Fundamental Frequency Wave Research Articles

The interaction of Airy waves and solitons in a three-wave system

We employ the generic three-wave system, with the interaction between two components of the fundamental frequency (FF) wave and the second-harmonic (SH) wave, to consider the collisions of truncated Airy waves (TAWs) and three-wave solitons in a setting which is not available in other nonlinear systems. The advantage of this is that single-wave TAWs, carried by either one of the FF components, are not distorted by the nonlinearity and are stable, three-wave solitons being stable too in the same system. The collision between mutually symmetric TAWs, carried by the different FF components, transforms them into a set of solitons, the number of which decreases with the increase of the total power. The TAW absorbs an incident small-power soliton, and a high-power soliton absorbs the TAW. Between these limits, the collision with an incident soliton converts the TAW into two solitons, with a remnant of the TAW attached to one of them, or leads to the formation of a complex TAW-soliton bound state. At large velocities, the collisions become quasi-elastic.

A Four-Band Rectifier With Adaptive Power for Electromagnetic Energy Harvesting

This letter presents a novel adaptive power rectifier operating at four bands to harvest the electromagnetic energy in the low and wide-range power density conditions. The power range of the rectifier is extended by two operation modes controlled adaptively by a FET switch according to the input power level. A cross-shaped match stub connected by a stepped impedance microstrip line is designed to make the rectifier work at four bands. Two cascaded radial open stubs act as a dc-pass filter to block the fundamental frequency wave and the high order harmonics to further improve the RF-DC (radio frequency-direct current) efficiency, and to smooth the output dc power. When the input power level is −10dBm, the measured maximum RF-DC efficiencies are 47.8%, 33.5%, 49.7% and 36.2% at the frequencies of 0.89GHz, 1.27GHz, 2.02GHz and 2.38GHz, respectively. The efficiency is above 30% in every band when the input power is from −12dBm to 12dBm, which shows a wide input power range.

Broadband and Efficient Femtosecond Second-Harmonic Generation With Temperature-Dependent Group Velocity Matching

In this paper, a method to achieve the simultaneous quasi-phased-matched and group-velocity-matched second harmonic (SH) generation for femtosecond pulses at 1550 nm band was proposed. Under the polarization configuration (e+e-o), group velocity can be matched by control of temperature. The described coupling equations were applied to MgO doped periodically poled lithium niobate crystal, and the temporal and spectral characteristics of interaction waves were investigated. The fractional time delay between the fundamental frequency wave and the SH wave is as a function of temperature and the input pulse duration, resulting in optimal conversion efficiency. Such method can be useful for the broadband and efficient ultrafast SH pulse generation and pulse compression applications.

High-efficiency blue light generation at 426 nm in low pump regime

We report high-efficiency Ti:sapphire-laser-based frequency doubling at the cesium D2 line 852 nm using a 20 mm-long periodically-poled potassium titanyl phosphate crystal in a bow-tie four-mirror ring enhancement cavity. The relatively complete cavity design procedure is presented. Focusing that is over twice as loose as optimal focusing is used, and both the fundamental frequency wave and second harmonic beam absorption-induced thermal lensing effects are weakened. Blue light of 210 mW at 426 nm, where absorption is severe, was obtained with 310 mW mode-matched fundamental light, corresponding to conversion efficiency of up to 67%. The blue light beam power showed 1.5% RMS fluctuation over 40 min.

Effect of pulse slippage on density transition-based resonant third-harmonic generation of short-pulse laser in plasma

The resonant third-harmonic generation of a self-focusing laser in plasma with a density transition was investigated. Because of self-focusing of the fundamental laser pulse, a transverse intensity gradient was created, which generated a plasma wave at the fundamental wave frequency. Phase matching was satisfied by using a Wiggler magnetic field, which provided additional angular momentum to the third-harmonic photon to make the process resonant. An enhancement was observed in the resonant third-harmonic generation of an intense short-pulse laser in plasma embedded with a magnetic Wiggler with a density transition. A plasma density ramp played an important role in the self-focusing, enhancing the third-harmonic generation in plasma. We also examined the effect of the Wiggler magnetic field on the pulse slippage of the third-harmonic pulse in plasma. The pulse slippage was due to the group-velocity mismatch between the fundamental and third-harmonic pulses.

