Opto-Mechanical Effects in Superradiant Light Scattering by Bose-Einstein Condensate in an Optical Cavity

We investigate the effects of a movable mirror (cantilever) of an optical cavity on the superradiant light scattering from a Bose-Einstein condensate (BEC) in an optical lattice. We show that the mirror motion has a dynamic dispersive effect on the cavity-pump detuning. Varying the intensity of the pump beam, one can switch between the pure superradiant regime and the Bragg scattering regime. The mechanical frequency of the mirror strongly influences the time interval between two Bragg peaks. We find that when the system is in the resolved side band regime for mirror cooling, the superradiant scattering is enhanced due to coherent energy transfer from the mechanical mirror mode to the cavity field mode.     

Opto-Mechanical Effects in Superradiant Light Scattering by Bose-Einstein Condensate in an Optical Cavity

We investigate the effects of a movable mirror (cantilever) of an optical cavity on the superradiant light scattering from a Bose-Einstein condensate (BEC) in an optical lattice. We show that the mirror motion has a dynamic dispersive effect on the cavity-pump detuning. Varying the intensity of the pump beam, one can switch between the pure superradiant regime and the Bragg scattering regime. The mechanical frequency of the mirror strongly influences the time interval between two Bragg peaks. We find that when the system is in the resolved side band regime for mirror cooling, the superradiant scattering is enhanced due to coherent energy transfer from the mechanical mirror mode to the cavity field mode.     

Correlation of Bragg scattering from the sea surface at different polarizations

The phase interference fading in Bragg backscattering from the sea surface at moderate incidence angles is considered using both moment method calculation of the scattering from measured water profiles and an implementation of the slightly rough, tilted facet model. The fading of the instantaneous scattering cross-section is shown to be independent of the instantaneous phase of the illuminating signal. The vertical and horizontal polarization fading responses are therefore strongly correlated when identical carrier frequencies and modulations are used at both polarizations since the electromagnetic energy is Bragg resonant with the same small-scale roughness in both cases, independent of whether the polarization channels are phase locked. Instantaneous horizontally polarized Bragg backscattering (HH) exceeding that at vertical polarization (VV) is extremely unlikely in this case. Use of an offset in the frequencies of monochromatic signals used at the two polarizations can lead to reduced correlation between the fading if the illumination footprint length is sufficiently large so that the frequency shift introduces a significant additional phase shift between the scattering from the leading and trailing edges of the footprint. The fading shows only a very weak correlation when this phase shift exceeds 400°. HH Bragg backscattering exceeding VV will be much more common under these specialized conditions.     

Acoustic scattering from a thermally driven buoyant plume revisited

Far-field weak scattering theory is applied to the case of high-frequency broad-bandwidth acoustic scattering from a thermally generated buoyant plume in a controlled laboratory environment. To first order, the dominant scattering mechanism is thermally driven sound-speed variations that are related to temperature deviations from ambient. As a result, the received complex acoustic scattering is a measure of the one-component three-dimensional Fourier transform of the temperature difference field measured at the Bragg wave number. The Bragg wave number vector is the difference between the scattered and incident wave vectors. Solving for its magnitude yields the Bragg scattering condition; this is the Fourier component of the plume variability that produces scattering. Results are presented for multistatic scattering from unstable and turbulent plumes using a parallel scattering geometry. The data justify application of the far-field weak scattering theory to the present case of a thermal plume. As a consequence, quantitative results on medium variability can be inferred using high-frequency broad-bandwidth acoustic scattering. Particular attention is given to the role of anisotropy of the variability of the scattering field in determining the validity of far-field Bragg scattering.     

Frequency response of second-order extremely asymmetrical scattering in wide uniform holographic gratings

Second-order extremely asymmetrical scattering (EAS) and grazing-angle scattering (GAS) are types of Bragg scattering in slanted wide periodic gratings. They occur when the second diffracted order satisfies the Bragg condition and has a wavevector parallel (for EAS) and almost parallel (for GAS) to the grating boundaries. In this paper, for the first time, a rigorous numerical study of the frequency responses of second-order EAS and GAS is presented for bulk TE electromagnetic waves in planar holographic gratings. A highly unusual pattern of strong optical resonances in the side-lobe structure of these frequency responses is predicted. A relationship between these resonances and the previously predicted GAS resonances (at zero detunings of the Bragg condition) is established and analysed. A special new type of eigenmodes in slanted wide periodic gratings with strong frequency detunings are predicted in the case of second-order EAS and GAS. The eigenmodes are shown to be guided by the grating alone without any conventional guiding effect in the structure. The typical field structure in such eigenmodes is investigated and discussed. PACS 42.25Fx; 42.79Dj; 42.40Eq     

