Analysis of beam-quality degradation in nonlinear frequency conversion

Based on the ripple transfers of electric-field amplitude and phase in frequency tripling, simple formulas are derived for the harmonic laser's beam-quality factor M-3omega(2), with an arbitrary fundamental incidence to ideal nonlinear crystals. Whereas the harmonic beam's quality is generally degraded, the beam's divergence is similar to that of the fundamental after nonlinear frequency conversion. For practical crystals with periodic surface ripples that are caused by their machining, a multiorder diffractive model is presented with which the focusing properties of harmonic beams can be studied. Predictions of the theories are shown to be in excellent agreement with full numerical simulations. (C) 2002 Optical Society of America.

Super-resolution scanning laser microscopy with a third-order optical nonlinear thin film

In a configuration of optical far-field scanning microscopy, super-resolution achieved by inserting a third-order optical nonlinear thin film is demonstrated and analyzed in terms of the frequency response function. Without the thin film the microscopy is diffraction limited; thus, subwavelength features cannot be resolved. With the nonlinear thin film inserted, the resolution is dramatically improved and thus the microscopy resolves features significantly smaller than the smallest spacing allowed by the diffraction limit. A theoretical model is established and the device is analyzed for the frequency response function. The results show that the frequency response function exceeds the cutoff spatial frequency of the microscopy defined by the laser wavelength and the numerical aperture of the convergent lens. The main contribution to the improvement of the cutoff spatial frequency is from the phase change induced by the complex transmission of the nonlinear thin film. Experimental results are presented and are shown to be consistent with the results of theoretical simulations.

Laser tunable Toraldo superresolution with a uniform nonlinear pupil filter

We demonstrate that it is possible to reduce the focal spot size by inserting a uniform nonlinear thin film at the aperture of a focusing lens. The reduction of spot size is tunable by adjusting the incoming laser power. In comparison with the original diffraction spot, the transverse spot size can be reduced 0.65 times. The nonlinear thin film acts effectively as a Toraldo filter, and the phase and amplitude modulation stems from the laser-induced variances in the transmission of the thin film. The proposed technique removes the need of fabricating annular pupil filters. (C) 2008 Optical Society of America.

The separation of beta-BBO phase in alpha-BBO crystal by the irradiation of femtosecond laser

We observed and described some phenomena, which were that when a alpha-BBO crystal was irradiated by a focused femtosecond laser beam, the temperature effect happened in a minute area of focus, then the induced beta-BBO phase was separated within the minute area in the alpha-BBO crystal. (C) 2007 Elsevier B.V. All rights reserved.

Solution-phase exfoliation of graphite for ultrafast photonics

We exfoliate graphite in both aqueous and non-aqueous environments through mild sonication followed by centrifugation. The dispersions are enriched with monolayers. We mix them with polymers, followed by slow evaporation to produce optical quality composites. Nonlinear optical measurements show similar to 5% saturable absorption. The composites are then integrated into fiber laser cavities to generate 630 fs pulses at 1.56 mu m. This shows the viability of solution phase processing for graphene based photonic devices. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

The nonlinear heat release response of stratified lean-premixed flames to acoustic velocity oscillations

This paper analyzes the forced response of swirl-stabilized lean-premixed flames to high-amplitude acoustic forcing in a laboratory-scale stratified burner operated with CH4 and air at atmospheric pressure. The double-swirler, double-channel annular burner was specially designed to generate high-amplitude acoustic velocity oscillations and a radial equivalence ratio gradient at the inlet of the combustion chamber. Temporal oscillations of equivalence ratio along the axial direction are dissipated over a long distance, and therefore the effects of time-varying fuel/air ratio on the response are not considered in the present investigation. Simultaneous measurements of inlet velocity and heat release rate oscillations were made using a constant temperature anemometer and photomultiplier tubes with narrow-band OH*/CH* interference filters. Time-averaged and phase-synchronized CH* chemiluminescence intensities were measured using an intensified CCD camera. The measurements show that flame stabilization mechanisms vary depending on equivalence ratio gradients for a constant global equivalence ratio (φg=0.60). Under uniformly premixed conditions, an enveloped M-shaped flame is observed. In contrast, under stratified conditions, a dihedral V-flame and a toroidal detached flame develop in the outer stream and inner stream fuel enrichment cases, respectively. The modification of the stabilization mechanism has a significant impact on the nonlinear response of stratified flames to high-amplitude acoustic forcing (u'/U∼0.45 and f=60, 160Hz). Outer stream enrichment tends to improve the flame's stiffness with respect to incident acoustic/vortical disturbances, whereas inner stream stratification tends to enhance the nonlinear flame dynamics, as manifested by the complex interaction between the swirl flame and large-scale coherent vortices with different length scales and shedding points. It was found that the behavior of the measured flame describing functions (FDF), which depend on radial fuel stratification, are well correlated with previous measurements of the intensity of self-excited combustion instabilities in the stratified swirl burner. The results presented in this paper provide insight into the impact of nonuniform reactant stoichiometry on combustion instabilities, its effect on flame location and the interaction with unsteady flow structures. © 2011 The Combustion Institute.

