Amplitude Gratings Research Articles

Common-path intrinsically achromatic optical diffraction tomography.

In this work we propose an open-top like common-path intrinsically achromatic optical diffraction tomography system. It operates as a total-shear interferometer and employs Ronchi-type amplitude diffraction grating, positioned in between the camera and the tube lens without an additional 4f system, generating three-beam interferograms with achromatic second harmonic. Such configuration makes the proposed system low cost, compact and immune to vibrations. We present the results of the measurements of 3D-printed cell phantom using laser diode (coherent) and superluminescent diode (partially coherent) light sources. Broadband light sources can be naturally employed without the need for any cumbersome compensation because of the intrinsic achromaticity of the interferometric recording (holograms generated by -1st and +1st conjugated diffraction orders are not affected by the illumination wavelength). The results show that the decreased coherence offers much reduced coherent noise and higher fidelity tomographic reconstruction especially when applied nonnegativity constraint regularization procedure.

Frequency Conversion of Lasers in a Dynamic Plasma Grating

When a dynamic medium in which the laser propagates changes its refractive index in time, the laser changes its frequency while keeping its wavevector unchanged to fullfil the dispersion relation. This is usually applied to upshift the laser frequency with ionizing plasma. We propose an alternative technique to modify light frequency. A transient plasma grating can be generated by two identical counterpropagating laser pulses via strongly coupled stimulated Brillouin scattering (SC SBS). The rapid evolution of the plasma grating affects the wave-dispersion relation and a band gap develops around the laser frequency, dependent on the grating amplitude. As a result, the lasers convert their frequency downward to the low edge of the band gap, while a free-traveling laser converts its frequency to both the upper and lower edge of the band gap. Depending on the considered setup, practical applications of this technique include either laser-frequency downshift or spectral splitting can be exploited. The former can be used for Raman amplification in plasma and the latter for dual-color x-ray generation by Thomson and/or Compton scattering.

Diffraction by perfect and imperfect amplitude grating.

The paper presents theoretical formulas for calculation of diffraction by perfect infinite and finite amplitude gratings with Fresnel and Fraunhofer approximations. Further, general formulas for diffraction by an imperfect diffraction grating are derived where edges of the grating are described with general harmonic functions. Such a formalism provides enough power to accurately characterize imperfections of diffraction gratings, and it serves as a simple tool for a solution to a diffraction problem.

Efficient characterization of optical vortices via diffraction from parabolic-line linear gratings

The diffraction from a linear grating having a quadratic curvature on its lines is proposed for vortex beam characterization. Three types of transmission functions are considered for the gratings, including pure amplitude, pure phase, and hybrid amplitude and phase profiles. The first-order diffraction of the vortex beam through such gratings is only a set of elongated intensity spots. The number of spots determines the value of the topological charge (TC), and the sign of the TC can be distinguished with the elongation (and rotation) direction of the spots. This method is effective because over a given diffraction order, all of the energy of the beam transfers into the bright bar-like spots. Another advantage of the method is its ease of use, because it is not sensitive to the relative location of the beam axis and the grating center. Using a spatial light modulator, we provide different hybrid amplitude and phase linear gratings with a quadratic curvature on their lines and demonstrate the effectiveness of the proposed method experimentally. Also, the same justification was done in the diffraction of vortex beams from printed pure amplitude gratings. We have also investigated the effect of lateral shearing between the amplitude and phase parts of the hybrid grating on the resulted diffraction pattern. It is shown that for given values of lateral shear, one of the first-order diffraction patterns is eliminated, and the intensity of the other one is maximized. Finally, we present the key results of the diffraction of optical vortices from annular amplitude and phase gratings and from phase objects having linearly increasing phase functions along the radial direction. It is shown that the diffraction of optical vortices only from the parabolic-line linear gratings is insensitive to the off-axis value of the beam and grating centers.

Single-chip holographic beam steering for lidar by a digital micromirror device with angular and spatial hybrid multiplexing.

A digital micromirror device (DMD) based holographic beam steering technique is reported that multiplexes fine-steering binary amplitude gratings with a coarse-steering programmable blazed grating. The angular spatial light modulation (ASLM) technique encodes the spatial pattern of the binary amplitude grating at the same plane as the angular modulation set by a phase map of the DMD-based beam steering technique. The beam steering technique is demonstrated at 532 nm and implemented into a 905 nm lidar system. The results of the lidar system tests are presented, achieving a 44° field-of-view, 0.9°×0.4° (H×V) angular resolution, 1 m max distance, 1.5 kHz sampling, and 7.8 FPS video. Scalability techniques are proposed, including max distance increases to over 100 m.