Bragg scattering of cooper pairs in an ultracold Fermi gas

We present a theoretical treatment of Bragg scattering of a degenerate Fermi gas in the weakly interacting BCS regime. Our numerical calculations predict correlated scattering of Cooper pairs into a spherical shell in momentum space. The scattered shell of correlated atoms is centered at half the usual Bragg momentum transfer, and can be clearly distinguished from atoms scattered by the usual single-particle Bragg mechanism. We develop an analytic model that explains key features of the correlated-pair Bragg scattering, and determine the dependence of that scattering on the initial pair correlations in the gas.     

Wave-front reversal of multifrequency continuous emission by Bragg scattering from phase regular inhomogeneities

The possibility of wave-front reversal of continuous multifrequency emission with a wide line spectrum (in particular, emission of lasers operating on cascade vibrational-rotational transitions of diatomic molecules, e.g., HF or CO) is analyzed; the reversal is based on Bragg scattering from a spatial phase hologram that is recorded in a resonance-absorbing medium by emission with a frequency different from any of the reversed-signal frequencies. The mechanism of formation of a spatial phase hologram and the features of optical Bragg scattering on such structures are analyzed. It is shown that a scattered wave-front is complex conjugate to one of the waves recording the phase grating. An optical system for wave-front reversal is proposed and the Bragg scattering efficiency is estimated for a particular example. The analysis indicates that the proposed system does not exhibit frequency selectivity and is basically suitable for wave-front reversal of emission with a broad line spectrum. The main problem is to choose a medium with resonance absorption at the center of a multifrequency emission spectrum and with complete transparency for the reversed signal.     

Low-noise chip-based frequency conversion by four-wave-mixing Bragg scattering in SiN(x) waveguides

Low-noise, tunable wavelength-conversion through nondegenerate four-wave mixing Bragg scattering in SiN(x) waveguides is experimentally demonstrated. Finite element method simulations of waveguide dispersion are used with the split-step Fourier method to predict device performance. Two 1550 nm wavelength band pulsed pumps are used to achieve tunable conversion of a 980 nm signal over a range of 5 nm with a peak conversion efficiency of ≈5%. The demonstrated Bragg scattering process is suitable for frequency conversion of quantum states of light.     

Stokes-space formalism for Bragg scattering in a fiber

Optical frequency conversion by four-wave mixing (Bragg scattering) in a fiber is considered. The evolution of this process can be modeled using the signal and idler amplitudes, which are complex, or Stokes-like parameters, which are real. The Stokes-space formalism allows one to visualize power and phase information simultaneously, and produces a simple evolution equation for the Stokes parameters.     

Grazing-angle scattering of electromagnetic waves in periodic Bragg arrays

A new powerful approximate approach for the theoretical analysis of Bragg scattering in oblique strip-like periodic arrays with the scattered wave propagating almost parallel to the array boundaries – grazing-angle scattering (GAS) – is introduced and justified. This approach is based on allowance for the diffractional divergence of the scattered wave by means of the parabolic equation of diffraction and Fourier analysis. The divergence is demonstrated to be an intrinsic physical cause of GAS. Detailed theoretical analysis of steady-state GAS is carried out for bulk and guided optical modes. It is demonstrated that the most interesting feature of GAS in arrays of width that is greater than a critical width is a unique combination of two strong simultaneous resonances with respect to frequency and angle of scattering. In such wide arrays, GAS is demonstrated to be not only unusually sensitive to angle of scattering, but also to small variations of array width and grating amplitude. Entire concentration of the resonantly strong scattered wave inside the array is shown to be possible. A relationship between GAS, conventional Bragg scattering, and extremely asymmetrical scattering (i.e. where the scattered wave propagates parallel to the array boundaries) is analysed. Applicability conditions for the used approximations and obtained results are derived and discussed.     

