Amplitude Gratings Research Articles

Traveling Wave Amplification in Stationary Gratings.

We show that a grating amplitude stationary in space but oscillating in time can be modeled as independent gratings traveling in opposite directions, interacting almost exclusively with waves traveling in the same direction. We reproduce the key features of traveling gratings: Amplification, field compression, and photon production are evident when the local wave speed equals the grating velocity. We speculate that these stationary but oscillating gratings may prove easier to realize experimentally than traveling gratings.

Multiplexing of color images by theta modulation with laser beam in amplitude grating

Multiplexing of color images by theta modulation with laser beam in amplitude grating

Manufacture of phase diffraction gratings by acid immersion

In this work, the manufacturing, characterization, and optical testing of phase diffraction gratings is performed. The fabrication is carried out in a very simple way: by immersion of a common amplitude diffraction gratings on acid and a posterior chemical procedure. The process makes it achievable for almost any scientist, since expensive equipment is not required. We have tested three different acids and evaluated the engraving depth (phase retardation) in terms of the immersion time. With this analysis, phase diffraction gratings with the desired phase delay could be manufactured. The quality of the gratings has been evaluated by means of their profiles and histograms of the surface, using confocal microscopy. To conclude, we have measured the near-field behavior of one of the phase gratings and compared it with that obtained analytically, showing high agreement.

Simulation of the spatial distribution of scattered light under illumination of a resonant diffraction grating with structured light

In this paper, a comparative theoretical analysis and numerical simulation of the operation of various types of diffraction gratings in the far field is carried out using a Fourier transform. In more detail is discussed the spatial spectrum of binary amplitude gratings, including the diffraction patterns in the far field and in the focal plane and while taking into account variations in the fill-factor. When analyzing characteristics of experimentally created halide perovskite resonant gratings, the influence of the illuminating beam type on the formation of the first three diffraction orders is considered.

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.

Analysis of laser-induced transient population gratings by different types of exciting pulse

Motivated by atomic response to different initial coherent optical fields, we comparatively studied transient population grating (TPG) induced by successive pulse train. Time delay and pump pulse duration dependence of TPG is achieved by numerically solving the density matrix equations. Results reveal that the creation and erasure of TPG is possible by choosing the appropriate pulse parameters, which is illustrated by Bloch sphere model and quantitative validation. To obtain desired large grating amplitude for rectangular pulse, the allowed pulse duration can be extended to one order wider than that of Gaussian pulse. Population grating can be erased to near zero by a third pulse with time delay by an odd multiple of half the pulse width, and it also can be erased further to recover atom assembly back to the initial state by a fourth pulse with time delay equal to an integer multiple of pulse width. Atomic behaviors excited by different types of pulse presented here may be significant to manipulate TPG during coherent light-matter interaction.

Error analysis and realization of a phase-modulated diffraction grating used as a displacement sensor.

A grating-based interferometric cavity produces coherent diffraction light field in a compact size, serving as a promising candidate for displacement measurement by taking advantage of both high integration and high accuracy. Phase-modulated diffraction gratings (PMDGs) make use of a combination of diffractive optical elements, allowing for the diminishment of zeroth-order reflected beams and thus improving the energy utilization coefficient and sensitivity of grating-based displacement measurements. However, conventional PMDGs with submicron-scale features usually require demanding micromachining processes, posing a significant challenge to manufacturability. Involving a four-region PMDG, this paper establishes a hybrid error model including etching error and coating error, thus providing a quantitative analysis of the relation between the errors and optical responses. The hybrid error model and the designated process-tolerant grating are experimentally verified by micromachining and grating-based displacement measurements using an 850 nm laser, confirming the validity and effectiveness. It is found the PMDG achieves an energy utilization coefficient (the ratio of the peak-to-peak value of the ±1st order beams to the 0th-order beam) improvement of nearly 500% and a four-fold reduction in 0th-order beam intensity compared with the traditional amplitude grating. More importantly, this PMDG maintains very tolerant process requirements, and the etching error and coating error can be up to 0.5 µm and 0.6 µm, respectively. This offers attractive alternatives to the fabrication of PMDGs and grating-based devices with wide process compatibility. This work first systematically investigates the influence of fabrication errors and identifies the interplay between the errors and the optical response for PMDGs. The hybrid error model allows further avenues for the fabrication of diffraction elements with practical limitations of micromachining fabrication.

