Bragg Regime Research Articles

Kapitza-Dirac scattering of electrons from a bichromatic standing laser wave

Coherent scattering of an electron beam by the Kapitza-Dirac effect from a standing laser wave which comprises two frequency components is studied. To this end, the Schr\"odinger equation is solved numerically with a suitable ponderomotive potential. Besides, an analytical solution for electron diffraction in the asymptotic domain of large field amplitudes is obtained and a mathematical model in reduced dimensionality for the scattering amplitude in the Bragg regime is presented. We demonstrate distinct interference signatures and relative phase effects when the standing wave contains a fundamental frequency and its second harmonic. The influence of the relative field intensities on the Rabi oscillation dynamics is also discussed.

Influence of laser pulse shape and spectral composition on strong-field Kapitza-Dirac scattering

Diffractive scattering of an electron beam from an intense standing wave of light (Kapitza-Dirac effect) is analyzed theoretically. The corresponding Schrödinger equation is solved in the Bragg regime by combined analytical and numerical means. Our goals are twofold: On the one hand, we examine the influence of the nature of the field's turning- on phase and demonstrate that a smooth, adiabatic envelope restricts the transitions to those satisfying the Bragg condition. On the other hand, we study signatures of quantum mechanical interference when the standing light wave comprises two commensurate frequencies. Characteristic modifications of the Rabi oscillation dynamics and a dependence on the relative phase between the frequency modes are revealed.

Spatial filtering with photonic crystals

Photonic crystals are well known for their celebrated photonic band-gaps—the forbidden frequency ranges, for which the light waves cannot propagate through the structure. The frequency (or chromatic) band-gaps of photonic crystals can be utilized for frequency filtering. In analogy to the chromatic band-gaps and the frequency filtering, the angular band-gaps and the angular (spatial) filtering are also possible in photonic crystals. In this article, we review the recent advances of the spatial filtering using the photonic crystals in different propagation regimes and for different geometries. We review the most evident configuration of filtering in Bragg regime (with the back-reflection—i.e., in the configuration with band-gaps) as well as in Laue regime (with forward deflection—i.e., in the configuration without band-gaps). We explore the spatial filtering in crystals with different symmetries, including axisymmetric crystals; we discuss the role of chirping, i.e., the dependence of the longitudinal period along the structure. We also review the experimental techniques to fabricate the photonic crystals and numerical techniques to explore the spatial filtering. Finally, we discuss several implementations of such filters for intracavity spatial filtering.

Spectral hole filters using tilt-modulated chiral sculptured thin films

A defect-free chiral sculptured thin film (STF) reflects light of one circular polarization state and transmits that of the other in a spectral regime, called the Bragg regime. A tilt-modulated chiral STF reflects light of both circular polarization states in the Bragg regime if the amplitude of modulation is sufficiently large. A twist defect in an unmodulated chiral STF results in either a narrow passband or an ultranarrow stopband filter depending upon the thickness of that STF. An ultranarrow passband filter can also be realized using a twist defect in the tilt-modulated chiral STF, if that STF is sufficiently thick. Furthermore, it was seen that the polarization-insensitive mirrors fabricated using tilt-modulated chiral STFs are very tolerant of twist defects if the amplitude of modulation is sufficiently large.

Biasing a coin after the toss: asymmetric delayed choice quantum eraser via Bragg regime cavity QED

Quantum eraser (QE), on the one hand, is treated as the most intriguing phenomenon that puts a conception of the time in classical and quantum physics in contrast whereas, on the other hand, the same phenomenon is considered fallacious and based on the wrong arguments. Here, we propose an asymmetric delayed choice QE based on a Mach–Zandher–Bragg (MZB) atom interferometer that marks the intriguing effects more explicitly through delayed choice, tunable manipulation of the de Broglie matter wave interference. We also plot distinguishability D and fringe visibility V as a function of the atom–field interaction time utilized for the delayed choice eraser to highlight the counter-intuitive nature of the phenomenon. The interferometric scheme is based on Bragg diffraction of neutral two-level atoms through cavity fields. It is shown that the proposal is deterministic in nature and can be demonstrated experimentally with overall good fidelity utilizing the available technical resources.

