We perform a detailed analysis of how the interplay between the residual binding potential and a strong laser field influences above-threshold ionization (ATI), employing a semi-analytical, Coulombcorrected strong-field approximation (SFA) in which the Coulomb potential is incorporated in the electron propagation in the continuum. We find that the Coulomb interaction lifts the degeneracy of some SFA trajectories, and we identify a set of orbits which, for high enough photoelectron energies, may be associated with rescattering. Furthermore, by performing a direct comparison with the standard SFA, we show that several features in the ATI spectra can be traced back to the influence of the Coulomb potential on different electron trajectories. These features include a decrease in the contrast, a shift towards lower energies in the interference substructure, and an overall increase in the photoelectron yield. All features encountered exhibit a very good agreement with the ab initio solution of the time-dependent Schrödinger equation.

We study photoelectron angular distributions (PADs) near the ionization threshold with a newly developed Coulomb quantum-orbit strong-field approximation (CQSFA) theory. The CQSFA simulations exhibit an excellent agreement with the result from the time-dependent Schrödinger equation. We show that the low-energy fan-shaped pattern in the PADs corresponds to a subcycle time-resolved holographic structure and stems from the significant influence of the Coulomb potential on the phase of the forward-scattered electron trajectories, which affects different momenta and scattering angles unequally. Our work provides a direct explanation of how the fan-shaped structure is formed, based on the quantum interference of direct and forward-scattered orbits. Moreover, our work shows that the fan-shaped pattern can be used to extract information on the target structure, as the number of fringes in the PADs depends strongly on the symmetry of the electronic bound state.

Elemental boron arouses great interest from both scientific and technological areas of research because it has unique chemical and physical properties and its theoretical tubular structures may have higher electrical conductivity than carbon nanotubes. [1][2][3][4][5][6][7] High conductivity and chemical stability of boron or boride nanostructures have made it an attractive candidate for future applications in ideal cold-cathode materials, high-temperature semiconductor devices, or fieldeffect transistors. [8][9][10][11][12][13][14] In particular, for the application of field emission (FE), it is especially useful to synthesize large, vertical arrays of boron nanowires (BNWs) with the desired surface work function and FE behavior. So far, to our knowledge, while both amorphous [15][16][17][18][19][20] and crystalline boron nanowires [21,22] have been fabricated by magnetron sputtering, laser ablation, or chemical vapor methods, vertical arrays of single-crystal boron nanowires over a large area have not been synthesized in a one-step process. In addition, little attention [23][24][25] has been paid to the measurements of the physical properties of an individual boron nanowire. In this Communication, we report the successful synthesis of high-density, vertically aligned single-crystal boron nanowire arrays with a nanowire diameter of approximately 20-40 nm by a thermal carbon-reduction method. Moreover, we have measured the FE behavior and surface work function of a single boron nanowire, which is critical to evaluate the possibility of using boron nanowires as field-emission materials. For the purpose of better understanding the field-emission mechanism of a boron nanowire, the field-emission properties of a BNW film are also measured to compare with those of an individual nanowire. Figure 1 shows large-scale boron nanowire arrays on a Si(001) substrate after approximately 2-4 h of growth. As shown in Figure 1A, the high-density arrays are aligned vertically on the silicon substrate. Figure 1B is the highresolution scanning electron microscopy (SEM) image of the aligned BNWs, in which one can see that the length of the BNW is about 5 mm and the morphology of the nanowires is uniform. The aspect ratio of each boron nanowire is about 200, which is high enough for a field-emission application. The side and top views of the boron nanowire are shown in Figure 1C and D, respectively, which reveals the detailed morphology of the BNWs. The boron nanowires have a diameter of about 20-40 nm and no catalyst is found at their tip. The catalysts, however, were found to lie on the substrate arbitrarily when we peeled off some nanowire film from the substrate, as shown in Figure 1C. Thus, we believe that the growth is through a vapor-liquid-solid (VLS) mechanism and the binding force between the Fe 3 O 4 catalyst and the silicon substrate is strong. This strong binding leads to good conductivity between the boron nanowires and the substrate, which may contribute to their good field-emission properties. The alignment of BNWs can...

