Complicated Interference Pattern Research Articles

Directional decomposition of internal tides propagating from multiple generation sites

Internal tides generated from multiple sites create complicated interference patterns, often making it difficult to identify the origin, direction of propagation, and dissipation of individual waves. To identify these constituent waves, we apply a directional Fourier filter (DFF) method to analyse multimodal, broad-wavenumber, internal wave fields found over varying topography. We apply the method to data derived from both a numerical model and satellite remote sensing observations. Using a series of two-dimensional (i.e. x–z) simulations, we first demonstrate the capability of the DFF method to separate incoming and reflected internal tides emanating from a supercritical slope. The results show the DFF method requires model sampling rates of Δt∕T<0.15 and horizontal cell sizes of Δx∕λ<0.2, where T is the wave period and λ is the wavelength. Remote internal tides can significantly affect the generation and propagation of local internal tides in regional ocean simulations. Using a gridded satellite altimetry product at three globally diverse regions, we demonstrate how the DFF method can be used to specify the internal tide boundary conditions at the open boundaries of regional ocean models. Lastly, we apply the DFF method to a three-dimensional hydrostatic numerical simulation of the southern Australian North West Shelf to estimate the energy decay characteristics of internal tides. The energy decay length scale, for offshore-propagating waves from the continental slope, in the model was estimated to be two mode-1 wavelengths (i.e. 240 km), in close agreement with an estimate derived from a satellite-derived sea surface height anomaly.

Identification of incident parameters of interference beams using angular power spectral density

Laser interference lithography is attracting increasing interest among researchers because of its high-efficiency and low-cost in fabrication of patterns. However, there are always operational errors in the setup of interference systems, which have a significant effect on the finally produced interference pattern. This paper has systematically investigated the influence of incident parameters including the incident angle, azimuth angle, and polarization angle on interference patterns. An algorithm has been proposed to extract interference fringes from complicated multibeam interference patterns using the angular power spectral density (APSD) function. The incident parameters were calculated based on the data extracted from the APSD images. Simulations were carried out to validate the effectiveness of the proposed algorithm. 3-D periodic patterns were fabricated on silicon wafers using three-beam interference lithography. The topographies of the samples were measured using an optical profiler. Based on the established model, incident parameters of the interference system setup were calculated. The computational results are in good agreement with the preset values. The results have demonstrated the validation of the developed algorithm for incident parameter identification of interference beams.

Bogoliubov-Cherenkov radiation in an atom laser

We develop a simple yet powerful technique to study Bogoliubov-Cherenkov radiation by producing a pulsed atom laser from a strongly confined Bose-Einstein condensate. Such radiation results when the atom laser pulse falls past a Bose-Einstein condensate at high-hypersonic speeds, modifying the spatial profile to display a characteristic twin jet structure and a complicated interference pattern. The experimental observations are in excellent agreement with mean-field numerical simulations and an analytic theory. Due to the highly hypersonic regime reached in our experiment, this system offers a highly controllable platform for future studies of condensed-matter analogs of quantum electrodynamics at ultrarelativistic speeds.

The influence of mode coupling on waveguide invariant

The waveguide invariant β is typically discussed in terms of either a range-independent environment or a range-dependent environment under the adiabatic approximation, with few studies considering the effects of mode coupling. In this work, how internal solitary waves (ISWs) affect the waveguide invariant is investigated, and it is shown that mode-coupling effects introduce many additional components in the acoustic interference intensity. It is found that the striation slope and value of β for these additional components are determined not only by the acoustic modal dispersion, but are also dependent on the position where the mode coupling occurs. This can lead to a very complicated acoustic interference pattern and result in multiple peaks in the distribution of β. The sensitivity of β to the parameters of ISWs, such as amplitude, horizontal scale, and position, is analyzed. It is found that although all parameters can affect the energy of the peaks, only the position of the internal wave has an obvious impact on the peak values. This indicates that the peak values of β can be utilized for monitoring the position of the internal wave.

