Related Experiment Video
Updated: Jun 17, 2026
11:08
Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities
Published on: November 30, 2012
Summary
This study presents a simple expression for the response of misaligned degenerate cavities using complex ray optics. The method simplifies calculations for Gaussian beam coupling factors, offering accurate results for conventional and nonorthogonal misaligned cavities.
Area of Science:
- Optics and Photonics
- Electromagnetism
- Cavity Resonator Theory
Background:
- Degenerate cavities are crucial in various optical systems.
- Accurate modeling of misalignments is essential for performance prediction.
- Existing methods may be complex for arbitrary misalignment scenarios.
Purpose of the Study:
- To develop a simplified analytical expression for the response of misaligned degenerate cavities.
- To provide numerical results validating the derived expression.
- To extend the analysis to cases with large and nonorthogonal misalignments.
Main Methods:
- Utilizing complex ray representation of Gaussian beams for resonance excitation.
- Identifying the modulus and phase of complex rays with beam radius and on-axis field phase.
- Calculating the coupling factor between Gaussian beams analytically.
Main Results:
- A simple analytical expression for the response of misaligned degenerate cavities.
- Numerical results demonstrating the accuracy of the derived expression.
- Agreement with established Laguerre-Gauss and Hermite-Gauss mode theories for conventional cavities.
- Discussion of degenerate cavities with large, nonorthogonal misalignments.
Conclusions:
- The complex ray method offers an efficient approach to analyze misaligned degenerate cavities.
- The derived expression is applicable to both conventional and complex misalignment cases.
- This work facilitates the design and analysis of optical systems employing degenerate cavities.
Related Concept Videos
01:25Imperfections in Crystal Structure: Point, Line and Plane Defects
A perfect crystal, in theory, has a uniform structure with the same unit cell and lattice points throughout. However, any deviation from this periodic arrangement is known as an imperfection or defect. These defects can be categorized into three types: point, line, and plane defects.Point defects occur when there is a deviation from the ideal due to missing atoms, displaced atoms, or additional atoms. These imperfections might occur due to imperfect packing during crystallization or because of...
01:26Imperfections in Crystal Structure: Stoichiometric Point Defects
Schottky defects arise when some lattice points in a crystal, such as those in NaCl, remain unoccupied, creating lattice vacancies without disturbing the overall electrical neutrality of the crystal. This defect is common in ionic crystals where the positive and negative ions are similar in size, as seen in sodium chloride and cesium chloride. The presence of Schottky defects enables the crystal to conduct electricity to a small extent through an ionic mechanism. Electric fields cause nearby...
01:28Standing 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:
01:21Deformations in a Transverse Cross Section
When a material is subjected to uniaxial stress, it elongates or contracts in the direction of the applied force, and also undergoes changes in the perpendicular directions. This behavior is crucial for understanding how materials behave under stress and is governed by mechanical properties such as Poisson's ratio v, which measures the ratio of transverse strain to axial strain.
As the material stretches, it expands or contracts in orthogonal directions to the load. This phenomenon varies...
As the material stretches, it expands or contracts in orthogonal directions to the load. This phenomenon varies...
01:29Imperfections in Crystal Structure: Non-Stoichiometric Defects
Non-stoichiometric defects refer to a type of defect in the crystal structure of a compound where the ratio of its constituent elements deviates from the ideal stoichiometric ratio. There are two main types of non-stoichiometric defects: metal excess defects and metal deficiency defects.Metal excess defects occur when there is a slight surplus of metal ions than what is required by the stoichiometric ratio of the compound. For example, heating a sodium chloride crystal in sodium vapor results...