Density Grating Research Articles

Phase demodulation method of high line density grating interferometric signal based on wavelet transform

The increasing line density of the reference grating and the accelerating miniaturization of ultra-precision displacement measurement technology necessitate more stable interferometric signal processing methods for high line density gratings, particularly in low signal-to-noise ratio scenarios. This paper presents a phase demodulation method for dynamic interferometric signals for high line density gratings. The Morlet wavelet transform is utilized to obtain the instantaneous frequency of the interferometric signal, integration of which yields the relative displacement, while adding adjacent relative displacements without gaps provides the absolute displacement during dynamic motion of the grating. In simulations with a signal-to-noise ratio ranging from 40 to 70 dB, the proposed method demonstrates greater robustness compared to the traditional method. By establishing a platform for repeated experiments and comparing it with traditional methods, it was found that the maximum deviation between calculation results obtained using this method and traditional methods is 0.8 nm, further confirming its potential application.

Bidirectional two-degree-of-freedom grating interferometer with biased Littrow configuration

Traditional grating interferometer with Littrow configuration suffer from low optical subdivision factor and high grating base surface shape error. To solve these problems, a grating interferometer with bidirectional Littrow configuration is proposed. Using a high linear density grating of 1800 gr/mm with quadruple optical subdivision is achieved on the optical path. A three-dimensional contour analysis method is proposed to calculate the influence of surface shape error. The experimental result shows that the error of the 10 mm/2 mm displacement test in the X/Z direction fluctuates in the range of ±25 nm, and the actual resolution in the X and Z direction is all 1.5 nm. In summary, the system has good repeatability and high resolution, and can achieve nanoscale displacement measurement in the X/Z direction, and has broad application prospects in the field of precision machining and manufacturing.

Advances in free-electron-laser based scattering techniques and spectroscopic methods

<sec>In 2005, the FLASH soft X-ray free-electron laser (FEL) in Hamburg, Germany, achieved its first lasing, which began an intensive phase of global FEL construction. Subsequently, the United States, Japan, South Korea, China, Italy, and Switzerland all began building such photon facilities. Recently, the new generation of FEL has started to utilize superconducting acceleration technology to achieve high-repetition-rate pulse output, thereby improving experimental efficiency. Currently completed facility is the European XFEL, ongoing constructions are the LCLS-II in the United States and the SHINE facility in Shanghai, and the facility in preparation is the Shenzhen superconducting soft X-ray free-electron laser (S<sup>3</sup>FEL).</sec><sec>These FEL facilities generate coherent and tunable ultrashort pulses ranging from the extreme ultraviolet to hard X-ray spectrum, which advances the FEL-based scattering techniques such as ultrafast X-ray scattering, spectroscopy, and X-ray nonlinear optics, thereby transforming the way we study correlated quantum materials on an ultrafast timescale.</sec><sec>The self-amplified spontaneous emission (SASE) process in FEL leads to timing jitter between FEL pulses and the synchronized pump laser, influencing the accuracy of ultrafast time-resolved measurements. To address this issue, timing tools have been developed to measure these jitters and reindexed each pump-probe signal after measurement. This success enables ultrafast X-ray diffraction (UXRD) to be first realized, and a systematic study of Peierls distorted materials is demonstrated. In addition, the high flux of FEL pulses enables Fourier transform inelastic X-ray scattering (FT-IXS) method, which can extract the phonon dispersion curve of the entire Brillouin zone by performing the Fourier transform on the measured momentum dependent coherent phonon scattering signals, even when the system is in a non-equilibrium state.</sec><sec>The UXRD is typically used to study ultrafast lattice dynamics, which requires hard X-ray wavelengths. In contrast, time resolved resonant elastic X-ray scattering (tr-REXS) in the soft X-ray regime has become a standard method of investigating nano-sized charge and spin orders in correlated quantum materials on an ultrafast time scale.</sec><sec>In correlated quantum materials, the interplay between electron dynamics and lattice dynamics represents another important research direction. In addition to Zhi-Xun Shen's successful demonstration of the combined tr-ARPES and UXRD method at SLAC, this paper also reports the attempts to integrate UXRD with resonant X-ray emission spectroscopy (RXES) for the simultaneous measurement of electronic and lattice dynamics.</sec><sec>Resonant inelastic X-ray scattering (RIXS) is a powerful tool for studying elementary and collective excitations in correlated quantum materials. However, in FEL-based soft X-ray spectroscopy, the wavefront tilt introduced by the widely used grating monochromators inevitably stretches the FEL pulses, which degrades the time resolution. Therefore, the new design at FEL beamlines adopts low line density gratings with long exit arms to reduce pulse stretch and achieve relatively high energy resolution. For example, the Heisenberg-RIXS instrument at the European XFEL achieves an energy resolution of 92 meV at the Cu <i>L</i><sub>3</sub> edge and approximately 150 fs time resolution.</sec><sec>In recent years, scientists at SwissFEL’s Furka station have drawn inspiration from femtosecond optical covariance spectroscopy to propose a new method of generating two-dimensional time-resolved resonant inelastic X-ray scattering (2D tr-RIXS) spectra. This method involves real-time detection of single-shot FEL incident and scattered spectra, followed by deconvolution calculation to avoid photon waste and wavefront tilt caused by monochromator slits. The SQS experimental station at European XFEL, built in 2023, features a 1D-XUV spectrometer that utilizes subtle variations in photon energy absorption across the sample to induce spatial energy dispersion. Using Wolter mirrors, it directly images spatially resolved fluorescence emission from the sample onto the detector to generate 2D tr-RIXS spectra without the need for deconvolution. However, this design is limited to specific samples. Currently, the S<sup>3</sup>FEL under designing has a novel 2D tr-RIXS instrument that uses an upstream low line density grating monochromator to generate spatial dispersion of the beam spot, allowing the full bandwidth of SASE to project spatially dispersed photon energy onto the sample. Subsequently, an optical design similar to the 1D-XUV spectrometer will be employed to achieve 2D tr-RIXS spectra, thereby expanding the applicability beyond specific liquid samples. These new instruments are designed to minimize pulse elongation by fully utilizing SASE’s full bandwidth, approaching Fourier-transform-limited RIXS spectra in both time and energy resolution.</sec><sec>Nonlinear X-ray optical techniques, such as sum-frequency generation (SFG) and second-harmonic generation, are adapting to X-ray wavelengths and opening up new avenues for detecting elementary excitations. The X-ray transient grating spectroscopy extends its capabilities to studying charge transport and spin dynamics on an ultrafast timescale. The future development of these scattering methods provides unique opportunities for detecting dynamical events in various systems, including surface and interface processes, chirality, nanoscale transport, and so-called multidimensional core-level spectroscopy.</sec>

