Diffraction Regime Research Articles

Spatiotemporal instability in a periodic structure consisting of negative-index and positive-index materials

In this paper, we apply the conventional method of linear stability to investigate the dynamical behaviors of spatiotemporal instability in a periodic structure consisting of negative-index materials and positive-index materials. It is found that the high-order diffraction (HOD) originating from spatial dispersion in such physical setting not only leads to the appearance of new instability regimes, but also may exert significant influence on the original instability, depending on the combined signs of both diffraction and dispersion. In the conventional positive diffraction regime, the most notable property is that HOD shrinks the regime of the original instability for the normal dispersion case through suppressing the higher-frequency components growth while it leads to the appearance of new instability regimes in addition to deforming the original instability for the anomalous dispersion case. However, in the negative diffraction regime, HOD may lead to the occurrence of spatiotemporal instability even for the normal dispersion case while it mainly shrinks the regimes of the original instability for the anomalous dispersion case.

Optic, acoustic and acousto-optic properties of tellurium in close-to-axis regime of diffraction

We examined the optic, acoustic, photoelastic and acousto-optic (AO) properties of single crystal tellurium. We also determined the Bragg angle dependences on the acoustic frequency at 10.6 μm. The phenomenon of optical activity and its influence on the Bragg matching condition during anisotropic diffraction near the optic axis of the crystal are discussed in detail. Based on the results of our calculations, we designed, fabricated and characterized an AO cell to determine parameters of the anisotropic interaction with longitudinal acoustic waves propagating along the X axis in the crystal. In our experiments, we also measured the value of one of the important photoelastic coefficient in tellurium, p41 = 0.14 ± 0.01 and demonstrated that this coefficient determines the efficiency of the anisotropic diffraction in the employed geometry.

Neutron diffraction from superparamagnetic colloidal crystals

We fabricated a superparamagnetic ordered structure via self-assembly of a colloidal crystal from a suspension of maghemite nanoparticles and polystyrene beads. Such crystals are potential candidates for novel polarizing beam-splitters for cold neutrons, complementing the available methods of neutron polarization. Different bead sizes and nanoparticle concentrations were tested to obtain a crystal of reasonable quality. Neutron diffraction experiments in the presence of an external magnetic field were performed on the most promising sample. We demonstrate that the diffraction efficiency of such crystals can be controlled by the magnetic field. Our measurements also indicate that the Bragg diffraction regime can be reached with colloidal crystals.

Monte Carlo study of particle production in diffractive proton\u2013proton collisions at sqrt{s} = 13 TeV with the very forward detector combined with central information

Very forward (VF) detectors in hadron colliders, having unique sensitivity to diffractive processes, can be a powerful tool for studying diffractive dissociation by combining them with central detectors. Several Monte Carlo simulation samples in p–p collisions at sqrt{s} = 13 TeV were analyzed, and different nondiffractive and diffractive contributions were clarified through differential cross sections of forward neutral particles. Diffraction selection criteria in the VF-triggered-event samples were determined by using the central track information. The corresponding selection applicable in real experiments has approx 100% purity and 30–70% efficiency. Consequently, the central information enables classification of the forward productions into diffraction and nondiffraction categories; in particular, most of the surviving events from the selection belong to low-mass diffraction events at log _{10}(xi _{x}) < -5.5. Therefore, the combined method can uniquely access the low-mass diffraction regime experimentally.

Ultrafast transmission electron microscope for studying the dynamics of the processes induced by femtosecond laser beams

We have developed an ultrafast transmission electron microscope for studying dynamic processes in samples excited by femtosecond laser pulses and for probing transient processes occurring under irradiation by a pulsed (~7 ps) photoelectron beam with an adjustable delay with respect to the excitation pulse. A 75-keV photoelectron beam is formed using a silver photocathode irradiated by a femtosecond laser beam. This microscope is shown to have a high spatial resolution in the photoelectron regime: nanoscale in the imaging regime and atomic in the electron diffraction regime. It is used for experimental observation of ultrafast interaction of a laser-induced electron cloud with a pulsed photoelectron beam. Using this effect, a method of spatial and temporal alignment of excitation laser and probe electron pulsed beams on a sample is experimentally implemented.

