Generation Of Odd Harmonics Research Articles

Transient renormalization of the Josephson plasma frequency

Layered superconductors are emerging as compact sources of intense, continuous and coherent terahertz (THz) waves [Welp et al., Nat. Photonics 7, 702 (2013)]. Apart from that, they also represent nonlinear media that can exhibit a host of nonlinear optical effects such as odd harmonic generation, slowing down of THz waves, self-focusing and self-induced transparency [Savel'ev et al., Nat. Phys. 2, 521 (2006)] that further widen their range of applications. In the linear regime, electromagnetic waves can penetrate them only if their frequency is larger than a gap-frequency, the so-called Josephson plasma frequency, whose signature is characterized by an edge in the THz reflectivity spectrum. In this work, transient renormalization of the Josephson plasma frequency in THz-perturbed La1.84Sr0.16CuO4 has been experimentally observed using the time-resolved THz time-domain spectroscopy. As the perturbing THz field evolves in time, the reflectivity edge measured from the raw-reflectivity data is found to exhibit a red shift, thus implying a reduction in the Josephson plasma frequency. This is a nonlinear effect that renders the layered superconductor transparent over a narrow spectral range close to the Josephson plasma frequency—THz waves with frequencies smaller than the unperturbed Josephson plasma frequency can penetrate the sample. The results presented in this paper should stimulate the development of nonlinear physics in layered superconductors and contribute in developing new concepts for well-controllable THz devices.

Light bullets formation accompanied by odd harmonics generation under Mid-IR femtosecond filamentation in LiF

The formation of light bullets in mid-IR femtosecond filamentation is investigated numerically by means of the unidirectional pulse propagation equation (UPPE). A general approach for light bullets formation is presented for condensed media under anomalous GVD. The main parameters of the light bullets are evaluated. The features of super continuum and odd harmonic generation accompanying the light bullets formation are analyzed.

Nonlinear properties of multiphase high-temperature superconductors of the Bi–Sr–Ca–Cu–O system in the temperature range of the superconducting transition

The nonlinear characteristics of high-temperature superconductors of the Bi–Sr–Ca–Cu–O system have been experimentally investigated in the temperature range of the superconducting transition under the influence of a harmonic alternating magnetic field. The effect of the generation of odd harmonics in the signal of response to a harmonic alternating magnetic field for multiphase high-temperature superconductors containing regions with different values of the critical temperature in their bulk has been observed for the first time. The mechanism of harmonic generation in a superconductor in the resistive state, which is associated with the switch effect, i.e., with the redistribution of eddy current density between the local regions of the superconductor, has been considered.

Mid-infrared laser filaments in air at a kilohertz repetition rate

Laser filamentation overcomes diffraction over a highly extended distance, making itself a powerful tool for long-range stand-off detection and light detection and ranging (LIDAR) applications. Mid-infrared (mid-IR) wavelengths are optimal for detecting biochemicals and air pollutants due to molecular fingerprints. Here, we demonstrate mid-IR laser filamentations in ambient air at a kilohertz repetition rate for the first time. Laser filaments significantly longer than the linear confocal parameter are generated with a pump power exceeding the critical power in air using a kilohertz, 2.1 μm, femtosecond, multi-millijoule optical parametric chirped-pulse amplifier. Odd-harmonic generation up to the ninth order at ultraviolet and the mid-IR spectral extensions up to 3.5 μm are observed. The highest third and fifth harmonic efficiencies from ambient air are obtained, to our knowledge, thanks to the extended interaction length within the filaments. Numerical simulations reproduce the harmonic generation with good agreement and confirm that the plasma effect dominates over the higher-order Kerr effect as the main defocusing mechanism of laser filamentation in our experiment. The detection of atmospheric CO2 is demonstrated via mid-IR absorption spectroscopy. High-flux ultrabroadband mid-IR filaments are useful for the fast and sensitive detection of multiple chemical species in air.

Nonperturbative model of harmonic generation in undoped graphene in the terahertz regime

We present a formalism to calculate the nonlinear terahertz response of monolayer graphene using a two-band tight-binding model of graphene. We develop the dynamic equations for the electron density matrix in the length gauge to calculate the interband and intraband carrier dynamics at terahertz frequencies. Using the calculated nonlinear interband and intraband current densities, we obtain the nonlinear transmitted and reflected terahertz fields. We find that when the conditions are such that the interband and intraband current densities are comparable, strong generation of odd harmonics is observed. We examine the response of undoped graphene as a function of a wide variety of system parameters, including operating temperature, Fermi velocity, pulse duration, and terahertz central frequency. We find that the response is generally most sensitive to the operating temperature and the terahertz central frequency. In particular, changing the ambient temperature from 10 to 100 K reduces the third harmonic field by a factor of 20, while increasing the terahertz central frequency from 0.5 to 5 THz results in an increase in the ratio of the generated third harmonic field to the fundamental of the reflected field from 19% to 49%. The very strong dependence on the temperature and central frequency is found to be due to the strong dependence of the nonlinear generation on the strength of the interplay between the intraband and interband dynamics. Our work demonstrates that, under the right conditions of low temperature and moderate THz field central frequency, third harmonic generation should be experimentally observable in undoped monolayer graphene at moderate THz field amplitudes of only 1 kV cm−1.

