Aperiodic Domain Research Articles

On the discrepancies between POD and Fourier modes on aperiodic domains

The application of Fourier analysis in combination with the Proper Orthogonal Decomposition (POD) is investigated. In this approach to turbulence decomposition, which has recently been termed Spectral POD (SPOD), Fourier modes are considered as solutions to the corresponding Fredholm integral equation of the second kind along homogeneous-periodic or homogeneous coordinates. In the present work, the notion that the POD modes formally converge to Fourier modes for increasing domain length is challenged. A family of analytical correlation functions parametrized by the Taylor macro/micro scale ratio (MMSR) is investigated numerically. The results of the analysis indicate that the discrepancy between POD and Fourier modes along locally translationally invariant coordinates is coupled to the MMSR of the flow. Increasing discrepancies are observed for smaller MMSRs, which are characteristic of low Reynolds number flows. The asymptotic convergence rate of the eigenspectrum matches the corresponding convergence rate of the exact analytical Fourier spectrum of the kernel in question, even for extremely small domains and small MMSRs where the corresponding DFT spectra suffer heavily from windowing effects. The Taylor micro scales are consistently underestimated when reconstructed using Fourier modes—failing to converge to the correct value even if all Fourier modes are used—while these are accurately reconstructed using POD modes.

Chiral spiral cyclic twins. II. A two-parameter family of cyclic twins composed of discrete circle involute spirals.

A mathematical toy model of chiral spiral cyclic twins is presented, describing a family of deterministically generated aperiodic point sets. Its individual members depend solely on a chosen pair of integer parameters, a modulus m and a multiplier μ. By means of their specific parameterization they comprise local features of both periodic and aperiodic crystals. In particular, chiral spiral cyclic twins are composed of discrete variants of continuous curves known as circle involutes, each discrete spiral being generated from an integer inclination sequence. The geometry of circle involutes does not only provide for a constant orthogonal separation distance between adjacent spiral branches but also yields an approximate delineation of the intrinsically periodic twin domains as well as a single aperiodic core domain interconnecting them. Apart from its mathematical description and analysis, e.g. concerning its circle packing densities, the toy model is studied in association with the crystallography and crystal chemistry of α-uranium and CrB-type crystal structures.

Is the “Bricks-and-Mortar” Mesophase Bicontinuous? Dynamic Simulations of Miktoarm Block Copolymer/Homopolymer Blends

A new mesophase in binary blends of A–b–(BA′)3 miktoarm star block copolymers and A homopolymers has recently been discovered experimentally and explored with field-theoretic simulations. This mesophase has been reported to consist of aperiodic discrete domains of A embedded in a continuous matrix of B up to very high concentrations of A. Because of the material’s potential as a thermoplastic elastomer, a deeper understanding of its structural and dynamic-mechanical properties, including its domain connectivity, linear rheological behavior, response to shear, and response to uniaxial tension, is warranted. These properties are explored here using dissipative particle dynamics in three dimensions, for the first time. These simulations establish that the so-called “bricks-and-mortar” phase, while appearing discrete in two dimensions, is bicontinuous. The simulations focusing on dynamics establish that the role of molecular bridging dominates the mechanical behavior and outweighs the influence of microphase segregation (contributions from the interfacial tension alone) even at the highest homopolymer concentrations we study. Additionally, it appears that the bricks-and-mortar phase is sensitive to the application of sufficiently high shear, leading to nonisotropic mechanical responses, which has ramifications for the processability of such materials. We find that upon application of shear the phase becomes closer in structure to its speculated discrete nature. Molecular simulations on our longest accessible timescales show that the material is unable to relax back to its original structure, suggesting that the morphology observed depends heavily on the material process pathway.

Effective Group Velocity and Shape of Twin Beams

The shape and propagation velocities of pulsed twin beams generated in the process of parametric light down-conversion have been theoretically studied in the case where the delays caused by the dispersion of group velocities exceed the length of a pump pulse. It has been shown that the effective group velocity of the scattered pulse is determined by the arithmetic mean of the group velocities at the scattered radiation and pump frequencies. The scattering matrix elements for the large parametric gain have been numerically found. It has been shown that mixing of the spectral components of scattered radiation can cause a significant narrowing of the twin beam pulses. Finally, for the case of generation of broadband twin beams sequentially in two crystals with an aperiodic domain structure, it has been shown that the visibility of the three-frequency interference decreases as the pump pulse lags behind the scattered radiation pulses.