Modulation instability in second harmonic generation in metamaterials with quadratic nonlinearity

Modulation instability (MI) in second harmonic generation in metamaterials (MMs) with quadratic nonlinearity is studied. The analytical expressions for MI gain spectra are obtained, from which the generation condition of MI and the respective roles of dispersion, group velocity mismatch and phase mismatch in MI are identified. It is found that the region of phase mismatch where the MI can take place in MMs is in contrast with its counterpart in conventional materials due to the negative wave vector direction. The MI gains mainly rely on the phase mismatch. Since magnetic permeability is dominant for negative refraction, so the refractive index difference of the fundamental frequency (FF) and second harmonic (SH) wave can fluctuate in a large range in MMs. While the frequency is near the critical point, the refractive index difference of the FF and SH wave is small, so the phase mismatch is small and the MI gain is low. However, while the frequency is far away from the critical point, the refractive index difference of the FF and SH wave becomes large, this leads to a large phase mismatch, and the giant gain with more sidelobes can be obtained for the large phase mismatch occurring in MMs with quadratic nonlinearity.

Enhanced generation of a second-harmonic wave in a composite of metamaterial and microwave plasma with various permittivities.

The generation of a second-harmonic wave, which is one typical nonlinear feature, is enhanced in a composite of plasma and metamaterial. When we generate plasma by an injection of microwaves, whose frequencies are fundamental, we observe intensified second-harmonic waves in the cases of negative-refractive-index states in which both metamaterial permeability and plasma permittivity are negative for the fundamental waves. We performed the measurements at multiple levels of microwave input power up to 300 W to regulate permittivity in the negative polarity for the fundamental wave and in the transient region, including the positive-zero-negative values, for the second-harmonic wave. We clarified that the observed enhancement results from high electron density in negative-permittivity plasma, the propagating fundamental frequency wave not being attenuated in the negative-refractive-index state, and partial phase matching between the fundamental and second-harmonic waves.

Quasi-phase-matching of the dual-band nonlinear left-handed metamaterial

We demonstrate a type of nonlinear meta-atom creating a dual-band nonlinear left-handed metamaterial (DNLHM). The DNLHM operates at two distinct left-handed frequency bands where there is an interval of one octave between the two center frequencies. Under the illumination of a high-power signal at the first left-handed frequency band corresponding to fundamental frequency (FF), second-harmonic generation (SHG) is observed at the second left-handed band. This means that our DNLHM supports backward-propagating waves both at FF and second-harmonic (SH) frequency. We also experimentally demonstrate quasi-phase-matching configurations for the backward SHG. This fancy parametric process can significantly transmits the SH generated by an incident FF wave.

Highly efficient second-harmonic generation from a two-dimensional linear–nonlinear photonic crystal heterostructure

The theory of second-harmonic generation (SHG) in two-dimensional (2D) linear–nonlinear photonic crystal (PC) heterostructure has been developed by means of transmission matrices and a Green’s function approach based on lattice sums. Using this method, we can calculate the conversion efficiency of second-harmonic waves in various 2D PC heterostructures. Not only has great enhancement of SHG been observed when the frequencies of both fundamental frequency and second frequency waves are located at the photonic band edges, but some unique phenomena for the SHG based on resonant states in the heterostructure have also been found. The resonant SHG can appear at the corresponding frequency of the resonant state in the range of 160° of the incident angle around the normal direction, although the value of the SHG changes with the incident angle. The second-harmonic conversion efficiency appears to have a higher value in the heterostructure containing several nonlinear PC slabs because of the competition between phase matching and the decrease in transmittance. We believe that these findings are very beneficial for the design of SHG devices.

