Nath Regime Research Articles

Second‐Harmonic Generation via Nonlinear Raman–Nath Diffraction in an Optical Fibonacci Superlattice

AbstractNonlinear Raman–Nath diffraction is an effective method for frequency conversion in the presence of phase mismatch. In a structure featuring periodically modulated quadratic nonlinearity, the available frequency‐doubled patterns generated from nonlinear Raman–Nath diffraction constitute uniformly spaced points due to the one parametric decided reciprocal lattice vectors. Herein, nonlinear Raman–Nath second‐harmonic generation from the optical Fibonacci superlattice is theoretically investigated, and a propagation equation that describes the properties of frequency‐doubled waves is presented. Abundant diffraction peaks that are substantially more varied than the traditional Raman–Nath regime are observed. The dependence of the generated second‐harmonic signals on the structural parameters and fundamental laser performance is also comprehensively discussed.

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.

Transitions Between Quantized Standing Waves at Interactions with an Atom in the Raman–Nath Regime

The interaction of an atom with an electromagnetic field induces transitions between its quantized modes, in which cos- and sin-standing waves are chosen as the basis for quantization. The number of photons in the modes were calculated in the Raman–Nath regime in the approximation of adiabatic following. It is shown that in the course of transitions an initially populated mode is generally not completely emptied, and the oscillating part of photons increases with the total number in the system.

Small dosage of holographic exposure via a He-Ne laser to fabricate tunable liquid crystal phase gratings operated with low electric voltages

ABSTRACTThe fabrication processes of tunable liquid crystal (LC) phase gratings via small dosage of holographic exposure of a He-Ne laser beam were investigated. The initial LC cells were filled with various ratios of ingredients mainly including LCs and photocurable monomers. The fabricated LC phase gratings shown in the Raman–Nath regime possessed a maximum value of first-order diffraction efficiency close to 33.3% at 5.8 Vrms. Furthermore, optimised grating was demonstrated and used as an interference recorder in holography.

Liquid crystal light valve operating at near infrared spectral range

A near infrared sensitive liquid crystal light valve, based on Ru-doped Bi12TiO20 (BTO:Ru) inorganic crystal and liquid crystal is proposed. The two-beam mixing experiments at Raman–Nath regime show promising gain value at 1064 nm. An image evolution through the proposed device is demonstrated supporting all optical switching property.

Light diffraction by acoustophotorefractive dynamic gratings in Raman―Nath regime

Raman–Nath light diffraction on acoustophotorefractive holographic gratings that was recorded in cubic photorefractive crystals according to a synchronous detection mechanism was investigated. It was shown that the diffraction efficiency in sillenite-type gyrotropic crystals depended weakly on the incident light polarization and the external electric field strength. The highest diffraction efficiency in non-gyrotropic crystals was reached for p-polarized light (writing and reading) and a strong external electric field.

Loss of atom interference due to a random phase

We suggest a model where the influence of an environment on the atom interference is associated with a random phase. The model consists of sending a two-level state atom through two cavities, both containing a standing wave field in the Bragg regime and Raman–Nath regime, respectively. In view of this model, we can visualize the loss of interference fringes if the randomness of the phase increases, and the restoration of the pattern when it decreases, as which-path information. Then, the controllable random noise acts as a decoherence that would destroy the quantum features.

Slow and fast light in photorefractive GaAs–AlGaAs multiple quantum wells in transverse geometry

We show theoretically that, based on the dispersive phase coupling effect during the wave mixing process, both slow and fast light can be achieved in GaAs–AlGaAs photorefractive multiple quantum wells (PRMQWs) films applied with a transverse direct-current electric field. The general formula for the group velocity of the diffracted beams in the Raman–Nath regime during the wave mixing process in a nonlinear thin film is derived and is then applied to the case of the PRMQWs films in the transverse geometry. The simulation results in the transverse-geometry PRMQWs films show that the group velocity and bandwidth of slow light can be on the order of centimeter per second and 100 kHz, respectively. The extremely low group velocity and the relatively broad bandwidth are mainly originated from the strong quadratic electro-optic effect and the fast response rate of the PRMQWs films, respectively. Our results show that the delay-bandwidth product of slow light can be significantly improved in PRMQWs films as compared to the reported results in other photorefractive materials.