Concept of waveguide invariant spectrum and algorithm for its extraction

There are two kinds of definitions for waveguide invariant β. One is defined according to the striation slope of acoustic interference patterns, and the other is defined on the basis of dispersion characteristics of acoustic modes. The first definition is appropriate for engineering applications, while the second is suitable for theoretical analysis. However, the two definitions are not consistent with each other for a waveguide with thermoclines, because modal dispersion in such a waveguide can be very different for different modes and different frequencies. In such cases, the waveguide invariant defined according to modal dispersion can take many different values, which are referred to as the spectrum of waveguide invariant (β spectrum for short) in the paper. Each β spectrum can be related to some interference striation patterns with corresponding striation slopes. The sound field is composed of many modes, so the interference pattern is the summation of many components of different striation slopes and may be very complicated as a result of the diversity of β spectrum. In such a case one single β is not able to describe the complicated interference pattern adequately; instead multiple values of β spectrum are required. From the point of view of engineering application, however, the present β-extracting methods can only give one optimal value, and thus a lot of information is lost. In this paper an algorithm for doing so, called β spectrum separation technique, is proposed. By adopting the concept of integral projection used in digital image processing, the image of acoustic intensity is projected at different angles to separate out the striations of different slopes; and then fast Fourier transform (FFT) is applied to the projected curve in order to isolate striations of different spacing from each other. The values for β spectrum can be computed according to striation slopes, which are also mapped into the positions of their corresponding acoustic modal horizontal wavenumber differences in the wavenumber domain. The applicability of this algorithm for the extraction of β spectrum is tested and verified by simulation results and experiment data. It is shown that the algorithm can separate out each β spectrum of different intensity components from acoustic interference structure. The algorithm maps β spectrum into a two-dimensional plane thereby being able to suppress noise more effectively and work in the condition of low signal-to-noise ratio compared with the already-existing β-extracting algorithms.

Refractometric micro-sensor using a mirrored capillary resonator.

We report on a flow-through optical sensor consisting of a microcapillary with mirrored channels. Illuminating the structure from the side results in a complicated spectral interference pattern due to the different cavities formed between the inner and outer capillary walls. Using a Fourier transform technique to isolate the desired channel modes and measure their resonance shift, we obtain a refractometric detection limit of (6.3 ± 1.1) x 10-6 RIU near a center wavelength of 600 nm. This simple device demonstrates experimental refractometric sensitivities up to (5.6 ± 0.2) x 102 nm/RIU in the visible spectrum, and it is calculated to reach 1540 nm/RIU with a detection limit of 2.3 x 10-6 RIU at a wavelength of 1.55 µm. These values are comparable to or exceed some of the best Fabry-Perot sensors reported to date. Furthermore, the device can function as a gas or liquid sensor or even as a pressure sensor owing to its high refractometric sensitivity and simple operation.

Simplified Cartesian basis model for intrapolyad emission intensities in the bent-to-linear electronic transition of acetylene.

The acetylene emission spectrum from the trans-bent electronically excited à state to the linear ground electronic X̃ state has attracted considerable attention because it grants Franck–Condon access to local bending vibrational levels of the X̃ state with large-amplitude motion along the acetylene ⇌ vinylidene isomerization coordinate. For emission from the ground vibrational level of the à state, there is a simplifying set of Franck–Condon propensity rules that gives rise to only one zero-order bright state per conserved vibrational polyad of the X̃ state. Unfortunately, when the upper level involves excitation in the highly admixed ungerade bending modes, ν4′ and ν6′, the simplifying Franck–Condon propensity rule breaks down--as long as the usual polar basis (with v and l quantum numbers) is used to describe the degenerate bending vibrations of the X̃ state--and the intrapolyad intensities result from complicated interference patterns between many zero-order bright states. In this article, we show that, when the degenerate bending levels are instead treated in the Cartesian two-dimensional harmonic oscillator basis (with vx and vy quantum numbers), the propensity for only one zero-order bright state (in the Cartesian basis) is restored, and the intrapolyad intensities are simple to model, as long as corrections are made for anharmonic interactions. As a result of trans ⇌ cis isomerization in the à state, intrapolyad emission patterns from overtones of ν4′ and ν6′ evolve as quanta of trans bend (ν3′) are added, so the emission intensities are not only relevant to the ground-state acetylene ⇌ vinylidene isomerization, they are also a direct reporter of isomerization in the electronically excited state.

