Direction-dependent Phase Research Articles

A micromechanics-informed phase field model for brittle fracture accounting for unilateral constraint

We propose a new direction-dependent model for the unilateral constraint involved in the phase field approach to fracture and also in the continuous damage mechanics models. The construction of this phase field model is informed by micromechanical modeling through the homogenization theory, where the representative volume element (RVE) has a planar crack in the center. The proposed model is made closely match the response of the RVE, including the frictionless self-contact condition. This homogenization approach allows to identify a direction-dependent phase field model with the tension–compression split obtained from cracked microstructures. One important feature of the proposed model is that unlike most other models, the material degradation is consistently determined without artificial assumptions or ad hoc parameters with no physical interpretation, thus, a more realistic modeling is resulted. With standard tests such as uniaxial loadings, three-point bending, simple shear, and through-crack tests, the proposed model predicts reasonable crack paths. Moreover, with the RVE response as a benchmark, the proposed model gives rise to an accurate stress–strain curve under shear loads, more accurate than most existing models.

Guiding and confining of light in a two-dimensional synthetic space using electric fields

Synthetic dimensions provide a promising platform for photonic quantum simulations. Manipulating the flow of photons in these dimensions requires an electric field. However, photons do not have charge and do not directly interact with electric fields. Therefore, alternative approaches are needed to realize electric fields in photonics. One approach is to use engineered gauge fields that can mimic the effect of electric fields and produce the same dynamical behavior. Here, we demonstrate such an electric field for photons propagating in a two-dimensional synthetic space. Generation of electric fields in a two-dimensional synthetic lattice provides the possibility to guide photons and to trap them through the creation of quantum confined structures. We achieve this using a linearly time-varying gauge field generated by direction-dependent phase modulations. We show that the generated electric field leads to Bloch oscillations and the revival of the state after a certain number of steps dependent on the field strength. We measure the probability of the revival and demonstrate a good agreement between the observed values and the theoretically predicted results. Furthermore, by applying a nonuniform electric field, we show the possibility of waveguiding photons. Ultimately, our results open up new opportunities for manipulating the propagation of photons with potential applications in photonic quantum simulations.

Solving the Christoffel equation: Phase and group velocities

We provide christoffel, a Python tool for calculating direction-dependent phase velocities, polarization vectors, group velocities, power flow angles and enhancement factors based on the stiffness tensor of a solid. It is built in a modular way to allow for efficient and flexible calculations, and the freedom to select and combine results as desired. All derivatives are calculated analytically, which circumvents possible numerical sampling problems. GNUPlot scripts are provided for convenient visualization. Program summaryProgram title: ChristoffelCatalogue identifier: AFAT_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFAT_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 2631No. of bytes in distributed program, including test data, etc.: 14958Distribution format: tar.gzProgramming language: Python.Computer: Workstations.Operating system: Linux/UNIX/Windows/MacOS.Classification: 7.8.External routines: NumPyNature of problem: Calculating acoustic phase and group velocities in homogeneous solidsSolution method:Solving the Christoffel equation eigenvalue problem by diagonalization; calculating group velocities and enhancement factors analytically as derivatives.Running time:Seconds/minutes

Resonator-free realization of effective magnetic field for photons

We propose to create an effective magnetic field for photons in a two-dimensional waveguide network with strong scattering at waveguide junctions. The effective magnetic field is realized by imposing a direction-dependent phase along each waveguide link. Such a direction-dependent phase can be produced by dynamic modulation or by the magneto-optical effect. Compared to previous proposals for creating an effective magnetic field for photons, this scheme is resonator-free, thus potentially reduces the experimental complexity. We also show that such a waveguide network can be used to explore photonic analogue of integer quantum Hall effect for massless particles.

Non-reciprocal phase shift induced by an effective magnetic flux for light

Photons are neutral particles that do not interact directly with a magnetic field. However, recent theoretical work has shown that an effective magnetic field for photons can exist if the phase of light changes with its direction of propagation. This direction-dependent phase indicates the presence of an effective magnetic field, as shown experimentally for electrons in the Aharonov–Bohm experiment. Here, we replicate this experiment using photons. To create this effective magnetic field we construct an on-chip silicon-based Ramsey-type interferometer. This interferometer has been traditionally used to probe the phase of atomic states and here we apply it to probe the phase of photonic states. We experimentally observe an effective magnetic flux between 0 and 2π corresponding to a non-reciprocal 2π phase shift with an interferometer length of 8.35 mm and an interference-fringe extinction ratio of 2.4 dB. This non-reciprocal phase is comparable to those of common monolithically integrated magneto-optical materials.

