Phase Plate Research Articles

Spatial shaping of low- and high-order harmonics generated using vortex beams

We demonstrate the generation of the low- and high-order harmonic vortex beams from a single spiral phase plate illuminated by different laser wavelengths. The second harmonic (532 nm) originates from the application of the wavefront-structured 1064 nm femtosecond pulses with fractional orbital angular momentum (OAM) during propagation through a lithium triborate crystal, while the third harmonic (500 nm) originates from the application of the wavefront-structured near-IR (1500 nm) femtosecond pulses with integer OAM during propagation through a 150 μm thick fused silica plate. The topological charges (TCs) of the second and third harmonics are measured and compared. The increase in TC and the peculiarities in OAM variations during modification of the polarisation of the incident radiation are analysed and discussed. The two-colour-pump-driven second-harmonic vortex radiation interacted with an Ar gas jet to generate vortex harmonics up to the 14th order with double-lobe complex spatial profiles in the extreme ultraviolet region.

Improving millimeter-wave imaging quality using the vortex phase method

This paper investigates a new vortex wave imaging approach to improve the imaging quality of small metal targets of size less than 1.5 mm. Antennas with different spiral phase plates are designed to efficiently transmit vortex beams with orbital angular momentums (OAMs). By analyzing the OAM spectrum of the target, it was discovered that the predominant reflection contains a particular OAM mode that carries abundant azimuthal information. This can be explained by the OAM selectivity of the target and the guidance of the vortex transmitting beam. A simple reflection vortex imaging system was designed to capture the phase information. Measurement results show that the high image contrast reaches 14.9%, which is twice as high as that of the imaging without OAM. Both of simulations and experiments demonstrate that the vortex phase imaging approach proposed in this paper can effectively improve the imaging quality at 80 GHz. This approach is suitable for other millimeter wave imaging systems and is helpful to improve the resolution in anti-terrorism security checks.

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.

Synthesizing polarization singularity lattices using phase ramps

In this paper, a novel methodology for generating polarization singularity lattices using ramp phase structures in a polarization interferometer is presented. By applying differential tilts to distinct regions within the wavefront using a spatial light modulator, a phase-discontinuity line separating the two regions is formed. During propagation along this line, phase vortices are formed at discrete points about which the phase difference on either side of the ramp is π. This wavefront with phase vortices is superimposed with a plane wave in orthogonal polarization in a polarization interferometer, giving rise to polarization singularities. A common-path polarization interferometer is constructed using a spatial light modulator to reduce errors and complexity. Polarization fringes instead of intensity fringes obtained in this interferometer host polarization singularities. Lattices made up of a linear chain of polarization singularities—unusually of the same index polarity—are found here. Experimental results corroborate the theoretical predictions. This study shows that singularities can be produced with non-spiral phase plates by using linear phase ramps. The method discussed in this paper may find potential applications in optical trapping and particle steering.

Optical vortices by an adaptive spiral phase plate

An Adaptive Spiral Phase Plate (ASPP) based on liquid crystal (LC) and the transmission electrode technique is theoretically and experimentally demonstrated. This ASPP design enables the generation of high-quality optical vortices with topological charges ranging from ±1 to ±4 using a single device, with higher charges being directly achievable by employing higher-birefringence LC or thicker cells. The continuous reconfigurability of the optical phase shift, achieved through a simple control mechanism involving only two low voltages and 100 electrodes that distribute the voltage, sets this device as an accurate approximation to a continuous ASPP. The measured conversion efficiency ranges between almost 100% and 95% for the first and fourth topological charges, respectively. This device offers remarkable advantages, such as complete reconfigurability, allowing adjustment of operating wavelengths and topological charges. The fabrication process mirrors that of a standard LCD cell, ensuring a cost-effective and reliable solution. In summary, the proposed ASPP is a key advancement, providing superior light conversion efficiency, simplicity, and the capability for on-the-fly reconfiguration in various optical applications.

Hollow vortex Gaussian beam expressed in terms of cylindrical wave

The electrical field of hollow vortex Gaussian beam (HVGB) with an arbitrary combination of the beam order and topological charge is formulated by using the cylindrical wave spectrum representation (CWSR), which satisfies Maxwell’s equations rigorously and allows to study analytically and numerically the evolution of the beam along its propagation in the source region and the near/far- field regions. It is found that in the source region there exists a sharp and very narrow peak, due to the contribution of evanescent waves when the beam order and the topological charge satisfy specific relations. The effect of the spiral phase plate (SPP) in generating a non-vortex Gaussian beam to a vortex one is explained. Besides, it is found that the divergence of the beam is mainly determined by the topological charge and the hollow structure is mainly determined by the beam order.

Application of Hilbert-Differential Phase Contrast to Scanning Transmission Electron Microscopy.