Inverse scattering for the one-dimensional Helmholtz equation: fast numerical method

The inverse scattering problem for the one-dimensional Helmholtz wave equation is studied. The equation is reduced to a Fresnel set that describes multiple bulk reflection and is similar to the coupled-wave equations. The inverse scattering problem is equivalent to coupled Gel'fand-Levitan-Marchenko integral equations. In the discrete representation its matrix has T?plitz symmetry, and the fast inner bordering method can be applied for its inversion. Previously the method was developed for the design of fiber Bragg gratings. The testing example of a short Bragg reflector with deep modulation demonstrates the high efficiency of refractive-index reconstruction.     

Bragg spectroscopy of discrete axial quasiparticle modes in a cigar-shaped degenerate Bose gas

We propose an experiment in which long wavelength discrete axial quasiparticle modes can be imprinted in a 3D cigar-shaped Bose-Einstein condensate by using two-photon Bragg scattering experiments, similar to the experiment at the Weizmann Institute [J. Steinhauer et al., Phys. Rev. Lett. 90, 060404 (2003)] where short wavelength axial phonons with different number of radial modes have been observed. We provide values of the momentum, energy and time duration of the two-photon Bragg pulse and also the two-body interaction strength which are needed in the Bragg scattering experiments in order to observe the long wavelength discrete axial modes. These discrete axial modes can be observed when the system is dilute and the time duration of the Bragg pulse is long enough.     

Fluctuations of the acoustic field Bragg-backscattered from rough surfaces

A rigorous theory of backscattering from slightly rough, statistically non-stationary surfaces is developed. The development proceeds through the application of two ensemble averages: the first is applied to all realizations of the surface having fixed non-stationary features, and the second over all non-stationary surface characteristics. The resulting theory is applied to acoustic sea-floor reverberation, where it is found that non-stationarity must be assumed to obtain agreement with observed reverberation fluctuations. The analysis is further extended to the time domain where it is demonstrated that, for Bragg scatter, no reduction in the predicted fluctuations occurs for frequency diverse waveforms, thus providing a method of differentiating Bragg scatter from other non-resonant scattering processes.     

Specific features of mode spectrum of planar structures with two-dimensional Bragg corrugation (theory and “cold” experiment)

Electrodynamic properties of two-dimensional-periodic Bragg structures of planar geometry are theoretically analyzed within the framework of the geometrical-optics approximation. Specific features of two-dimensional structures with different profiles, such as two-dimensional sinusoidal and “chess-board” corrugation and corrugation in the form of rectangular grooves, are studied. “Cold” testing of the Bragg structures in frequency ranges of 60 and 75 GHz is performed. The measured frequency dependences of the coefficients of reflection, transmission, and scattering in the transverse direction are in good argeement with the calculations. Existence of high-quality modes near the frequency of exact Bragg resonance is experimentally confirmed.     

Matryoshka locally resonant sonic crystal

The results of numerical modeling of sonic crystals with resonant array elements are reported. The investigated resonant elements include plain slotted cylinders as well as their various combinations, in particular, Russian doll or Matryoshka configurations. The acoustic band structure and transmission characteristics of such systems have been computed with the use of finite element methods. The general concept of a locally resonant sonic crystal is proposed that utilizes acoustic resonances to form additional band gaps that are decoupled from Bragg gaps. An existence of a separate attenuation mechanism associated with the resonant elements that increases performance in the lower frequency regime has been identified. The results show a formation of broad band gaps positioned significantly below the first Bragg frequency. For low frequency broadband attenuation, a most optimal configuration is the Matryoshka sonic crystal, where each scattering unit is composed of multiple concentric slotted cylinders. This system forms numerous gaps in the lower frequency regime, below Bragg bands, while maintaining a reduced crystal size viable for noise barrier technology. The finding opens alternative perspectives for the construction of sound barriers in the low frequency range usually inaccessible by traditional means including conventional sonic crystals.     