Two-wave mixing in erbium-doped-fibers with spectral-hole burning at 77K

Experimental results on effective two-wave mixing (TWM) via dynamic population gratings in saturable erbium doped fibers (EDFs) at liquid nitrogen temperature (77 K) are reported. It is shown that formation of the spectral holes (SHs) by the recording coherent waves in the wavelength region 1500–1540 nm results in a complex dynamics of the transient TWM response. In addition to conventional slow, even-type response due to amplitude grating formation via spectrally uniform EDF absorption saturation we also observed a dominating contribution due to SH formation. In particular, at the recording wavelength 1527 nm the relaxation time of the SH contribution to the TWM process was significantly shorter (< 4.7 ms) and with the effective recording power ∼4 times lower than that for conventional EDF population grating.

Diffraction of bessel beams on 2D amplitude gratings—a new branch in the talbot effect study

In this paper, an analytical theory for the diffraction of a Bessel beam of arbitrary order Jl(κr) on a 2D amplitude grating is presented. The diffraction pattern behind the grating turned out to be more complicated in comparison with the classical Talbot effect observed under illumination by a plane wave. In particular, the patterns in the main and fractional Talbot planes under certain conditions that are found in the article, are lattices of ring microbeams, the diameters of which depend on the period of the grating, the diameter of the illuminating beam, the number of the Talbot plane, and the topological charge l. For the rings near the optical axis, the latter reproduces l of the illuminating beam. The diffraction patterns observed in experiments on the Novosibirsk free electron laser behind gratings with periods of 1 to 6 mm, illuminated by zero- to second-order Bessel beams at a radiation wavelength λ = 141 µm, are in good agreement with both theoretical predictions and numerical calculations. We emphasize that an analytical theory based on the scalar theory of diffraction perfectly describes resulting diffraction patterns with hole diameters down to 0.25 mm, which are less than 2λ, when, formally speaking, the scalar theory becomes incorrect. Since the Laguerre–Gaussian beams can be represented as a superposition of Bessel beams, results of this paper can be applied to analysis of the Talbot effect with the Laguerre–Gaussian beams. A regular lattice of ring-like vortex microbeams, which can be formed in the Talbot planes, can be applied, for example, to creation of a lattice of optical traps, transmission of orbital angular momentum to elements of micromechanical devices, and to launching surface plasmon polaritons on an array of metal wires by ‘the end-fire coupling technique’.

Tunneling induced two-dimensional phase grating in a quantum well nanostructure via third and fifth orders of susceptibility

We study the nonlinear optical properties in an asymmetric double AlGaAs/GaAs quantum well nanostructure by using an external control field and resonant tunneling effects. It is found that the resonant tunneling can modulate the third-order and fifth-order of susceptibilities via detuning frequency of coupling light. In presence of the resonant tunneling and when the coupling light is in resonance with the corresponding transition, the real parts of third-order and fifth-order susceptibilities are enhanced which are accompanied by nonlinear absorption. However, in off-resonance of coupling light, real parts of third-order and fifth-order susceptibilities enhance while the nonlinear absorption vanishes. We investigate also the two-dimensional electromagnetically induced grating (2D-EIG) of the weak probe light by modulating the third-order and fifth-order susceptibilities. In resonance of coupling light, both amplitude and phase grating are formed in the medium due to enhancement of third-order and fifth-order probe absorption and dispersion. When the coupling light is out of resonance, most of probe energy is transferred from zero-order to higher-order directions due to resonant tunneling effect. The efficiency of phase grating for third-order of susceptibility is higher than phase grating for fifth-order susceptibility. Our proposed model may be useful for optical switching and optical sensors based on semiconductor nanostructures.

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.

Grating deployed total-shear 3-beam interference microscopy with reduced temporal coherence.

Interference microscopy is a powerful optical imaging technique providing quantitative phase distribution information to characterize various type technical and biomedical objects. Static and dynamic objects and processes can be investigated. In this paper we propose very compact, common-path and partially coherent diffraction grating-based interference microscopy system for studying small objects like single cells with low densities being sparsely distributed in the field of view. Simple binary amplitude diffraction grating is the only additional element to be introduced into a conventional microscope optical system. By placing it at a proper distance in front of the microscope image plane the total-shear operation mode is deployed resulting in interferograms of the object-reference beam type. Depending on the grating to image plane separation distance two or three-beam interferograms are generated. The latter ones are advantageous since they contain achromatic second harmonics in the interferogram intensity distributions. This feature enables to use reduced temporal coherence light sources for the microscope to reduce coherent noise and parasitic interference patterns. For this purpose we employ the laser diode with driving current below the threshold one. Results of conducted experiments including automatic computer processing of interferograms fully corroborate analytical description of the proposed method and illustrate its capabilities for studying static and dynamic phase objects.