Enhanced damage localization for complex structures through statistical modeling and sensor fusion

Ultrasonic guided waves represent a promising technique for detecting and localizing structural damage, but their application to realistic structures has been hampered by the complicated interference patterns produced by scattering from geometric features. This work presents a new damage localization paradigm based on a statistical approach to dealing with uncertainty in the guided wave signals. A bolted frame and a section of a fuselage rib are tested with different simulated damage conditions and used to conduct a detailed comparison between the proposed solution and other sparse-array localization approaches. After establishing the superiority of the statistical approach, two novel innovations to the localization procedure are proposed: an approach to sensor fusion based on the Neyman–Pearson criterion, and a method of constructing simple models of geometrical features. Including the sensor fusion and geometrical models produces a substantial improvement in the system׳s localization accuracy. The final result is a robust and accurate framework for single-site damage localization that moves structural health monitoring towards practical implementation on a much broader range of structures.

Young Double Slit Interference Effects at Quantum Level

The currently accepted model for quantum interference resulting from the emission of electron waves from two scattering centers induced by either light or charged particle impact is analogous to Young's emission of two light waves from two slits. In this work we show that this simple classical wave model is incomplete and that there is a more complicated quantum interference pattern for low energy ionization caused by electron impact.

Tomography and the global predictability of mode‐1 internal tides

Twenty years ago, temporally coherent, mode-1 internal tides were detected in the central North Pacific using acoustic tomography. The spatial sampling of tomography is a natural filter for these internal waves. The signals were conjectured to have originated from the Hawaiian Ridge 2000 km to the south, and shortly thereafter Ray and Michum found radiation of internal tides from that undersea ridge using satellite altimetry. The two data types are complementary: tomography demonstrates astonishing temporal coherence, altimetry demonstrates astonishing spatial coherence. In the Atlantic, diurnal internal tides, resonantly trapped between Puerto Rico and their 30N turning latitude, were observed by AMODE tomography, while the semidiurnal variability consisted of a complicated interference pattern. While several conventional in situ observations indicated incoherent components to mode-1 internal-tide variability, both tomography (directly) and altimetry (indirectly) show the incoherent component is minimal. Resolution of mode-1 is challenging, but, without basis, oceanographers have been reluctant to accept the tomography measurements. A combined frequency and wavenumber tidal analysis of altimetry data has recently demonstrated that the amplitude and phase of mode‐1 internal tides are predictable, except, perhaps, in more variable regions. Attenuation appears to be negligible, and waves coherent in time and space extend across ocean basins.

Coherence in multistate resonance-enhanced four-photon ionization of lithium atoms

A joint experimental and theoretical study of four-photon ionization of Li is performed using a pump-probe setup with the laser frequency tuned in between the excitation energies of the $2s$--$4p$ and $2s$--$4f$ three-photon transitions. The three-dimensional photoelectron momentum pattern is recorded as a function of the delay time between two otherwise identical laser pulses. The process is modeled by numerically solving the time-dependent Schr\"odinger equation. While complicated interference patterns arise in the electron spectrum when the two pulses partially overlap in time, the expected quantum-beat phenomenon between Li atoms in either the $4p$ or the $4f$ state are seen when the fast oscillations involving the $2s$ initial state are averaged over. The qualitative agreement between the predicted and observed beating patterns is very good.

Two-State Double-Continuum Fano Resonance at the Si(100) Surface

Fano resonances are well-known manifestations of the interference between a direct and an indirect ionization process. Here we report on a more complicated interference pattern observed in two-photon photoemission at the Si(100) surface. This two-dimensional Fano profile involves two discrete surface resonances which couple as initial and intermediate states to the silicon valence and conduction band, respectively. Tuning the photon energy across the surface resonance reveals asymmetric line profiles with pronounced destructive interference in the two-photon photoelectron intensities of both initial and intermediate states. The interference pattern is explained by an analytic extension of Fano's model to describe the coupling of two discrete states with two continua. This coupling strongly modifies the photoabsorption and is of general importance for light conversion in nanostructures and light-harvesting devices.