Formation and properties of spatially inhomogeneous plasma density gratings.

Volume plasma density gratings receive increasing interest since, compared to solid-state optical media, they posses significantly higher damage thresholds. The gratings are produced by counterpropagating laser pulses in underdense plasma. When analyzing their optical properties, usually they are assumed to be homogeneous in space. The latter assumption, however, breaks down, especially when the gratings are produced by short high-power laser pump pulses. Then, generically the plasma grating posses an inhomogeneous envelope which results from the superposition of the pump pulses envelopes. The present paper discusses the effect of grating inhomogeneity on reflection and transmission of probe pulses. A Gaussian plasma density grating becomes an apodized grating which offers significant improvement over homogeneous gratings due to side-lobe suppression while maintaining reflectivity and a narrow bandwidth. On the other hand, the reflected probe pulses receive a chirp which depends on the spatial scale. For a Gaussian grating a cubic spectral phase appears. Numerical particle-in-cell simulations are supported by theoretical analysis based on coupled mode equationsas well as an effective medium approach.

Measuring carrier diffusion in MAPbI3 solar cells with photocurrent-detected transient grating spectroscopy.

Conventional time-of-flight methods can be used to determine carrier mobilities for photovoltaic cells in which the transit time between electrodes is greater than the RC time constant of the device. To measure carrier drift on sub-ns timescales, we have recently developed a two-pulse time-of-flight technique capable of detecting drift velocities with 100-ps time resolution in perovskite materials. In this method, the rates of carrier transit across the active layer of a device are determined by varying the delay time between laser pulses and measuring the magnitude of the recombination-induced nonlinearity in the photocurrent. Here, we present a related experimental approach in which diffractive optic-based transient grating spectroscopy is combined with our two-pulse time-of-flight technique to simultaneously probe drift and diffusion in orthogonal directions within the active layer of a photovoltaic cell. Carrier density gratings are generated using two time-coincident pulse-pairs with passively stabilized phases. Relaxation of the grating amplitude associated with the first pulse-pair is detected by varying the delay and phase of the density grating corresponding to the second pulse-pair. The ability of the technique to reveal carrier diffusion is demonstrated with model calculations and experiments conducted using MAPbI3 photovoltaic cells.