Low-Field High-Harmonic Studies in Hg-1223 High-Temperature Polycrystalline Superconductor

We have studied harmonic generation in the ultra-weak magnetic fields of bulk sample of the HgBa2Ca 2Cu 3 O 8+δ polycrystalline superconductor. Dependence of the odd and even harmonics on the dc magnetic field, amplitude of the ac magnetic field, and the temperature was investigated. We observe very high-order odd harmonics generation when H=0. When dc field H≠0 is applied, even harmonics also appear and shape of the odd harmonics does not change. Our experiments show that the amplitudes of the odd harmonics squarely depend on the magnitude of the dc field. Numerical results of our experiments have demonstrated that the $J_{c}=J_{c}(0)H_{0}^{2}/\left (H+H_{0}^{2}\right )$ critical-state theoretical model is preferable for investigating the sample.

Bifurcation properties of the bremsstrahlung harmonics generated by a pumping field in plasmas

Nonlinear generation of odd harmonics of the electromagnetic pumping field in a fully ionized plasma is briefly surveyed. Two threshold bifurcation properties of the harmonics are discussed, viz. the splitting of the peak of their intensity as a function of the degree of circular polarization of the pumping field and, at a somewhat higher threshold, the emergence of nonzero-intensity harmonics with complete circular polarization in a pumping field with a partial circular polarization.

Low-cost PWM speed controller for an electric mini-baja type vehicle

This paperwork presents a Pulse Width Modulation (PWM) speed controller for an electric mini-baja-type car. A battery-fed 1-kW three-phase induction motor provides the electric vehicle traction. The open-loop speed control is implemented with an equal voltage/frequency ratio, in order to maintain a constant amount of torque on all velocities. The PWM is implemented by a low-cost 8-bit microcontroller provided with optimized ROM charts for distinct speed value implementations, synchronized transition between different charts and reduced odd harmonics generation. This technique was implemented using a single passenger mini-baja vehicle, and the essays have shown that its application resulted on reduced current consumption, besides eliminating mechanical parts.

Generation of harmonics by a focused laser beam in the vacuum

Abstract We consider generation of odd harmonics by a super strong focused laser beam in the vacuum. The process occurs due to the plural light-by-light scattering effect. In the leading order of perturbation theory, generation of ( 2 k + 1 ) th harmonic is described by a loop diagram with ( 2 k + 2 ) external incoming, and two outgoing legs. A frequency of the beam is assumed to be much smaller than the Compton frequency, so that the approximation of a constant uniform electromagnetic field is valid locally. Analytical expressions for angular distribution of generated photons, as well as for their total emission rate are obtained in the leading order of perturbation theory. Influence of higher-order diagrams is studied numerically using the formalism of Intense Field QED. It is shown that the process may become observable for the beam intensity of the order of 10 27 W / cm 2 .

Infrared radiation harmonic generation in degenerate semiconductors

The basic properties of infrared laser radiation odd harmonic generation due to electron-charged impurity collisions in degenerate semiconductors are investigated. It is found that in the case of relatively weak fields, the electron Fermi distribution is the cause of an anomalous suppression of harmonic radiation. In the case of strong fields, the effect of the selective suppression of single harmonics is established.

Generation of even harmonics in aMgB2 bulk superconductor: an indication of the presence of weak link grain boundaries

In this paper we report the generation of higher harmonics in a bulk polycrystallineMgB2 superconductor when it is subjected to ac and dc magnetic field. TheMgB2 sample shows the generation of higher odd harmonics when an ac field is applied. Theapplication of a small dc field ( gauss) in addition to an ac field also leads to the generation of second and fourthharmonics, which is an indication of the presence of some weak link grain boundaries in aMgB2 superconductor. We have studied the variation of the amplitude of higher harmonics withtemperature for different values of amplitude of ac field. The observed results areinterpreted in terms of weak link grain boundaries and a critical state model.

