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

Experimental Determination of Chemical Formula02:37

Experimental Determination of Chemical Formula

The elemental makeup of a compound defines its chemical identity, and chemical formulas are the most concise way of representing this elemental makeup. When a compound’s formula is unknown, measuring the mass of its constituent elements is often the first step in determining the formula experimentally.
Maxwell's Thermodynamic Relations01:23

Maxwell's Thermodynamic Relations

Maxwell's thermodynamic relations are very useful in solving problems in thermodynamics. Each of Maxwell's relations relates a partial differential between quantities that can be hard to measure experimentally to a partial differential between quantities that can be easily measured. These relations are a set of equations derivable from the symmetry of the second derivatives and the thermodynamic potentials.
All thermodynamic potentials are exact differentials. Therefore, their second-order...
Mason's Rule01:20

Mason's Rule

Mason's rule is a powerful tool in control systems and signal processing. It simplifies the calculation of transfer functions from signal-flow graphs. This method leverages various elements, including loop gains, forward-path gains, and non-touching loops, to determine the transfer function efficiently.
Loop gain is determined by identifying and tracing a path from a node back to itself. This involves computing the product of branch gains along the loop. Each loop's gain is crucial for further...
Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
Gravitational Potential Energy for Extended Objects01:07

Gravitational Potential Energy for Extended Objects

Consider a system comprising several point masses. The coordinates of the center of mass for this system can be expressed as the summation of the product of each mass and its position vector divided by the total mass:
Euler's Formula to Columns with Other End Conditions01:15

Euler's Formula to Columns with Other End Conditions

Euler's formula is very important in the field of structural engineering, providing a foundation for understanding the critical loading conditions of pin-ended columns. This formula links the modulus of elasticity, the moment of inertia of the cross-section, and the column's length, offering a precise calculation of the critical load at which a column is prone to buckling.

You might also read

Related Articles

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

Sort by
Same author

Trained nnU-Net model for semantic segmentation of human adult cervical vertebrae from CT-Scans.

Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference·2025
Same author

Fatherhood experiences: A qualitative approach of cisgender and transgender fathers in assisted reproductive technologies (ART) situation with sperm donation.

Heliyon·2024
Same author

Alternative climatic steady states near the Permian-Triassic Boundary.

Scientific reports·2024
Same author

American Football On-Field Head Impact Kinematics: Influence of Acceleration Signal Characteristics on Peak Maximal Principal Strain.

Annals of biomedical engineering·2024
Same author

Automatic detection of spinal injuries under dynamic compressive loading using high-speed cine-radiography.

Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference·2023
Same author

Contribution of impactor misalignment to the neurofunctional variability in porcine spinal cord contusion models.

Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference·2023
Same journal

Denoising algorithm of Φ-OTDR systems based on adaptive fractional wavelet transform denoising.

Optics express·2026
Same journal

Millisecond photon-to-photon latency and high-speed volumetric projection system for optogenetics.

Optics express·2026
Same journal

Polarization-encoded coaxial structured light for high-precision 3D surface profilometry.

Optics express·2026
Same journal

Discrete freeform optical design based on collaborative optimization of point cloud and local normals.

Optics express·2026
Same journal

Ultrafast ghost imaging with 25 GHz speckle switching and wavelength-division multiplexing.

Optics express·2026
Same journal

Atomic vapor cells fabricated by femtosecond laser welding of standard-optical-quality glass.

Optics express·2026
See all related articles

Related Experiment Video

Updated: Jun 13, 2026

Reliable Mechanochemistry: Protocols for Reproducible Outcomes of Neat and Liquid Assisted Ball-mill Grinding Experiments
13:05

Reliable Mechanochemistry: Protocols for Reproducible Outcomes of Neat and Liquid Assisted Ball-mill Grinding Experiments

Published on: January 23, 2018

Generalized Miller formulae.

W Ettoumi1, Y Petit, J Kasparian

  • 1Université de Genève, GAP-Biophotonics, 20 rue de l'Ecole de Médecine, 1211 Geneva 4, Switzerland.

Optics Express
|April 15, 2010
PubMed
Summary
This summary is machine-generated.

This study generalizes Sellmeier equations to describe non-linear optical properties of materials. The non-linear susceptibility and refractive indices are fully determined by the material's linear dispersion.

More Related Videos

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels
11:34

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels

Published on: September 8, 2016

Related Experiment Videos

Last Updated: Jun 13, 2026

Reliable Mechanochemistry: Protocols for Reproducible Outcomes of Neat and Liquid Assisted Ball-mill Grinding Experiments
13:05

Reliable Mechanochemistry: Protocols for Reproducible Outcomes of Neat and Liquid Assisted Ball-mill Grinding Experiments

Published on: January 23, 2018

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels
11:34

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels

Published on: September 8, 2016

Area of Science:

  • Non-linear optics
  • Materials science
  • Spectroscopy

Background:

  • The Sellmeier equation describes linear optical dispersion.
  • Miller's formula relates non-linear susceptibility to linear properties but is limited in order.
  • Understanding non-linear optical responses is crucial for advanced photonic applications.

Purpose of the Study:

  • To generalize the Sellmeier equation for any order of non-linear susceptibility.
  • To establish a direct link between linear dispersion and non-linear optical properties.
  • To provide a framework for calculating spectral dependence of non-linear refractive indices.

Main Methods:

  • Derivation of spectral dependence for higher-order non-linear susceptibility.
  • Generalization of existing formulas (e.g., Miller formula).
  • Analysis of the frequency-degenerate case for non-linear refractive indices.

Main Results:

  • A generalized formula for spectral dependence of non-linear susceptibility of any order was derived.
  • This dependence is shown to be entirely determined by the linear dispersion of the medium.
  • The generalized formula extends Miller's formula to arbitrary non-linearity orders.

Conclusions:

  • The derived framework provides a comprehensive method for predicting non-linear optical behavior.
  • Linear dispersion data is sufficient to characterize higher-order non-linear optical responses.
  • This work simplifies the analysis of non-linear optical materials and phenomena.