Related Experiment Video
Updated: Jun 15, 2026
11:08
Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities
Published on: November 30, 2012
Comparison of various diffraction formulas in a study of open resonators
Applied Optics
|March 6, 2010
Summary
The study computed resonator modes and losses using diffraction theory approximations. Confocal resonators showed significant differences based on approximation methods, unlike planar Fabry-Perot resonators.
Area of Science:
- Optics and Photonics
- Electromagnetism
- Mathematical Physics
Background:
- Resonator design is crucial for laser and optical systems.
- Diffraction theory approximations impact optical simulations.
- Understanding resonator behavior requires accurate theoretical models.
Purpose of the Study:
- To compute modes and losses for planar Fabry-Perot and confocal resonators.
- To evaluate the influence of different diffraction theory kernels on resonator computations.
- To identify the impact of approximation methods on resonator characteristics.
Main Methods:
- Utilized various kernels derived from diffraction theory approximations.
- Computed modes and losses for planar Fabry-Perot resonators.
- Computed modes and losses for confocal resonators.
- Analyzed results for varying Fresnel numbers (N).
Main Results:
- Planar Fabry-Perot resonators showed minimal influence from kernel shape for N up to 42.25.
- Confocal resonators exhibited significant differences based on approximation methods, even for small N (>=1).
- Qualitative differences emerged between parabolic approximation and Rayleigh-Luneberg diffraction theory kernels for confocal resonators.
- Differences highlight the importance of amplitude considerations in diffraction approximations.
Conclusions:
- The choice of diffraction theory approximation significantly affects confocal resonator analysis.
- Planar Fabry-Perot resonators are less sensitive to approximation methods within the studied Fresnel number range.
- Amplitude variations in approximations play a critical role in diffraction-based resonator modeling.
Related Concept Videos
02:18Interference and Diffraction
Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.
02:18X-ray Crystallography
The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
01:14Sound Waves: Resonance
Resonance is produced depending on the boundary conditions imposed on a wave. Resonance can be produced in a string under tension with symmetrical boundary conditions (i.e., has a node at each end). A node is defined as a fixed point where the string does not move. The symmetrical boundary conditions result in some frequencies resonating and producing standing waves, while other frequencies interfere destructively. Sound waves can resonate in a hollow tube, and the frequencies of the sound...
01:23Parallel Resonance
The parallel RLC circuit is an arrangement where the resistor (R), inductor (L), and capacitor (C) are all connected to the same nodes and, as a result, share the same voltage across them. The parallel RLC circuit is analyzed in terms of admittance (Y), which reflects the ease with which current can flow. The admittance is given by:
02:16Resonance and Hybrid Structures
According to the theory of resonance, if two or more Lewis structures with the same arrangement of atoms can be written for a molecule, ion, or radical, the actual distribution of electrons is an average of that shown by the various Lewis structures.
Resonance Structures and Resonance Hybrids
The Lewis structure of a nitrite anion (NO2−) may actually be drawn in two different ways, distinguished by the locations of the N–O and N=O bonds.
Resonance Structures and Resonance Hybrids
The Lewis structure of a nitrite anion (NO2−) may actually be drawn in two different ways, distinguished by the locations of the N–O and N=O bonds.
01:29Determination of Crystal Structures
In the late 1800s, the revelation that light extended beyond visible wavelengths led to the discovery of X-rays by Wilhelm Roentgen. Recognized as high-energy electromagnetic radiation with short wavelengths, X-rays prompted exploration into their interaction with crystals. Max von Laue proposed in 1912 that the periodic arrangement of atoms, ions, or molecules in crystals would cause them to diffract X-rays, a hypothesis confirmed through experiments with copper sulfate and zinc sulfide...