Simulations Of Harmonic Generation Research Articles

Harmonic generation: Quantum-electrodynamical theory of the harmonic photon-number spectrum

Simulations of harmonic generation in the single-atom limit usually describe the harmonic radiation as proportional to the squared magnitude of the Fourier transform (FT) of the expectation value of either the dipole moment or the dipole acceleration. However, no derivation of an explicit single-atom representation of the typical experimental measurement (i.e., the number of harmonic photons produced versus the frequency of the harmonic) has been given. By means of the first principles of quantum electrodynamics a formula for this ``harmonic photon-number spectrum'' is derived, which is proportional to the double FT of the time-autocorrelation function of the dipole velocity of the whole system. Within the long-wavelength approximation the time-correlation function can be recast as the FT of the squared magnitude of the expectation value of the dipole velocity of a single representative atom.

Monte Carlo simulation of harmonic generation in GaAs structures operating under large-signal conditions

By using a multiparticles Monte Carlo technique, with a self-consistently coupled one-dimensional Poisson solver, we investigate the dependence of the nonlinear carrier dynamics in GaAs n+nn+ micro e submicro-structures operating under very intense sub-terahertz signals by: (i) the frequency and the intensity of the excitation signal and (ii) the length of the n region.

Monte Carlo simulation of harmonic generation in InP

Harmonics spectra in an n-type InP bulk semiconductor showing up to the 13th harmonic are reported. The external field is linearly polarized with the frequency ν = 100 GHz. Calculations are based on a Monte Carlo simulation for the electron motion in the conducting band and on an electrodynamics equation for the harmonics generation. The effect of a significant reduction of efficiency in the generation of particular harmonics is found, and is traced back to a sort of alternating field Gunn effect. A short analysis of the different physical mechanisms giving rise to harmonics generation is presented.

Hysteresis and two‐dimensional nonlinear wave propagation in Berea Sandstone

We have further developed a two‐dimensional endochronic constitutive model applicable to rock in the intermediate strain regime, i.e., approximately 10−6 to 10−3, where nonlinear losses, pulse distortion, and harmonic distortions have been documented in the laboratory. An accurate and efficient computation algorithm has been established and used to fit a set of triaxial laboratory data on Berea Sandstone, obtained by G. N. Boitnott of New England Research, Inc., including nonlinear hysteresis for both hydrostatic compression and shear deformation. The constitutive model has been incorporated into a two‐dimensional pseudospectral scheme for simulating nonlinear wave propagation. We compare our numerical pseudospectral scheme with the perturbation solutions to nonlinearly elastic plane wave propagation and find that the two solutions are in close agreement. Applying the numerical scheme to the endochronic constitutive model for Berea Sandstone, we find the following results, which confirm and extend previous results obtained with a one‐dimensional model: (1) nonlinear propagation from a monochromatic source excites odd harmonics of the source frequency, (2) the interaction of two monochromatic wave fields leads to energy transfer to other bands corresponding to various combinations of the two source frequencies, (3) amplitudes of the harmonics change with distance and show a trade‐off between nonlinearity, intrinsic attenuation (hysteresis), and geometrical spreading, (4) for a broadband pressure source, energy is transferred from the principal band to a higher band at the expense of the components at intermediate frequencies; this is diagnostic of nonlinear interactions, and (5) the harmonic amplitude and energy transfer increase nonlinearly with strain amplitude; i.e., higher strain levels lead to higher energy exchange. These simulations of harmonic generation, interaction, and band expansion, based on a model developed from quasistatic experimental observations, agree with dynamic experimental observations.

Generation and propagation of high-order harmonics in a rapidly ionizing medium.

We present the results from simulations of harmonic generation using intense ultrashort laser pulses, both for single atoms and in an extended gaseous medium. Using a windowing technique on the single-atom spectrum, we show that the highest-order harmonics are generated simultaneously with rapid ionization, and that these harmonics have a phase dependence which is consistent with a quasiclassical tunneling model. By solving the atomic dynamics simultaneously with the propagation equations, we have obtained spectra that directly show the effects of phase mismatching and blueshifting produced by an ionizing medium. At experimental pressures, the plasma-induced phase mismatch is only important for the highest-order harmonics near the plateau cutoff. All harmonic orders, however, are seen to be blueshifted, by an amount consistent with a blueshifting of the fundamental as it propagates through the ionizing medium.