Bragg Regime Research Articles

Structural Colors from Amyloid-Based Liquid Crystals.

The helical periodicity and layered structure in cholesteric liquid crystals (CLCs) may be tuned to generate structural color according to the Bragg's law of diffraction. A wide range of natural-based materials such as condensed DNA, collagen, chitin, cellulose, and chiral biopolymers exhibit cholesteric phases with left-handed helixes and ensued structural colors. Here, the possibility of using amyloid CLCs is reported to prepare films with iridescent color reflection and opposite handedness. Right-handed CLCs assembled by left-handed amyloid fibrils are dried into layered structures with variable pitch controlled by the addition of glucose. Circularly polarized light with the same handedness of amyloid CLCs helix is reflected in the Bragg regime. Varying the drying speed leads to the switching between films with a rainbow-like color gradient and large area uniform color. It is confirmed that the origin of the colors derives from the layered structures of the amyloid CLCs, given the negligeable birefringence of the films, calculated from optical rotatory dispersion. These findings provide a facile approach to constructing biosourced cholesteric materials and introduce an original class of proteinaceous materials for the generation of structural colors from right-handed circularly polarized light.

Frequency doubling of femtosecond laser pulses in three dimensional nonlinear photonic crystals

Quasi-phase matched nonlinear frequency conversion in three dimensional nonlinear photonic crystals (NPCs) has been considered for implementation of the second harmonic generation of transform-limited and chirped femtosecond laser pulses. Spatial distribution of the second harmonic intensity is shown to be caused by Cherenkov- and Raman–Nath-type nonlinear diffraction. These types of nonlinear diffraction may occur simultaneously resulting in an efficient multi-order nonlinear diffraction in the Bragg regime, which can be realized by a proper choice of the modulation period of NPC structure in longitudinal direction for considered transverse diffraction order. Three dimensional NPCs open up new possibilities for ultrafast nonlinear photonics and parametric interactions in optics.

Generalized elliptical retarder design and construction using nematic and cholesteric phase liquid crystal polymers.

Elliptical retarders have important applications in interferometry and polarimetry, as well as imaging and display technologies. In this work, we discuss the traditional elliptical retarder decomposition using Pauli matrices as basis sets and then introduce a solution to the inverse problem: how an arbitrary elliptical retarder with desired eigenpolarizations and retardance can be constructed using a combination of linear and circular retarders. We present a simple design process, based on eigen-decomposition, with a solution determined by the intrinsic properties of each individual retarder layer. Additionally, a novel use of cholesteric liquid crystal polymer as a circular retarder is presented. Through simulation and experimental validation, we show cholesteric phase liquid crystal has an achromatic region of circular retardance at shorter wavelengths, outside of the Bragg regime. Finally, we verify our design process by fabricating and testing an elliptical retarder using both nematic and cholesteric phase liquid crystal polymers. The performance of the elliptical retarders shows excellent agreement with theory.

Characterization of an atom interferometer in the quasi-Bragg regime

We provide a comprehensive study of ultra-cold atom diffraction by an optical lattice. We focus on an intermediate regime between the Raman-Nath and the Bragg regimes, the so-called quasi-Bragg regime. The experimental results are in a good agreement with a full numerical integration of the Schr\"odinger equation. We investigate the long pulse regime limited by a strong velocity selection and the short pulse regime limited by non-adiabatic losses. For each of these regimes, we estimate the multi-port features of the Bragg interferometers. Finally, we discuss the best compromise between these two regimes, considering the diffraction phase shift and the existence of parasitic interferometers.

Acousto-optic spatial frequency filter operating in the intermediate region of acousto-optic interaction

The characteristics of an acousto-optic spatial frequency filter designed for processing of two-dimensional images and operation in the intermediate region of acousto-optic diffraction are investigated. The advantage of such filters over filters operating in a Bragg regime is the possibility of operation at significantly lower acoustic frequencies, which allows the passband of spatial frequencies to be increased and the limiting resolution to be decreased. Transfer functions of diffraction orders are obtained. The use of the first diffraction order is demonstrated to allow selection of the two-dimensional image contour. The two-dimensional image edge enhancement of the image transmitted by optical emission at a wavelength of 0.63×10−4cm is experimentally demonstrated using a TeO2 spatial filter operating at a frequency of 15 MHz.