A Method to Improve Mounting Tolerance of Open-Type Optical Linear Encoder.

Accuracy becomes progressively important in the wake of development in advanced industrial equipment. A key position sensor to such a quest is the optical linear encoder. Occasionally, inappropriate mounting can cause errors greater than the accuracy grade of the optical linear encoder itself, especially for open-type optical linear encoders, where the mounting distance between the reading head and main scale must be accurately controlled. This paper analyzes the diffraction fields of a traditional scanning reticle made by amplitude grating and a newly designed combined grating; the latter shows a more stable phase in mathematical calculation and simulations. The proposed combined gratings are fabricated in a laboratory and assembled into the reading heads. The experimental results indicate that the mounting tolerance between the reading head and the main scale of the optical linear encoder can be improved.

Optical vortex beam controlling based on fork grating stored in a dye-doped liquid crystal cell.

In this paper, we investigate the generation and controlling of the optical vortex beam using a dye-doped liquid crystal (DDLC) cell. The spatial distribution of the quasi-sinusoidal orientation of the liquid crystal molecules creates a quasi-sinusoidal phase grating (PG) in the DDLC cell. Depending on the incident light pattern, Trans to Cis photoisomerization of the dye molecules affects the orientation of the liquid crystal molecules. To do so, an amplitude fork grating (FG) is used as a mask, and its pattern is stored in the cell by a pattern printing method as the PG. One of the particular features of the stored grating in the cell is its capability in the diffraction efficiency controlled by the applied electric field. The results show, based on the central defect in the FG pattern, the diffracted probe beam in different orders is optical vortices. As a new technique, this type of stored pattern acts like an amplitude grating but according to the results, its structure is in fact a PG. This technique leads to the vortex beam switching capability by applying an electric field to the cell. The results show that by applying 22V, all the diffraction orders vanish. Meanwhile, the vortex beams reappear by removing the applied voltage. The diffraction efficiency of the vortex beams as well as its generation dependency on the polarization of the incident beam studied. The maximum efficiency of the first diffraction order for linear polarized incident beam was obtained at 0V, about 8%. Based on the presented theory, a simulation has been done which shows the Cis form of the dye molecules has been able to change the angle of LC molecules on average about 12.7°. The study of diffracted beam profiles proves that they are electrically controllable vortex beams.

Simulating spatiotemporal dynamics of ultra-intense ultrashort lasers through imperfect grating compressors.

The upcoming 100 Petawatt (PW) laser is going to provide a possibility to experimentally study vacuum physics. Pulse compression and beam focusing, which can be affected by the spatiotemporal coupling, are two key processes of generating a 100 PW laser and then determine whether its physical objective can be achieved or not. We improved our previous model of the spatiotemporal coupling where only the grating wavefront error and the output optical field of a common compressor configuration were included, and in the improved model, the grating amplitude modulation, the spatio-spectral clipping, and the optical field inside the compressor were added. By using it, we theoretically investigated the spatiotemporal dynamics of an ultra-intense ultrashort laser passing through an imperfect grating compressor for different cases, especially the spatio-temporal/spectral coupling and the on-target intensity variation induced by the phase and amplitude modulation at different grating positions in two different compressor configurations. This study is of importance for both engineering development and physical application of the upcoming Exawatt-class laser.

Polarization Properties of the Electrically Controlled Twist-Planar Liquid Crystal Di.raction Structure

The properties of the designed anisotropic diffraction structures based on the spatially structured electrically-controlled liquid crystal elements have been studied. Such a di.raction structure represents interchanging layers of a nematic liquid crystal with planar and twist orientations of the director. It is formed when a photosensitive polymer is subjected to the e.ect of polarized ultraviolet radiation through a photolithographic mask. It is shown that increase in voltages leads to transformations of the liquid crystal structure. At minor voltages the diffraction structure may be considered as two amplitude gratings with orthogonal polarizations at the output. At the voltage associated with the broken Mauguin condition (optical threshold of the twist effect) the amplitude-to-phase transformation of the di.raction structure takes place and its diffraction e.ciency becomes higher. The proposed theoretical model enables one to explain the relationship between di.raction characteristics of a di.raction element and applied voltage or polarization of light. A good agreement of theoretical and experimental results is demonstrated.