H-PDLC/Clay Nanocomposites

Holographic polymer-dispersed liquid crystals (H-PDLCs) filled with layer-structured montmorillonite (MMT) clay were fabricated by wave mixing of two coherent argon-ion laser beams. The effects of MMT doping were investigated by comparing a pristine sodium-type MMT and an organophilic MMT (OMMT) via modification. In order to gain insights into the complex formation of the ternary nematic/polymer/clay nanocomposites, wide-angle X-ray diffraction experiments were carried out on pure liquid crystal, MMT clay, and clay dispersed in the liquid crystal in the mesophase as well as isotropic state. Self-diffraction experiments in the Raman–Nath regime revealed that the first-order diffraction efficiency was enhanced in the H-PDLCs consisting of pristine MMT nanoparticles and yet suppressed by the incorporation of OMMT. Holographic nature of the polymer-matrix nanocomposites was confirmed by optical polarizing microscopy. The results of this study may open up great promise held by such ternary polymer-matrix nanocomposites for photonic applications.

Regime independent coupled-wave equations in anisotropic photorefractive media

An extension to coupled wave theory suitable for all regimes of diffraction is presented. The model assumes that the refractive index grating has an arbitrary profile in one direction and is periodic (but not necessarily sinusoidal) in the other. Higher order diffracted terms are considered and appropriate mismatch terms dealt with. It is shown that this model is analytically equivalent to both the Bragg and Raman–Nath regime coupling models under an appropriate set of assumptions. This model is applied to cases such as optical coupling in liquid crystal cells with photoconductive layers. Its predictions are successfully compared to finite element simulations of the full Maxwell’s equations.

Measurement of the Wigner function via atomic beam deflection in the Raman–Nath regime

A method for the reconstruction of photon statistics and even the Wigner function of a quantized cavity field state is proposed. The method is based on the measurement of momentum distribution of two-level atoms in the Raman–Nath regime. Both the cases of resonant and off-resonant atom–field interaction are considered. The Wigner function is reconstructed by displacing the photon statistics of the cavity field. This reconstruction method is straightforward and does not need much mathematical manipulation of experimental data.

Characterization of thin real-time holographic media by dithered four-wave mixing

Photosensitive optical media of the types that are used in real-time holography generally exhibit both photorefractive and photochromic response. The parameters that characterize each of these types of response can be extracted by detailed quantitative analysis of four-wave mixing experiments in the Raman–Nath regime. This principle has been tested using reactive eyeglass lenses. The techniques of Fourier optics have been applied to the analysis of diffraction from amplitude/phase gratings produced in the photochromic glass by laser illumination. Dithering of a laser-induced fringe pattern produces a combination of two-wave and four-wave mixing that can be analysed in terms of amplitudes proportional to products of Bessel functions of different orders. The incident and diffracted beams are predicted, and observed, to be modulated at the dither frequency and its harmonics. The small dither amplitudes that were employed, made possible by use of a phase-sensitive detection technique, allowed Bessel function expansions to be truncated after only a few terms for the purpose of parameter estimation. The technique has allowed the very small refractive index change associated with dispersion of the photo-induced absorption in silver halide doped photochromic glass to be measured for the first time.

Characterization of an inorganic photorefractive liquid crystal hybrid cell

High birefringent liquid crystals are attractive for photorefractive applications but device operation, usually restricted to the Raman–Nath regime, can be degraded by small phase shifts between the optical and refractive index gratings and coarse grating spacings with narrow beam intersection angles. Applying external electric fields and having to tilt the cell at an angle to the grating k-vector cause further complications. In this paper, two-beam coupling in hybrid photorefractive cells comprising a nematic liquid crystal layer between inorganic photorefractive windows is described. Photorefractive properties are determined by the windows, while the liquid crystal amplifies the overall refractive index modulation. Bragg matched liquid crystal gain coefficients >1600 cm−1, grating periods <300 nm and wide beam intersection angles with perfect 90° phase shifts between the optical and refractive index gratings at normal incidence without the need for an external field are demonstrated.

High-Performance Material for Holographic Gratings by Means of a Photoresponsive Polymer Liquid Crystal Containing a Tolane Moiety with High Birefringence

Formation of intensity gratings was studied with two s-polarized (s+s) writing beams in polymer liquid crystals (PLCs) containing a photochromic moiety (azobenzene) and a mesogenic unit (tolane, T-AB; cyanobiphenyl, CB-AB) by means of photoinduced change in alignment of PLCs. Remarkable differences were observed between these two PLCs. T-AB showed higher values of the diffraction efficiency (η) and a faster response than CB-AB. In photoinduced alignment behavior of the PLCs, T-AB exhibited a faster change in alignment than CB-AB with the value of η about 30% in the Raman−Nath regime and the maximum value for modulation of the refractive index (Δn‘) of about 0.08. It was revealed that η and Δn‘ are dependent on the structure of the mesogenic unit. In addition, we attempted the holographic image storage of three-dimensional (3-D) objects in the T-AB films. The 3-D object was reconstructed with high resolution (>5000 lines/mm).

