Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

14.5K
It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...
14.5K
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

593
James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...
593
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

128
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
128
Plane Electromagnetic Waves I01:30

Plane Electromagnetic Waves I

4.1K
The existence of combined electric and magnetic fields that propagate through space as electromagnetic (EM) waves is the most significant prediction of Maxwell's equations. As Maxwell's equations hold in free space, the predicted electromagnetic waves do not require a medium for their propagation. An EM wave comprises an electric field, defined as the force per charge on a stationary charge, and a magnetic field, which is the force per charge on a moving charge.
The EM field is assumed...
4.1K
Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

3.5K
Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
3.5K
Gauss's Law in Dielectrics01:17

Gauss's Law in Dielectrics

4.6K
Consider a polar dielectric placed in an external field. In such a dielectric, opposite charges on adjacent dipoles neutralize each other, such that the net charge within the dielectric is zero. When a polar dielectric is inserted in between the capacitor plates, an electric field is generated due to the presence of net charges near the edge of the dielectric and the metal plates interface. Since the external electrical field merely aligns the dipoles, the dielectric as a whole is neutral. An...
4.6K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Mapping Molecular/Nanocrystal Orientation with Nano-FTIR.

The journal of physical chemistry letters·2026
Same author

Anharmonic Coupling in a Strong Intramolecular H-Bond System: Contributions to Static and Time-Resolved Vibrational Spectra.

The journal of physical chemistry letters·2025
Same author

Mode-Specific Coherent Interference of Vibrational Sum-Frequency Generation Imaging: An Approach to Differentiate Lung Tumors through Collagen Interfibrillar Distances.

Journal of the American Chemical Society·2025
Same author

Ultrafast transient s-SNOM nanoscopic measurement of charge transfer between a ruthenium complex and a MoS<sub>2</sub> monolayer.

Chemical communications (Cambridge, England)·2025
Same author

Tip-enhanced nanocavities amplify the sum frequency generation.

Light, science & applications·2025
Same author

Overcoming energy disorder for cavity-enabled energy transfer in vibrational polaritons.

Science (New York, N.Y.)·2025

Related Experiment Video

Updated: Aug 26, 2025

Spectral and Angle-Resolved Magneto-Optical Characterization of Photonic Nanostructures
08:01

Spectral and Angle-Resolved Magneto-Optical Characterization of Photonic Nanostructures

Published on: November 21, 2019

7.2K

Neumann's principle based eigenvector approach for deriving non-vanishing tensor elements for nonlinear optics.

Zishan Wu1, Wei Xiong1

  • 1Department of Chemistry and Biochemistry, UC San Diego, La Jolla, California 92093, USA.

The Journal of Chemical Physics
|October 8, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a new matrix-based method for determining non-vanishing tensor elements in physical properties, simplifying calculations for symmetric systems. The approach, grounded in Neumann's principle, offers a more intuitive and accurate way to analyze material symmetries and their impact on optical and magnetic properties.

More Related Videos

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.1K
Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements
14:18

Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements

Published on: February 28, 2016

11.5K

Related Experiment Videos

Last Updated: Aug 26, 2025

Spectral and Angle-Resolved Magneto-Optical Characterization of Photonic Nanostructures
08:01

Spectral and Angle-Resolved Magneto-Optical Characterization of Photonic Nanostructures

Published on: November 21, 2019

7.2K
Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.1K
Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements
14:18

Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements

Published on: February 28, 2016

11.5K

Area of Science:

  • Solid State Physics
  • Materials Science
  • Quantum Information Technologies

Background:

  • Physical properties are often described by tensors, like optical susceptibilities.
  • Conventional methods for deriving tensor elements in symmetric systems are complex and error-prone, relying on intuitive sign-flipping after symmetry operations.
  • Neumann's principle, stating that physical property symmetries mirror geometric symmetries, provides a foundation for a more systematic approach.

Purpose of the Study:

  • To develop a novel matrix-based approach for deriving non-vanishing tensor elements of physical properties.
  • To provide a physically intuitive and mathematically rigorous method for analyzing tensor properties based on Neumann's principle.
  • To extend the method for higher-rank tensors and applications involving magnetization for spin polarization measurements.

Main Methods:

  • Mathematical application of Neumann's principle to tensor expressions.
  • Development of a procedure based on eigensystems to derive non-vanishing tensor elements.
  • Implementation of a generalized Mathematica code for arbitrary symmetries and nonlinear processes.

Main Results:

  • Demonstrated the approach's validity for second and third-order nonlinear susceptibilities in chiral/achiral surfaces with complex symmetries (D6, Oh).
  • Successfully applied the method to higher-rank tensors relevant for 2D and high-order spectroscopy.
  • Extended the approach to derive nonlinear tensor elements involving magnetization, crucial for surface spin polarization analysis.

Conclusions:

  • The matrix-based approach offers a simplified, intuitive, and accurate method for determining tensor elements in physical properties.
  • This generalized method is applicable to a wide range of symmetries, tensor ranks, and nonlinear optical/magnetic phenomena.
  • The provided Mathematica code facilitates the analysis of complex material properties for fundamental research and technological applications, including quantum information.