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Articles 1 - 8 of 8
Full-Text Articles in Physical Sciences and Mathematics
A Brief On Characteristic Functions, Austin G. Vandegriffe
A Brief On Characteristic Functions, Austin G. Vandegriffe
Graduate Student Research & Creative Works
Characteristic functions (CFs) are often used in problems involving convergence in distribution, independence of random variables, infinitely divisible distributions, and stochastics. The most famous use of characteristic functions is in the proof of the Central Limit Theorem, also known as the Fundamental Theorem of Statistics. Though less frequent, CFs have also been used in problems of nonparametric time series analysis and in machine learning. Moreover, CFs uniquely determine their distribution, much like the moment generating functions (MGFs), but the major difference is that CFs always exists, whereas MGFs can fail, e.g. the Cauchy distribution. This makes CFs more robust in …
Waveforms For Optimal Sub-Kev High-Order Harmonics With Synthesized Two- Or Three-Colour Laser Fields, Cheng Jin, Guoli Wang, Hui Wei, Anh-Thu Le, C. D. Lin
Waveforms For Optimal Sub-Kev High-Order Harmonics With Synthesized Two- Or Three-Colour Laser Fields, Cheng Jin, Guoli Wang, Hui Wei, Anh-Thu Le, C. D. Lin
Physics Faculty Research & Creative Works
High-order harmonics extending to the X-ray region generated in a gas medium by intense lasers offer the potential for providing tabletop broadband light sources but so far are limited by their low conversion efficiency. Here we show that harmonics can be enhanced by one to two orders of magnitude without an increase in the total laser power if the laser's waveform is optimized by synthesizing two- or three-colour fields. The harmonics thus generated are also favourably phase-matched so that radiation is efficiently built up in the gas medium. Our results, combined with the emerging intense high-repetition MHz lasers, promise to …
Influence Of Gas Pressure On High-Order-Harmonic Generation Of Ar And Ne, Guoli Wang, Cheng Jin, Anh-Thu Le, C. D. Lin
Influence Of Gas Pressure On High-Order-Harmonic Generation Of Ar And Ne, Guoli Wang, Cheng Jin, Anh-Thu Le, C. D. Lin
Physics Faculty Research & Creative Works
We study the effect of gas pressure on the generation of high-order harmonics where harmonics due to individual atoms are calculated using the recently developed quantitative rescattering theory, and the propagation of the laser and harmonics in the medium is calculated by solving the Maxwell's wave equation. We illustrate that the simulated spectra are very sensitive to the laser focusing conditions at high laser intensity and high pressure since the fundamental laser field is severely reshaped during the propagation. By comparing the simulated results with several experiments we show that the pressure dependence can be qualitatively explained. The lack of …
Analysis Of Effects Of Macroscopic Propagation And Multiple Molecular Orbitals On The Minimum In High-Order Harmonic Generation Of Aligned Co₂, Cheng Jin, Anh-Thu Le, C. D. Lin
Analysis Of Effects Of Macroscopic Propagation And Multiple Molecular Orbitals On The Minimum In High-Order Harmonic Generation Of Aligned Co₂, Cheng Jin, Anh-Thu Le, C. D. Lin
Physics Faculty Research & Creative Works
We report theoretical calculations of the effect of the multiple-orbital contribution in high-order harmonic generation (HHG) of aligned CO₂ with the inclusion of macroscopic propagation of harmonic fields in the medium. Our results show very good agreement with recent experiments for the dynamics of the minimum in HHG spectra as laser intensity or alignment angle changes. Calculations are carried out to check how the position of the minimum in HHG spectra depends on the degrees of molecular alignment, laser-focusing conditions, and the effects of alignment-dependent ionization rates of the different molecular orbitals. These analyses help to explain why the minima …
Medium Propagation Effects In High-Order Harmonic Generation Of Ar And N₂, Cheng Jin, Anh-Thu Le, C. D. Lin
Medium Propagation Effects In High-Order Harmonic Generation Of Ar And N₂, Cheng Jin, Anh-Thu Le, C. D. Lin
Physics Faculty Research & Creative Works
We report theoretical calculations of high-order harmonic generation (HHG) by intense infrared lasers in atomic and molecular targets taking into account the macroscopic propagation of both fundamental and harmonic fields. On the examples of Ar and N₂, we demonstrate that these ab initio calculations are capable of accurately reproducing available experimental results with isotropic and aligned target media. We further present detailed analysis of HHG intensity and phase under various experimental conditions, in particular, as the wavelength of the driving laser changes. Most importantly, our results strongly support the factorization of HHG at the macroscopic level into a product of …
Quantitative Rescattering Theory For High-Order Harmonic Generation From Molecules, Anh-Thu Le, R. R. Lucchese, S. Tonzani, Toru Morishita, C. D. Lin
Quantitative Rescattering Theory For High-Order Harmonic Generation From Molecules, Anh-Thu Le, R. R. Lucchese, S. Tonzani, Toru Morishita, C. D. Lin
Physics Faculty Research & Creative Works
The quantitative rescattering theory (QRS) for high-order harmonic generation (HHG) by intense laser pulses is presented. According to the QRS, HHG spectra can be expressed as a product of a returning electron wave packet and the photorecombination differential cross section of the laser-free continuum electron back to the initial bound state. We show that the shape of the returning electron wave packet is determined mostly by the laser. The returning electron wave packets can be obtained from the strong-field approximation or from the solution of the time-dependent Schrödinger equation (TDSE) for a reference atom. The validity of the QRS is …
Probing Molecular Frame Photoionization Via Laser Generated High-Order Harmonics From Aligned Molecules, Anh-Thu Le, R. R. Lucchese, M. T. Lee, C. D. Lin
Probing Molecular Frame Photoionization Via Laser Generated High-Order Harmonics From Aligned Molecules, Anh-Thu Le, R. R. Lucchese, M. T. Lee, C. D. Lin
Physics Faculty Research & Creative Works
Present experiments cannot measure molecular frame photoelectron angular distributions (MFPAD) for ionization from the outermost valence orbitals of molecules. We show that the details of MFPAD can be retrieved with high-order harmonics generated by infrared lasers from aligned molecules. Using accurately calculated photoionization transition dipole moments for fixed-in-space molecules, we show that the dependence of the magnitude and phase of the high-order harmonics on the alignment angle of the molecules observed in recent experiments can be quantitatively reproduced. This result provides the needed theoretical basis for ultrafast dynamic chemical imaging using infrared laser pulses.
Retrieving Photorecombination Cross Sections Of Atoms From High-Order Harmonic Spectra, Shinichiro Minemoto, Toshihito Umegaki, Yuichiro Oguchi, Toru Morishita, Anh-Thu Le, Shinichi Watanabe, Hirofumi Sakai
Retrieving Photorecombination Cross Sections Of Atoms From High-Order Harmonic Spectra, Shinichiro Minemoto, Toshihito Umegaki, Yuichiro Oguchi, Toru Morishita, Anh-Thu Le, Shinichi Watanabe, Hirofumi Sakai
Physics Faculty Research & Creative Works
We observe high-order harmonic spectra generated from a thin atomic medium, Ar, Kr, and Xe, by intense 800-nm and 1300-nm femtosecond pulses. A clear signature of a single-atom response is observed in the harmonic spectra. Especially in the case of Ar, a Cooper minimum, reflecting the electronic structure of the atom, is observed in the harmonic spectra. We successfully extract the photorecombination cross sections of the atoms in the field-free condition with the help of an accurate recolliding electron wave packet. The present protocol paves the way for exploring ultrafast imaging of molecular dynamics with attosecond resolution.