Nondestructive characterization of wood by monitoring of local elastic anisotropy and dynamic nonlinearity

Abstract The results of non-contact measurements of local in-plane elastic anisotropy in wood by monitoring the flexural plate wave velocity as a function of azimuth angle of propagation are reported. The Focused Slanted Transmission of air-coupled ultrasound is used to generate and detect locally the flexural waves in wood as well as to measure their velocities. The analysis presented shows that for thin plates the flexural wave velocity can be readily used to evaluate the anisotropy of Young’s modulus. This conclusion is confirmed by measurements of the plate wave anisotropy factors for veneer laminae and cross-ply laminates of spruce and beech. The technique is sensitive enough to detect the anisotropy variation of earlywood caused by the incorporation of latewood areas in growth rings. A new approach based on dynamic nonlinearity of wood is developed and applied to acoustic imaging of wood structure and detecting of defects in wood. The hysteresis mechanism of the dynamic nonlinearity is shown to dominate in clear wood and to manifest in a primary generation of odd acoustic harmonics. Local maxima of the odd higher harmonic amplitudes in the LR- and LT-planes of softwood are observed in the earlywood area close to latewood/earlywood transition interface that indicates the lower stiffness and strength of wood in those areas. The higher-order even harmonics and subharmonics in the nonlinear vibration spectra of wood are mostly produced by “clapping” in defect areas. Measurements of local amplitudes of these modes are applied to nonlinear acoustic imaging of cracks, delaminations and knots in wood and wood composites.

Controlling harmonic generation in molecules with intense laser and static magnetic fields: Orientation effects

We solve exactly the three-dimensional time-dependent Schr\"odinger equation for the ${\mathrm{H}}_{2}^{+}$ molecular ion in a combination of intense short laser pulses and static magnetic fields using a newly developed adaptive grid method. This allows for a study of the control of high-order harmonic generation in molecules by various orientations of the magnetic and laser fields in order to control electron recollision with nuclei. In particular, we find regimes of pure even harmonic or even and odd harmonic generation for particular field and frequency configurations. Furthermore, magnetic fields are found to extend harmonic generation plateaus to higher order as a result of further nonlinear coupling between charges and fields.

Stress induced conditioning and thermal relaxation in the simulation of quasi-static compression experiments

Local interaction simulation approach simulations of the ultrasonic wave propagation in multi-grained materials have succeeded in reproducing most of the recently observed nonclassical nonlinear effects, such as stress–strain hysteresis and discrete memory in quasi-static experiments and a downwards shift of the resonance frequency and the generation of odd harmonics at specific amplitude rates in dynamics experiments. By including a simple mechanism of thermally activated random transitions, we can predict the occurrence of experimentally observed effects, such as the conditioning and relaxation of the specimen. Experiments are also suggested for a quantitative assessment of the validity of the model.

Electron–ion collision-induced harmonics generation in a plasma with an isotropic bi-Maxwellian distribution

A treatment is given of harmonics generation resulting from nonlinear inverse bremsstrahlung in a plasma with an anisotropic bi-Maxwellian electron velocity distribution function. A complete characterization of the process is reported. In particular, analytically and numerically we established how the efficiency of the odd harmonics generation and their polarization depend on such process parameters as: (1) the degree of effective temperature anisotropy, (2) the frequency and the intensity of the fundamental wave, and (3) the angle between the fundamental wave field direction and the symmetry axis of the electron distribution function.

Generation of Harmonics by Sea Breeze in Nontidal Water Bodies

The sea breeze introduces harmonics of its diurnal cycle into water bodies, which can be notable for strong sea breeze and microtidal and nontidal conditions. The harmonics can be of the same magnitude as those produced by bottom friction and dominate those produced by nonlinear terms in the equations of motion. A closed-form analytic solution of the linearized depth-averaged equations of motion including friction is discussed for the situation of a sea breeze blowing on an idealized one-dimensional basin of constant depth. The solution reveals the generation of odd harmonics introduced by the quadratic wind stress and role of (linearized) friction. Sea-breeze forcing on the idealized basin is numerically modeled, and agreement with the analytic solution is found. The numerical model is then run with quadratic bottom friction and nonlinear terms to compare relative contributions to the generation of harmonics. Harmonics of the water motion are distinguished as forced, or arising from the wind forcing, and as response, or arising from the interactions within the water. The hydrodynamics of Baffin Bay, Texas, are modeled and spatial variation and relative strength of the harmonics investigated. Baffin Bay is a large shallow embayment with a weak connection to the Gulf of Mexico that experiences a strong southeast wind and sea breeze during the summer. The wind induces even and odd forced harmonics through the combined quasi-steady southeast wind and sea breeze. At Baffin Bay, ratios of the semidiurnal to diurnal amplitudes of water level and current speed are found to be comparable to M4/M2 ratios for U.S. Atlantic coast embayments.

