High-order harmonic generation (HHG) has become an indispensable process for generating attosecond pulse trains and single attosecond pulses used in the observation of nuclear and electronic motion. As such, improved control of the HHG process is desirable, and one such possibility for this control is through the use of structured laser pulses. We present numerical results from solving the one-dimensional time-dependent Schrödinger equation for HHG from hydrogen using Airy and Gaussian pulses that differ only in their spectral phase. Airy pulses have identical power spectra to Gaussian pulses, but different spectral phases and temporal envelopes. We show that the use of Airy pulses results in less ground state depletion compared to the Gaussian pulse, while maintaining harmonic yield and cutoff. Our results demonstrate that Airy pulses with higher intensity can produce similar HHG spectra to lower intensity Gaussian pulses without depleting the ground state. The different temporal envelopes of the Gaussian and Airy pulses lead to changes in the dynamics of the HHG process, altering the time-dependence of the ground state population and the emission times of the high harmonics.
High-order harmonic generation (HHG) using an Airy pulse with a third order spectral phase results in less ground state depletion, but similar harmonic yield, compared to a Gaussian pulse. Top – schematic depiction of the 3-step HHG process for different intensity pulses. Bottom left – time-dependent ground state populations for Gaussian pulses showing that a more intense pulse causes more ground state depletion. Bottom middle – final ground state populations for Airy and Gaussian pulses as a function of intensity showing that Airy pulses result in less ground state depletion for a given intensity. Bottom right – HHG spectra for a more intense Airy pulse and a less intense Gaussian pulse exhibit similar shapes, magnitudes, and plateau cutoff values
The dynamics of hyperbolic secant beams under the competition between the fractional diffraction and rectangular potential is investigated. It is found that the beams can exhibit the reflection, tunneling and interference, forming the bound states, optical lattices or fringes, or solitons under different conditions. In linear regime, when the potential is wide, the beam exhibits the total reflection for deeper potential and smaller incident angle, and presents the reflection and tunneling for shallower potential and larger incident angle. The irregular interference pattern and bound states are generated for the narrow potential. Moreover, the initial chirp causes the appearance of side lobes during beam propagation. When two hyperbolic secant beams are symmetrically incident from inside or outside the potential, the interference lattices or interference fringes are generated inside the potential, which are related to the Lévy index, initial chirp and incident angle of the beams. In nonlinear regime, the hyperbolic secant beam undergoes the collapse, splitting or formation of the periodic-like soliton by selecting appropriate parameters including the Lévy index, initial chirp and incident angle. In addition, the dynamics of two hyperbolic secant beams under the interaction of the nonlinear effect and fractional diffraction is also investigated in detail. This work provides more possibilities for optical lattice generation and optical manipulation.
Most of the previously proposed methods for nonreciprocal light transmission are based on the unequal couplings of the nanocavity with the input waveguide and the output waveguide, which will inevitably affect the contrast ratio and working bandwidth. Here, we present a simple approach just via the side coupling between one nonlinear resonator and a coupling-tunable waveguide, demonstrating that a high transmission contrast, broad operation bandwidth, and controllable nonreciprocal light transmission can be realized even though the coupling is symmetric. The underlying physics is revealed. This approach may open a way for the study of on-chip optical information processing and quantum computing.