Performance analysis of double-amplitude population gratings by non-overlapping unipolar pulses

We investigate the performance of the induced double-amplitude population grating (DAPG) based on spatially periodic modulation by the optical non-overlapping interaction of unipolar pulses. Considering the two typical allowed pulse configurations, the time delay requirements and the relationship between the grating amplitude, phase shift and the time delay were analyzed in detail. The results reveal that the grating amplitudes and phase can be dynamically controlled by the suitable time delay between the excited pulses. The population gratings presented here maybe offer more potential applications in nonlinear optics.

Understanding diffraction grating behavior: including conical diffraction and Rayleigh anomalies from transmission gratings

With the wide-spread availability of rigorous electromagnetic (vector) analysis codes for describing the diffraction of electromagnetic waves by specific periodic grating structures, the insight and understanding of nonparaxial parametric diffraction grating behavior afforded by approximate methods (i.e., scalar diffraction theory) is being ignored in the education of most optical engineers today. Elementary diffraction grating behavior is reviewed, the importance of maintaining consistency in the sign convention for the planar diffraction grating equation is emphasized, and the advantages of discussing “conical” diffraction grating behavior in terms of the direction cosines of the incident and diffracted angles are demonstrated. Paraxial grating behavior for coarse gratings (<italic>d</italic> ≫ λ) is then derived and displayed graphically for five elementary grating types: sinusoidal amplitude gratings, square-wave amplitude gratings, sinusoidal phase gratings, square-wave phase gratings, and classical blazed gratings. Paraxial diffraction efficiencies are calculated, tabulated, and compared for these five elementary grating types. Since much of the grating community erroneously believes that scalar diffraction theory is only valid in the paraxial regime, the recently developed linear systems formulation of nonparaxial scalar diffraction theory is briefly reviewed, then used to predict the nonparaxial behavior (for transverse electric polarization) of both the sinusoidal and the square-wave amplitude gratings when the +1 diffracted order is maintained in the Littrow condition. This nonparaxial behavior includes the well-known Rayleigh (Wood’s) anomaly effects that are usually thought to only be predicted by rigorous (vector) electromagnetic theory.

Photofunctionalizable Hydrogel for Fabricating Volume Optical Diffractive Sensors

AbstractVolume amplitude gratings made of mesoporous hydrogels are beneficial for sensing, but are difficult to fabricate because they involve creating high aspect ratio features in soft materials. A novel photofunctionalizable hydrogel is reported and its suitability for fabricating grating sensors is demonstrated comprising of features with an aspect ratio of ≈3.2. To make a photofunctionalizable hydrogel with high optical quality that can be patterned using widely available light sources, a water‐soluble photoactive monomer and sensitizer are synthesized. A transmission amplitude grating is subsequently fabricated in a ≈100 µm thick photofunctionalizable hydrogel film by reaction of the free amines generated in the photoexposed regions with pH‐responsive fluorescein isothiocyanate. The volume hydrogel grating described herein is shown to be suitable for real‐time sensing of pH as an exemplar analyte. This work will have a significant impact on the fabrication of diffractive optical structures in thick films of hydrogels that are highly promising for biomolecular sensing in disease diagnosis and healthcare monitoring.

Colorful radial Talbot carpet at the transverse plane.

In this work we theoretically and experimentally investigate the diffraction of spatially coherent and collimated white light beam from radial amplitude gratings. Theoretical part of the work is resolved with the Fresnel-Kirchhoff integral. In the experimental part, a collimated wave-front of a white light beam emitting from a halogen lamp is transmitted through a radial amplitude grating. We digitally record the diffraction pattern in various distances from the grating using a CCD camera. The resulted diffraction pattern that we call it "Colorful radial Talbot carpet at the transverse plane" has a shape-invariant form under propagation. The other significant aspects of this pattern are the existence of a quite patternless dark area located around the optical axis and an intense rainbow-like ring in the vicinity of the patternless area. The rainbow color changes radially from the violet in the vicinity of the patternless area to red by increasing the radius in which the purity of the colors in the inner side is dominant. We call this phenomena "diffraction-based rainbow". In addition, the transverse plane Talbot carpet pattern consists colorful self-images of the grating's spokes at the larger radii. The theoretical calculations and experimental results verify each other completely. The introduced diffraction-based rainbow can be utilized in spectrometry.

