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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:
Modes of Standing Waves - I01:03

Modes of Standing Waves - I

A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. A building may vibrate for several seconds with a driving frequency matching the building's natural frequency of vibration; this produces a resonance that results in one building collapsing while the neighboring buildings do not. Often, buildings of a certain height are devastated, while other taller buildings remain intact. This phenomenon...
Modes of Standing Waves: II01:04

Modes of Standing Waves: II

The starting point for expressing the modes of standing waves is understanding the boundary conditions that the waves must follow. The boundary conditions are derived from the physical understanding of how the standing waves are sustained, that is, how the vibrating particles of the medium behave at the boundaries imposed on them.
For a tube open at one end and closed at the other filled with air, the modes are such that there is always an antinode at the open end and a node at the closed end.

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Related Experiment Video

Updated: May 31, 2026

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

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Localized modes in one-dimensional nonlinear periodic photonic structures.

V M Apalkov1

  • 1Department of Physics and Astronomy, Georgia State University, Atlanta, GA 30303, USA.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|June 23, 2011
PubMed
Summary

We investigated second-harmonic generation in photonic crystals with phase slip defects. Optimal crystal parameters were found to enhance second-harmonic mode generation and improve resonance stability.

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Area of Science:

  • Photonics
  • Nonlinear Optics
  • Condensed Matter Physics

Background:

  • Photonic crystals offer unique control over light propagation.
  • Localized in-gap modes can arise from defects like phase slips.
  • Nonlinear optical effects enable frequency conversion within materials.

Purpose of the Study:

  • To study the generation of localized second-harmonic modes in a 1D photonic crystal with a phase slip defect.
  • To identify conditions for achieving resonance in second-harmonic generation.
  • To optimize photonic crystal parameters for stable second-harmonic mode generation.

Main Methods:

  • Theoretical analysis of a one-dimensional photonic crystal with a phase slip defect.
  • Investigation of nonlinear optical properties, specifically second-harmonic generation.
  • Parameter-dependent analysis of mode localization and intensity.

Main Results:

  • Localized second-harmonic modes are generated from a fundamental mode in the first bandgap.
  • Sharp intensity maxima for the second-harmonic mode occur at resonance conditions.
  • Resonance is achieved when the second-harmonic mode frequency matches a localized mode in the second bandgap.
  • Optimal parameters were identified to reduce sensitivity to resonance condition violations.

Conclusions:

  • Phase slip defects in 1D photonic crystals enable efficient localized second-harmonic generation.
  • Resonance conditions are crucial for maximizing second-harmonic intensity.
  • Tuning photonic crystal parameters can lead to robust second-harmonic generation.