Bragg Interference Research Articles

Elastodynamic metasurface: Depolarization of mechanical waves and time effects

We report the concept of microstructured surfaces with inner resonance in the field of elastodynamics, so-called elastodynamic metasurfaces. Such metasurfaces allow for wavefield manipulation of mechanical waves by tuning the boundary conditions at specific frequencies. In particular, they can be used to depolarize elastic waves without introducing heterogeneities in the medium itself; the physical means to do so in homogeneous elastic media used to remain, surprisingly, an open question while depolarization is commonplace in electromagnetism. The principle relies on the anisotropic behaviour of a subwavelength array of resonators: Their subwavelength configuration confines the Bragg interferences scattered by resonators into a boundary layer. The effective behaviour of the resonating array is expressed with homogenization as an unconventional impedance, the frequency-dependence, and anisotropy of which lead to depolarization and time effects. The concept of the elastodynamic metasurface is tested experimentally and results bear testament to its efficacy and robustness. Elastodynamic metasurfaces are easily realized and analytically predictable, opening new possibilities in tomography techniques, ultrasonics, geophysics, vibration control, materials and structure design.

ISOLATION OF SURFACE WAVE-INDUCED VIBRATION USING PERIODICALLY MODULATED PILES

The isolation of surface wave-induced vibration using periodically modulated piles in soil is investigated. We demonstrate through simulations the dependence of complete bandgaps on the lattice symmetries, geometric parameters of the piles and material properties of the soil. The simulated results suggest that the piles modulated with square and hexagonal lattices are much more favorable for the formation of complete bandgaps than those modulated with honeycomb lattice. The height of the piles also plays a significant role in governing the evolution of complete bandgaps. Besides, complete bandgaps can be tuned by tailoring the volume fraction of the piles and the geometries of the pile cross section. Our results indicate that the contrast in the Young's modulus and the density is vital for the evolution of complete bandgaps and the viscosity of the soil should be considered as well. The analysis of surface wave propagation in a finite number of piles confirms the simulated complete bandgaps and also reveals that the complete bandgaps stem from Bragg interferences. This paper not only demonstrates the promising application of periodically modulated piles as wave barriers but also provides design guidelines for civil engineers.

Surface acoustic waves in pillars-based two-dimensional phononic structures with different lattice symmetries

The theoretical study deals with the propagation of surface acoustic waves in two-dimensional arrays of resonant elements with different symmetry lattices. The resonant elements are cylindrical pillars on the surface of a semi-infinite substrate. The obtained band structures show the interaction of the pillars acoustic resonances with the semi-infinite medium which form additional band gaps that are decoupled from Bragg gaps. Especially, the frequency position of the lowest band gap is invariant with respect to lattice symmetries. Thereby, this position is independent of the lattice pitch, which is unexpected in band gaps based on Bragg interferences. However, the role of the period remains important for defining the non-radiative region limited by the slowest bulk mode and influencing the existence of the guided modes. Numerical simulations are based on the efficient finite element method and considered silicon pillars on a silicon substrate.

PHOTON-PHOTON INTERACTION IN STRUCTURED QED VACUUM

In spatially structured strong laser fields, quantum electrodynamical vacuum behaves like a nonlinear Kerr medium with modulated third-order susceptibility where new coherent nonlinear effects arise due to modulation. We consider the enhancement of vacuum polarization and magnetization via coherent spatial vacuum effects in the photon-photon interaction process during scattering of a probe laser beam on parallel focused laser beams. Both processes of elastic and inelastic four wave-mixing in structured QED vacuum accompanied with Bragg interference are investigated. The phase-matching conditions and coherent effects in the presence of Bragg grating are analyzed for photon-photon scattering.

Bragg Scattering of Light in Vacuum Structured by Strong Periodic Fields

Elastic scattering of laser radiation due to vacuum polarization by spatially modulated strong electromagnetic fields is considered. The Bragg interference arising at a specific impinging direction of the probe wave concentrates the scattered light in specular directions. The interference maxima are enhanced with respect to the usual vacuum polarization effect proportional to the square of the number of modulation periods within the interaction region. The Bragg scattering can be employed to detect the vacuum polarization effect in a setup of multiple crossed superstrong laser beams with parameters envisaged in the future Extreme Light Infrastructure.

