Second-order Optical Susceptibility Advances Material Characterization with Perturbative Calculations

The ability to precisely predict how materials interact with light underpins advances in diverse fields, from telecommunications to material science, and researchers continually seek more accurate methods for calculating a material’s optical properties. Angiolo Huaman, Luis Enrique Rosas-Hernandez from the University of Arkansas and MonArk NSF Quantum Foundry, and Salvador Barraza-Lopez from the University of Arkansas, MonArk NSF Quantum Foundry and Institute for Solid State Physics, University of Tokyo, have developed a new approach to calculating second-order optical susceptibility, a key property determining a material’s nonlinear optical response. Their work represents a return to calculations based on localized atomic orbitals, but with a crucial innovation: a symmetry-enforced method for determining interactions between these orbitals that significantly improves computational efficiency and accuracy. This achievement allows for more reliable prediction of optical behaviour in materials like silicon carbide and gallium arsenide, paving the way for the design of novel photonic devices and materials with tailored optical properties.

Theoretical Calculation of Second Harmonic Generation Properties

This compilation details a comprehensive body of research concerning the theoretical calculation of nonlinear optical properties, specifically second-harmonic generation (SHG), in materials. The focus lies heavily on semiconductors and two-dimensional materials, such as molybdenum disulfide and hexagonal boron nitride, alongside silicon carbide. The research encompasses both fundamental theoretical frameworks and advanced computational methods.

A central theme is the application of ab initio methods, meaning calculations based on first principles without empirical parameters, like Density Functional Theory. A significant portion of the research addresses the SHG properties of semiconductors and increasingly, two-dimensional materials, reflecting their unique optical properties and potential for novel optoelectronic devices. Many studies investigate the role of excitons, bound pairs of electrons and holes, in enhancing or modifying the nonlinear optical response, particularly in two-dimensional materials where these effects are pronounced. Accurate determination of a material’s electronic band structure is fundamental to calculating its nonlinear optical properties. Alongside Density Functional Theory, tight-binding methods are used as alternative or complementary approaches for calculating electronic structure and optical properties. The research also highlights the importance of symmetry in determining the nonlinear optical response, with references to group theory and selection rules.

Semiconductor Susceptibility via Pseudoatomic Orbitals Calculated

Scientists have developed a method for calculating the second-order optical susceptibility of semiconductors, a property crucial for applications in metrology, spectroscopy, telecommunications, and material characterization. The work centers on utilizing numerical pseudoatomic orbitals within a perturbation approach, successfully tested on both cubic silicon carbide and gallium arsenide. This approach builds Bloch wavefunctions, which describe the quantum state of electrons in a crystal, from these non-orthogonal pseudoatomic orbitals, currently restricted to spinless systems exhibiting time-reversal symmetry.

The process begins by retrieving radial functions from existing calculations, reconstructing the pseudoatomic orbitals in real space, and extracting Hamiltonian and overlap matrix elements. The team meticulously constructed a basis set for each chemical species, silicon and carbon in the case of silicon carbide, considering valence configurations and polarization orbitals. For silicon, the basis includes orbitals representing the arrangement of electrons, while carbon utilizes a similar configuration, both incorporating orbitals with d-character to expand the basis. These radial functions are defined up to cutoff radii, ensuring accurate representation of the electron distribution. To accurately represent the angular dependence of the pseudoatomic orbitals, scientists employed linear combinations of spherical harmonics, utilizing a specific phase convention crucial for quantum mechanical representations of angular momentum. These calculations provide a robust framework for understanding and predicting the optical properties of semiconductors, paving the way for advancements in various technological fields.

Semiconductor Susceptibility via Pseudoatomic Orbitals

This work presents a new method for calculating the second-order optical susceptibility of semiconductors, a property crucial for applications in areas like metrology and telecommunications. The researchers successfully developed an approach based on numerical pseudoatomic orbitals, allowing for efficient calculation of this complex property. A key achievement lies in the formulation of a method to calculate two-center integrals, essential components in determining optical susceptibility, using symmetry-adapted pseudoatomic orbitals.

The method was rigorously tested on cubic silicon carbide and gallium arsenide, demonstrating its accuracy and applicability to important semiconductor materials. Results obtained using this approach align with established calculations of linear optical responses, validating the new formulation. The authors acknowledge that the current implementation is limited to spinless systems, meaning it does not account for the effects of electron spin, and future work could extend the method to include these effects. This advancement provides a valuable tool for materials scientists seeking to understand and optimize the optical properties of semiconductors.