High Absorption and Second‐Harmonic Generation in Split Ring Resonator Multilayer Nanostructure

Second‐harmonic generation in split ring resonator multilayer nanostructure is studied with the finite‐difference time‐domain (FDTD) method. The fundamental frequency wave and the second‐harmonic generation at the resonant absorption wavelength are highly localized in the dielectric layer, and the absorption peak is sensitive to dielectric constant of the dielectric layer. Under the excitation of the plasmon resonances mode, the strong local field induces an expected increase of the second‐harmonic generation with conversion efficiencies 10−6‐10−7. The distributions of fundamental frequency electric field and second‐harmonic electric field inside the central dielectric layer region are also shown.

Second-Order Nonlinearity in Triangular Lattice Perforated Gold Film due to Surface Plasmas Resonance

We have studied the excitation second-order nonlinearity through a triangular lattice perforated gold film instead of square lattice in many papers. Under the excitation of surface plasmas resonance effect, the second order nonlinearity exists in the noncentrosymmetric split-ring resonators arrays. Reflection of fundamental frequency wave through a triangular lattice perforated gold film is obtained. We also described the second harmonic conversion efficiencies in the second order nonlinear optical process with the spectra. Moreover, the electric field distributions of fundamental frequency above the gold film region are calculated. The light propagation through the holes results in the enhancement of the second order nonlinearity including second harmonic generation as well as the sum (difference) frequency generation.

Dynamic Analysis of Flexible Rotor-Ball Bearings System with Unbalance-Misalignment-Rubbing Coupling Faults

Dynamic responses of flexi rotor-ball-bearing system under unbalance misalignment rubbing coupling faults are studied. Coupling faults dynamic control model of flexi-multi-system of rotor-ball-bearing system is established, based on finite element analysis and numerical integral combined simulate method. Then nonlinear bearing force and rub-impact force models are programmed in MATLAB. Analysis and compare vibration characteristics of system while under faults-free, unbalance and rub-impact faults. The result demonstrates that when system under unbalance faults, vibration frequency brought by eccentric mass is agreed with rotating speed frequency, its fundamental frequency wave add high frequency component, can show the characteristics of unbalance-rubbing faults efficiently; when system under misalignment faults, with frequency double vibration and high harmonics; when system under unbalance-misalignment-rubbing coupling faults, support force of shafting of rotor system appears high frequency responses like saw tooth based on sine wave, causing aggravation of rub-impact faults.

Nonlinear instabilities of a non-self-similar boundary layer on an airfoil: Experiments, DNS, and theory

Transition prediction of a laminar boundary layer developing on a two-dimensional airfoil section at pure subsonic speeds is still a challenge, because the commonly used semi-empirical prediction tools are mainly based on results derived from the linear stability theory (LST). This approach completely neglects non-linear interactions at later stages of the transition development and therefore provides limited accuracy for cases when the non-linear part has significant length in comparison to the linear stage. Nevertheless, the later one can be of significant importance for airfoil design. The onset and further development of non-linear, in general resonant wave interactions is depending on the pre-history of the boundary layer and the specific linear and non-linear stability characteristics driven by the pressure gradient, which varies in streamwise direction for typical airfoil sections. The variation of the pressure gradient leads to a non self-similar boundary layer development connected with a continuous change of the resonance conditions for wave interactions. The present paper is devoted to the detailed experimental, numerical and theoretical study of weakly nonlinear subharmonic resonant interactions of Tollmien–Schlichting waves in such a two-dimensional non self-similar boundary layer on an airfoil. The experimental approach is based on phase locked hot-wire measurements under controlled disturbance conditions in a low turbulence wind tunnel at a Reynolds number of Re=0.7×10 6. Direct numerical simulations (DNS) based on the vorticity–velocity formulation of the complete Navier–Stokes equations are utilized to provide a detailed comparison for the test cases. The results of weakly non-linear theory (WNT) enabled a profound understanding of the underlying physical mechanisms observed in the experiments and simulations. The joint study provides a complete set of data, starting from the base flow and stability characteristics up to non-linear disturbance development with different involved wave triplets. The phase synchronization mechanism is investigated in detail as well as the resonance efficiency for tuned cases with respect to the exact subharmonic frequency. In general, a good agreement between the experiment, DNS and WNT is found. The essential non-self-similarity of the airfoil boundary layer does not prevent strong resonant interactions and in accordance with investigations in self-similar flows, rapid, close to double-exponential amplification of subharmonic modes is observed. At the resonant stage, the phase-synchronization condition is shown to be satisfied, which provides equal phase speeds for all involved modes. For tuned cases, the initial phase relation between fundamental and subharmonic modes can lead, partly, to a suppression of the subharmonic wave amplification. Variation of the fundamental wave frequency shows that the integral resonance efficiency is significantly decreased with the reduction of the frequency. This effect is explained as a frequency dependence of the nonlinear coupling coefficients as well as the detuning of the subharmonic-fundamental phase speed associated mainly with the base-flow non-self-similarity. Depending on the frequency content of the initial disturbances this can lead to a direct influence on the corresponding transition position.