The Klein-Cook parameter in analyzing acousto-optic interaction in acoustically anisotropic media

A theoretical study of acousto-optic interaction in acoustically anisotropic media is performed. A new criterion for estimating the Raman-Nath and Bragg regimes of light diffraction by means of ultrasound in acoustic crystals is proposed. The modified Klein-Cook parameter is found to consider the walkoff of ultrasonic wave energy as a result of the elastic anisotropy of a medium.

Suppression of circular Bragg phenomenon in tilt-modulated chiral-sculptured thin films at oblique incidence

By using a piecewise uniform approximation method, the reflectance and transmittance of light for an obliquely incident circularly polarized plane wave on a tilt-modulated chiral sculptured thin film (STF) were computed. The circular Bragg phenomenon was found to vanish when the amplitude of the modulation was high enough for oblique incidence. The tilt-modulated chiral STF then acts like a conventional mirror in the Bragg regime.

The circular Bragg phenomenon

Exhibited by structurally chiral materials—such as Reusch piles, cholesteric liquid crystals (CLCs), and chiral sculptured thin films (STFs)—due to their helical nonhomogeneity along a fixed axis, the circular Bragg phenomenon is the almost total reflection of the incident light of the co-handed circular-polarization state but very little reflection of the incident light of the cross-handed circular-polarization state. Manifesting itself in spectral regimes that depend on the angle of incidence, the structural period, and the relative permittivity dyadic, the phenomenon amounts to the formation of a light pipe that bleeds energy backward under appropriate conditions. Mild dissipation and dispersion do not significantly affect the circular Bragg regime. Every structurally chiral material of sufficient thickness is essentially a circular-polarization-sensitive band-rejection filter. Cascades of these materials with or without structural defects can be used to satisfy complex filtering requirements, such as multiband, narrowband, and ultra-narrowband filtering. A shift in the circular Bragg regime due to infiltration of a chiral STF by a fluid enables optical sensing. Sources of circularly polarized light can be fabricated by embedding emission sources in CLCs and chiral STFs.

Near-infrared sensitive photorefractive device using polymer dispersed liquid crystal and BSO:Ru hybrid structure.

A near-infrared sensitive hybrid device, based on a Ru-doped BSO photorefractive substrate and polymer dispersed liquid crystal (PDLC) layer, is reported. It is found that the photoexcited charge carriers generated in the BSO:Ru substrate create an optically induced space charge field, sufficient to penetrate into the PDLC layer and to re-orient the LC molecules inside the droplets. Beam-coupling measurements at the Bragg regime are performed showing prospective amplification values and high spatial resolution. The proposed structure does not require indium tin oxide (ITO) contacts and alignment layers. Such a device allows all the processes to be controlled by light, thus opening further potential for real-time image processing at the near-infrared range.

Beam coupling in hybrid photorefractive inorganic-cholesteric liquid crystal cells: Impact of optical rotation

We develop a theoretical model to describe two-beam energy exchange in a hybrid photorefractive inorganic-cholesteric cell. A cholesteric layer is placed between two inorganic substrates. One of the substrates is photorefractive (Ce:SBN). Weak and strong light beams are incident on the hybrid cell. The interfering light beams induce a periodic space-charge field in the photorefractive window. This penetrates into the cholesteric liquid crystal (LC), inducing a diffraction grating written on the LC director. In the theory, the flexoelectric mechanism for electric field-director coupling is more important than the LC static dielectric anisotropy coupling. The LC optics is described in the Bragg regime. Each beam induces two circular polarized waves propagating in the cholesteric cell with different velocities. The model thus includes optical rotation in the cholesteric LC. The incident light beam wavelength can fall above, below, or inside the cholesteric gap. The theory calculates the energy gain of the weak beam, as a result of its interaction with the pump beam within the diffraction grating. Theoretical results for exponential gain coefficients are compared with experimental results for hybrid cells filled with cholesteric mixture BL038/CB15 at different concentrations of chiral agent CB15. Reconciliation between theory and experiment requires the inclusion of a phenomenological multiplier in the magnitude of the director grating. This multiplier is cubic in the space-charge field, and we provide a justification of the q-dependence of the multiplier. Within this paradigm, we are able to fit theory to experimental data for cholesteric mixtures with different spectral position of cholesteric gap relative to the wavelength of incident beams, subject to the use of some fitting parameters.