Locally resonant surface acoustic wave band gaps in a two-dimensional phononic crystal of pillars on a surface

We investigate theoretically the propagation of acoustic waves in a two-dimensional array of cylindrical pillars on the surface of a semi-infinite substrate. Through the computation of the band structure of the periodic array and of the transmission of waves through a finite length array, we show that the phononic crystal can support a number of surface propagating modes in the nonradiative region of the substrate, or sound cone, as limited by the slowest bulk acoustic wave. The modal shape and the polarization of these guided modes are more complex than those of classical surface waves propagating on a homogeneous surface. Significantly, an in-plane polarized wave and a transverse wave with sagittal polarization appear that are not supported by the free surface. In the band structure, guided modes define band gaps that appear at frequencies markedly lower than those expected from the Bragg interference condition. We identify them as originating from local resonances of the individual cylindrical pillars and show their dependence on the geometrical parameters, in particular with the height of the pillars. The transmission of surface acoustic waves across a finite array of pillars shows the signature of the locally resonant band gaps for surface modes and their dependence on the symmetry of the source and its polarization. Numerical simulations are performed by using the finite element method and considering silicon pillars on a silicon substrate.

Coherent Scattering of a Multiphoton Quantum Superposition by a Mirror BEC

We present the proposition of an experiment in which the multiphoton quantum superposition consisting of N approximately 10{5} particles generated by a quantum-injected optical parametric amplifier, seeded by a single-photon belonging to an Einstein-Podolsky-Rosen entangled pair, is made to interact with a mirror-Bose-Einstein condensate (BEC) shaped as a Bragg interference structure. The overall process will realize a macroscopic quantum superposition involving a microscopic single-photon state of polarization entangled with the coherent macroscopic transfer of momentum to the BEC structure, acting in spacelike separated distant places.

Experimental and calculated research on a large band gap constituting of tubes with periodic narrow slits

A new band gap structure composed of a square array of parallel steel tubes with narrow slits is presented. The propagation of acoustic waves in a two-dimensional composite medium constituted of slit tubes in air is investigated both theoretically and experimentally. The band gap is calculated with the finite element method in which the acoustic-solid coupling is taken into account. The transmissions of the band system with both different single-width narrow slits and multi-width narrow slits are analyzed. Experimental measurements show that the transmission through an array of slit tubes with periodic narrow slits drops to noise level throughout frequency interval in good agreement with the calculated forbidden band. The large band gap and low starting frequency is obtained by arranging different width of slits embedded in the tubes. The experiments and theoretical results show that this new band gap structure has an especial character based on the resonant cavity playing an important role on the band gap besides the traditional Bragg interference.

MACROSCOPIC QUANTUM ENTANGLEMENT IN LIGHT REFLECTION FROM BOSE-EINSTEIN CONDENSATES

The present work investigates quantum phenomena with large size systems generated in the microscopic world and then transferred in the macro one through an amplification process. Precisely, a microscopic entangled photon state is created by a nonlinear optical process, then one subsystem is injected into an optical parametric amplifier and then converted into a macro — state consisting of N ≈ 3.5 × 104 photons in a quantum superposition. By adopting a local filtering technique, we then demonstrate the entanglement of the bipartite system. The new conceptual framework paves the way toward the generation of light-matter entangled states by coupling the output radiation with a Bose-Einstein condensate. The multiphoton superposition generated by a quantum-injected optical parametric amplifier (QI-OPA) can be made to interact with a Mirror-BEC shaped as a Bragg interference structure.

Modulation optical spectroscopy of excitons in structures with GaAs multiple quantum wells separated by tunneling-nontransparent barriers