Hydrogen-induced morphotropic phase transformation of single-crystalline vanadium dioxide nanobeams.

We report a morphotropic phase transformation in vanadium dioxide (VO2) nanobeams annealed in a high-pressure hydrogen gas, which leads to the stabilization of metallic phases. Structural analyses show that the annealed VO2 nanobeams are hexagonal-close-packed structures with roughened surfaces at room temperature, unlike as-grown VO2 nanobeams with the monoclinic structure and with clean surfaces. Quantitative chemical examination reveals that the hydrogen significantly reduces oxygen in the nanobeams with characteristic nonlinear reduction kinetics which depend on the annealing time. Surprisingly, the work function and the electrical resistance of the reduced nanobeams follow a similar trend to the compositional variation due mainly to the oxygen-deficiency-related defects formed at the roughened surfaces. The electronic transport characteristics indicate that the reduced nanobeams are metallic over a large range of temperatures (room temperature to 383 K). Our results demonstrate the interplay between oxygen deficiency and structural/electronic phase transitions, with implications for engineering electronic properties in vanadium oxide systems.

Nonlinear phenomena in thermoacoustics: A comparison between single-mode and multi-mode methods

Nonlinear analysis of thermoacoustic instability is essential for prediction of frequencies and amplitudes of limit cycles. In frequency domain analyses, a quasi-linear transfer function between acoustic velocity and heat release rate perturbations, called the flame describing function (FDF), is obtained from a flame model or experiments. The FDF is a function of the frequency and amplitude of velocity perturbations but only contains the heat release response at the forcing frequency. While the gain and phase of the FDF provide insight into the nonlinear dynamics of the system, the accuracy of its predictions remains to be verified for different types of nonlinearity. In time domain analyses, the governing equations of the fully coupled problem are solved to find the time evolution of the system. One method is to discretize the governing equations using a suitable basis, such as the natural acoustic modes of the system. The number of modes used in the discretization alters the accuracy of the solution. In our previous work we have shown that predictions using the FDF are almost exactly the same as those obtained from the time-domain using only one mode for the discretization. We call this the single-mode method. In this paper we compare results from the single-mode and multi-mode methods, applied to a thermoacoustic system of a premixed flame in a tube. For some cases, the results differ greatly in both amplitude as well as frequency content. This study shows that the contribution from higher and subharmonics to the nonlinear dynamics can be significant and must be considered for an accurate and comprehensive analysis of thermoacoustic systems. Hence multi-mode simulations are necessary, and the single-mode method or the FDF may be insufficient to capture some of the complex nonlinear behaviour in fhermoacoustics.

Phase synchronization through entrainment by a consensus input

The paper proposes a synchronization mechanism in a set of nonlinear oscillators interconnected through a communication network. In contrast to many existing results, we do not employ strong, diffusive couplings between the individual oscillators. Instead, each individual oscillator is weakly forced by a linear resonator system. The resonator systems are synchronized using results from consensus theory. The synchronized resonator systems force the frequencies of the nonlinear oscillators to a constant frequency and thereby yield synchronization of the oscillators. We prove this result using the theory of small forcings of stable oscillators. This synchronization scheme allows for synchronization of nonlinear oscillators over uniformly connected communication graphs. ©2010 IEEE.

Trading the stability of finite zeros for global stabilization of nonlinear cascade systems

This note analyzes the stabilizability properties of nonlinear cascades in which a nonminimum phase linear system is interconnected through its output to a Stable nonlinear system. It is shown that the instability of the zeros of the linear System can be traded with the stability of the nonlinear system up to a limit fixed by the growth properties of the cascade interconnection term. Below this limit, global stabilization is achieved by smooth static-state feedback. Beyond this limit, various examples illustrate that controllability of the cascade may be lost, making it impossible to achieve large regions of attractions.

Trading the stability of finite zeros for global stabilization of nonlinear cascade systems

This paper analyzes the stabilizability properties of nonlinear cascades in which a nonminimum phase linear system is interconnected through its output to a stable nonlinear system. It is shown that the instability of the zeros of the linear system can be traded with the stability of the nonlinear system up to a limit fixed by the growth properties of the cascade interconnection term. Below this limit, global stabilization is achieved by smooth static state feedback. Beyond this limit, various examples illustrate that controllability of the cascade may be lost, making it impossible to achieve large regions of attractions.

