Theory for the Nonlinear Optical Response of Transition-Metals: Polarization Dependence as a Fingerprint of the Electronic Structure at Surfaces and Interfaces

Since the first observation of second harmonic generation (SHG), there have been extensive studies on this nonlinear phenomenon not only to clarify its physical origin but also to realize unconventional functionalities. Nonetheless, a widely accepted model of SHG with rigorous experimental verification that describes the contributions of different underlying microscopic mechanisms is still under debate. Here, we examine second harmonic far-field radiation patterns over a wide...

We present a theory for the electron-temperature dependence $T_{el}$ of optical second harmonic generation (SHG). Such an analysis is required to study the dynamics of metallic systems with many hot electrons not at equilibrium with the lattice. Using a tight-binding theory for the nonlinear susceptibility \cwtel and the Fresnel coefficients we present results for the SHG intensity \iwtel for a Cu monolayer. In the case of linear optical response we find that the intensity wi...

We theoretically investigate the second harmonic generation (SHG) of topological insulator surface states in a perpendicular magnetic field. Our theory is based on the microscopic expression of the second-order magneto-optical conductivity developed from the density matrix formalism, taking into account hexagonal warping effects on the surface states' band structure. Using numerically exact Landau level energies and wavefunctions including hexagonal warping, we calculate the ...

Second harmonic generation (SHG) spectroscopy ubiquitously enables the investigation of surface chemistry, interfacial chemistry as well as symmetry properties in solids. Polarization-resolved SHG spectroscopy in the visible to infrared regime is regularly used to investigate electronic and magnetic orders through their angular anisotropies within the crystal structure. However, the increasing complexity of novel materials and emerging phenomena hamper the interpretation of e...

The nonlinear magneto-optical Kerr-effect (NOLIMOKE) is determined for freestanding Fe monolayers with several in-plane structures from first principles. Based on the theory of nonlinear magneto-optics by H\"ubner and Bennemann [Phys. Rev. B, {\bf 40}, 5973 (1989)] we calculate the nonlinear susceptibilities of the monolayers using the ab initio FLAPW-method WIEN95 with the additional implementation of spin-orbit coupling and the calculation of the dipole transition matrix el...

Metal-organic molecular adsorbates on metallic surfaces offer the potential to both generate materials for future (spin-)electronics applications as well as a better fundamental understanding of molecule-substrate interaction, provided that the electronic properties of such interfaces can be analyzed and/or manipulated in a targeted manner. To investigate electronic interactions at such interfaces, we measure optical second harmonic generation (SHG) from iron-octaethylporphyr...

We use ultrafast laser pulses to experimentally demonstrate that the second-order optical response of bulk single crystals of the topological insulator Bi$_2$Se$_3$ is sensitive to its surface electrons. By performing surface doping dependence measurements as a function of photon polarization and sample orientation we show that second harmonic generation can simultaneously probe both the surface crystalline structure and the surface charge of Bi$_2$Se$_3$. Furthermore, we fin...

Nonlinear optics, and particularly second harmonic generation (SHG), is increasingly used in many modern disciplines from material characterization in physical sciences to bio-imaging in medicine and optical signal processing in information technology. We present a theoretical analysis providing a strong estimate for the energy-integrated SHG response. Requirements of symmetry in time and space are fully respected in the calculation, and estimates of natural and magnetic circ...

The interface between two different semiconductors is crucial in determining the electronic properties at the heterojunction, therefore novel techniques that can probe these regions are of particular interest. Recently it has been shown that heterojunctions of two-dimensional transition metal dichalcogenides have sharp and epitaxial interfaces that can be used to the next generation of flexible and on chip optoelectronic devices. Here, we show that second harmonic generation ...

Polarized and azimuthal dependencies of optical second harmonics generation (SHG) at the surface of noncentrosymmetric semiconductor crystals have been measured on polished surfaces of ZnSe(100), using a fundamental wavelength of 1.06$\mu m$. The SHG intensity patterns were analyzed for all four combination of p- and s-polarized incidence and output, considering both the bulk and surface optical nonlinearities in the electric dipole approximation. We found that the measuremen...