The quantum acousto-optic effect in Bose-Einstein condensate

We investigate the interaction between a single mode light field and an elongated cigar shaped Bose-Einstein condensate (BEC), subject to a temporal modulation of the trap frequency in the tight confinement direction. Under appropriate conditions, the longitudinal sound like waves (Faraday waves) in the direction of weak confinement acts as a dynamic diffraction grating for the incident light field analogous to the acousto-optic effect in classical optics. The change in the refractive index due to the periodic modulation of the BEC density is responsible for the acousto-optic effect. The dynamics is characterised by Bragg scattering of light from the matter wave Faraday grating and simultaneous Bragg scattering of the condensate atoms from the optical grating formed due to the interference between the incident light and the diffracted light fields. Varying the intensity of the incident laser beam we observe the transition from the acousto-optic effect regime to the atomic Bragg scattering regime, where Rabi oscillations between two momentum levels of the atoms are observed. We show that the acousto-optic effect is reduced as the atomic interaction is increased.     

Measurement for Scattering Media by Synthesis of Optical Coherence Function with Super-Structure Grating Distributed Bragg Reflector Laser Diode

The application of the technique of synthesis of optical coherence function for detection in scattering media is investigated. By modulating the optical frequency, the technique synthesizes the coherence function into a delta-function-like peak at an arbitrary location, and thus can select interferometrically the information at that location. The location is adjustable by the modulation parameter or additional phase modulation. A multi-section super-structure grating distributed Bragg reflector laser diode (SSG-DBR-LD) of THz-order tunable range is employed to enhance the spatial resolution for suppressing the multiple scattering from locations other than that detected. In a preliminary experimental demonstration, a reflectometry of 550 μm spatial resolution was achieved and was used to detect scattering media.     

Double-resonant extremely asymmetrical scattering of electromagnetic waves in periodic arrays separated by a gap

Two strong simultaneous resonances of scattering – double-resonant extremely asymmetrical scattering (DEAS) – are predicted in two parallel, oblique, periodic Bragg arrays separated by a gap, when the scattered wave propagates parallel to the arrays. One of these resonances is with respect to frequency (which is common to all types of Bragg scattering), and another is with respect to phase variation between the arrays. The diffractional divergence of the scattered wave is shown to be the main physical reason for DEAS in the considered structure. Although the arrays are separated, they are shown to interact by means of the diffractional divergence of the scattered wave across the gap from one array into the other. It is also shown that increasing separation between the two arrays results in a broader and weaker resonance with respect to phase shift. The analysis is based on a recently developed new approach allowing for the diffractional divergence of the scattered wave inside and outside the arrays. Physical interpretations of the predicted features of DEAS in separated arrays are also presented. Applicability conditions for the developed theory are derived.     

Generalized Bloch's theorem for viscous metamaterials: Dispersion and effective properties based on frequencies and wavenumbers that are simultaneously complex

It is common for dispersion curves of damped periodic materials to be based on real frequencies as a function of complex wavenumbers or, conversely, real wavenumbers as a function of complex frequencies. The former condition corresponds to harmonic wave motion where a driving frequency is prescribed and where attenuation due to dissipation takes place only in space alongside spatial attenuation due to Bragg scattering. The latter condition, on the other hand, relates to free wave motion admitting attenuation due to energy loss only in time while spatial attenuation due to Bragg scattering also takes place. Here, we develop an algorithm for 1D systems that provides dispersion curves for damped free wave motion based on frequencies and wavenumbers that are permitted to be simultaneously complex. This represents a generalized application of Bloch's theorem and produces a dispersion band structure that fully describes all attenuation mechanisms, in space and in time. The algorithm is applied to a viscously damped mass-in-mass metamaterial exhibiting local resonance. A frequency-dependent effective mass for this damped infinite chain is also obtained.     

Growth of ultrasmall nanoparticles based on thermodynamic size focusing

A physical mechanism of phononic band gap and resonant nanoacoustic scattering in an aggregate of two elastic nanospheres is presented in this paper. By considering the Van der Waals (VdW) force between two nanospheres illuminated by nanoacoustic wave, phononic band gap and frequency shift at the lower frequency side, and largely enhanced nanoacoustic scattering at the other frequency range have been found through calculating the form function of the acoustic scattering from the nanosystem. This VdW-force-induced band gap is different from the known mechanisms of Bragg scattering and local resonances for periodic media. It is shown that when the separation distance between two nanospheres is decreasing from 20 to 1?nm, due to the increasing VdW force, the nanoacoustic scattering is much heightened by two order of magnitude, and meanwhile the frequency shift and phononic band gap at the low frequencies are both widened. These results could provide potential applications of nanoacoustic devices.