Second harmonic generation with zero phase velocity waves

We design a dual-band nonlinear composite right-left handed transmission line with phase-matching achieved between the fundamental frequency and second harmonic when both interacting waves have zero phase velocity. Additionally, we show that such a transmission line supports a new regime where the generation of backward second harmonic waves is achieved from a backward fundamental frequency wave.

Spatial structure of first and higher harmonic internal waves from a horizontally oscillating sphere

An experimental study is presented on the spatial structure of the internal wave field emitted by a horizontally oscillating sphere in a uniformly stratified fluid. The limits of linear theory and the nonlinear features of the waves are considered as functions of oscillation amplitude. Fourier decomposition is applied to separate first harmonic waves at the fundamental frequency and higher harmonic waves at multiples of this frequency. For low oscillation amplitude, of 10% of the sphere radius, only the first harmonic is significant and the agreement between linear theory and experiment is excellent. As the oscillation amplitude increases up to 30% of the radius, the first harmonic becomes slightly smaller than its linear theoretical prediction and the second and third harmonics become detectable. Two distinct cases emerge depending on the ratio Ω between the oscillation frequency and the buoyancy frequency. When Ω > 0.5, the second harmonic is evanescent and localized near the sphere in the plane through its centre perpendicular to the direction of oscillation, while the third harmonic is negligible. When Ω < 0.5, the second harmonic is propagative and appears to have an amplitude that exceeds the amplitude of the first harmonic, while the third harmonic is evanescent and localized near the sphere on either side of the plane through its centre perpendicular to the direction of oscillation. Moreover, the propagative first and second harmonics have radically different horizontal radiation patterns and are of dipole and quadrupole types, respectively.

Two phenomena: Honji instability, and ringing of offshore structures

Honji instability and ringing of offshore structrures are two different phenomena. Honji instability occurs at a circular cylinder in transverse periodic finite motion in a water tank. It is superposed on the streaming flow induced by the cylinder's boundary layer. Its oscillation period is half of the period of the cylinder oscillation. Finite volume calculations of the filtered Navier-Stokes equations visualize the three-dimensional instability, where fluid particles transported by the circumferencial roll pairs exhibit a periodic mushroom-like pattern. Force is the same with and without the Honji instability. The large eddy simulation calculations for high Reynolds number support a drag coefficient in accordance with the Stokes-Wang solution below separation and conform with experimental measurements of the damping force on a harmonically oscillating cylinder. Ringing of offshore structures are vibrations which appear at natural frequencies and concern fatigue. It is generated by a higher harmonic force oscillating with frequency being 3–4 times the fundamental wave frequency. Together with a strong inertia load in phase with the incoming wave's acceleration, a secondary load cycle appears in strong seas when the wave crest leaves the structure; this occurs about 1/4 wave period after the main force peak, it starts when the wave crest is about one cylinder radius behind the cylinder, lasts for about 15–20 percent of the wave period and has a magnitude up to 11 % of the peak-to-peak total force. It is a gravity effect and appears in strong irregular seas when kA > 0.18 and um/gD>0.4 (k wavenumber, A amplitude, um maximal wave induced velocity, g acceleration of gravity, D cylinder diameter).