Developing an Advanced Prototype of the Acousto-Optical Radio-Wave Spectrometer for Studying Star Formation in the Milky Way

The designed practically prototype of an advanced acousto-optical radio-wave spectrometer is presented in a view of its application to investigating the Milky Way star formation problems. The potential areas for observations of the cold interstellar medium, wherein such a spectrometer can be exploited successfully at different approximations, are: 1) comparison of the Milky Way case with extragalactic ones at scale of the complete galactic disk; 2) global studies of the Galactic spiral arms; and 3) characterization of specific regions like molecular clouds or star clusters. These aspects allow us to suggest that similar instrument will be really useful. The developed prototype of spectrometer is able to realize multi-channel wideband parallel spectrum analysis of very-high-frequency radio-wave signals with an improved resolution power exceeding 103. It includes the 1D-acousto-optic wide-aperture cell as the input device for real-time scale data processing. Here, the current state of developing this acousto-optical spectrometer in frames of the astrophysical instrumentation is briefly discussed, and the data obtained experimentally with a tellurium dioxide crystalline acousto-optical cell are presented. Then, we describe a new technique for more precise spectrum analysis within an algorithm of the collinear wave heterodyning. It implies a two-stage integrated processing, namely, the wave heterodyning of a signal in an acoustically square-law nonlinear medium and then the optical processing in the same solid-state cell. Technical advantage of this approach lies in providing a direct multi-channel parallel processing of ultra-high-frequency radio-wave signals with the resolution power exceeding 104. This algorithm can be realized on a basis of exploiting a large-aperture effective acousto-optical cell, which operates in the Bragg regime and performs the ultra-high-frequency co-directional collinear acoustic wave heterodyning. The general concept and basic conclusions here are confirmed by proof-of-principle experiments with the specially designed cell of a new type based on a lead molybdate crystal.

Double Bragg diffraction: A tool for atom optics

The use of retro-reflection in light-pulse atom interferometry under microgravity conditions naturally leads to a double-diffraction scheme. The two pairs of counterpropagating beams induce simultaneously transitions with opposite momentum transfer that, when acting on atoms initially at rest, give rise to symmetric interferometer configurations where the total momentum transfer is automatically doubled and where a number of noise sources and systematic effects cancel out. Here we extend earlier implementations for Raman transitions to the case of Bragg diffraction. In contrast with the single-diffraction case, the existence of additional off-resonant transitions between resonantly connected states precludes the use of the adiabatic elimination technique. Nevertheless, we have been able to obtain analytic results even beyond the deep Bragg regime by employing the so-called "method of averaging," which can be applied to more general situations of this kind. Our results have been validated by comparison to numerical solutions of the basic equations describing the double-diffraction process.

On optical rotation and selective transmission in ambichiral sculptured thin films

The optical rotation and selective transmission spectra of ambichiral sculptured thin films were calculated using the transfer matrix method. The results of optical modeling showed that at lower angular rotations the optical characteristics of ambichiral sculptured thin films are the same as chiral sculptured thin films. At higher angular rotations, two circular Bragg regimes appear. An ambichiral sculptured thin film in one regime reflects left circularly polarized (LCP) light and in a second regime reflects right circularly polarized (RCP) light. The optical properties of ambichiral sculptured thin films with twist and layer defects as spectral holes are also reported.

Diffraction of Light by Acoustic Waves in Liquids

For the acusto-optic interactions in liquids, an equation for the diffraction light intensity was obtained in terms of Klein Cook parameter Q. With optimized parameters for Q, incident light wave length of λ = 633 nm, sound wave length of Λ = 0.1 mm, acusto-optic interaction length L=0.1 m, and refractive index of the liquid in the range of 1 to 2, the existence of ideal Raman-Nath and Bragg diffractions were investigated in terms of phase delay and incident angle. The ideal Raman-Nath diffraction slightly deviated when the Klein Cook parameter was increased from 0 to 1 for low phase delay values and for large phase delay, the characteristics of the Bessel function disappeared. Higher value of Klein Cook parameter gave Bragg diffraction and ideal Bragg diffraction was obtained for Q ~100. A slight variation of the incident angle from Bragg angle had a considerable effect on Bragg diffraction pattern. Klein Cook parameter with the change of acoustic wave frequency was investigated for liquids with refractive index in the range1.3-1.7 and their diffraction patterns were compared with practically applicable acusto-optic crystals. For acusto-optic diffractions in liquids, sound velocity plays an important role in Bragg regime with Q increasing with increasing acoustic frequency. As acoustic wave frequency exceeded 10 MHz most of the liquids reached Bragg regime before these crystals.