Population density gratings produced by a pair of nonharmonic unipolar rectangular attosecond pulses in a resonant medium

Recently, the possibility of obtaining non-harmonic unipolar electromagnetic pulses with a specific electric field strength’s dependence on time (e.g. a rectangular pulse) has been actively discussed in optics. Unipolar pulses have a nonzero electric area and a wide spectrum: from zero frequency up to the visible region. This could open up wide application of such pulses, for example, for faster and more efficient control of the quantum systems’ properties with a high temporal resolution compared to conventional bipolar multicycle pulses. In this paper, based on an approximate solution of the time dependent Schrödinger equation and a numerical solution of the equation system for the density matrix, we show the possibility of creating electromagnetically induced population density gratings in an atomic medium using a pair of unipolar rectangular attosecond light pulses that do not overlap in the medium. The formation of such gratings can be explained on the basis of the concept of ‘interference’ of electric pulse areas, recently introduced into optics.

Depolarization of intense laser beams by dynamic plasma density gratings

Abstract As a typical plasma-based optical element that can sustain ultra-high light intensity, plasma density gratings driven by intense laser pulses have been extensively studied for wide applications. Here, we show that the plasma density grating driven by two intersecting driver laser pulses is not only nonuniform in space but also varies over time. Consequently, the probe laser pulse that passes through such a dynamic plasma density grating will be depolarized, that is, its polarization becomes spatially and temporally variable. More importantly, the laser depolarization may spontaneously take place for crossed laser beams if their polarization angles are arranged properly. The laser depolarization by a dynamic plasma density grating may find application in mitigating parametric instabilities in laser-driven inertial confinement fusion.

Al/Mo/SiC multilayer diffraction gratings with broadband efficiency in the extreme ultraviolet.

Al/Mo/SiC periodic and aperiodic multilayers were optimized and deposited on high groove density gratings to achieve broadband efficiency in the extreme ultraviolet (EUV). Grating efficiencies were measured by monochromatic synchrotron radiation under 5° and 45° incident angles in the wavelength ranges 17-25 nm and 22-31 nm, respectively. We study the influence of the number of deposited periods on the initial trapezoidal profile and the EUV diffraction efficiency. We propose models of periodic and aperiodic coatings based on a combination of characterizations and compare rigorous coupled-wave analysis (RCWA) simulations with experimental data. We demonstrate the possibility to select the optimal balance between peak efficiency and bandwidth by adjusting the number of periods in the case of periodic multilayer grating. We also report unprecedented broadband diffraction efficiency with an Al/Mo/SiC aperiodic multilayer grating.

Population density gratings creation and control in resonant medium by half-cycle terahertz pulses

Electromagnetically induced gratings (EIG) are created by standing-wave laser field in resonant media. Such gratings can be also created by few-cycle electromagnetic pulses counter-propagating in the medium via coherent Rabi oscillations of atomic inversion. In this case, instantaneous cross-section of the pulses in the medium is not necessary for grating formation. In this paper, we revise our recent results in study of such grating formation and their control by few-cycle pulses coherently propagating in a resonant medium. We demonstrate the grating formation and their control in three-level medium excited by three subcycle THz pulses.

Dynamical density wave order in an atom–cavity system

We theoretically and experimentally explore the emergence of a dynamical density wave (DW) order in a driven dissipative atom–cavity system. A Bose–Einstein condensate is placed inside a high finesse optical resonator and pumped sideways by an optical standing wave. The pump strength is chosen to induce a stationary superradiant checkerboard DW order of the atoms stabilized by a strong intracavity light field. We show theoretically that, when the pump is modulated with sufficient strength at a frequency ω d close to a systemic resonance frequency ω >, a dynamical DW order emerges, which oscillates at the two frequencies ω > and ω < = ω d − ω >. This order is associated with a characteristic momentum spectrum, also found in experiments in addition to remnants of the oscillatory dynamics presumably damped by on-site interaction and heating, not included in the calculations. The oscillating density grating, associated with this order, suppresses pump-induced light scattering into the cavity. Similar mechanisms might be conceivable in light-driven electronic matter.

