven inertial confinement fusion experiments, the direct-drive and the indirect-drive, CBET is of great importance because it governs the coupling of laser energy to the plasma. We use the two-dimensional wave-coupling code Harmony to simulate the transfer between two laser beams with speckle structure that overlap in a plasma with an inhomogeneous flow profile. We compare the CBET dynamics for laser beams with spatial incoherence and with spatio-temporal incoherence; in particular we apply the smoothing techniques using random phase plates (RPPs) and smoothing by spectral dispersion (SSD), respectively. It is found that for laser beams (wavelength λ0) with intensities (IL) above IL ∼ 2 × 1015 W cm−2(λ0/0.35 µm)−2(Te/keV), both the so-called plasma-induced smoothing as well as self-focusing in intense laser speckles induce temporal incoherence; the latter affects the CBET and the angular distribution of the light transmitted behind the zone of beam overlap. For RPP-smoothed incident beams, the resulting band width of the transmitted light can already be of the same order as the effective band width of the SSD available at major laser facilities. We examine the conditions when spatio-temporal smoothing techniques become efficient for CBET.This article is part of a discussion meeting issue ‘Prospects for high gain inertial fusion energy (part 1)’.

Phase smoothing and polarisation-phase synchronous smoothing based on liquid crystal Pancharatnam-Berry phase devices

ABSTRACT In this paper, we proposed and fabricated a liquid crystal random-phase plate (LCRPP) for laser beam phase smoothing, while the simulation and experimental verification of LCRPP applied to laser beam’s smoothing were also carried out simultaneously. A new beam smoothing technology named polarisation-phase synchronous smoothing and an improved algorithm based on G-S algorithm specially designed for polarisation-phase synchronous beam smoothing are also proposed based on liquid crystal Pancharatnam-Berry (LC PB) phase devices. Our work on beam smoothing taking advantage of LC PB phase devices not only simplifies the process, deduces the cost and greatly improves the precision and effect of beam smoothing but also provides a novel way for spatial beam shaping, which is of wide applications in laser processing.

Wavefront sensing for low-coherent sources through spatial coherence revival

An interferometry based wavefront sensing scheme applicable to low-coherent light sources is proposed and demonstrated. Using a pair of cascaded Sagnac interferometers, spatial frequency multiplexed interference of three sheared copies of the wavefront is recorded. The independent vector gradients obtained are used to reconstruct the wavefront. We overcome the spatio-temporal coherence limitations of the light source through the choice of spatial and spectral distribution of the light source. A Gaussian spectral distribution enables the measurement of the phase gradient corresponding to the central wavelength. Introduction of aperture for controlling the spatial distribution of the extended light source, we revive the spatial coherence of the optical field at the detector plane. We revive the spatial coherence of the field for the set value of lateral shear to maintain the visibility of the interference at the detectable level. Validating the scheme through measurement of changes in wavefront as a function of a collimation lens position, we apply it to reconstruct the wavefront of a light beam passing through a pseudo random phase plate, an atmospheric turbulence simulator.

Speckle-free smoothing of coherence laser beams by a homogenizer on uniaxial high birefringent crystal

We report on a new type of a random phase plate (RPP) that can be applied for effective homogenization of coherent laser beams. The RPP is fabricated on a uniaxial birefringent crystal, ensuring the absence of speckles within the processing plane due to two orthogonally polarized beamlets with π phase difference. High fabrication speed ∼ 2 mm2/s of RPP takes at least 10 minutes to fabricate it. RPPs test showed the transformation of Gauss intensity distribution to the flat-top one characterized by low-intensity modulation ∼1% of the coherent laser beam. Then, RPP was applied in a picosecond laser setup for ZnO film microprocessing.