Photoionization microscopy of the hydrogen atom in parallel electric and magnetic fields

In photoionization microscopy experiments, an atom in an electric field is ionized by a laser with sharply defined frequency, the electron is drawn toward a position-sensitive detector, and the current is measured as a function of position. Multiple classical paths lead from the atom to any point in the classically allowed region on the detector, and waves traveling along these paths produce an interference pattern. If a magnetic field is added parallel to the electric field, trajectories become chaotic. There is an infinite set of different families of trajectories, leading to an extremely complicated interference patterns on the detector. We present calculations predicting the kind of structure that will be seen in experiments.

Above-threshold ionization, energy-resolved photoelectron angular distributions, and momentum distributions ofH2+in intense femtosecond laser pulses

We study above threshold ionization, energy-resolved photoelectron angular distributions and photoelectron momentum distributions for the initial ${^{2}\ensuremath{\Sigma}}_{g}^{+}(1s{\ensuremath{\sigma}}_{g})$ ground and the ${^{2}\ensuremath{\Sigma}}_{u}^{+}(2p{\ensuremath{\sigma}}_{u})$ first-excited state in $\text{H}_{2}{}^{+}$, driven by an arbitrary orientated linearly polarized 800 nm laser pulse of different intensities and temporal durations. When the pulse duration is reduced, multiphoton structure is erased, and continuum states of gerade $(g)$ and ungerade $(u)$ inversion symmetry start to overlap. A strong localization of the photoelectron emission occurs as a consequence of the $g\text{\ensuremath{-}}u$ mixing. Furthermore, as the pulse length is reduced, effects of the carrier-envelope phase show up, and a number of complicated interference patterns in the momentum distribution radially as well angularly are predicted. Such patterns were previously reported in the atomic case. In the molecules, additional structures appear due to the interference between electronic waves emerging from different nuclear centers.

The interference component of the acoustic field corresponding to the Long-Range Ocean Acoustic Propagation Experiment

Propagation of energy along the sound channel axis cannot be formally described in terms of geometrical acoustics due to repeated cusped caustics along the axis. In neighborhoods of these cusped caustics, a very complicated interference pattern is observed. Neighborhoods of interference grow with range and overlap at long ranges. This results in the formation of a complex interference wave--the axial wave--that propagates along the sound channel axis like a wave belonging to a crescendo of near-axial arrivals. The principal properties of this wave are calculated for the actual space-time configuration realized during a 2004 long-range propagation experiment conducted in the North Pacific. The experiment used M-sequences at 68.2 and 75 Hz, transmitter depths from 350 to 800 m, and ranges from 50 to 3200 km. Calculations show that the axial wave would be detectable for an optimal geometry-both transmitter and receiver at the sound channel axis--for a "smooth" range-dependent sound speed field. The addition of sound speed perturbations--induced here by simulated internal waves--randomizes the acoustic field to the extent that the axial wave becomes undetectable. These results should be typical for mid-latitude oceans with similar curvatures about the sound speed minimum.

NEAR-AXIAL INTERFERENCE EFFECTS IN LONG-RANGE OCEAN ACOUSTIC PULSE PROPAGATION

In many long-range ocean propagation experiments the source and receiver are placed close to the depth of the waveguide axis. In this case, rays emerging from the source at sufficiently small angles intersect the sound-channel axis many times and form in its vicinity a large number of caustics with caustics cusps located repeatedly along the axis. In neighborhoods of cusped caustics there exists a very complicated interference pattern. Neighborhoods of interference grow with range and at long ranges they overlap. As a result, a complex interference wave (axial wave), that propagates along the waveguide axis, appears. The goal of this paper is to obtain the representation for the axial wave in the time domain and calculate its magnitude for a realistic model of a three-dimensional range-independent medium. Numerical computations are done for the average profile from the Acoustic Engineering Test (AET) experiment. The pulse center frequency of 75 Hz with 30-Hz bandwidth is used that corresponds to broadband acoustic signals which were transmitted during November 1994 in the eastern North Pacific Ocean as a part of the AET. The propagation range is 3250 km. The sound source is located on the waveguide axis, and the receiver is placed close to the depth of the axis. Through numerical simulation the dependencies of the magnitude of the axial wave on depth of the receiver and propagation range are studied.