Vector characteristics of light beams in acousto-optic cells studied in the regime of Bragg diffraction

An experimental setup is proposed in this work that allows measurement of beat signals during the superposition of the related components of the orthogonal expansion describing the electric field of the total light wave. The results of experimental studies obtained in real time via optical heterodyning accompanied by the acousto-optic interaction of two light waves in the Bragg diffraction regime are presented.

Influence of light-induced gratings on acousto-optic interaction of Bessel light beams in uniaxial gyrotropic crystals

The influence of light-induced gratings, caused by cubic optical nonlinearity, on the Bragg diffraction of Bessel light beams by ultrasound in uniaxial gyrotropic crystals was studied theoretically. It was shown that, when Bessel light beams are used, the threshold for a substantial manifestation of optical nonlinearity during Bragg diffraction is significantly reduced. It was established that the efficiency of the acousto-optic interaction increases with increasing light intensity in the anti-Stokes regime of diffraction and decreases monotonically in the Stokes regime. Satisfactory qualitative agreement between the theoretical and experimental dependences of the diffraction efficiency on the light and ultrasound intensities was demonstrated using a uniaxial gyrotropic quartz crystal.

How many photons are needed to reconstruct random objects in coherent X-ray diffractive imaging?

This paper presents an investigation of the reconstructibility of coherent X-ray diffractive imaging diffraction patterns for a class of binary random `bitmap' objects. Combining analytical results and numerical simulations, the critical fluence per bitmap pixel is determined, for arbitrary contrast values (absorption level and phase shift), both for the optical near- and far-field. This work extends previous investigations based on information theory, enabling a comparison of the amount of information carried by single photons in different diffraction regimes. The experimental results show an order-of-magnitude agreement.

Experimental evidence of transition between dynamical and kinematical diffraction regimes in ion-implanted Si observed through X-ray multiple-beam diffraction mappings

In this paper, the dependence of a Laue diffraction streak on the crystalline perfection of Xe-implanted Si(001) substrates is presented, based on the observation in the X-ray multiple diffraction (XRMD) mappings, as an experimental evidence of the transition between dynamical and kinematical diffraction regimes. A direct observation of the implanted region by transmission electron microscopy revealed an amorphous Si layer, which recrystallizes into a heavily twinned and faulted microstructure after thermal treatment at 800 °C. Besides the lattice damages, the annealing induces the formation of Xe bubbles. Both singularly affect the XRMD pattern, primarily the four-fold streaks profile of the (000)(002)(11¯1¯)(11¯3) four-beam simultaneous case when compared with the pristine Si pattern, highlighting the intra- and inter-block diffractions and the role played by the primary extinction effect. Such features provide information on the dominant diffraction regime. The findings are also discussed and compared to the conventional reciprocal space mappings via the asymmetric Si(113) reflection.

Acousto-optic Bragg diffraction in paratellurite by the sidelobes of the spatial radiation spectrum of an acoustic transducer

Acousto-optic Bragg diffraction in paratellurite is investigated within the two first diffraction orders for the case of diffraction by the sidelobes of the spatial radiation spectrum of an acoustic transducer. One of the diffraction orders is due to anisotropic diffraction, and the other, to isotropic diffraction. Such a diffraction regime is achieved when the diffraction plane is inclined toward the optical axis of the crystal. For light with a wavelength of 0.63 × 10–4 cm diffracted by a “slow” sound wave with a frequency of 26 MHz, the effect manifests itself when the angle between the acousto-optic diffraction plane and the optical axis of paratellurite is ~3°. The effect is experimentally verified. The diffraction efficiency is 20% for each of the diffraction orders for a microwave signal of 8 V at the transducer.

Transition from two-dimensional photonic crystals to dielectric metasurfaces in the optical diffraction with a fine structure.

We study experimentally a fine structure of the optical Laue diffraction from two-dimensional periodic photonic lattices. The periodic photonic lattices with the C4v square symmetry, orthogonal C2v symmetry, and hexagonal C6v symmetry are composed of submicron dielectric elements fabricated by the direct laser writing technique. We observe surprisingly strong optical diffraction from a finite number of elements that provides an excellent tool to determine not only the symmetry but also exact number of particles in the finite-length structure and the sample shape. Using different samples with orthogonal C2v symmetry and varying the lattice spacing, we observe experimentally a transition between the regime of multi-order diffraction, being typical for photonic crystals to the regime where only the zero-order diffraction can be observed, being is a clear fingerprint of dielectric metasurfaces characterized by effective parameters.

