Related Concept Videos
01:07Gauss's Law
If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
01:17NMR Spectrometers: Radiofrequency Pulses and Pulse Sequences
A pulse is a short burst of radio waves distributed over a range of frequencies that simultaneously excites all the nuclei in the sample. Upon passing a radio frequency pulse along the x-axis, the nuclei absorb energy corresponding to their Larmor frequencies and achieve resonance. This shifts the net magnetization vector from the z-axis toward the transverse plane. This angle of rotation of the magnetization vector, or the flip angle, is proportional to the duration and intensity of the pulse.
01:08IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations
Identical bonds within a polyatomic group can stretch symmetrically (in-phase) or asymmetrically (out-of-phase). Similar to hydrogen bonding, these vibrations also influence the shape of the IR peak. Generally, asymmetric stretching frequencies are higher than symmetric stretching frequencies. For example, primary amines exhibit two distinct IR peaks between 3300–3500 cm−1 corresponding to the symmetric and asymmetric N-H stretching, while secondary amines exhibit a single stretching vibration...
01:30Plane Electromagnetic Waves I
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 to be a...
The EM field is assumed to be a...
01:19Rectangular and Triangular Pulse Function
The unit rectangular pulse function is mathematically represented by a rectangular function centered at the origin with a height of one unit. This function is defined by two parameters: T, which specifies the center location of the pulse along the time axis, and τ, which determines the pulse duration.
For example, consider a rectangular pulse with a 5V amplitude, a 3-second duration, and centered at t=2 seconds. This pulse can be expressed using the rectangular function, written as,
For example, consider a rectangular pulse with a 5V amplitude, a 3-second duration, and centered at t=2 seconds. This pulse can be expressed using the rectangular function, written as,
01:02¹H NMR: Interpreting Distorted and Overlapping Signals
Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
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Related Experiment Video
Updated: Jun 22, 2026
07:11
ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
Published on: August 19, 2021
Summary
This study introduces a cyclo-stationary model for Gaussian-Schell pulses, analyzing their power spectrum. Pulse correlation was found to alter the spectrum
Area of Science:
- Optics and Photonics
- Statistical Optics
- Signal Processing
Background:
- The Gaussian-Schell (G-S) model is foundational for describing Gaussian light pulses.
- Existing research has explored non-stationary random functions for G-S pulse analysis.
- A need exists for advanced models to capture complex pulse dynamics.
Purpose of the Study:
- To develop and present a cyclo-stationary model for Gaussian-Schell pulses.
- To derive the power spectrum of the proposed cyclo-stationary G-S pulse model.
- To investigate the impact of pulse correlation on the power spectrum's characteristics.
Main Methods:
- Development of a cyclo-stationary mathematical framework for G-S pulses.
- Derivation of the power spectrum using the established cyclo-stationary model.
Main Results:
- A novel cyclo-stationary model for Gaussian-Schell pulses is successfully formulated.
- The power spectrum associated with this cyclo-stationary model has been derived.
- Pulse correlation is demonstrated to modify the Gaussian nature of the power spectrum.
Conclusions:
- The cyclo-stationary model offers a more comprehensive description of G-S pulse variations.
- Understanding pulse correlation is crucial for predicting and controlling optical pulse characteristics.
- This work advances the statistical description of non-stationary optical fields.