Effect of Pump Depletion on the Spectrum of Twin Beams

The effect of pump depletion on the spectrum of twin beams, which appear in the process of collinear parametric down-conversion in a nonlinear crystal with an aperiodic domain structure and have a high degree of simultaneity, has been described. A system of equations describing the interaction of pump with all modes of scattered light simultaneously has been derived. It has been shown that pump depletion results in a noticeable broadening of the spectrum of twin beams for a quadratic-hyperbolic law of variation of the reciprocal lattice vector of the domain structure. The effect of narrowing of the coherent peak in the sum-frequency generation signal from twin beams has been demonstrated. This effect increases as the pump is depleted.

Noncolinear Second-Harmonic Generation Pairs and Their Scatterings in Nd3+:SBN Crystals with Needle-Like Ferroelectric Domains**Supported by the National Natural Science Foundation of China under Grant No 61675101.

Second-harmonic generation in Nd3+:SBN crystal with needle-like ferroelectric with aperiodic domain structures is investigated. Two pairs of second harmonic (SH) waves appearing in lines are observed in unpoled Nd3+:SBN crystals with aperiodic needle-like domains. A pair of SH waves emit from the exit face, whose intensities are angle-dependent. The angular dependence is corresponding to the spatial frequency spectrum of the aperiodic domain structure. Another pair of SH waves emit from both the side surfaces, which are mainly the scattered SH waves by needle-like domain walls and obey the theory of Rayleigh scattering.

Additive solc action in aperiodically poled MgBaF4 for deep UV applications

A novel scheme of additive Solc filter (ASF) is proposed in a single aperiodically poled BaMgF4 biaxial crystal comprising of aperiodic domains having four different grating periods. This filter is designed to reject a narrow band of selected wavelength in Deep ultra-violet (DUV) region. The fibonacci sequence is followed in domains of aperiodic optical super lattice for poling design. Proposed filter finds its application in Swept Wavelength Optical Resonance Raman Diagnostic process utilizing tunable lasers, the condition for blocking multiple discrete wavelengths by one filter can be particularly useful.

Design and analysis of dual periodic optical superlattices using Walsh–Hadamard transform matrix

We propose a systematic approach for designing dual periodic optical superlattices using Walsh–Hadamard transform, one of the widely used transforms in signal and image processing. We identify a family of dual periodic optical superlattices from vairous columns of the Walsh–Hadamard transform matrix. We provide closed form expressions for the second harmonic spectral response of the designed optical superlattices, by explicitly performing the Fourier sum corresponding to finite domain by domain calculation. As the number of aperiodic domains in the dual periodic optical superlattice designed increases, the dual peak separation also increases and it provides larger band width for multiple peak second harmonic generation.

Characterization of aperiodic domain structure in lithium niobate by spontaneous parametric down-conversion spectroscopy

We develop a technique for detailed analysis of aperiodically poled crystalline nonlinear transfer functions. The method allows precise evaluation of 1D aperiodic domain structure amplitude spectra. It also allows determining the angle of periodic poling in respect to the crystalline z axis, as well as the dispersion of both ordinary and extraordinary refractive indexes in a broad spectral range. The measurement is non-destructive, and all data can be extracted from two frequency-angular spontaneous parametric down-conversion (SPDC) spectra. The precision of the domain structure analysis for aperiodically poled lithium niobate is increased by an order of magnitude in comparison to previously reported techniques based on spontaneous parametric down-conversion.

Ferroelectric domain building blocks for photonic and nonlinear optical microstructures in LiNbO3

The ability to manipulate the size and depth of poling inhibited domains, which are produced by UV laser irradiation of the +z face of lithium niobate crystals followed by electric field poling, is demonstrated. It is shown that complex domain structures, much wider than the irradiating laser spot, can be obtained by partially overlapping the subsequent UV laser irradiated tracks. The result of this stitching process is one uniform domain without any remaining trace of its constituent components thus increasing dramatically the utility of this method for the fabrication of surface microstructures as well as periodic and aperiodic domain lattices for nonlinear optical and surface acoustic wave applications. Finally, the impact of multi exposure on the domain characteristics is also investigated indicating that some control over the domain depth can be attained.

Dynamics of difference frequency radiation generation in the field of few-cycle laser pulse propagating in GaAs crystal with domain structure

We consider the process of generation of difference frequency in a GaAs crystal with periodic domain structure during propagation of a few-cycle laser pulse in the crystal in the regime of weakly expressed chromatic dispersion. Method of lines is used to obtain numerical solution to the system of coupled nonlinear differential equations in partial derivatives describing the evolution of the electric field of a few-cycle laser pulse in GaAs crystal both with periodic and aperiodic domain structure. It is shown that employing GaAs crystal with domain structure allows controlling the instantaneous frequency of broadband pulse radiation at difference frequency.