We report a novel class of scanning transmission electron microscopy with Hilbert-differential phase contrast (HDP-STEM) that displays nanostructures of thin samples in a topographical manner. A semicircular π phase plate (PP) was used as an optical device for manipulating electron waves in HDP-STEM. This is the different design from the Zernike PP used in our previous phase plate STEM (P-STEM), but both must be placed in the front focal plane of the condenser lens. HDP-STEM images of multi-walled carbon nanotubes showed higher contrast than those obtained by conventional bright-field STEM. Since the PP of the HDP-STEM is nonsymmetrical, several different images were obtained by changing the detection conditions. A two-dimensional electron detector was also used to remove the scattering contrast component in the same way as with the Zernike PP and obtain an image containing only (differential) phase contrast.

Encoding terahertz holographic bits with a computer-generated 3D-printed phase plate

A sub-terahertz holographic image of a two-dimensional 576-bit data code is produced using a diffractive phase-plate element. The phase plate was designed using a modified Gerchberg-Saxton iterative algorithm to encode a focused image of the data code into a phase modulation profile. The complex phase plate structure is fabricated from polylactic acid using fused deposition modeling, a common three-dimensional-printing technique. The design achieves a significantly simplified optical setup, consisting of a 0.14 THz diverging source, the holographic phase plate and a scanning detector, without the need for additional optical elements. The information stored in the data code is an example of a cryptographic private key. Specifically, the private key for a Bitcoin wallet address. Successful retrieval of the encoded information demonstrates a potential use case for terahertz holographic memory, using a storage medium that can be fabricated with consumer-level three-dimensional-printing techniques.

3D printable PLA spiral phase plate with horn feed for OAM beam generation for 6G communication

3D printable PLA spiral phase plate with horn feed for OAM beam generation for 6G communication

Divide and structure: generating and interswitching orthogonal eigenstates of complementary petal beams using a π-shifted Sagnac interferometer.

One of the many facets of structured light are Ferris wheel/petal beams that can be generated by the addition/superposition of two beams with opposite vorticity/orbital angular momentum (OAM). We demonstrate a simple scheme employing a π-shifted Sagnac interferometer (SI) containing a spiral phase plate (SPP) that divides and structures an incoming beam into two azimuthally complementary petal beams representing orthogonal eigenstates. The half-wave plate in the SI can interswitch/route these intensity patterns between the two outputs of the interferometer. The results are interpreted as a double symmetry breaking--that of helicity due to SPP and handedness due to HWP--experienced by counterpropagating beams in the π-shifted SI. In general, for a Laguerre-Gaussian (LG) incoming mode, the SI produces two orthogonal output states, each consisting of a sum or difference of distinct SPP-modified LG modes and resulting in complementary petal beams convoluted with the incoming mode. We also introduce a three-mirror π-shifted SI that can switch on and switch off opposite sign vortices into different SI arms. The scheme can find applications in particle trapping, information transmission/development of communications protocols, and signal processing (i.e.,multiplexing/demultiplexing when using beams with high vorticity/OAM).

Optical design of a novel near-infrared phase contrast imaging (NI-PCI) diagnostic on the HL-2A tokamak

The optical design of near-infrared phase contrast imaging (NI-PCI) diagnosis on HL-2A is introduced in this paper. This scheme benefits from the great progress of near-infrared laser technology and is a broadening of traditional phase contrast technology. This diagnostic can work as a keen tool to measure plasma wavenumber spectra by inferring string-integrated plasma density fluctuations. Design of both the front optical path which is the path before the laser transmitting into the tokamak plasma and the rear optics which is the path after the laser passing through the plasma is detailed. The 1550 nm laser is chosen as the probe beam and high-precision optical components are designed to fit the laser beam, in which a phase plate with a 194-nm-deep silver groove is the key. Compared with the conventional 10.6 m laser-based PCI system on HL-2A, NI-PCI significantly overcomes the unwanted phase scintillation effect and promotes the measurement capability of high-wavenumber turbulence with an increased maximal measurable wavenumber from 15 cm−1 to 32.6 cm−1.

Dynamic structured illumination for confocal microscopy.

Structured illumination enables the tailoring of an imaging device's optical transfer function to enhance resolution. We propose the incorporation of a temporal periodic modulation, specifically a rotating mask, to encode multiple transfer functions in the temporal domain. This approach is demonstrated using a confocal microscope configuration. At each scanning position, a temporal periodic signal is recorded. By filtering around each harmonic of the rotation frequency, multiple images of the same object can be constructed. The image carried by the nth harmonic is a convolution of the object with a phase vortex of topological charge n, similar to the outcome when using a vortex phase plate as an illumination. This enables the collection of chosen high spatial frequencies from the sample, thereby enhancing the spatial resolution of the confocal microscope.

High-order optical vortex beam generation based on watt-class spatial phase plate-integrated photonic-crystal surface-emitting lasers.

We develop spatial phase plate (SPP)-integrated photonic-crystal surface-emitting lasers featuring double-lattice photonic-crystal structures embedded using a crystal regrowth technique. SPPs possessing eight segmentations per phase rotation number l are fabricated on the top surface to generate optical vortex beams (OVBs) with l = 1-3. The beams exhibit a high output power of ∼5 W and high mode purities of 85%, 78%, and 72% for l = 1-3, respectively. These purity values are comparable with those of a pure Gaussian mode passing through an SPP. The compact, high-power, and high-purity OVB sources can be used in the fields of material processing, optical manipulation, and microscopy.

