Numerical investigation of the Rayleigh hypothesis for electromagnetic scattering by a particle

The validity of the Rayleigh hypothesis has been a long-standing issue in the applicability of the T-matrix method to near-field calculations, and despite numerous theoretical works, the practical consequences for numerical simulations have remained unclear. Such calculations are increasingly important in the field of nanooptics, for which accurate and efficient modeling tools are in high demand. We here tackle this challenge by investigating numerically the convergence behavior of series expansions of the electric field around spheroidal particles, which provides us with unambiguous examples to clarify the conditions of convergence. This study is made possible by the combination of alternative methods to compute near-fields accurately, and crucially, the recent improvements in the calculation of T-matrix elements free from numerical instabilities, as such errors would otherwise obfuscate the intrinsic convergence properties of the field series. The resulting numerical confirmation for the range of validity of the Rayleigh hypothesis, complemented by a better understanding of the convergence behavior of the field expansions, is a crucial step toward future developments

Theoretical analysis of dynamic chemical imaging with lasers using high-order harmonic generation

We report theoretical investigations of the tomographic procedure suggested by Itatani {\it et al.} [Nature, {\bf 432} 867 (2004)] for reconstructing highest occupied molecular orbitals (HOMO) using high-order harmonic generation (HHG). Using the limited range of harmonics from the plateau region, we found that under the most favorable assumptions, it is still very difficult to obtain accurate HOMO wavefunction, but the symmetry of the HOMO and the internuclear separation between the atoms can be accurately extracted, especially when lasers of longer wavelengths are used to generate the HHG. We also considered the possible removal or relaxation of the approximations used in the tomographic method in actual applications. We suggest that for chemical imaging, in the future it is better to use an iterative method to locate the positions of atoms in the molecule such that the resulting HHG best fits the macroscopic HHG data, rather than by the tomographic method.Comment: 13 pages, 14 figure

Retrieval of interatomic separations of molecules from laser-induced high-order harmonic spectra

We illustrate an iterative method for retrieving the internuclear separations of N$_2$, O$_2$ and CO$_2$ molecules using the high-order harmonics generated from these molecules by intense infrared laser pulses. We show that accurate results can be retrieved with a small set of harmonics and with one or few alignment angles of the molecules. For linear molecules the internuclear separations can also be retrieved from harmonics generated using isotropically distributed molecules. By extracting the transition dipole moment from the high-order harmonic spectra, we further demonstrated that it is preferable to retrieve the interatomic separation iteratively by fitting the extracted dipole moment. Our results show that time-resolved chemical imaging of molecules using infrared laser pulses with femtosecond temporal resolutions is possible.Comment: 14 pages, 9 figure