Analysis of a phase reversal quasi-phase matching device for the dual peak second harmonic response

Phase reversal quasi-phase matching devices are fairly capable of yielding a dual peak second harmonic spectral response. However, it does suffer from uneven intensity and overlapping of the peaks. In this paper, we analyze the effect of the errors to which these devices are prone. Such unavoidable errors are bound to happen during the poling process even under controlled conditions. The second harmonic spectral response is analyzed by introducing two sorts of possible errors in an ideal phase reversal quasi-phase matching device. Initially, the aperiodic domain is kept fixed at the center of the device and its width is altered to determine the intensity variation of the peaks. When the width of the aperiodic domain is not equal to twice the periodic domain width, an unequal peak response is observed. Secondly, the aperiodic domain width is kept constant while the aperiodic domain is moved along the length of the device to determine the interference between the peaks. If the aperiodic domain is not positioned exactly at the center, a disturbance of the peaks’ intensities is noticed.

Tunable all-optical wavelength broadcasting in a PPLN with multiple QPM peaks

We experimentally demonstrate tunable multiple-idler wavelength broadcasting of a signal to selective channels for wavelength division multiplexing (WDM). This is based on cascaded χ(2) nonlinear mixing process in a novel multiple-QPM 10-mm-long periodically poled LiNbO3 having an aperiodic domain in the center. The idlers' spacing is varied utilizing detuning of the pump wavelength within the SHG bandwidth. The temperature-assisted tuning of QPM pump wavelengths allows shifting the idlers together to different set of WDM channels. Our experimental results indicate that an overall idler wavelength shift of less than 10 nm realized by selecting pump wavelengths via temperature tuning, is sufficient to cover up to 40 WDM channels for multiple idlers broadcasting.

GENERATION OF DIFFERENCE FREQUENCY RADIATION IN THE FIELD OF FEW-CYCLE LASER PULSE PROPAGATING IN GaAs CRYSTAL WITH PERIODIC AND APERIODIC DOMAIN STRUCTURE

We consider process of generation of difference frequency in a GaAs crystal with periodic domain structure during propagation of a few-cycle laser pulse in the crystal in the regime when chromatic dispersion is expressed weakly. Method of lines is used to obtain numerical solution to the system of coupled nonlinear differential equations in partial derivatives describing the evolution of the electric field of a few-cycle laser pulse in GaAs crystal both with periodic and aperiodic domain structure. Time-frequency distribution is obtained, with use of Wigner transformation, for linearly-polarized femtosecond laser pulse and for orthogonally polarized difference-frequency pulse generated via filtration of the orthogonally-polarized pulse at the crystal output.

Strain relaxation induced spin reorientation in Fe films on W(110)

We studied Fe double layer films on W(110) to investigate the role of strain relaxation in determination of the magnetic ground states. The spin reorientation transition (SRT) between perpendicular and in-plane magnetization takes place with varying density of dislocation lines as imaged with spin polarized scanning tunneling microscopy/spectroscopy. Unexpected domain wall orientation along W[001] and aperiodic magnetic domain patterns suggest that strain relaxation-induced domain has an easy axis along W[001] rather than W[11¯0] in conjunction with the Dzyaloshinskii-Moriya interaction. Furthermore, we confirmed that the SRT can be suppressed by reducing the density of the dislocation lines with lower temperature annealing.

Agent-based simulations of complex droplet pattern formation in a two-branch microfluidic network.

We develop an agent-based computational simulation to investigate the complex behavior exhibited by an initially regularly spaced train of immiscible droplets passing through a simple two-branch microfluidic network wherein a channel splits into two asymmetric branches that reconnect downstream. As observed by Fuerstman et al. (M. J. Fuerstman, P. Garstecki and G. M. Whitesides, Science, 2007, 315, 828-832), variations in the flow rates within each segment induced by the droplets cause complex droplet spacing patterns to occur in the outlet, leading to periodic and aperiodic behavior. Our model utilizes a highly efficient agent-based modeling approach, where the flow-rates in each section of the network are determined using fundamental concepts of viscous and interfacial flows. Simulations spanned physical parameter space that includes variation in droplet spacing, surface tension, viscosity and geometry. These simulations demonstrate qualitative agreement with the findings of Fuerstman et al., including the prediction of interspersed periodic and aperiodic domains. We predict that decreasing droplet contribution to the overall pressure drop (reducing the tube radius or surface tension, increasing the viscosity) would result in increased complexity. The geometric configuration of the system is also critical to pattern formation; a greater disparity in branch length generally results in higher-order periodicities in the outflow channel. The aperiodic results indicate the likelihood of chaotic behavior arising from this purely deterministic system. The consideration of fundamental fluid mechanical principles coupled to the agent-based simulation technique may provide a highly efficient means for the design and analysis of more complex systems.