Anisoplanatic effects on wave propagation through dynamic pseudo-random phase plate mimicking atmospheric turbulence

Atmospheric turbulence significantly impacts the performance of optical systems, causing wavefront distortions that degrade image quality and limit the capabilities of remote sensing, astronomical observations, and free-space communication. The phenomenon of angular anisoplanatism, where the angular extent of the isoplanatic patch becomes limited due to varying turbulence conditions across the field of view, poses a substantial challenge in achieving high-resolution imaging of extended objects through turbulent atmospheres. This paper presents a comprehensive investigation into angular anisoplanatism using a laboratory-based environment that employs a pseudo-random phase plate to generate Kolmogorov turbulence. Angular anisoplanatism has been studied by generating two beams using a robust cyclic interferometer type arrangement, such that one beam is considered as a reference and the other beam as a target. Here, we have investigated experimentally the correlation of Zernike coefficients, mean square error (MSE), and beam centroid displacement, as a function of the angular separation of two beams. Furthermore, we have also reported the correlation of Zernike coefficients of the Laguerre Gaussian beam with different charges and eventually compared its MSE with that of the Gaussian beam.

Robustness of partially coherent vortex beams to the impact of dynamic Kolmogorov kind of turbulence

The wave propagation characteristics of Gaussian-Schell model vortex beams passing through a dynamic Kolmogorov type of turbulence are analyzed at the laboratory level. The effect of a rotating pseudo-random phase plate, which simulates Kolmogorov-type atmospheric turbulence, on the Gaussian-Schell model beams carrying twist phase is characterized by calculating the scintillation index and intensity line profiles. Our analysis proves the resilience of Gaussian-Schell model vortex beams to the impact of dynamic turbulence. Simulation studies are further used to validate the experimental results. Because of the resemblance between our investigation conditions and real-world atmospheric turbulence, these findings have potential applications in free-space communication systems.

Fast and robust 3D MINFLUX excitation with a variable phase plate

Fast and robust 3D MINFLUX excitation with a variable phase plate

3D tracking using a multi-spectral 4th-generation phase plate

3D tracking using a multi-spectral 4th-generation phase plate

Key technology of vector removal decoupling in a slope-based figuring model and application in continuous phase plate fabrication.

For the high-precision fabrication of a continuous phase plate (CPP), a combined decoupling algorithm of single-step decoupling based on the Clairaut-Schwarz theorem and global decoupling by stagewise iteration is proposed. It attempts to address the problem of the low accuracy and limitation of the existing slope-based figuring (SF) model in two-dimensional applications caused by the vector removal coupling between the tool slope influence function and the material removal slope due to the inherent convolution effect in the SF model. The shortcomings of CPP interferometry and the application bottleneck of the Hartmann test in traditional height-based figuring model are studied. The generation mechanism of vector removal coupling is analyzed and compensated. A CPP of 85m m×85m m was successfully machined by the decoupled slope-based figuring model, and the root mean square (RMS) of the surface height error accounted for 6.01% of the RMS of the design value. The research results can effectively improve the convergence and certainty of CPP fabrication using the slope-based figuring model.

Development of a polarimetric thermal imager calibration method

Measurement of thermal imager characteristics is important for the reliable and efficient operation of the device in various fields, including science, medicine, and industry. Incorrect measurements can lead to errors, which can be critical, especially for military-grade thermal imagers.
 This article is dedicated to developing a method for monitoring the output parameters of polarimetric thermal imagers based on calibration. During calibration, the following operations are proposed: visual inspection, functionality check, measurement of polarimetric thermal imager parameters, and evaluation of measurement uncertainties. In this article, the controlled parameters of the polarimetric thermal imager are the measured for device temperature and NETD, Noise Equivalent Temperature Difference. For these parameters, a measurement model, a measurement function, and an uncertainty budget have been developed. The uncertainty budget includes only the main and most influential uncertainty components. This methodology can only be used for one type of polarimetric thermal imager, where the determination of the radiation polarization state is achieved by rotating a phase plate.

Metasurface-based varifocal Alvarez lens at microwave frequencies.

Lenses with a tunable focus are highly desirable but remain a challenge. Here, we demonstrate a microwave varifocal meta-lens based on the Alvarez lens principle, consisting of two mechanically movable tri-layer metasurface phase plates with reversed cubic spatial profiles. The manufactured multilayer Alvarez meta-lens enables microwave beam collimation/focusing at frequencies centered at 7.5 GHz, and shows one octave focal length tunability when transversely translating the phase plates by 8 cm. The measurements reveal a gain enhancement up to 15 dB, 3-dB beam width down to 3.5∘, and relatively broad 3-dB bandwidth of 3 GHz. These advantageous characteristics, along with its simplicity, compactness, and lightweightness, make the demonstrated flat Alvarez meta-lens suitable for deployment in many microwave systems.