Contribution from the secondary harmonics of a disturbance to the separatrix map of the Hamiltonian system

The special role of low-frequency secondary harmonics with frequencies that are sums of and differences between primary frequencies entering into the Hamiltonian in explicit form has been already discussed in the literature. These harmonics are of the second order of smallness and constitute a minor fraction of the disturbance. Nevertheless, under certain conditions, their contribution to the amplitude of the separatrix map of the system may be several orders of magnitude higher than the contributions from primary harmonics and, thereby, govern the formation of dynamic chaos. This work generalizes currently available theoretical and numerical data on this issue. The role of secondary harmonics is demonstrated with a pendulum the disturbance of which in the Hamiltonian is represented by two asymmetric closely spaced high-frequency harmonics. An analytical expression for the contribution of the secondary harmonics to the separatrix map amplitude for this system is derived, and the range of very low secondary frequencies not studied earlier is considered using this equation. The domains where the separatrix map amplitude linearly grows with frequency and the chaotic layer size is frequency-independent are indicated. Theoretical predictions are compared with numerical data.     

相位匹配法在毛细管波导中产生高次谐波的分析

在理论上研究了超短强激光脉冲与毛细管中惰性气体相互作用产生高次谐波的最佳相位匹配条件,在计算中发现了特定级次 相位匹配中截止驱动光强的存在。分析表明要想使高次谐波获得相位匹配,需要超短脉宽的驱动脉冲以及电离能大的气体工作介质。讨论了毛细管波导中的强场高次谐波选择性并指出了改善谐波选择性的措施。     

Frequency mixing in a bistable system in the presence of noise

The dynamics of a bistable system resulting from the action of several periodic perturbations and noise is studied. The response of the system at combination harmonics and the changes in the response caused by high-frequency modulation and a constant field that removes the degeneracy in the bistable system are calculated. The mixing of harmonics is investigated experimentally in an iron garnet thin film. It is shown that the higher harmonics exhibit behavior characteristic of stochastic resonance and that the form and symmetry of the dependence of harmonics on the constant field removing the degeneracy can be used to determine the characteristics of a bistable system with respect to its response to external periodic modulation. Zh. éksp. Teor. Fiz. 112, 628–642 (August 1997)     

Anisotropic multiple scattering of collimated irradiance

Spherical harmonics are often used to solve multi-scatter transport problems. For a collimated incident beam, we describe a technique similar to the familiar P_N approximation except that we manage the infinite set of coupled equations in a novel way that permits the use of hundreds of harmonics to represent very pointed angular distributions. We split some equations into two approximate ones that depend on the angle of incidence. For plane slab geometry, the harmonics of low degree are solved in a coordinate system aligned to the boundary while the high harmonics use coordinates pointed at the source. We illustrate the technique with an extreme example: a scattering function having an integrable singularity in the forward direction. We give a time-dependent example along with several time-independent ones.     

Space-time considerations in the phase locking of high harmonics

The combination of several high order harmonics can produce an attosecond pulse train, provided that the harmonics are locked in phase to each other. We present calculations that evaluate the degree of phase locking that is achieved in argon and neon gases interacting with an intense, 50 fs laser pulse, for a range of macroscopic conditions. We find that phase locking depends on both the temporal and the spatial phase behavior of the harmonics, as determined by the interplay between the intrinsic dipole phase and the phase matching in the nonlinear medium. We show that, as a consequence of this, it is not possible to compensate for a lack of phase locking by purely temporal phase manipulation.     

Characterisation of parallel misalignment in rotating machines by means of the modulated signal of incremental encoders

There are many defects in rotating machines which, when analysed by means of the Fourier spectrum of transversal vibration, show several harmonics of the rotational speed, more specifically the first and the second, although higher harmonics may also be present. Misalignments, looseness, the breakage of fastening screws, broken mechanical seals, are just some of the problems. Nevertheless, the effects of some of these defects differ when the angular vibration is measured using an incremental rotating encoder, which offers an additional aid for diagnosing the problem.     

平面镜反射率的标定及修正

 研究了用同步辐射源标定软X光掠入射平面镜的反射率。实验采用北京同步辐射装置(BSRF)-3W1B束线及反射率计靶室,在50~1 500 eV能区,做了C,Si,Ni和Au材料平面镜在1°~7°掠射角下的反射率标定曲线。由于3W1B束线的单色器采用变间距光栅作色散元件,光栅分光必然存在高次谐波,高次谐波严重影响光源的单色性,从而给平面镜的反射率标定值带来误差。前置滤片虽然能有效抵制高次谐波,但不能完全消除高次谐波。为此,利用透射光栅对光源做了单色性研究,给出高次谐波在不同能区所占光源强度的比例,从而对平面镜反射率标定值做出修正。     

