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Gauss's Law

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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.

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Related Experiment Video

Updated: Jun 19, 2026

Determination of the Excitation and Coupling Rates Between Light Emitters and Surface Plasmon Polaritons

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Reactive power in the full Gaussian light wave.

¹s.r.seshadri@att.net

Journal of the Optical Society of America. A, Optics, Image Science, and Vision

|November 4, 2009

Summary

This study identifies electric current sources for Gaussian beams and light waves. It analyzes their power, revealing reactive power depends on beam parameters and can become infinite.

Area of Science:

Electromagnetics
Optics
Wave Physics

Background:

Gaussian beams are fundamental in optics and laser physics.
Understanding wave excitation and power generation is crucial for optical system design.

Purpose of the Study:

To determine the electric current sources required for exciting fundamental Gaussian beams and full Gaussian light waves.
To analyze the electromagnetic fields and complex power generated by these sources.
To investigate the dependence of real and reactive power on key beam parameters.

Main Methods:

Mathematical derivation of electric current sources on a secondary source plane.
Evaluation of electromagnetic fields and complex power.
Analysis of power variations with parameters like Rayleigh distance (b), beam waist (w0), and wavenumber (k).

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Determination of the Excitation and Coupling Rates Between Light Emitters and Surface Plasmon Polaritons

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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

Main Results:

For the fundamental Gaussian beam, reactive power is zero, with real power normalized to 2 W.
Full Gaussian waves are characterized by a length parameter b(t) (0 ≤ b(t) ≤ b, where b is Rayleigh distance).
Reactive power for full Gaussian waves increases with b(t)/b, becoming infinite at b(t)/b=1, and approaches zero for paraxial beams as kw0 increases.

Conclusions:

The study provides a framework for understanding Gaussian beam excitation and power characteristics.
The findings highlight the critical role of beam parameters in determining reactive power, with implications for optical energy management.
The analysis extends to non-paraxial regimes, offering insights into wave behavior beyond simplified models.