Nonlinear phenomena in thermoacoustic systems with premixed flames

Nonlinear analysis of thermoacoustic instability is essential for prediction of frequencies, amplitudes and stability of limit cycles. Limit cycles in thermoacoustic systems are reached when the energy input from driving processes and energy losses from damping processes balance each other over a cycle of the oscillation. In this paper an integral relation for the rate of change of energy of a thermoacoustic system is derived. This relation is analogous to the well-known Rayleigh criterion in thermoacoustics, but can be used to calculate the amplitudes of limit cycles, as well as their stability. The relation is applied to a thermoacoustic system of a ducted slot-stabilized 2-D premixed flame. The flame is modelled using a nonlinear kinematic model based on the G-equation, while the acoustics of planar waves in the tube are governed by linearised momentum and energy equations. Using open-loop forced simulations, the flame describing function (FDF) is calculated. The gain and phase information from the FDF is used with the integral relation to construct a cyclic integral rate of change of energy (CIRCE) diagram that indicates the amplitude and stability of limit cycles. This diagram is also used to identify the types of bifurcation the system exhibits and to find the minimum amplitude of excitation needed to reach a stable limit cycle from another linearly stable state, for single- mode thermoacoustic systems. Furthermore, this diagram shows precisely how the choice of velocity model and the amplitudedependence of the gain and the phase of the FDF influence the nonlinear dynamics of the system. Time domain simulations of the coupled thermoacoustic system are performed with a Galerkin discretization for acoustic pressure and velocity. Limit cycle calculations using a single mode, as well as twenty modes, are compared against predictions from the CIRCE diagram. For the single mode system, the time domain calculations agree well with the frequency domain predictions. The heat release rate is highly nonlinear but, because there is only a single acoustic mode, this does not affect the limit cycle amplitude. For the twenty-mode system, however, the higher harmonics of the heat release rate and acoustic velocity interact resulting in a larger limit cycle amplitude. Multimode simulations show that in some situations the contribution from higher harmonics to the nonlinear dynamics can be significant and must be considered for an accurate and comprehensive analysis of thermoacoustic systems. Copyright © 2012 by ASME.

Nonlinear thermoacoustics of ducted premixed flames: The influence of perturbation convection speed

When a premixed flame is placed within a duct, acoustic waves induce velocity perturbations at the flame's base. These travel down the flame, distorting its surface and modulating its heat release. This can induce self-sustained thermoacoustic oscillations. Although the phase speed of these perturbations is often assumed to equal the mean flow speed, experiments conducted in other studies and Direct Numerical Simulation (DNS) conducted in this study show that it varies with the acoustic frequency. In this paper, we examine how these variations affect the nonlinear thermoacoustic behaviour. We model the heat release with a nonlinear kinematic G-equation, in which the velocity perturbation is modelled on DNS results. The acoustics are governed by linearised momentum and energy equations. We calculate the flame describing function (FDF) using harmonic forcing at several frequencies and amplitudes. Then we calculate thermoacoustic limit cycles and explain their existence and stability by examining the amplitude-dependence of the gain and phase of the FDF. We find that, when the phase speed equals the mean flow speed, the system has only one stable state. When the phase speed does not equal the mean flow speed, however, the system supports multiple limit cycles because the phase of the FDF changes significantly with oscillation amplitude. This shows that the phase speed of velocity perturbations has a strong influence on the nonlinear thermoacoustic behaviour of ducted premixed flames. © 2013 The Combustion Institute.

Sparse recovery of complex phase-encoded velocity images using iterative thresholding

In this paper we propose a new algorithm for reconstructing phase-encoded velocity images of catalytic reactors from undersampled NMR acquisitions. Previous work on this application has employed total variation and nonlinear conjugate gradients which, although promising, yields unsatisfactory, unphysical visual results. Our approach leverages prior knowledge about the piecewise-smoothness of the phase map and physical constraints imposed by the system under study. We show how iteratively regularizing the real and imaginary parts of the acquired complex image separately in a shift-invariant wavelet domain works to produce a piecewise-smooth velocity map, in general. Using appropriately defined metrics we demonstrate higher fidelity to the ground truth and physical system constraints than previous methods for this specific application. © 2013 IEEE.

APSK coded modulation schemes for nonlinear satellite channels with high power and spectral efficiency

A new class of 16-ary Amplitude Phase Shift Keying (APSK) coded modulations deemed double-ring PSK modulations best suited for (satellite) nonlinear channels is proposed. Constellation parameters optimization has been based on geometric and information-theoretic considerations. Furthermore, pre- and post-compensation techniques to reduce the nonlinearity impact have been examined. Digital timing clock and carrier phase have been derived and analyzed for a Turbo coded version of the same new modulation scheme. Finally, the performance of state-of the art Turbo coded modulation for this new 16-ary digital modulation has been investigated and compared to the known TCM schemes. It is shown that for the same coding scheme, double-ring APSK modulation outperforms classical 16-QAM and 16-PSK over a typical satellite nonlinear channel due to its intrinsic robustness against the High Power Amplifier (HPA) nonlinear characteristics. The new modulation is shown to be power- and spectrally-efficient, with interesting applications to satellite communications. © 2002 by the American Institute of Aeronautics and Astronautics, Inc.