Analysis of the sound of the Japanese voice using real-time spectral analysis

Voice signal processing requires real-time processing. For this reason, a new method which updates the spectrum by using input data is proposed. In this method, analysis in the time-frequency domain is executed as well as wavelet transform. Vowels /i/ and /e/ consist of fundamental, harmonic, and high frequency waves. These high frequency waves determine the sounds of /i/ and /e/. These high frequency waves may also exist in /a/ and /o/. In this article, we analyze these high frequency waves by using a new analyzing method, and we show the constitution of high frequency waves. Since the waveform of a consonant does not repeat, the analysis cannot be performed like the analysis of the high frequency wave of a vowel. In a consonant, we show the fluctuation of the spectrum with time.

Electrically controlled second harmonic generation of circular polarization in a single LiNbO3 optical superlattice

We demonstrate theoretically that a linearly polarized fundamental frequency wave (FW) can be effectively converted into a circularly polarized frequency doubling one in a single LiNbO3 optical supperlattice (OSL) by applying an appropriate electric field. The numerical results show that at 30°C, for a single OSL with a 91.235 V/mm applied electric field, a 100 MW/cm2 and 1064 nm laser beam can be converted into a right-handed circularly polarized (RHCP) light at 10 mm or a left-handed circularly polarized (LHCP) light at 25.747 mm. The quasi-periodic domain optimized process for minimizing the applied electric field can be obtained by changing the structural parameter, e.g., the positive or negative domain length of the OSL. It is also found that the generation of the second harmonic (SH) circularly polarized light (CPL) is insensitive to the fabrication errors of domains of the OSL; moreover, the bandwidth of conversion efficiency from the e-polarized FW to SH CPL is about 0.062 nm corresponding to a 60.85 ps FW pulse.

Theoretical analysis of second-harmonic conversion efficiency in negative-index materials

For negative-index materials(NIM) of second-harmonic wave(SHW) and positive-index materials of fundamental frequency wave(FFW)，the equations of the coupled wave was deduced，taking account of absorption coefficient，walk-off effect，phase mismatching capacity and the approximation of slow-varying amplitudes of the plane wave. On the basis of the equations，a formulation of SHW conversion efficiency was obtained in condition of small signal approximation for FFW. Through numerical simulation, the effects of phase mismatching capacity，walk-off angle and absorption coefficient of SHW on the conversion efficiency of SHW were scrutinized respectively. The maximum conversion efficiency of SHW was realized via increasing the length of NIM，that is，there exists an optimum length of NIM; however, the conversion efficiency of SHW shows an evidencet periodic evolution and the maximum conversion efficiency always diminishes. The conversion efficiency decreases with the increases of the phase mismatching capacity and the absorption coefficient. The influence of walk-off effect is not evident so that it may be neglected with respect to the conversion efficiency of SHW. This study provides a basis for investigating nonlinear theory of negative-index materials.

Broadband characteristics of piezoelectric transducer bonded to a thick plate resonator.

The piezoelectric transducer bonded to a thick plate resonator wholly vibrates as a single transducer. Since the distribution of stress in the thickness direction is asymmetric, the transducer resonates at even order harmonic frequencies as well as odd order ones. The back of the resonator is bonded to a quarter‐wavelength matching layer to transmit backward the fundamental frequency wave through the layer. The front of piezoelectric transducer is bonded to another matching layer to transmit forward the ultrasonic wave of higher order frequencies. If both the piezoelectric transducer and the resonator are made of low Q materials, the admittance curve including troughs among resonance peaks is flattened and shows broadband characteristics. Such broadband characteristic transducers made of one to three composite piezoelectric materials were experimentally studied. The thickness of the piezoelectric transducer and the resonator were designed for resonance frequencies of 7 and 1 MHz, respectively. The back of matching layer was bonded to the absorbing material not to reflect forward the ultrasonic waves of 1 MHz. As a result, the ultrasound of center frequency of 5 MHz and fractional bandwidth of 100% were transmitted from the transducer driven by an impulsive signal.