Optical amplification in nematics doped with carbon nanotubes

We present results on the orientational photorefractive effect in a mesogenic nematic doped with multiwalled carbon nanotubes. Efficient coherent-beam amplification of a signal beam by energy exchange with a pump beam was observed in homogeneous cells of the doped liquid crystal E7 at electric fields of ∼0.5 V/μm. Photorefractive gains as high as 103 cm−1 are achieved in the Raman–Nath regime. It is found that the gain coefficient depends strongly on the externally applied dc voltage, the pump/probe intensity ratio and the total input intensity.

Achromatic optical device for generation of a broadband frequency spectrum with high-frequency stability and sharp termination

We have implemented a new optical scheme to produce a broadband frequency spectrum with customizable shape and high stability. The scheme consists of the generation of a mode structure by allowing a frequency-stabilized single-mode laser to pass through an acousto-optical modulator working in the Raman–Nath regime. Diffraction yields several diffracted beams, which are shifted in frequency (ΔνM) by acoustic waves in the acousto-optical modulator. Then the diffracted beams are merged into one beam by means of a telescope. The scheme has worked in both the visible and the UV: Frequency spectra as wide as nΔνM with n=7 have been achieved, resulting in widths of 225 and 150 MHz for the visible and the UV spectral regions, respectively. The spectra possess the same stability as the primary single-mode laser. Their profiles may exhibit a sharp termination on one side of the spectrum, a feature that allows them to be utilized for high-efficiency laser cooling of an ion beam in a storage ring.

Arc field states, photon statistics probes and quantum lenses: field evolution and atomic motion in a dispersive interaction model

We study the interaction of a quantized single-mode standing-wave cavity field with a two-level atom de Broglie wave. For the sake of simplicity we consider the field to be far detuned and the atom to be moving in the Raman - Nath regime. We show that the Wigner function of the field is a superposition of the Wigner functions for the coherent states aligned on an arc in phase space. The back action of the measurement of the atomic internal state leads to the modification of the diagonal as well as of the off-diagonal elements of the field density matrix. We investigate the formation of nonclassical field states via atomic deflection and internal-state measurement and show that the coherence of the field and the interference between the constituent coherent states disappear in the limit of large interaction times. The width of the atomic momentum distribution allows us to determine the mean photon number and the width of the photon distribution. We find that, for an appropriate choice of the initial state of the atomic centre-of-mass motion, the form of the atomic momentum distribution is identical to that of the photon distribution. The field near a node or an antinode acts as a focusing or defocusing lens for atoms, depending on the detuning and on the initial internal state of the atom.

Shift-invariant photorefractive joint-transform correlator using Fe:LiNbO_3 crystal plates

We report the results of our experimental investigation on a shift-invariant photorefractive image correlator that uses a thin crystal plate of Fe:LiNbO(3), which operates in the Raman-Nath regime of diffraction.

Electron wave diffraction by semiconductor gratings: Rigorous analysis and design parameters

An exact rigorous coupled-wave analysis has been developed to model ballistic electron wave diffraction by gratings with periodic effective mass and/or potential energy variations. Design expressions have been derived to calculate diffracted angles, to identify evanescent orders, and to identify the Bragg condition. Design expressions for Bragg regime (up to 100% diffraction efficiency in a single order) and Raman–Nath regime (high diffraction efficiency divided among multiple orders) diffraction are presented along with example Ga1−xAlxAs grating designs. Design procedures for ballistic electron switches, multiplexers, spectrometers, and electron waveguide couplers are described.

Acousto-optic control and modulation of optical coherence by electronically synthesized holographic gratings

We introduce a new technique to modify the coherence properties and the far-field intensity distributions of optical fields. Use is made of a combination of Bragg diffraction and Raman–Nath diffraction in an acousto-optic deflector. The high-frequency Bragg grating in the deflector is phase modulated by a synthetic low-frequency Raman–Nath regime grating that has a structure of an optimized phase-only computer-generated hologram. We demonstrate, e.g., electronic control of the state of spatial coherence of light, Gaussian to flat-top conversion, and the generation of arrays of equally intense but mutually incoherent light spots.