Regular mode-hopping dynamics in Erbium-doped ring fiber laser with saturable absorber

We report on transition from single longitudinal mode operation to regular mode-hopping dynamics in Erbium-doped ring fiber laser with a saturable absorber. The laser can be switched from wavelength stabilization (with stability time of up to tens of seconds) to a wavelength self-sweeping regime (in the range of about 20 pm near 1560 nm) with an increase of the pump power and with elongation of the absorbing fiber length. The observed effect is associated with an interplay of amplitude and phase dynamic gratings. Additionally, a continuous wave single-frequency self-sweeping operation in an Erbium-doped fiber laser is demonstrated for the first time. The results are useful both for single-frequency and self-sweeping laser development.

Spectral analysis and correction of the structure of computer-generated fan-out Dammann gratings at their fabrication

A technique for quickly finding the optimal time of liquid etching the amplitude masks of two-dimensional Dammann gratings, the structure of which is synthesized by direct laser writing in a polar coordinate system, is studied theoretically and experimentally. Thin chromium films are used as the recording material for laser writing, which are oxidized during laser writing and form an amplitude mask during their liquid etching (when using the thermochemical technology for their processing). The change in the etching time here occurs in the form of etching and displacement of the edges of the exposed zones. To find the optimal etching time for chromium films, it is proposed to use a procedure of measuring the spectra of amplitude gratings, by quick operational measurement and analysis of the intensity distribution of high diffraction orders, and by minimization of the root-mean-square deviation of these intensities. It is shown that higher diffraction orders in the spectra of binary-amplitude structures correlate well with the same orders of binary-phase structures. This conclusion can be effectively used to determine the moment when the optimum zone size is reached during liquid etching.

Analysis of circular gratings as image plane coronagraph filters

Coronagraphy is an efficient technique for identifying and characterizing extra-solar planets orbiting in the habitable zone of their parent star. An important family of coronagraphs is based on amplitude or phase filters placed at an intermediate image plane of the optical system, spreading starlight outside of the so-called “Lyot stop” located at the exit pupil plane of the instrument. This article explores the potential of circular amplitude and phase gratings employed as image plane coronagraph filters. It presents a theoretical analysis of the simplest case of an amplitude circular grating and introduces an inversion paradigm with respect to classical Lyot coronagraph, by exchanging its image and pupil masks. Various types of circular gratings are considered and their performance is evaluated with the help of numerical simulations. The most promising solutions are presented and discussed. The main conclusion is that high attenuation ratios of the parent star are feasible, provided that the system is properly optimized with a Lyot stop especially tailored to the grating filter.

Accurate Morphology-Related Diffraction Behavior of Light-Induced Surface Relief Gratings on Azopolymers

Holographic relief gratings can be fabricated directly on the surface of azobenzene-containing materials (or simply azomaterials) without additional development steps. Despite often being described to have ideal sinusoidal profiles, the developing surface morphology in large amplitude gratings can affect the light distribution of the writing interferogram, causing profile deformations and deviations in the expected diffraction behavior. In this work, we characterize the temporal evolution of the surface relief grating (SRG) morphology fabricated by means of interference lithography on azopolymer films, quantitatively relating the results of a Fourier analysis of their surface profiles to the accurate measurement of efficiencies in the transmitted diffraction orders. A reliable surface structuration dynamics is empirically extracted from the analysis and used to formulate a simple but detailed diffraction model that, within the scalar diffraction theory, exhaustively describes the diffraction behavior of real SRGs without the need of complex rigorous electromagnetic theories. Our results add a deeper insight in the quantitative description of the morphology and the diffraction behavior of SRGs, which can contribute to their adoption for operating high-performance, reconfigurable, compact, and lightweight diffractive optical devices.

Low-coherence quantitative differential phase-contrast microscopy using Talbot interferometry.

This paper presents a simple, cost-efficient, and highly stable quantitative differential phase-contrast (PC) microscopy based on Talbot interferometry. The proposed system is composed of an optical microscope coupled with a pair of Ronchi amplitude gratings that utilizes a light-emitting diode as a low temporal coherence light source. The quantitative differential PC images of the microscopic transparent samples are reconstructed by analyzing the deformation of moiré patterns using a phase-shifting procedure. Low temporal coherence leads to eliminating speckle noise and undesirable interferences to obtain high-quality images. The spatial phase stability of the system is investigated and compared to two other common-path interferometers. Additionally, the performance of the method is verified by the experimental results of a standard resolution test target and phase biological samples.