Effect of ocean internal waves on the interference component of the acoustic field in the Long-range Ocean Acoustic Propagation Experiment

The propagation of energy along the sound‐channel axis cannot be described in terms of geometrical acoustics because of the presence of cusped caustics repeatedly along the axis. In neighborhoods of these cusped caustics a very complicated interference pattern is observed. Neighborhoods of interference grow with range and at long ranges they overlap. This results in the formation of a complex interference wave‐the axial wave‐that propagates along the sound‐channel axis like a wave belonging to a crescendo of near‐axial arrivals. In this paper, the axial wave is simulated for the LOAPEX CTD data measured at seven different ranges from the vertical line array. A signal with the center frequency of 75 Hz and 37.5‐Hz bandwidth is used for computations. This signal well approximates one transmitted m‐sequence in the LOAPEX experiment. The effect of environmental variability, induced by internal waves, on the axial wave is studied. The sound‐speed fluctuations caused by ocean internal waves are obtained with the use of the buoyancy frequency profile measured in the LOAPEX. Calculations are based on the integral representation of the axial wave in a local coordinate system introduced in the vicinity of the range‐variable sound‐channel axis. [Work supported by ONR.]

Biosensing Using Porous Silicon Double-Layer Interferometers: Reflective Interferometric Fourier Transform Spectroscopy

A simple, chip-based implementation of a double-beam interferometer that can separate biomolecules based on size and that can compensate for changes in matrix composition is introduced. The interferometric biosensor uses a double-layer of porous Si comprised of a top layer with large pores and a bottom layer with smaller pores. The structure is shown to provide an on-chip reference channel analogous to a double-beam spectrometer, but where the reference and sample compartments are stacked one on top of the other. The reflectivity spectrum of this structure displays a complicated interference pattern whose individual components can be resolved by fitting of the reflectivity data to a simple interference model or by fast Fourier transform (FFT). Shifts of the FFT peaks indicate biomolecule penetration into the different layers. The small molecule, sucrose, penetrates into both porous Si layers, whereas the large protein, bovine serum albumin (BSA), only enters the large pores. BSA can be detected even in a large (100-fold by mass) excess of sucrose from the FFT spectrum. Detection can be accomplished either by computing the weighted difference in the frequencies of two peaks or by computing the ratio of the intensities of two peaks in the FFT spectrum.

An algorithm for extremely complicated interference pattern evaluation

A description of an easy algorithm for evaluation of interference patterns recording the light beam deflection in phase objects is presented in this paper. The method is suitable for digitizing and evaluating complicated interference patterns containing heavily distorted, double or closed interference fringes. The created algorithm and evaluation procedure result from the lines’ approximation and Delaunay triangulation. They were applied to a complex interference pattern taken in the pinch discharge burning in low-pressure deuterium. The results obtained were used for calculation of electron density values in the discharge channel. The influence of the phase shift deformation outside the region under study on the accuracy of results and on electron density estimation inside the shock wave of the pinch was also analyzed. The gathered data were verified with a calculation of the electron temperature in the discharge channel, which was performed providing kinetic and magnetic pressure equilibriums.

Long-range acoustic transmission in a deterministic range-dependent ocean: Contribution from interference of near-axial waves

The propagation of energy along the waveguide axis cannot be described in terms of geometrical acoustics because of the presence of cusped caustics repeatedly along the axis. In neighborhoods of these cusped caustics a very complicated interference pattern is observed. Neighborhoods of interference grow with range and at long ranges they overlap. For an arbitrary range-independent ocean, it was shown in [N. S. Grigorieva and G. M. Fridman, J. Comp. Acoust. 12, 127–147 (2004)] that the interference of wave fields corresponding to near-axial rays results in a diffractive (as opposed to geometrical acoustics) component of the field which can be viewed as distinct, ‘‘axial’’ wave and effectively calculated using its integral representation. In this paper the integral representations of the axial wave in the frequency and time domains are obtained for a range-dependent ocean. In the frequency domain this representation has the form of a linear superposition of the solutions of the Helmholtz equation that are concentrated in a neighborhood of the sound-channel axis. The weight function is selected in such a way that the localization principle holds. The axial wave is simulated for a deterministic model of a range-dependent ocean corresponding to AET experiment. [Work supported by ONR Global.]