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Related Concept Videos

Symmetry Elements in a Crystal01:27

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...
Determination of Crystal Structures01:29

Determination of Crystal Structures

In the late 1800s, the revelation that light extended beyond visible wavelengths led to the discovery of X-rays by Wilhelm Roentgen. Recognized as high-energy electromagnetic radiation with short wavelengths, X-rays prompted exploration into their interaction with crystals. Max von Laue proposed in 1912 that the periodic arrangement of atoms, ions, or molecules in crystals would cause them to diffract X-rays, a hypothesis confirmed through experiments with copper sulfate and zinc sulfide...
X-ray Crystallography02:18

X-ray Crystallography

The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
The Seven Crystal Systems: Overview01:24

The Seven Crystal Systems: Overview

Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific requirements are not imposed on the...
Standing Waves in a Cavity01:28

Standing Waves in a Cavity

A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:
Crystallographic Point Groups01:29

Crystallographic Point Groups

Crystallographic point groups represent the various symmetry operations that can occur within crystals. They are unique in that at least one point will always remain unchanged during these actions. For instance, consider the triclinic system. This system, devoid of any axis or plane of symmetry, aligns with the C1 and Ci point groups.where Cᵢ is characterized solely by a center of inversion.Contrastingly, the monoclinic system introduces an element of symmetry. This system with one plane and...

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Related Experiment Video

Updated: Jul 9, 2026

Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities
11:08

Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities

Published on: November 30, 2012

Reflected fourth-harmonic radiation from a centrosymmetric crystal.

Y S Lee, M C Downer

    Optics Letters
    |December 19, 2007
    PubMed
    Summary

    We measured fourth-harmonic generation in silicon and silicon dioxide. The surface

    Area of Science:

    • Nonlinear optics
    • Surface science
    • Materials science

    Background:

    • Second-harmonic generation (SHG) is a well-established nonlinear optical technique for probing surfaces and interfaces.
    • Fourth-harmonic generation (4HG) offers potential for enhanced surface sensitivity but is less explored.
    • Centrosymmetric materials like silicon (Si) and silicon dioxide (SiO2) typically exhibit weak nonlinear optical responses.

    Purpose of the Study:

    • To investigate fourth-harmonic generation (4HG) at the Si(001)-SiO2 interface.
    • To compare the surface and bulk contributions to 4HG.
    • To assess the potential of 4HG as a surface-sensitive probe.

    Main Methods:

    • Femtosecond laser pulses were used for 4HG measurements.
    • Measurements were performed in reflection geometry.

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    Hyperspectral Imaging as a Tool to Study Optical Anisotropy in Lanthanide-Based Molecular Single Crystals
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    Hyperspectral Imaging as a Tool to Study Optical Anisotropy in Lanthanide-Based Molecular Single Crystals

    Published on: April 14, 2020

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    Last Updated: Jul 9, 2026

    Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities
    11:08

    Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities

    Published on: November 30, 2012

    Applying X-ray Imaging Crystal Spectroscopy for Use as a High Temperature Plasma Diagnostic
    06:46

    Applying X-ray Imaging Crystal Spectroscopy for Use as a High Temperature Plasma Diagnostic

    Published on: August 25, 2016

    Hyperspectral Imaging as a Tool to Study Optical Anisotropy in Lanthanide-Based Molecular Single Crystals
    07:24

    Hyperspectral Imaging as a Tool to Study Optical Anisotropy in Lanthanide-Based Molecular Single Crystals

    Published on: April 14, 2020

  • The Si(001)-SiO2 interface was studied below the optical damage threshold.

    • Main Results:

    • Fourth-harmonic generation was successfully measured from the Si(001)-SiO2 interface.
    • Analysis of signal amplitudes and rotational anisotropy indicated a strong surface contribution.
    • The surface dipole contribution to 4HG was found to be significantly more dominant than the bulk quadrupole contribution.

    Conclusions:

    • Fourth-harmonic generation is a highly surface-sensitive nonlinear optical process at centrosymmetric interfaces.
    • The surface dipole contribution to 4HG is substantially stronger than previously anticipated.
    • 4HG shows promise for advanced surface and interface characterization, surpassing SHG in surface sensitivity.