Effects of optically biaxial anisotropy in orthogonal-circular polarization gratings operating in the Raman–Nath to Bragg regimes

The incident angle dependences of the diffraction properties of orthogonal-circular polarization gratings (OCPGs) fabricated using a polymer liquid crystal exhibiting biaxial anisotropy have been investigated. The investigations were conducted with the plane orthogonal to the surface of the OCPGs as the plane of incidence. It was found that a specific biaxial anisotropy reduces the incident angle dependence of optically thin OCPGs against the wavelength of the incident light, and is less effective on thick OCPGs. In addition, a method also has been proposed to determine the biaxial anisotropic shape that most reduces the incident angle dependence in thin OCPGs.

Quantum Borrmann effect for dissipation-immune photon-photon correlations

We study theoretically the second-order correlation function $g^{(2)}(t)$ for photons transmitted through a periodic Bragg-spaced array of superconducting qubits, coupled to a waveguide. We demonstrate that photon bunching and anti-bunching persist much longer than both radiative and non-radiative lifetimes of a single qubit. The photon-photon correlations become immune to non-radiative dissipation due to the Borrmann effect, that is a strongly non-Markovian collective feature of light-qubit coupling inherent to the Bragg regime. This persistence of quantum correlations opens new avenues for enhancing the performance of setups of waveguide quantum electrodynamics.

Quantum three-box paradox: a proposal for atom optics implementation

Quantum three-box paradox is one of the major mysteries revealed through two-state vector formalism of the quantum theory in conjunction with the weak measurements. We suggest a proposal for the experimental implementation of the paradox using time tested tools of Bragg regime atom optics with a two-level atom diffracted from a cavity field in the momentum space. The proposed schematics can be easily executed within the limits of contemporary laboratory resources using either quantized or classical fields.

Large-angle two-dimensional grating with hybrid mechanisms

We demonstrate a large-diffraction-angle two-dimensional (2D) grating based on cholesteric liquid crystal (CLC). One dimension is a polarization volume grating (PVG) working in the Bragg regime, which is produced by a patterned photoalignment layer. The other dimension is a CLC grating working in the Raman-Nath regime, which is introduced by CLC self-assembly under a weak anchoring energy condition. The condition for the coexistence of the CLC Raman-Nath grating (RNG) and PVG is analyzed, and the efficiency and grating period of the CLC RNG are also characterized. Potential application of this 2D grating for enlarging the eyebox of augmented reality displays is discussed.

Modeling the Polarization Ratio in the Upper Microwave Band for Sea Clutter Analysis

The two-scale model (TSM) based on Bragg tilting is widely employed to model the normalized radar cross section (NRCS) from the sea surface in the microwave bands. It also leads to the compound distribution model when used to represent the distribution of intensity in high-resolution sea clutter. While the TSM satisfactorily describes the dynamical behavior of the polarized NRCS at moderate incidence angles for various sea states and radar frequencies, it fails to consistently describe the polarized sea clutter distribution in the upper microwave band. The hidden reason is an overestimation of the Bragg polarization ratio (PR) at larger local incidence angles. Following the concept of universal analytical scattering models and based on the experimental evidence of two independent X-band airborne data sets, we propose a simple correction to the facet NRCS which brings the PR in closer agreement to the observations and makes it analytically very close to the popular Thompson empirical model. This amended model preserves the simple structure of Bragg scattering; it admits one single extra parameter which makes a dynamical transition between the asymptotic Bragg and Kirchhoff regime depending on the sea state and the radar frequency. This allows to correctly describe the angular variations of the PR in the upper microwave regime (C-, X-, and Ku-bands) with minimal <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> information regarding the sea surface. Once this correction is incorporated in the TSM, a consistent modeling of the polarized sea clutter statistics can be obtained with the compound distribution model.

Fresnel Gaussian shape invariant applied to optical diffraction grating calculation

We present numerical results on the diffraction produced by optical gratings in the Raman–Nath, Bragg and intermediate regimes calculated by means of the Fresnel Gaussian Shape Invariant. We describe how this numerical method based on a superposition of Gaussian wavelets, allows propagating, in an iterative manner within the grating, the illuminating beams, providing accurate calculations of the diffractive orders. We also include results due to a truncated, non-diffractive Airy illuminating beam.

