A real-time approach to frequency-mixing spectroscopies: application to sum and difference frequency generation in two-dimensional crystals

Abstract

We propose a computational framework to extract non-linear response functions from real-time simulations in the presence of more than one external field. We apply this approach to the calculation of sum frequency generation (SFG) and difference frequency generation (DFG). SFG and DFG are second-order nonlinear processes where two lasers with frequencies ${\omega }_1$ and ${\omega }_2$ combine to produce a response at frequency $\omega ={\omega }_1\pm {\omega }_2$. Compared with other nonlinear responses such as second-harmonic generation, SFG and DFG allow for tunability over a larger range. Moreover, the optical response can be enhanced by selecting the two laser frequencies in order to match specific electron-hole transitions. To assess the approach, we calculate the SFG and DFG of two-dimensional crystals, hBN and MoS2 monolayers, from real-time solution of an effective Schrödinger equation. Within the effective Schrödinger equation, one can select from various levels of theory for the effective one-particle Hamiltonian to account for local-field effects and electron-hole interactions. We compare results obtained within the independent-particle picture and including many-body effects. Such comparison allows us to identify and characterize excitonic features in the obtained spectra. Additionally, we demonstrate that our approach can also extract higher-order response functions, such as field-induced second-harmonic generation. We provide an example using the hBN bilayer.

References in corpus (18)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Advanced capabilities for materials modelling with Quantum ESPRESSO
• The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table
• The GW method
• Many-body perturbation theory calculations using the yambo code
• Effect of spin-orbit interaction on the excitonic effects in single-layer, double-layer, and bulk MoS2
• Excitons in boron nitride nanotubes: dimensionality effects
• A real-time approach to the optical properties of solids and nano-structures: the time-dependent Bethe-Salpeter equation
• Theory of second harmonic generation in few-layered MoS2
• Dynamics of Berry-phase polarization in time-dependent electric fields
• Second Harmonic Generation in h-BN and MoS${}_2$ monolayers: the role of electron-hole interaction
• Nonlinear optics from an ab-initio approach by means of the dynamical Berry phase: Application to second- and third-harmonic generation in semiconductors
• Quantum interference effects in resonant Raman spectroscopy of single- and triple-layer MoTe${}_2$ from first principles
• First-principles study of excitonic effects in Raman intensities
• Exciton enhanced nonlinear optical responses in monolayer h-BN and MoS2: Insight from first-principles exciton-state coupling formalism and calculations
• Isolating the Nonlinear Optical Response of a MoS${}_2$ Monolayer under Extreme Screening of a Metal Substrate
• Extracting Nonlinear Dynamical Response Functions from Time Evolution
• Twisted nonlinear optics in monolayer van der Waals crystals

Cited by in corpus (2)

• Shift current in 2D Janus Transition-Metal Dichalcogenides: the role of excitons
• Tangent equations of motion for nonlinear response functions