Multi-section images parallel encryption based on optical scanning holographic cryptography technology

In this paper, the function of parallel encrypting multiple images and reproducing arbitrary layers of images is realized by improving the double pupil function in optical scanning holography. In an optical scanning holography (OSH) system, a dual-pupil heterodyne incoherent image processing technique is used to record holographic images. By adjusting the two pupil functions in the optical system, the interference fringes can be modified to achieve different imaging effects. In this paper, the ring pupil and random phase plate are used to act as two pupil functions to interfere to form a ring random phase plate, and thus realizing the fast scanning of multi-layer images. Then the multi-layer images can be quickly encrypted by one imaging technique. The scanned signals are quickly collected by photoelectric detectors, and they synthesize encrypted holograms by computer. By using the digital holography to decrypt the holograms, the precise reproduction of any layer image can be achieved. The OSH system with random phase pupil is strongly dependent on the longitudinal position of the system in digital reconstruction. The defocusing noise can be converted into random noise and the effect of defocusing layer on imaging can be effectively suppressed. However, in practice, it is necessary to average multiple images to achieve better imaging effect, and the accuracy of random phase plate is required. In this paper, most of the random noise can be filtered with the aid of ring pupil, and all the information about multi-layer graphics can be recorded and reconstructed by one scan. In the process of reconstruction, the influence of defocusing image can be effectively eliminated, and the decryption of any layer image can be realized. This method collects encrypted image by photoelectric detector, and does not need complex algorithm reconstruction nor phase iteration, which greatly reduces the time expended in the encryption process. In the process of encryption, the key space of the system is increased, and the encrypted image obtained has high security. In this paper, correlation coefficient is used to evaluate the encryption effect of this method, and the effectiveness and security of this method are verified by simulation experiments. For cutting resistance, when 75% of the information is lost, the correlation coefficient can still reach more than 0.5. For the sensitivity of information, the integrity of decrypted image will be seriously damaged when the wavelength and distance shift very little. For the anti-noise ability, under the influence of Gauss noise and salt and pepper noise, the correlation coefficient and image recognition degree are high. This method is very time-saving, and the result of encryption has high security, high sensitivity, strong ability to resist clipping and noise.

Implementation of a phase plate for the generation of homogeneous focal-spot intensity distributions at the high-energy short-pulse laser facility PHELIX

We propose and demonstrate the use of random phase plates (RPPs) for high-energy sub-picosecond lasers. Contrarily to previous work related to nanosecond lasers, an RPP poses technical challenges with ultrashort-pulse lasers. Here, we implement the RPP near the beginning of the amplifier and image-relay it throughout the laser amplifier. With this, we obtain a uniform intensity distribution in the focus over an area 1600 times the diffraction limit. This method shows no significant drawbacks for the laser and it has been implemented at the PHELIX laser facility where it is now available for users.

An online diagnosis technique for simultaneous measurement of the fundamental, second and third harmonics in one snapshot

A three-wavelength coherent-modulation-imaging (CMI) technique is proposed to simultaneously measure the fundamental, second and third harmonics of a laser driver in one snapshot. Laser beams at three wavelengths (1053 nm, 526.5 nm and 351 nm) were simultaneously incident on a random phase plate to generate hybrid diffraction patterns, and a modified CMI algorithm was adopted to reconstruct the complex amplitude of each wavelength from one diffraction intensity frame. The validity of this proposed technique was verified using both numerical simulation and experimental analyses. Compared to commonly used measurement methods, this proposed method has several advantages, including a compact structure, convenient operation and high accuracy.

Single shot multi-wavelength phase retrieval with coherent modulation imaging.

A single shot multi-wavelength phase retrieval method is proposed by combining common coherent modulation imaging (CMI) and a low rank mixed-state algorithm together. A radiation beam consisting of multi-wavelength is illuminated on the sample to be observed, and the exiting field is incident on a random phase plate to form speckle patterns, which is the incoherent superposition of diffraction patterns of each wavelength. The exiting complex amplitude of the sample including both the modulus and phase of each wavelength can be reconstructed simultaneously from the recorded diffraction intensity using a low rank mixed-state algorithm. The feasibility of this proposed method was verified with visible light experimentally. This proposed method not only makes CMI realizable with partially coherent illumination but also can extend its application to various traditionally unrelated fields, where several wavelengths should be considered simultaneously.