Population difference gratings created on vibrational transitions by nonoverlapping subcycle THz pulses

We study theoretically a possibility of creation and ultrafast control (erasing, spatial frequency multiplication) of population density gratings in a multi-level resonant medium having a resonance transition frequency in the THz range. These gratings are produced by subcycle THz pulses coherently interacting with a nonlinear medium, without any need for pulses to overlap, thereby utilizing an indirect pulse interaction via an induced coherent polarization grating. High values of dipole moments of the transitions in the THz range facilitate low field strength of the needed THz excitation. Our results clearly show this possibility in multi-level resonant media. Our theoretical approach is based on an approximate analytical solution of time-dependent Schrödinger equation (TDSE) using perturbation theory. Remarkably, as we show here, quasi-unipolar subcycle pulses allow more efficient excitation of higher quantum levels, leading to gratings with a stronger modulation depth. Numerical simulations, performed for THz resonances of the H_20 molecule using Bloch equations for density matrix elements, are in agreement with analytical results in the perturbative regime. In the strong-field non-perturbative regime, the spatial shape of the gratings becomes non-harmonic. A possibility of THz radiation control using such gratings is discussed. The predicted phenomena open novel avenues in THz spectroscopy of molecules with unipolar and quasi-unipolar THz light bursts and allow for better control of ultra-short THz pulses.

Growth, saturation, and collapse of laser-driven plasma density gratings

The plasma density grating induced by intersecting intense laser pulses can be utilized as optical compressors, polarizers, waveplates, and photonic crystals for the manipulation of ultra-high-power laser pulses. However, the formation and evolution of plasma density grating are still not fully understood as linear models are adopted to describe them usually. In this paper, two theoretical models are presented to study the formation process of plasma density grating in the nonlinear stages. In the first model, an implicit analytical solution based on the fluid equations is presented, while in the second model, a particle-mesh method is adopted. It is found that both models can describe the plasma density grating formation at different stages, well beyond the linear growth stage. More importantly, the second model can reproduce the phenomenon of ion “wave-breaking” of plasma density grating, which eventually induces the saturation and collapse of plasma density grating. Using the second model, the saturation time and maximum achievable peak density of plasma density grating are obtained as functions of laser intensity and plasma density, which can be applied to estimate the lifetime and capability of plasma density grating in experiments. The results from these two newly developed models are verified using particle-in-cell simulations.

Relaxation Polarization Dependence of Circular Vector Gratings in Azobenzene Glassy Molecular Films

Holographic grating recording and relaxation is studied in different azobenzene molecular glassy films by circularly orthogonally polarized 532 nm laser beams L and R. The readout was made by circularly polarized (R or L) 632.8 nm laser beam. Sandwich-type samples (glass-film-glass) were also studied. Maximum diffraction efficiency of 81% has been achieved in sandwich-type AR-173 film. The following relaxation features have been found: after reaching diffraction efficiency (DE) maximum no DE decay took place; DE read out by R-polarized beam was always higher than that by L-polarized beam; in sandwich-type samples DE decayed until zero when read out by R-polarization whereas DE was zero when read out by L-polarization. 50% relaxation times varied from 4 to 44 minutes, and they mainly decreased when grating period was increased. The observed relaxation peculiarities can be understood if one assumes that volume birefringence grating (VBG) is recorded followed by volume density grating (VDG) and surface relief grating (SRG) recording. R-polarization "feels" all gratings whereas L-polarization only VDG and SRG. At large exposures VDG and SRG dominate. These results confirm the conclusion made by J.Mikelsone in her 2018 PhD thesis that birefringence grating recording in azobenzene materials is a neccessary condition for SRG appearance.

Analytical solution of phototransport problem under the presence of a small-signal photocurrent based on method of weighted residuals

The nonlinear phototransport differential equations are analytically solved for a small-signal steady-state photocarrier grating in the presence of external electric field using the method of weighted residuals. Two-term ansatz sinusoidal solution is initially considered as approximate and is then corrected to get the optimum derived expressions for density grating of photoelectrons and photoholes. Both the approximate and corrected expressions of the derived grating amplitudes of the two photocarriers are employed to find corresponding expressions of the coefficient β. The expressions of β are examined by re-producing the field-dependent experimental data of β obtained at room temperature from steady-state photocarrier grating (SSPG) technique for a hydrogenated nanocrystalline silicon sample. The fittings to experimental data are obtained using physical transport quantities as adjustable parameters. We believe that the average value of ambipolar diffusion length of 212 nm with an uncertainty of ~ 6%, obtained from this analysis, which is close to the experimental error of the SSPG measurements, is acceptable. The excess photoelectron and photohole densities in addition to electric field grating are demonstrated. The current analysis reveals that the spatial electric field grating exhibits an increase with increasing applied field and until a certain point where it starts slowly falling off at high values of applied field. This fall off becomes shallower with increasing grating periods.