On the relative influence of individual harmonics on pitch judgment

Spectral weighting functions were estimated in a pitch-comparison task to assess the relative influence of individual harmonics on listeners' pitch judgment. The stimuli were quasi-harmonic complex tones composed of the first 12 components, with fundamental frequencies ranging from 100 to 800 Hz. On each stimulus presentation the frequency of each harmonic was randomly jittered by a small amount. The perceptual weight for each harmonic was calculated as the correlation coefficient between the binary responses of the listener and the frequency jitters for that harmonic. Although in general the present results conform to previous ones showing the predominant role of several low-ranked harmonics, discrepancies exist in details. Contrary to some previous reports that the dominant harmonics were of fixed harmonic ranks regardless of their frequencies, the current results showed that the dominant harmonics were best described as close to a fixed absolute frequency of 600 Hz.     

核运动对非奇次谐波产生的影响

理论研究了H2+、D2+、T2+辐射高次谐波的特点.结果表明,在核运动影响下,不仅奇次谐波呈现红移现象,而且谐波光谱呈现非奇次谐波.随着核质量增大,奇次谐波频移和非几次谐波强度都减弱.但是随着激脉宽增大,非奇次谐波的产生明显被增强.理论分析表明,谐波频移是由谐波辐射在激光上升和下降区间的非对称性导致的;非奇次谐波是由于分子对称性在较大核间距离处遭破坏产生的.     

Higher Harmonic Operations of Submillimeter Wave Gyrotrons (Gyrotron FU Series)

Higher harmonic operation of gyrotrons is necessary to obtain high frequencies. Some gyrotrons included in the Gyrotron FU series developed at Fukui University have achieved operation at the third and even fourth harmonics of the electron cyclotron frequency. The output lies in the millimeter to submillimeter wavelength range and the output powers are several watts to several tens of watts. In this paper, the gyrotrons and the conditions under which they operate are described in detail.     

Nonlinear non-spherical oscillations of gas bubble under a periodic variation of ambient liquid pressure

A mathematical model is constructed for the bubble dynamics, in which the interphase surface variation is presented in the form of a series in spherical harmonics, and the equations are written with the accuracy up to the squared amplitude of the distortion of the spherical shape of the bubble. In the oscillation regimes close to periodic sonoluminescence of a single bubble in a standing acoustic wave, the character of air bubble oscillations in water was studied depending on the bubble initial radius and the amplitude of the liquid pressure variation. It was found that non-spherical oscillations of bounded amplitude can take place outside the region of linearly stable spherical oscillations. Both the oscillations with a period equal to one or several periods of the liquid pressure variation and aperiodic oscillations are observed. It is shown that neglecting the distortions in the form of spherical harmonics with large numbers (i > 3) may lead to a change of oscillation regimes. The influence of distortions on the bubble surface shape for the harmonics with i > 8 is insignificant.     

Characteristics of whistles from the acoustic repertoire of resident killer whales (Orcinus orca) off Vancouver Island, British Columbia

The acoustic repertoire of killer whales (Orcinus orca) consists of pulsed calls and tonal sounds, called whistles. Although previous studies gave information on whistle parameters, no study has presented a detailed quantitative characterization of whistles from wild killer whales. Thus an interpretation of possible functions of whistles in killer whale underwater communication has been impossible so far. In this study acoustic parameters of whistles from groups of individually known killer whales were measured. Observations in the field indicate that whistles are close-range signals. The majority of whistles (90%) were tones with several harmonics with the main energy concentrated in the fundamental. The remainder were tones with enhanced second or higher harmonics and tones without harmonics. Whistles had an average bandwidth of 4.5 kHz, an average dominant frequency of 8.3 kHz, and an average duration of 1.8 s. The number of frequency modulations per whistle ranged between 0 and 71. The study indicates that whistles in wild killer whales serve a different function than whistles of other delphinids. Their structure makes whistles of killer whales suitable to function as close-range motivational sounds.     

The role of load harmonics in audible noise of electrical transformers

Harmonic components in load currents have a larger impact on the load noise level of transformers than might be expected from their amplitude. There are several reasons for this larger impact: (a) the interaction of higher harmonics with the large fundamental load current at power frequency, (b) the increasing sound radiation efficiency with increasing frequency, and (c) the greater sensitivity of the human ear to higher frequencies, which is considered in sound measurements by applying the A-weighting filter. This paper describes the process of generation, transmission, and emission of load noise in the presence of load harmonics. A calculation scheme is presented that is able to estimate the noise increase and the noise spectrum of electrical transformers under non-sinusoidal load conditions. The proposed calculation scheme is applied to three practical examples.     