An Optical Diffraction Method for Controlling the Solid-Phase Recrystallization and Heating of Implanted Semiconductors during Pulse Light Annealing

t—The results of the improvement of the method of laser diagnostics for investigating the heating dynamics, solid-state recrystallization, and melting of implanted semiconductors directly during a pulse light annealing procedure are presented. This technique is based on recording Fraunhofer diffraction patterns from special periodic structures; it allows investigations of structural–phase transitions in ion-doped semiconductor layers simultaneously with sample temperature measurements with a high time resolution. For this purpose, two measuring diffraction gratings were preliminarily formed on the surface of a silicon wafer: a phase grating and an amplitude grating. The solid-phase recrystallization and melting processes were studied via the kinetics of the disappearance and appearance of the diffraction maxima from the amplitude grating. The sample temperature was monitored by the deflection of the diffraction angle of the probe laser beam from the phase diffraction grating. This deflection is caused by a change in the grating period due to its thermal expansion.

Talbot effect with a grating of period 1 μm

Under coherent plane wave illumination, the classical Talbot effect yields exact replica of the periodic input pattern in planes periodically distributed in the free propagation direction (paraxial regime). But when the period of the object is comparable with the wavelength, the Talbot phenomenon is considered to enter its non-paraxial regime(non-paraxial Talbot effect). In this contribution an experimental and theoretical report of this phenomenon is presented at non-paraxial regime with a amplitude grating of period 1μm, using a plane wave with wavelength of 616nm. The experimental self-images are registered by a confocal microscope and these self-images are contrasted with those obtained by the theory of diffraction in representation of plane waves. Contrary to what was expected, the remarkable results obtained is that it does not present quasi-self-images phenomenon and a detailed discussion of this behavior is included.

Three-level transmittance 2D grating with reduced spectrum and its self-imaging.

A simple method for generating 2D binary amplitude structure with additive superimposition of mutually orthogonal 1D amplitude gratings is proposed. Its implementation requires software generated three binary amplitude gratings, i.e., the crossed Ronchi, checker board and 1D Ronchi gratings with aspect ratio equal to 0.5. Their computer processing involves only two steps. First the checker grating is multiplied by a high frequency 1D grating. Next the product is added to the crossed grating. In result 3-level transmittance (0, 0.5, 1) hybrid diffraction structure is obtained. The intermediate level results from the use of a dense 1D grating. The zero diffraction order, well separated from the rest of the spectrum, consists of crossed spectra of additively superimposed 1D Ronchi gratings. Detailed heuristic explanation of the process aided by spectrum domain analyses is presented. Additionally, simulations and experiments conducted in the Fresnel diffraction field exemplify the invented structure properties in comparison with the multiplicative superimposition crossed Ronchi grating. Up to authors' best knowledge the Fresnel field (self-imaging phenomenon or Talbot effect) properties of 2D periodic structure with additive superimposition of component 1D gratings have not been published in the literature.

High density colloidal particle flux using modulated nondegenerate counter-propagating optical beams

Abstract We analyze, through numerical simulations, a method for generating unidirectional flux in colloidal systems using non-degenerate two-wave mixing. The approach uses a bidirectional PZT modulation and a laser grating amplitude modulation to suppress the reversal of the grating velocity with each cycle of the PZT. The dependence of the particle flux on modulation frequency is determined through numerical solution of the differential equations and the suppression of sedimentation in an extended colloidal system is analyzed.

Electromagnetically induced grating based on Zeeman coherence oscillations in cases beyond the multi-photon resonance condition

We present a theoretical study on the generation of an electromagnetically induced grating (EIG), based on Zeeman coherence oscillations, in a duplicated two-level atomic system. We show that the pure amplitude grating is obtained in the resonance case of multi-photon detuning. In this system, transferring of light energy from the zero order to the first order occurs by tuning the intensity and detuning of the coupling field. Physical mechanisms of the results are discussed using cases beyond the multi-photon resonance condition. Additionally, in the duplicated two-level system, we can create a two-dimensional EIG by splitting the coupling field into two orthogonal components. Optical properties of the proposed two-dimensional grating are also controlled by the intensity and detuning of the coupling field.

Advancement of X-ray radiography using microfocus X-ray source in conjunction with amplitude grating and SOI pixel detector, SOPHIAS.

We show how to improve microfocus X-ray radiography by using the SOPHIAS silicon-on-insulator pixel detector in conjunction with an amplitude grating. Single-exposure multi-energy absorption and differential phase contrast imaging was performed using the single amplitude grating method. The sensitivity in differential phase contrast imaging in a two-pixel-pitch setup was enhanced by 39% in comparison with the previously reported method [Rev. Sci. Instrum. 81, 113702 (2010).] by analyzing charge-sharing effects. Small-angle-scattering imaging was also possible in the two-pixel-pitch setup by counting the number of X-ray photons passing the pixel boundaries.