Contactless optical electroreflectance measurements at different temperatures are used to study exciton states in a structure involving a periodic system of 36 GaAs quantum wells separated by tunneling-nontransparent AlGaAs barriers with thickness 104 nm. In the structure, the width of 32 of the quantum wells is 15 nm, while the width of the remaining four quantum wells, numbered 5, 14, 23, and 32, is 20 nm. The periodicity of the structure corresponds to the Bragg interference condition at the excitonic frequency in quantum wells at the angle of incidence of light ∼43°. From the quantitative analysis of the shape of the contactless electroreflectance line, the parameters of the exciton ground states and excited states are determined for both types of quantum wells. It is established that, for the system of four 20-nm-wide quantum wells separated by a distance of 830 nm, the size-quantization energy in the ground state is 8.4 ± 0.1 meV, and the parameter of broadening of the excitonic peak is 1.8 ± 0.1 meV at 17 K and increases with temperature up to 2.0 ± 0.1 meV at 80 K. For the system of 32 wells with the width 15 nm, the quantum confinement energy in the ground state is 14.9 ± 0.1 meV, and the parameter of broadening of the excitonic peak is 2.2 ± 0.1 and 2.6 ± 0.1 meV at 17 and 80 K, respectively. The possible causes of radiative and nonradiative broadening of exciton states in the systems are discussed.

Room temperature operation of epitaxial lead-telluride detectors monolithically integrated on midinfrared filters

Epitaxial PbTe midinfrared photodetectors are monolithically integrated on optical filter structures, like λ∕4 antireflection layers or λ∕2 microcavities. The antireflection layers result in an increased photoresponsivity of the detectors by a factor of 2.2, measured at the target wavelength of 3.1μm. The microcavities, acting as efficient narrow band filters, consist of two PbEuTe∕EuTe Bragg interference mirrors separated by a PbEuTe cavity layer. The photoresponse spectra of the detectors integrated with the microcavity filters exhibit a single resonance at 3.6μm with a relative line width of 2.7%. The narrow photoresponse peak is in coincidence with a molecular absorption line typical for nonaromatic aldehydes. For all devices room temperature operation is demonstrated either in photoconductive or in photovoltaic operation mode.

Nanocrystal-based microcavity light-emitting devices operating in the telecommunication wavelength range

Highly luminescent colloidally prepared HgTe nanocrystals (NCs) are used to fabricate microcavity light-emitting devices operating around 1.5μm. They consist of a Bragg interference mirror from standard optical materials deposited on glass substrates, an active layer embedding the nanocrystals, and a metallic top mirror. These devices give highly directional narrow single-mode emission with a beam divergence below 3° and a spectral width smaller by a factor of 8 than that of a NC reference sample. The emission wavelength can be tuned between 1.4 and 1.75μm by changing the cavity length and thus, the cavity finesse. The influence of the latter on output power and beam divergence is discussed. Furthermore, operation up to 75 °C is demonstrated without degradation of the NCs, which is promising for potential applications.

Comparison of the sound attenuation efficiency of locally resonant materials and elastic band-gap structures

Numerical methods are applied to study the elastic wave propagation in a so-called locally resonant sonic material. The structure is a two-dimensional analog of a three-dimensional structure proposed recently, which offers interesting attenuation properties at low frequencies [K. M. Ho et al., Appl. Phys. Lett. 83, 5566 (2003)]. The present structure is based on heavy cylinders located on a square lattice, immersed in a soft polymer, and separated from each other by a rigid grid. It is demonstrated that the grid induces Fano resonances, improving the sound attenuation performances of the system compared with the mass law. The transmission characteristics of a stacking of different layers of this material are studied and compared with those of a 2D phononic crystal obtained by removing the grid. For equivalent mass and size, the latter is shown to have even better attenuation performances on a larger range of frequencies due to Bragg interference phenomena at low frequencies.

Highly directional emission from colloidally synthesized nanocrystals in vertical cavities with small mode spacing

The optical properties of light emitting devices based on colloidally synthesized CdSe/CdS core/shell semiconductor nanocrystals embedded in vertical cavities are investigated. The cavities are several micrometers, thick and formed by a metallic mirror and a dielectric Bragg interference mirror deposited on the opposite surfaces of cleaved pristine mica sheets. Due to the large cavity length, up to 30 resonances are found within the Bragg mirror stop band. The corresponding small mode spacing allows one to extract a large portion of the broad nanocrystal luminescence band from the cavity upon optical excitation. The spontaneous emission of these cavities is highly forward directed with a beam divergence smaller than 1.3°. Furthermore, the emission is linearly polarized which is a result of the birefringent properties of the mica sheets.