Nonlinear pulse compression in inhomogeneous photonic crystals upon backward second harmonic generation

Frequency doubling of phase-modulated laser pulses, which is caused by a quasi-synchronous interaction of counterpropagating waves, is studied theoretically in crystals with an aperiodic domain structure. The simultaneous influence of the change in the domain period and the phase-modulation depth of fundamental radiation on the formation of a second-harmonic pulse is analysed in the nonstationary regime. It is shown that there exists an optimal relation between chirps in an aperiodic crystal and the phase modulation of fundamental radiation at which the maximum nonlinear compression of the second-harmonic pulse duration is possible.

Dual-wavelength green laser with a 45 THz frequency difference based on self-frequency- doubling in Nd^3+-doped aperiodically poled lithium niobate

We report a dual-wavelength continuous-wave laser at 542.4 and 546.8 nm based on an Nd(3+)-doped aperiodically poled lithium niobate crystal. Two fundamental infrared (IR) wavelengths at 1084.8 and 1093.6 nm are simultaneously oscillated and self-frequency-doubled to green. The aperiodic domain distribution patterned in the crystal allows for quasi-phase matched self-frequency-doubling of both IR fundamentals while avoiding their sum-frequency mixing.

Micro-Raman and micro-infrared spectroscopic studies of Pb- and Au-irradiatedZrSiO4: Optical properties, structural damage, and amorphization

The optical properties of damaged periodic and aperiodic domains created by ${\mathrm{Pb}}^{+}$ $(280\phantom{\rule{0.3em}{0ex}}\mathrm{keV})$ and ${\mathrm{Au}}^{4+}$ $(10\phantom{\rule{0.3em}{0ex}}\mathrm{MeV})$ implantation of zircon were studied using micro-infrared (IR) and micro-Raman spectroscopy. The ${\mathrm{Pb}}^{+}$ and ${\mathrm{Au}}^{4+}$ irradiations caused a dramatic decrease in the IR reflectivity similar to that observed for metamict natural zircon. The irradiation with $10\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$ ${\mathrm{Au}}^{4+}$ ions (to fluences of $1\ifmmode\times\else\texttimes\fi{}{10}^{15}\phantom{\rule{0.3em}{0ex}}{\mathrm{Au}}^{4+}\phantom{\rule{0.3em}{0ex}}\mathrm{ions}∕{\mathrm{cm}}^{2}$) also results in the formation of an amorphized phase similar to that observed in metamict zircon. These results show that high-energy, heavy-ion irradiations provide a good simulation of the ballistic effects of the recoil nucleus of an alpha-decay event and, in both cases, the result is the creation of aperiodic domains. Additional IR and Raman features were recorded in samples irradiated with $280\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ ${\mathrm{Pb}}^{+}$ ions (to fluences of $1\ifmmode\times\else\texttimes\fi{}{10}^{14}$ and $1\ifmmode\times\else\texttimes\fi{}{10}^{15}\phantom{\rule{0.3em}{0ex}}{\mathrm{Pb}}^{+}\phantom{\rule{0.3em}{0ex}}\mathrm{ions}∕{\mathrm{cm}}^{2}$), indicating the formation of an irradiation-induced additional phase(s). The frequencies of the features are consistent with lead silicates, $\mathrm{Zr}{\mathrm{O}}_{2}$, and $\mathrm{Si}{\mathrm{O}}_{2}$. The results show that spectral features of the ${\mathrm{Au}}^{4+}$- and ${\mathrm{Pb}}^{+}$-irradiated zircon are different from those of quenched $\mathrm{Zr}\mathrm{Si}{\mathrm{O}}_{4}$ melts, and the finding further confirms that the amorphous state produced by high-energy ion irradiations is structurally different from the glassy state that results from quenching a high temperature melt. In contrast to significant changes in the frequency and width of the Raman ${\ensuremath{\nu}}_{3}$ band observed in metamict zircon, the ${\mathrm{Pb}}^{+}$ and ${\mathrm{Au}}^{4+}$ irradiations do not cause similar variations, indicating that the remaining zircon crystalline domains in irradiated samples have a crystalline structure with fewer defects than those of metamict zircon.

Optimized Second Harmonic Generation of Femtosecond Pulse by Phase-Blanking Effect in Aperiodically Optical Superlattice

In order to minimize the effect of the unconsidered frequency components on the generated compression pulse, the phasing-blanking effect is taken into account of designing the one-dimensional aperiodic domain reversal structure. Hierarchic genetic algorithm for the design of a domain reversal grating to modulate the spectrum and phase of the generated SH pulse simultaneously are presented. Our simulation shows that the quality of an output pulse is fairly improved.