Related Experiment Video
Updated: May 25, 2026

12:21
Stimulated Stokes and Antistokes Raman Scattering in Microspherical Whispering Gallery Mode Resonators
Published on: April 4, 2016
Second harmonic generation in three-dimensional structures based on homogeneous centrosymmetric metallic spheres
1School of Physics, Beijing Institute of Technology, Beijing, China.
Optics Express
|January 26, 2012
Summary
We developed a theory for second harmonic generation (SHG) in metallic nanoparticle structures. Localized surface plasmon resonances significantly influence the nonlinear optical response of these ensembles.
Area of Science:
- Physics
- Materials Science
- Optics
Background:
- Second harmonic generation (SHG) is a key nonlinear optical process.
- Understanding SHG in complex nanostructures is crucial for optical device development.
Purpose of the Study:
- To develop a theoretical framework for SHG in 3D arrangements of metallic spheres.
- To analyze the influence of localized surface plasmon-polariton resonances on SHG.
Main Methods:
- Multiple scattering theory of electromagnetic multipole fields.
- Calculation of electromagnetic fields and scattering cross-sections for various configurations.
Main Results:
- Developed a theory for SHG in arbitrary distributions of metallic spheres.
- Demonstrated strong influence of localized surface plasmon-polariton resonances on linear and nonlinear optical response.
- Analyzed the physical origin of this plasmonic influence.
Conclusions:
- The developed theory accurately describes SHG in metallic nanoparticle ensembles.
- Localized surface plasmon-polariton resonances are critical for tailoring nonlinear optical properties.
- This work provides insights into designing novel plasmonic nanostructures for nonlinear optics.
Related Concept Videos
Metallic Solids
Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms. The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. The atoms within such a metallic solid are held together by a unique force known as metallic bonding that gives rise to many useful and varied bulk properties.
All metallic solids exhibit high thermal and electrical conductivity, metallic luster, and malleability. Many...
All metallic solids exhibit high thermal and electrical conductivity, metallic luster, and malleability. Many...
Symmetry Elements in a Crystal
Crystal symmetry operations are isometric transformations that map objects onto indistinguishable copies while preserving distances, angles, and volumes. The simplest symmetry operation is translation, which shifts the entire infinite crystal lattice parallelly by a translation vector.Crystallographic rotations involve rotations by an angle of 2π/n around an axis without changing the positions of points on the axis. It is called the rotational axis of the symmetry, denoted by n. The combination...
Gauss's Law: Spherical Symmetry
A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...
Hybridization of Atomic Orbitals I
The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
Valence Bond Theory
Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
Lattice Centering and Coordination Number
The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
Types of Unit Cells
Imagine taking a large number of identical...