We provide approximate analytic expressions for above-threshold ionization (ATI) transition probabilities and photoelectron angular distributions. These analytic expressions are more general than those existing in the literature and include the residual binding potential in the electron continuum propagation. They successfully reproduce the ATI side lobes and specific holographic structures such as the near-threshold fan-shaped pattern and the spider-like structure that extends up to relatively high photoelectron energies. We compare such expressions with the Coulomb quantum orbit strong-field approximation (CQSFA) and the full solution of the timedependent Schrödinger equation for different driving-field frequencies and intensities, and provide an in-depth analysis of the physical mechanisms behind specific holographic structures. Our results shed additional light on what aspects of the CQSFA must be prioritized in order to obtain the key holographic features, and highlight the importance of forward scattered trajectories. Furthermore, we find that the holographic patterns change considerably for different field parameters, even if the Keldysh parameter is kept roughly the same.

Many nonlinear quantum phenomena of intense laser-atom physics can be intuitively explained with the concept of trajectory. In this paper, Bohmian mechanics (BM) is introduced to study a multiphoton process of atoms interacting with the intense laser field: above-threshold ionization (ATI). Quantum trajectory of an atomic electron in intense laser field is obtained from the Bohm-Newton equation first and then the energy of the photoelectron is gained from its trajectory. With energies of an ensemble of photoelectrons, we obtain the ATI spectrum which is consistent with the previous theoretical and experimental results. Comparing BM with the classical trajectory Monte-Carlo method, we conclude that quantum potential may play a key role to reproduce the spectrum of ATI. Our work may present a new approach to understanding quantum phenomena in intense laser-atom physics with the image of trajectory. * Electronic address: qycai@wipm.ac.cn

We unambiguously identify, in experiment and theory, an overlooked holographic interference pattern in strong-field ionization, dubbed "the spiral," stemming from two trajectories where the potential and laser field are equally critical. Because of the strong interaction with the core of the two trajectories, the spiral could be employed as an optimal tool for probing the target after ionization and for revealing obfuscated phases in the bound states. We find that the spiral is responsible for interference carpets, formerly ascribed to direct trajectories, and that the carpet-interference condition is derived from the field symmetry. This case of mistaken identity may have prevented the spiral from being used as a holographic tool.

We use orthogonally polarized two-color (OTC) laser pulses to separate quantum paths in the multiphoton ionization of Ar atoms. Our OTC pulses consist of 400 and 800 nm light at a relative intensity ratio of 10∶1. We find a hitherto unobserved interference in the photoelectron momentum distribution, which exhibits a strong dependence on the relative phase of the OTC pulse. Analysis of model calculations reveals that the interference is caused by quantum pathways from nonadjacent quarter cycles.

We introduce a concise methodology to detect the parity of atomic and molecular orbitals based on photoelectron holography, which is more general than the existing schemes. It fully accounts for the Coulomb distortions of electron trajectories, does not require sculpted fields to retrieve phase information and, in principle, is applicable to a broad range of electron momenta. By comparatively measuring the differential photoelectron spectra from strong-field ionization of N 2 molecules and their companion atoms of Ar, some photoelectron holography patterns are found to be dephased for both targets. This is well reproduced by the full-dimensional time-dependent Schrödinger equation and the Coulomb quantum-orbit strong-field approximation (CQSFA) simulation. Using the CQSFA, we trace back our observations to different parities of the 3p orbital of Ar and the highest-occupied molecular orbital of N 2 via interfering Coulomb-distorted quantum orbits carrying different initial phases. This method could in principle be used to extract bound-state phases from any holographic structure, with a wide range of potential applications in recollision physics and spectroscopy.