A laboratory study on the loading and motion of a heaving box

This paper concerns the nonlinear loading and dynamic response of a heaving rectangular box in two dimensions, using a series of experimental tests in regular and irregular wave conditions. Nonlinear forcing components are found to make major contributions to both the excitation problem and the motion response. Two main sources of nonlinearity are established: the first associated with higher-order wave–structure interactions, and the second associated with viscous dissipation. The present work quantifies the relative influence of these two sources. Adopting a series of regular wave cases, the first source, prevalent in steep wave conditions, is shown to be particularly significant in the diffraction regime, leading to significant excitation force amplifications. In deep water, these nonlinearities are primarily driven by interactions between incident and reflected wave components. The second source, due to vortex shedding, plays a minor role in the excitation problem, but has a major influence on the motion response. Vortex-induced effects are particularly important when the structure exhibits large motions, for example at resonance. To characterise the response in irregular waves, experimental data are provided comprising in excess of 100,000 individual waves, presenting one of the most substantial data sets of this kind to date. In considering these irregular sea states, the two aforementioned sources of nonlinearity are again found to be of critical importance. While wave-induced load amplifications of up to 60% may be observed in the excitation problem, the motion response is primarily governed by vortex-induced attenuations. In order to provide practical engineering solutions, two approaches are offered. For nonlinear forcing predictions, a two parameter Weibull fit is found to be both simple and accurate. In terms of the heave motion, a computationally efficient time-domain simulation, building upon a linear hydrodynamic description and a quadratic MOJS type drag term, leads to good agreement with experimental data.

Double-filtering method based on two acousto-optic tunable filters for hyperspectral imaging application.

A hyperspectral imaging system was demonstrated based on two acousto-optic tunable filters (AOTFs). Efficient regulation of the incoherent beam was executed by means of the wide-angular regime of Bragg diffraction in the birefringent materials. A double-filtering process was achieved when these two AOTFs operated with a central wavelength difference. In comparison with the single-filtering method, the spectral bandwidth was greatly compressed, giving an increment of 42.02% in spectral resolution at the wavelength of 651.62 nm. Experimental results and theoretical calculations are basically identical. Furthermore, the sidelobe was found to be suppressed by the double-filtering process with the first order maximum decreased from -9.25 dB to -22.35 dB. The results indicated high spectral resolution and high spectral purity were obtained simultaneously from this method. The basic spectral resolution performance was examined with a didymium glass by this configuration. We present our experimental methods and the detailed results obtained.

Refraction limit of miniaturized optical systems: a ball-lens example.

We study experimentally and theoretically the electromagnetic field in amplitude and phase behind ball-lenses across a wide range of diameters, ranging from a millimeter scale down to a micrometer. Based on the observation, we study the transition between the refraction and diffraction regime. The former regime is dominated by observables for which it is sufficient to use a ray-optical picture for an explanation, e.g., a cusp catastrophe and caustics. A wave-optical picture, i.e. Mie theory, is required to explain the features, e.g., photonic nanojets, in the latter regime. The vanishing of the cusp catastrophe and the emergence of the photonic nanojet is here understood as the refraction limit. Three different criteria are used to identify the limit: focal length, spot size, and amount of cross-polarization generated in the scattering process. We identify at a wavelength of 642 nm and while considering ordinary glass as the ball-lens material, a diameter of approximately 10 µm as the refraction limit. With our study, we shed new light on the means necessary to describe micro-optical system. This is useful when designing optical devices for imaging or illumination.

Acousto-optic modulator of depolarized laser radiation on the paratellurite crystal

An original acousto-optic modulator of depolarized laser radiation is based on a paratellurite crystal in the regime of anisotropic diffraction by a slow acoustic wave. Two acoustic waves with different frequencies are simultaneously excited in a single acousto-optic cell. Two diffraction orders of orthogonal polarizations at the exit from the cell are diffracted in opposite sides relative to the zero order. A polarization prism that is placed immediately behind the cell transforms the diffraction orders into a single output depolarized beam. The total efficiency is 96%.