Селективное возбуждение и создание инверсной населенности в квантовых системах с помощью униполярных аттосекундных и терагерцовых импульсов

The possibility of selective population of the energy levels of quantum systems was studied using a single unipolar subcycle pulse and a pair of pulses. Selective population of quantum levels is clearly illustrated based on the numerical solution of the system of equations for the density matrix of a three-level medium interacting with a pair of subcycle attosecond and terahertz pulses. The possibility of creating an population inversion in a three-level medium is shown using a pair of such pulses. The dynamics of population density gratings in a three-level medium is studied at the impact on the system of a pair of large-amplitude Gaussian pulses. If in a weak field the shape of the gratings is harmonic, according to analytical calculations performed according to perturbation theory, then in in the case of a strong field, the spatial profile of the gratings can differ from the sinusoidal one and has complex spike structure.

Plasma volume holograms for focusing and mode conversion of ultraintense laser pulses.

Beating of a broad laser reference beam with a quite general focused object beam inside a plasma volume generates a dynamic plasma hologram. Both beams may be of moderate intensity. The volume hologram can be read out by an ultraintense main beam (of similar structure as the reference beam) producing an object beam replica. For the latter, intensity in the focus may become extremely large. As an application, the possibility of a read-out focused Gaussian laser pulse with intensity of several 10^{19}W/cm^{2} in focus is shown by three-dimensional numerical simulations. Besides the focusing possibility, the hologram may also act as a mode converter for high-intensity laser pulses. Generating a plasma hologram with a focused Laguerre-Gaussian object beam results in a staggered plasma density grating, allowing the production of high-intensity vortex beam replica.

Multimode collective scattering of light in free space by a cold atomic gas

We have studied collective recoil lasing by a cold atomic gas, scattering photons from an incident laser into many radiation modes in free space. The model consists of a system of classical equations for the atomic motion of N atoms, where the radiation field has been adiabatically eliminated. We performed numerical simulations using a molecular dynamics code, Pretty Efficient Parallel Coulomb Solver or PEPC, to track the trajectories of the atoms. These simulations show the formation of an atomic density grating and collective enhancement of scattered light, both of which are sensitive to the shape and orientation of the atomic cloud. In the case of an initially circular cloud, the dynamical evolution of the cloud shape plays an important role in the development of the density grating and collective scattering. The ability to use efficient molecular dynamics codes will be a useful tool for the study of the multimode interaction between light and cold gases.

Optimized highly efficient multilayer-coated blazed gratings for the tender X-ray region.

The optimized design of multilayer-coated blazed gratings (MLBG) for high-flux tender X-ray monochromators was systematically studied by numerical simulations. The resulting correlation between the multilayer d-spacing and grating blaze angle significantly deviated from the one predicted by conventional equations. Three high line density gratings with different blaze angles were fabricated and coated by the same Cr/C multilayer. The MLBG with an optimal blaze angle of 1.0° showed a record efficiency reaching 60% at 3.1 keV and 4.1 keV. The measured efficiencies of all three gratings were consistent with calculated results proving the validity of the numerical simulation and indicating a more rigorous way to design the optimal MLBG structure.

A Phase Switch for Electromagnetically Induced Gratings in a Medium with Λ Atoms

We have theoretically studied the possibility of using the phenomenon of phase switching of coherent population trapping for creating a switch of light propagation direction in electromagnetically induced gratings in a medium with Λ-atoms. The permissible region of this effect application is determined and the parameters are found which ensure the obtaining of a high-efficiency scheme of the spatial redistribution of probing field intensity on atomic density gratings.

Фазовый переключатель для электромагнитно индуцированных решеток в среде с -атомами

The possibility to use phasic effect to turn off a coherent population trapping for creating a switcher of the light propagation direction in an electromagnetically induced gratings in the medium with Λ-atoms is studied theoretically in this paper. The allowable scope of the effect is determined. The parameters that allowed to obtain a highly efficient scheme of spatial redistribution of the intensity of the probe field on atomic density gratings were obtained and studied.