Влияние хлоридов на спектральные свойства серебряных ионообменных слоев фото-термо-рефрактивного стекла

The effect of chlorine on the spectral properties of silver nanoparticles in the ion-exchanged layers of photo-thermo-refractive glass was studied. It was shown that silver nanoparticles were precipitated only in the UV-irradiated region of the ion-exchanged chlorine-free photo-thermo-refractive glass and refractive index of the irradiated and non-irradiated was the same. It was founded that UV irradiation and subsequent thermal treatment resulted in a growth of NaF nanocrystals on AgCl/NaCl shells formed on the silver nanoparticles in the irradiated ion-exchanged chloride photo-thermo-refractive glass. The refractive index contrast of the irradiated and non-irradiated areas of photo-thermo-refractive glass with chlorine was achieved Δn=-3•10-3. Results of the study demonstrate that it is possible to record the amplitude gratings in the ion-exchanged layers of chlorine-free photo-thermo-refractive glass, and to record the amplitude-phase gratings in the ion-exchanged layers of chloride photo-thermo-refractive glass.

Near field diffraction of steel tape gratings illuminated with finite-size incoherent sources

Steel tape gratings are diffraction gratings engraved on a steel substrate, whose slits are commonly manufactured by laser ablation. They behave as amplitude diffraction gratings, since the engraved slits act as strong scatters. Here, we extend previous works to the case of finite-size illumination sources, as they are used in applications such as optical encoders, where LEDs are commonly used as illumination sources. We obtain an analytical formulation for the near field behavior of this kind of gratings. When the light source increases its size, a decreasing in the contrast of the self-images is added to the effect of the surficial roughness. The agreement between analytical and numerical results is high, validating the obtained formulation. Besides, these results could be crucial in metrological applications in which steel tape gratings or other diffractive optical elements engraved on steel substrates are used, providing with a theoretical formalism to analyze the near field propagation of light after reflecting in them.

High-resolution image multiplexing using amplitude grating for remote sensing applications

High-resolution images are essential in many remote sensing applications such as weather prediction, deforestation, crop monitoring, land mapping, urban growth, etc. In these applications, it is necessary to use multiple high-resolution images for proper analysis. These images carry a lot of information; therefore, multiplexing plays an important role for efficient storage of the images. Hence, we provide an idea of multiplexing high-resolution images using amplitude grating. Initially, images are modulated with variable spatial frequencies and orientation angles followed by the addition of modulated spectrums to form a single spectrum plane. The resultant spectrum plane is filtered before transmission to eliminate noise. To optimize storage space, only a part of the filtered spectrum is transmitted. A pixel intensity graph is plotted to identify the location of maximum information of the images, which is required during the retrieval process. The quality of the output images is analyzed by peak signal-to-noise ratio, structural similarity index measurement, and correlation coefficient methods. The entire work is done by simulation software, and we prove that our proposed multiplexing method is suitable for efficient storage of high-resolution images in remote sensing applications.

Moiré microstructure generated binary amplitude gratings for suppression of high diffraction orders

We propose 2D gratings with 2D sinusoidal-like transmittance for spectral analysis in a wide wavelength range. Our design deploys the concept of the multiplicative superimposition of two mutually inclined or orthogonally crossed 1D binary amplitude gratings with appropriately selected opening numbers. In result the trapezoidal transmittance function without the 3rd and even harmonics is obtained in two perpendicular directions corresponding to the so-called subtractive and additive moiré patterns. The distance between main diffraction orders, i.e., -1, 0 and +1 in both directions is easily controlled by adjusting the angle between component grating lines. The moiré microstructure acting as 2D diffraction grating comprises 4 sided parallelogram holes up to the angle of 90 degrees for which they become rectangles. Diffraction efficiencies and free-standing parameters of our grating and the solutions reported in the literature, i.e., the inclined rectangular aperture grating (IRAG) and the grating with hexagonal holes are calculated and compared. Additionally, the methods of design for the literature reported gratings which start from square or rectangular shape apertures are introduced for the sake of comprehensive treatment of gratings with suppressed high diffraction orders. Design considerations are corroborated by the moiré Fourier spectra numerical simulations, their visualizations and experimental works.