Generation of even harmonics in a relativistic laser plasma of atomic clusters

It is shown that the irradiation of atomic clusters by a superintense femtosecond laser pulse gives rise to various harmonics of the laser field. They arise as a result of elastic collisions of free electrons with atomic ions inside the clusters in the presence of the laser filed. The yield of even harmonics whose electromagnetic field is transverse is attributed to the relativism of the motion of electrons and the consideration of their drift velocity associated with the internal ionization of atoms and atomic ions of a cluster. These harmonics are emitted in the same direction as odd harmonics. The conductivities and electromagnetic fields of the harmonics are calculated. The generation efficiency of the harmonics slowly decreases as the harmonic number increases. The generation of even harmonics ceases when the drift velocity of electrons becomes equal to zero and only the oscillation velocity of electrons is nonzero. The results can also be applied to the irradiation of solid-state targets inside a skin layer.     

Study of second-harmonic generation of shear horizontal modes using modal analysis

In this work a modal analysis was employed to study generation of the second harmonics of shear horizontal (SH) modes in a solid plate. Under second order perturbation, second-harmonic generation will occur accompanying SH mode propagation due to the bulk elastic non-linearity of plate material. In solid plate the total second-harmonic fields of a SH mode propagation are regarded as sum of the fields of a series of double frequency Lamb modes (DFLMs). The contribution of each DFLM component to the total second-harmonic fields is dependent of the difference of phase velocities of the corresponding DFLM and SH mode. The analysis results show that the DFLM field component may have cumulative growth effect once its phase velocity exactly or approximately equals that of a SH mode. It is also found that the fields of the total second harmonics of a SH mode are only symmetrical. The examples of field distributions of several DFLMs on the plate surface are considered.     

High-order harmonic generation of the N2 molecule in two-color circularly polarized laser fields

The generation of high-order harmonics and the attosecond pulse of the N₂ molecule in two-color circularly polarized laser fields are investigated by the strong-field Lewenstein model. We show that the plateau of spectra is dramatically extended and a continuous harmonic spectrum with the bandwidth of 113 eV is obtained. When a static field is added to the x direction, the quantum path control is realized and a supercontinuum spectrum can be obtained, which is beneficial to obtain a shorter attosecond pulse. The underlying physical mechanism is well explained by the time-frequency analysis and the semi-classical three-step model with a finite initial transverse velocity. By superposing several orders of harmonics in the combination of two-color circularly polarized laser fields and a static field, an isolated attosecond pulse with a duration of 30 as can be generated.     

Non linear recording in silver halide planar volume holograms

A series of bromine-vapour bleached, planar, volume holograms were formed in silver halide emulsion. The holograms were characterised by measuring the variation in intensity of the transmitted replaying beam with angles at several wavelengths. The results were investigated using coupled-wave theory, allowing for the existence of grating harmonics and higher diffraction orders. The effects of first, second and third grating harmonics were found in the experimental results. Modulation profiles synthesised using the results suggested the presence of a small fourth harmonic in the higher exposure holograms.     

Role of excited states in coherent harmonic bremsstrahlung in a photoionized plasma

It is established for a photoionized plasma formed in the barrier-suppression ionization regime that the preliminary population of the excited states of the ionizing atoms plays an important role. It is established that in this case an anomalously strong (several orders of magnitude) increase occurs in the efficiency of generation of the harmonics of the pump radiation. It is shown that a relative decrease of the harmonics generation efficiency occurs with time as a result of collisions of the electrons produced by ionization.     

Generation of non-integer high-order harmonics and significant enhancement of harmonic intensity

High-order harmonics from helium atom in the orthogonally two-color(OTC) laser field are investigated by solving the two-dimensional time-dependent Schrodinger equation.Non-integer high-order harmonics are obtained in some ratio of frequencies of two components.Pure odd and even harmonics from atoms could be separated in two components by adjusting the ratio of frequencies in OTC scheme,and the resolution of harmonics is improved at the same time.The physical mechanism is explained by the periodicity of dipole.With the same intensity of the incident laser,the intensity of the high-order harmonics from the OTC field scheme is improved by three orders of magnitude compared to the monochromatic laser field scheme.A theoretical scheme is provided for experimentally achieving improving energy resolution and separation of pure odd and even harmonics in atoms.Also,we provide a means for improving harmonic intensity.     

Simulation of sound field in a tissue medium generated by a concave spherically annular transducer

The concave spherically annular transducer is regarded as a negative and a positive concave spherical transducer, and the spheroidal beam equation is used to simulate the linear and nonlinear sound field in a tissue medium generated by this transducer. It is found that the acoustic focus of the ring does not coincide with the acoustic focus of its central part. If the width of the ring increases, its acoustic focus will move toward the geometric focus and the amplitudes of nonlinear harmonics will increase obviously. If there are several coaxial rings placed on the concave spherical surface, more than one peak will appear along the axial direction for the fundamental, and high harmonics focus better. The distribution of sound field will change with the number and the excited signals of rings, so it maybe is a potential approach to treat locally big tumors.