Time-dependent electron-ion collision frequency at arbitrary laser intensity-temperature ratio.

In superintense laser beams collisional absorption exhibits a large amplitude modulation over a laser cycle. In this paper formulas for the time-dependent electron-ion collision frequency nu(ei)(t) are presented. On the basis of a ballistic interaction model we deduce an expression for nu(ei)(t) which holds for an arbitrary isotropic distribution function and arbitrary anharmonic oscillatory electron motion [Eq. (4)]. For a Maxwellian we present compact formulas for the various ratios v(os)(t)/v(th). It is shown that the strong time dependence over one laser cycle leads to the generation of intense odd harmonics. The cycle-averaged collision frequency nu(ei);(t) is compared with expressions derived from the more complex dielectric model. It is shown that the correct choice of cutoffs as a consequence of dynamical screening is essential.

Generation of higher harmonics in superconducting YNi2B2C

We report the generation of higher harmonics when superconductingintermetallic YNi2B2C is exposed to an ac magnetic fieldHac = H 0acsin (ωt) and a dc magnetic field Hdc. Application ofan ac magnetic field (H 0ac>Hc1) leads to the generation of higher oddharmonics as is expected in conventional intermetallic superconductors.Interestingly, the application of Hdc in addition to Hac also causesthe generation of even harmonics. This phenomenon is similar to that observed inhigh-Tc superconductors in which grain boundaries behave as Josephson weaklinks. We have studied the variation in amplitude of the higher harmonics as afunction of H 0ac, ω, Hdc and temperature. The observed resultsare explained in terms of grain boundary weak links and a critical state model.

Harmonic generation and wave mixing in a plasma in the presence of two linearly polarized laser fields

A theoretical treatment of the high-order harmonic generation by electrons undergoing collisions with ions in a plasma in the presence of two single-mode linearly polarized fields is presented. Except for polarization, the two radiation fields may have arbitrary parameters. The treatment is based on an approximate solution of the Fokker–Planck equation for the plasma electron velocity distribution function. A set of representative numerical calculations is carried out. It is found that the generation of odd harmonics of each field is followed by the generation as well of satellites at mixed frequencies. For a given odd harmonic of one field, the satellites are shifted from it by multiple numbers of twice the frequency of the other field. When there are no coincident frequencies among the generated ones, the intensity of the odd harmonics of one field is found to decrease owing to the action of the other field. When, instead, the satellite frequencies of low-order harmonics coincide with the frequencies of high-order harmonics, a considerable enhancement of the latter is predicted. It is shown also that the harmonic intensity and the polarization direction depend significantly on the angle between the polarization directions of the two mixing fields.

Interpretation of high-order harmonic generation in terms of transitions between quantum Volkov states

A theoretical perspective of high-order harmonic generation is presented in which transitions between quantum Volkov states\char22{}stationary solutions to Schr\odinger's equation for an electron interacting with a quantized optical field\char22{}are the dominant mechanism for producing radiation. The picture proposed here is one in which the interaction of an intense optical field with an electron forms a photon-electron ``quasiatom'' and the stationary states of this complex can be viewed as the high optical field analog of bound states of an atom. Consequently, although momentum conservation for the overall harmonic generation process requires that an electron eventually return to the parent atom, the electron and fundamental optical field are treated as an isolated system with well-defined energy and momentum. To introduce a secondary photon (harmonic) field, the matrix element describing the electron-photon field interaction through quantum Volkov states is modified in a perturbative manner. The result is the production of harmonic photons by Volko$\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}$Volkov-state transitions, a process which has no classical counterpart. The generation of odd harmonics of the fundamental field and the requirement that the final state of the electron be the initial bound state of the atom follow directly from the theory. A clear connection between harmonic generation and above-threshold ionization (ATI) is drawn by maintaining the discrete, nonzero energies of photoelectrons injected into the driving optical field by ATI. For experiments in which the laser pulse width is \ensuremath{\gtrsim}100\char21{}150 fs, only the lowest ATI photoelectron orders contribute significantly to harmonic generation, whereas higher-energy electrons escape from the parent atom during the pulse risetime. As the duration of the fundamental field is decreased, however, the rapid rise of the field intensity to its peak value effectively traps more energetic photoelectrons, thereby extending the harmonic response to shorter wavelengths. An analytic expression for the transition matrix for the harmonic generation process is derived and is compared with the predictions of semiclassical theory and published experimental results, including harmonic spectra and polarization data.