Nonadiabatic contributions to Bragg-regime dynamics in atomic Kapitza-Dirac scattering

Atomic Kapitza-Dirac Bragg regime scattering is a multiphoton process in which a neutral atom undergoes a change of momentum through an interaction with a coherent light source. When the Bragg conditions are met, the outgoing atom beams are spatially quantized. Counterpropagating lasers act as pump and probe scattering from far-off-resonant excited intermediate electronic states, leaving the atoms in the electronic ground state with quantized transverse momentum. Each nontrivial scattering event imparts transverse velocity and therefore kinetic energy to the deflected atoms through recoil. In the Bragg regime, the loss of energy in the light fields is equal to the gain of kinetic energy in the atom. Energy nonconserving intermediate states, which are described by nonadiabatic contributions, are not accounted for by first-order off-resonant states. By comparing the solutions of increasing orders of off-resonant intermediate states, it becomes clear that calculating the correct Pendell\"{o}sung frequencies and phases requires including an ever increasing number of off-resonant states in proportion to the square root of the field strength.

Narrowing of filters and laser mirror in tilt-modulated chiral sculptured thin films

Helicoidal multi-layered nanostructures obsess intriguing optical properties to develop various optical and photonic devices. The optical properties of such spiral materials are adjacent with helical rotation. Tilt-modulated chiral sculptured thin film (STF) can totally reflect or transmit light in the Bragg regime for varying amplitudes of oscillation angles. Particularly, twist defect chiral STFs of same handedness creating spectral hole for circularly polarized light at different oscillation amplitudes. A narrow bandstop or wide bandpass filters and Bragg reflectors are created in defect modulated chiral STF. While, increasing the number of oscillations in a structural half period of chiral STF, the filters are flattering and narrower having blue shift. For large number of oscillation, the modulated chiral STF behave as laser mirror and creating Bragg fringes in the Bragg regime. Similarly, for different angles of incidence light the spectral holes and optical filters are become narrowing and shifted to lower wavelength regime, eventually die out in the Bragg regime, with maximum reflection for large angle of incident light. Therefore, it is suggested that such chiral STF are very useful in optical devices which operating in different wavelength regime.

Acousto-optic Modulation of Terahertz Radiation in Liquefied Sulfur Hexafluoride at Room Temperature

Acousto-optic modulation of terahertz free-electron laser radiation was investigated using diffraction on an acoustic wave in liquefied sulfur hexafluoride at room temperature. At the wavelength 130 μ m, the diffraction efficiency in Bragg regime of interaction 1% was obtained at 75 V driving electrical signal applied to the transducer terminals.

Analysis of volume-phase-grating characteristics that a variety of refractive index distributions influence. Part 2: Analysis of spectral bandwidths and angular bandwidths, and the derivation of these equations.

To expand the spectral bandwidths with high diffraction efficiency of volume phase (VP) gratings, it is important to know the influence of a variety of refractive index distributions (RIDs) inside the recording material on the bandwidths. The influence of various graded types of RIDs on the full width at half the maximum of the spectral bandwidth (${\lambda _{\rm FWHM}}$λFWHM) and the angular bandwidth (${\theta _{\rm FWHM}}$θFWHM) is investigated in the Bragg regime. It becomes clear that various graded types of RIDs influence their bandwidths and the characteristics, and the combination of the RIDs and refractive index modulation (${{ n}_m}$nm) is the most important factor for obtaining the large bandwidths of VP gratings. Theoretically, the ${\lambda _{\rm FWHM}}$λFWHM are obtained as the values of 149.7 nm and 257.6 nm (${{ n}_m} = {0.045}$nm=0.045) for the wavelengths of 900 nm and 1550 nm, respectively. Furthermore, I have succeeded in developing the expression for ${\lambda _{\rm FWHM}}$λFWHM and ${\theta _{\rm FWHM}}$θFWHM, using the proportional characteristics of VP gratings investigated in this work. The correlative coupling-length coefficients "G-factors" devised as a variety of RID functions in the previous paper are introduced into them. It is apparent that the derived equations of the bandwidths can be adapted to any graded type of RID that changes continuously from a triangular type to a rectangular type of VP grating, which has not been reported yet. The equations have made it easy to design ${\lambda _{\rm FWHM}}$λFWHM and ${\theta _{\rm FWHM}}$θFWHM of VP gratings.