Effective magnetic field for photons based on the magneto-optical effect

We propose to create an effective magnetic field for photons in photonic crystal resonator lattices using the magneto-optical effect. The inter-resonator coupling is mediated by magneto-optical waveguides or magneto-optical resonators, and thus the coupling between the nearest-neighbor photonic crystal resonators acquire a direction-dependent phase. The effective magnetic field can be realized with a proper choice of the spatial distribution of such a direction-dependent phase.

Limits on the Superconducting Order Parameter in NdFeAsO1-xFy from Scanning SQUID Microscopy

Identifying the symmetry of the superconducting order parameter in the recently-discovered ferrooxypnictide family of superconductors, RFeAsO{sub 1-x}F{sub y}, where R is a rare earth, is a high priority. Many of the proposed order parameters have internal {pi} phase shifts, like the d-wave order found in the cuprates, which would result in direction-dependent phase shifts in tunneling. In dense polycrystalline samples, these phase shifts in turn would result in spontaneous orbital currents and magnetization in the superconducting state. We perform scanning SQUID microscopy on a dense polycrystalline sample of NdFeAsO{sub 0.94}F{sub 0.06} with T{sub c} = 48K and find no such spontaneous currents, ruling out many of the proposed order parameters.

Passive directional discrimination in laser-Doppler anemometry by the two-wavelength quadrature homodyne technique.

We report a method for passive optical directional discrimination in laser-Doppler anemometers. For this purpose frequency-shift elements such as acousto-optic modulators, which are bulky and difficult to align during assembly, have traditionally been employed. We propose to use a quadrature homodyne technique to achieve directional discrimination of the fluid flow without any frequency-shift elements. It is based on the employment of two laser wavelengths, which generate two interference fringe systems with a phase shift of a quarter of the common fringe spacing. Measurement signal pairs with a direction-dependent phase shift of +/- pi/2 are generated. As a robust signal-processing technique, the cross-correlation technique is used. The principles of quadrature homodyne laser-Doppler anemometry are investigated. A setup that provides a constant phase shift of pi/2 throughout the entire measurement volume was achieved with both single-mode and multimode radiation. The directional discrimination was successfully verified with wind tunnel measurements. The complete passive technique offers the potential of building miniaturized measurement heads that can be integrated, e.g., into wind tunnel models.

Angle estimation and binaural processing in animal echolocation.

Physical structures separate the ears of many mammals, and the ears themselves have complex transfer functions that depend upon the direction of a sound source. Neither of these observations is usually incorporated into standard array analysis. The conventional array problem generally assumes that individual elements are omnidirectional, and there are no physical structures between elements to provide partial isolation. This investigation of binaural angle estimation specifically incorporates the effects of partial isolation and directivity patterns that vary with angle and frequency. Cramér–Rao bounds for the variance of maximum likelihood angle estimates are derived. These bounds, along with a generalized ambiguity function, are used to evaluate the significance of isolation between the ears, angle-dependent magnitude, and phase variations in the spatial transfer functions of the ears, the use of wide-band and narrow-band signals in animal echolocation, symmetry of aural directivity patterns, the transmitted beam patterns that are employed by certain bats, and the angle-dependent signal variations that have been observed in cetacean echolocation. Only two broadband hydrophones are sufficient for accurate, unambiguous azimuth measurement if the width of the signal autocorrelation function is small relative to the distance between hydrophones. The analysis indicates that many past measurements of transmitted beam patterns and aural transfer functions in animals are incomplete, since they do not consider direction-dependent phase variations. It may also be necessary to reinterpret the meaning of time difference and pressure difference cues for localization. These insights can be used not only for better correlation of behavioral and physiological measurements, but also for better design of man-made systems for communication, radar, sonar, and ultrasonic medical diagnosis.