Related Experiment Video
Updated: Apr 25, 2026
12:18
Microwave Photonics Systems Based on Whispering-gallery-mode Resonators
Published on: August 5, 2013
16.4K
One-dimensional finite-elements method for the analysis of whispering gallery microresonators
Summary
This study reduces the 3D analysis of whispering gallery microresonators to a 2D problem using finite-element method (FEM) and Fourier analysis. The efficient numerical technique accurately calculates resonator modes considering all losses.
Area of Science:
- Photonics and Optics
- Computational Electromagnetics
Background:
- Whispering gallery microresonators are crucial for integrated optics.
- Accurate simulation of 3D microresonator behavior is computationally demanding.
Purpose of the Study:
- To develop an efficient numerical method for analyzing 3D whispering gallery microresonators.
- To reduce the computational complexity of microresonator simulations.
Main Methods:
- Leveraging axial symmetry to reduce the 3D problem to a 2D cross-section analysis.
- Combining the finite-element method (FEM) with Fourier expansion for field analysis.
- Solving the resulting sparse eigenvalue problem using numerical techniques.
Main Results:
- The formulation accurately accounts for both radiation and dielectric losses.
- The method is efficient for both high and low order resonator modes.
- Validation against commercial software confirms the method's accuracy.
Conclusions:
- The proposed 2D FEM-based approach offers an efficient and accurate solution for 3D whispering gallery microresonator analysis.
- This method simplifies complex simulations, enabling broader research and design applications.
Related Concept Videos
01:23Parallel Resonance
849
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:
849
01:28Standing Waves in a Cavity
1.7K
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:
1.7K
01:12Mesh Analysis for AC Circuits
794
In the domain of radio communication, the significance of impedance matching must be considered. It is crucial to ensure the efficient transmission of signals between radio transmitters and receivers. Achieving this balance involves using impedance-matching circuits, with one fundamental configuration comprising a resistor, capacitor, and inductor.
The process of harmonizing these impedances begins with a clear understanding of the input and output signals. Once these signals are known, the...
The process of harmonizing these impedances begins with a clear understanding of the input and output signals. Once these signals are known, the...
794
01:24Characteristics of Series Resonant Circuit
900
Series resonance occurs in a circuit containing inductive (L), capacitive (C), and resistive (R) elements connected sequentially. At the resonance frequency, the inductive and capacitive reactances are equal in magnitude but opposite in sign, effectively canceling each other. This causes the circuit's impedance is minimal, primarily determined by the resistance R. The resonant frequency of an RLC circuit is defined as:
900
01:17Design Example: Underdamped Parallel RLC Circuit
815
Consider designing an oscillator circuit, a crucial component in various electronic devices and systems. The objective is to create an oscillator circuit with specific characteristics: a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. To accomplish this, a parallel RLC circuit is employed, known for its ability to sustain oscillations at a resonant frequency. In this case, the damping factor is pivotal in achieving the desired performance.
Starting with a fixed...
Starting with a fixed...
815
01:14Sound Waves: Resonance
2.8K
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...
2.8K