Space-time phononic crystals with anomalous topological edge states

It is well known that an interface created by two topologically distinct structures could host nontrivial edge states that are immune to defects. In this letter, we introduce a one-dimensional space-time phononic crystal and study the associated anomalous topological edge states. A space-decoupled time modulation is assumed. While preserving the key topological feature of the system, such a modulation also duplicates the edge state mode across the spectrum, both inside and outside the band gap. It is shown that, in contrast to conventional topological edge states which are excited by frequencies in the Bragg regime, the time-modulation-induced frequency conversion can be leveraged to access topological edge states at a deep subwavelength scale where the entire phononic crystal size is merely 1/5.1 of the wavelength. This remarkable feature could open a new route for designing miniature devices that are based on topological physics.

Optical properties of gyrotropic polygonal chiral thin films

The optical response of gyrotropic and non-gyrotropic dielectric polygonal chiral thin films were investigated using transfer matrix method. The influence of gyrotropy factor, porosity and incident angle of light on Bragg regimes, selective reflection and transmission were reported. The results revealed that the Fabry-Perot oscillations were affected by gyrotropy factor and porosity of polygonal chiral thin films.

Generalized Space-Time-Periodic Diffraction Gratings: Theory and Applications

This paper studies the theory and applications of the diffraction of electromagnetic waves by space-time periodic (STP) diffraction gratings. We show that, in contrast with conventional spatially periodic grating, a STP diffraction grating produces spatial diffraction orders, each of which is formed by an infinite set of temporal diffraction orders. Such spatiotemporally periodic gratings are endowed with enhanced functionalities and exotic characteristics, such as asymmetric diffraction pattern, nonreciprocal and asymmetric transmission and reflection, and an enhanced diffraction efficiency. The theory of the wave diffraction by STP gratings is formulated through satisfying the conservation of both momentum and energy, and rigorous Floquet mode analysis. Furthermore, the theoretical analysis of the structure is supported by time and frequency domain FDTD numerical simulations for both transmissive and reflective STP diffraction gratings. Additionally, we provide the conditions for Bragg and Raman-Nath diffraction regimes for STP gratings. Finally, as a particular example of a practical application of the STP diffraction gratings to communication systems, we propose an original multiple access communication system featuring full-duplex operation. STP diffraction gratings are expected to find exotic practical applications in communication systems, especially for the realization of enhanced-efficiency or full-duplex beam coders, nonreciprocal beam splitters, nonreciprocal and enhanced-resolution holograms, and illusion cloaks.

Study of self-diffraction from laser generated plasma gratings in the nanosecond regime

We investigate the formation and diffraction efficiency of plasma gratings generated by the interference of two laser beams crossing at a small angle on the surface of a planar aluminum target. Such gratings were observed during National Ignition Facility experiments with the ratio of energy in the first-order to zeroth order of ≈60%. Recently, additional experiments were performed on the Optical Sciences Laser. These experiments with only two interfering beams showed high normalized energy (ratio of energy in diffracted order to zeroth order) of approximately 10% and 3% at the first and second diffracted order locations, respectively, for intensities less than 1012 W/cm2. The existence of the higher-orders is the characteristic of diffraction from gratings in the Raman-Nath as opposed to the Bragg regime. In addition, we show conical diffraction from the generated plasma grating. Using numerical simulations, we explore the large difference in diffraction efficiency observed in these two experiments and highlight the role of plasma temperature and density scale length. The simulations suggest a modulation depth of the plasma grating refractive index ranging from 1.77 × 10−4 to 3.5 × 10−2. These results are relevant to Inertial Confinement Fusion experiments or plasma photonics applications of gratings in high-field laser-physics and high-energy density science, specifically in the nanosecond regime.

Atomic Cheshire Cat: untying energy levels from the de Broglie motion

We suggest an idea to implement the Cheshire Cat in atomic media. The proposal is based on the time-tested tools of the Bragg regime atom interferometry and can be easily executed under the prevailing cavity quantum electrodynamics (QED) research environment. Our analysis, based on weak measurements, clearly demonstrates that under certain specific pre- and post-selected scenarios, the atom strangely behaves as being in one arm of the interferometer whereas the signatures of its energy levels exist in the other arm simultaneously.