Nonlinear loading of a two-dimensional heaving box

A numerical investigation is presented addressing the nonlinear heave response of a rectangular box. The work specifically concerns the importance of the relative body dimensions, expressed through the product of the half-beam b and the wavenumber k. When subjected to moderately steep incident waves, the second-harmonic content of the heave motion is found to be as large as 25% of the first-harmonic content. In considering the extent of this second-harmonic motion, three regimes may be defined: (i) the long wave regime, where kb≤0.4, (ii) the intermediate regime, where 0.4<kb<1.0 and (iii) the diffraction or short wave regime, where kb≥1.0. Expressed in terms of the wavelength λ=2π/k, these regimes correspond to (i) b≤0.06λ, (ii) 0.06λ<b<0.16λ and (iii) b≥0.16λ. The second-harmonic motion content is found to be particularly pronounced in regimes (i) and (iii). Perhaps surprisingly, this second-harmonic content is also found to be practically non-existent for some intermediate cases lying within regime (ii). Three sources of nonlinearity are shown to be particularly important. First, the interaction between the first-order incident waves and the first-order scattered waves is key to the nonlinear loading in regime (iii). Second, the generation of freely propagating second-harmonic radiated waves due to the body motion is important in (i). Third, the local standing wave field associated with the radiation problem is found to contribute to the loading in regime (iii). In addition, the location of the body resonance also plays a critical role in defining the extent of the second-harmonic motion content. The focus of the present work lies on a clear physical interpretation of the sources of these nonlinear loads, coupled with an analysis of the body dynamics.

Reflection of X-rays from a rough surface at extremely small grazing angles.

Peculiarities of X-ray diffraction from a rough surface at an extremely small grazing angle of an incident beam are theoretically studied. The interrelation of four diffraction channels (coherent reflectance, coherent transmittance, diffuse scattering in vacuum, and scattering into the matter depth) is analyzed for different limiting cases (large and small correlation length of roughness and large and extremely small grazing angle of incident radiation). Both the Debye-Waller and the Nevot-Croce factors are demonstrated to describe improperly the features of X-ray diffraction at extremely small grazing angles. More appropriate simple analytic expressions for the specular reflectivity and total integrated scattering in vacuum are obtained instead. Transformation of one limiting diffraction regime into another one with variation in the correlation length of roughness is discussed.

Nonadiabatic diffraction of matter waves

Diffraction phenomena usually can be formulated in terms of a potential that induces the redistribution of a wave's momentum. Using an atomic Bose-Einstein condensate coupled to the orbitals of a state-selective optical lattice, we investigate a hitherto unexplored nonadiabatic regime of diffraction in which no diffracting potential can be defined, and in which the adiabatic dressed states are strongly mixed. We show how, in the adiabatic limit, the observed coupling between internal and external dynamics gives way to standard Kapitza-Dirac diffraction of atomic matter waves. We demonstrate the utility of our scheme for atom interferometry and discuss prospects for studies of dissipative superfluid phenomena.

Diffraction of three-colour radiation on an acoustic wave

We study acousto-optic Bragg diffraction of three-colour radiation having wavelengths of 488, 514 and on a single acoustic wave propagating in a crystal. A technique is developed that allows one to find diffraction regimes with a proportional change in the intensity of all radiations by varying the acoustic power. According to the technique, radiation with a maximum wavelength has to be in strict Bragg synchronism with the acoustic wave, while other radiations diffract during the synchronism detuning. The results obtained using this technique are experimentally confirmed.

Quantum information processing by weaving quantum Talbot carpets

Single photon interference due to passage through a periodic grating is considered in a novel proposal for processing D-dimensional quantum systems (quDits) encoded in the spatial degrees of freedom of light. We show that free space propagation naturally implements basic single quDit gates by means of the Talbot effect: an intricate time-space carpet of light in the near field diffraction regime. Adding a diagonal phase gate, we show that a complete set of single quDit gates can be implemented. We then introduce a spatially-dependent beam splitter that allows implementation of controlled operations between two quDits. A new form of universal quantum information processing can then be implemented with linear optics and ancilla photons. Though we consider photons, our scheme should be directly applicable to a number of other physical systems. Interpretation of the Talbot effect as a quantum logic operation provides a beautiful and interesting way to visualize quantum computation through wave propagation and interference.