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Three alternative forms of harmonic spectra, based on the dipole moment, dipole velocity, and dipole acceleration, are compared by a numerical solution of the Schrödinger equation for a hydrogen atom interacting with a linearly polarized laser pulse, whose electric field is given by E͑t͒ = E 0 f͑t͒cos͑ 0 t + ͒ with Gaussian carrier envelope f͑t͒ = exp͑−t 2 / ␦ 2 ͒. The carrier frequency 0 is fixed to correspond to a wavelength of 800 nm. Spectra for a selection of pulses, for which the intensity I 0 = c 0 E 0 2 , duration T ϰ ␦, and carrier-envelope phase are systematically varied, show that, depending on , all three forms are in good agreement for "weak" pulses with I 0 Ͻ I b , the over-barrier ionization threshold, but that marked differences among the three appear as the pulse becomes shorter and stronger ͑I 0 Ͼ I b ͒. Except for scalings by powers of the harmonic frequency, the three forms differ from one another only by "limit contributions" proportional to the expectation values of the dipole moment ͗z͑t f ͒͘ or dipole velocity ͗ż͑t f ͒͘ at the end ͑t f ͒ of the pulse. For long, weak pulses the limit contributions are negligible, whereas for short, strong ones they are not. In the short, strong limit, where ͗ż͑t f ͒͘ 0 and therefore ͗z͑t͒͘ may increase without bound ͑i.e., the atom may ionize͒, depending on , an "infinite-time" spectrum based on the acceleration form provides a convenient computational pathway to the corresponding infinite-time dipole-velocity spectrum, which is related directly to the experimentally measured "harmonic photon number spectrum" ͑HPNS͒. For short, intense pulses the HPNS is quite sensitive to and exhibits not only the usual odd harmonics but also even ones. The analysis also reveals that most of the harmonic photons are emitted during the passage of the pulse. Because of the divergence of ͗z͑t͒͘ the dipolemoment form does not provide a numerically reliable route to the harmonic spectrum for very short ͑few-cycle͒, very intense laser pulses.

A two-step model of Coulomb explosions of diatoms in intense laser fields is presented. In this model the molecule loses several electrons when the atoms are at the equilibrium internuclear distance and then fast Coulomb explosions occur until the products reach a critical distance Rc approximately=9 Bohr, at which several additional electrons are lost due to a recently discovered maxima of ionization rates occurring at R=Rc. Then the subsequent Coulomb explosion for the higher-charged ions takes place. The total combined Coulomb explosion energy agrees well with experimental results, showing striking regularities. The origin and intensity dependence of unexpectedly high ionization rates of dissociating nuclei at preferential, large internuclear distances R=Rc is also discussed and an analytic expression for Rc is derived.

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