Kapitza-Dirac effect in the relativistic regime

A relativistic description of the Kapitza-Dirac effect in the so-called Bragg regime with two and three interacting photons is presented by investigating both numerical and perturbative solutions of the Dirac equation in momentum space. We demonstrate that spin-flips can be observed in the two-photon and the three-photon Kapitza-Dirac effect for certain parameters. During the interaction with the laser field the electron's spin is rotated, and we give explicit expressions for the rotation axis and the rotation angle. The off-resonant Kapitza-Dirac effect, that is, when the Bragg condition is not exactly fulfilled, is described by a generalized Rabi theory. We also analyze the in-field quantum dynamics as obtained from the numerical solution of the Dirac equation.

QUANTUM CATALOGUING VIA ATOM INTERFERENCE

A quantum cataloguing scheme to identify any unknown quantized cavity field state using the atom interference is proposed. The scheme consists of sending a two-level state atom through two cavities, with Bragg and Raman-Nath regimes, respectively. We inveterate the atom interference from the second cavity to achieve different interference patterns which depend on the photons statistics.

On circular Bragg regimes in ellipsometry spectra of ambichiral sculptured thin films

The generalized ellipsometry formalism was used for a right-handed ambichiral sculptured thin film. The amplitude ratios and phase differences were calculated using an experimental dielectric function for bulk titania. The results showed that the occurrence of the circular Bragg regimes can be adduced from ellipsometry spectra.

Suppression of circular Bragg phenomenon in chiral sculptured thin films produced with simultaneous rocking and rotation of substrate during serial bideposition

Chiral sculptured thin films (STFs) produced by substrate rotation during physical vapor deposition exhibit the circular Bragg phenomenon, whereby normally incident left- and right-circularly polarized plane waves are discriminated in a spectral regime called the circular Bragg regime. Theory had predicted that substrate rocking, in synchrony with substrate rotation, during deposition could suppress the propensity to exhibit the circular Bragg phenomenon. Therefore chiral STFs of a dielectric material were fabricated with/without substrate rocking, and their transmittance spectrums for incident linearly and circularly polarized plane waves were measured. With sufficient rocking amplitude, the discrimination between incident left- and right-circularly polarized light nearly vanished, whereas a Bragg phenomenon for all normally incident plane waves was observed. Thus, chiral STF technology can be used to produce both ordinary and circular-polarization Bragg filters.

Tuning circular Bragg phenomenon of TiO2 sculptured thin f ilms with chiral structure

TiO2 chiral sculptured thin films (CSTFs) prepared using glancing angle deposition (GLAD) method based on electron beam evaporation are studied. The relationship between structural parameters and circular Bragg phenomenon (CBP) is investigated. Results demonstrate that, the central wavelength of Bragg regime red-shifts with the increasing pitch of helix, and peak value of selective transmittance will increase after adding more turns to the helix. After annealing, the central wavelength blue-shifts and the peak value rises. Tuning CBP by modulating the deposition parameters and annealing can optimize the performance of circularly polarized devices fabricated from CSTFs.

Diffraction of Light by Acoustic Waves in Liquids

For the acusto-optic interactions in liquids, an equation for the diffraction light intensity was obtained in terms of Klein Cook parameter Q. With optimized parameters for Q, incident light wave length of λ = 633 nm, sound wave length of Λ = 0.1 mm, acusto-optic interaction length L=0.1 m, and refractive index of the liquid in the range of 1 to 2, the existence of ideal Raman-Nath and Bragg diffractions were investigated in terms of phase delay and incident angle. The ideal Raman-Nath diffraction slightly deviated when the Klein Cook parameter was increased from 0 to 1 for low phase delay values and for large phase delay, the characteristics of the Bessel function disappeared. Higher value of Klein Cook parameter gave Bragg diffraction and ideal Bragg diffraction was obtained for Q ~100. A slight variation of the incident angle from Bragg angle had a considerable effect on Bragg diffraction pattern. Klein Cook parameter with the change of acoustic wave frequency was investigated for liquids with refractive index in the range1.3-1.7 and their diffraction patterns were compared with practically applicable acusto-optic crystals. For acusto-optic diffractions in liquids, sound velocity plays an important role in Bragg regime with Q increasing with increasing acoustic frequency. As acoustic wave frequency exceeded 10 MHz most of the liquids reached Bragg regime before these crystals.