Applications of lead-salt microcavities for mid-infrared devices

Optically pumped lasers and light detectors based on microcavities with highly efficient Pb1 - x Eux Te/EuTe Bragg interference mirrors are described for the 3–6 µm wavelength range. The lasers operate up to and above room temperature with a minimum pump intensity threshold of about 15kW/cm2 The responses of the photodetectors show well pronounced cavity resonances. Furthermore, a microcavity is used to determine the absorption spectrum of a superlattice containing three-dimensionally ordered, self-organised PbSe quantum dots. The quantum dot absorption peak, with a width of only 9 meV, confirms the exceptionally high homogeneity of the quantum dot size distribution, observed so far only for these lead-salt quantum dots.

Spectroscopy on Vertical Microcavities for the Mid-Infrared

Mid-infrared microcavities from IV–VI semiconductors (lead salts) are investigated by infrared transmission measurements. Epitaxial Pb1—xEuxTe/EuTe multilayers with an refractive index contrast of more than 80% are used as Bragg interference mirrors with a very large mirror stop band width. Therefore, the polarization splitting of cavity modes which are strongly detuned in respect to the center of the mirror stop band can by studied. It is found to show a quadratic dependence as function of the detuning energy. Furthermore, by inspecting the ratio between the width and the height of cavity resonances, the absorption edge of ordered, self-organized PbSe quantum dots is clearly detected.

The Helmholtz–Kirchhoff approach to modeling penetration of acoustic waves into rough seabeds

The Helmholtz–Kirchhoff integral is applied to model the penetration of sound waves into sandy seafloors at grazing angles above and below the critical angle. Although the conditions for the validity of the Kirchhoff approximation can be limiting, this approximation should be valid at high frequency for gently undulating seafloor surfaces even at moderate to low grazing angles, providing that the self-shadowing effect is carefully removed. The analytical development of the method is first presented, followed by numerical examples and comparisons with the experimental data of Maguer et al. [SACLANTCEN report, SR-287, April 1998]. The model predicts, in agreement with the 2- to 15-kHz acoustic data, the frequency where the contributions due to roughness effects begin to dominate those due to the evanescent wave. Secondary effects such as Bragg interference patterns and the loss of signal coherence with grazing angle or depth are correctly predicted. The model simulations strongly suggest that roughness of the sediment interface is most likely the cause of anomalous sound penetration into the seabed.

Diffraction-like effects in a highly concentrated w/o emulsion: a PFG NMR study

Diffraction-like effects have been observed by applying pulsed field gradient (PFG) nuclear magnetic resonance (NMR) to a highly concentrated water-in-oil (W/O) emulsion, made up of the nonionic surfactant C 12E 4 [CH 3(CH 2) 11(OCH 2CH 2) 4OH], n-decane, and brine [1 wt% NaCl(aq) solution]. The pulsed field gradient NMR data show one pronounced maximum and the shoulder of a second maximum in the attenuation curve of the NMR signal from water, the so-called Bragg interference peaks. From the diffraction-like peaks, the average distance (center to center) between the emulsion droplets can be obtained, in this case related to the average size of an emulsion droplet. Furthermore, we note that the long-term stability of the emulsion can be followed by pulsed field gradient NMR.

Aspects of Resonant Enhancement of Nonlinear Optical Properties in Silica

This paper briefly reports two approaches toward improving the nonlinear response of glassy materials. Recent results demonstrate that the use of local-field resonance or Bragg interference effects provide improved figures of merit.

Interface study of W/Si multilayers with increasing number of periods

The X-ray reflectivity and diffuse-scattering measurements at grazing incidence on W/Si multilayers with increasing number of periodsN from 3 to 15 were performed using the CuKα1 radiation. The Fresnel optical computational code and distorted-wave Born approximation were used to evaluate the results. The multilayer Bragg interferences are observed fromN=6. The reflectivity on the 1st Bragg maximum increases from 20% to 55% on increasingN from 6 to 15. The r.m.s. interface roughness of 0.65 nm does not change withN. A model of vertically correlated interface profiles was successfully used to simulate the diffuse scattering results and confirmed a negligible cumulative interface roughness upwards the multilayers. The lateral correlation length of 10 nm is independent ofN. An additional roughness component of very large correlation length (“waviness”) had to be included to obtain self-consistent simulations of the sample and detector scans forN≥9. A gradual increase of the fractal parameter of the interface profiles fromh=0.15 forN=3 toh=0.75 forN=15 is the most pronounced effect of increasingN and implies the loss of the fractal behaviour.