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Related Concept Videos

Design Example: Underdamped Parallel RLC Circuit01:17

Design Example: Underdamped Parallel RLC Circuit

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...
Sound Waves: Resonance01:14

Sound 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...
Oscillations In An LC Circuit01:30

Oscillations In An LC Circuit

An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by
RLC Circuit as a Damped Oscillator01:30

RLC Circuit as a Damped Oscillator

An RLC circuit combines a resistor, inductor, and capacitor, connected in a series or parallel combination.
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...
Concept of Resonance and its Characteristics01:19

Concept of Resonance and its Characteristics

If a driven oscillator needs to resonate at a specific frequency, then very light damping is required. An example of light damping includes playing piano strings and many other musical instruments. Conversely, to achieve small-amplitude oscillations as in a car's suspension system, heavy damping is required. Heavy damping reduces the amplitude, but the tradeoff is that the system responds at more frequencies. Speed bumps and gravel roads prove that even a car's suspension system is not immune...
Double Resonance Techniques: Overview01:12

Double Resonance Techniques: Overview

Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
Spin decoupling is usually achieved by...

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Fabrication and Characterization of High-Q Silicon Nitride Membrane Resonators
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Ray method for unstable resonators.

S H Cho, L B Felsen

    Applied Optics
    |March 18, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study reviews a ray-optical method for unstable resonators, extending its application to complex structures like resonators with internal axicons. The method addresses diffraction, scattering, and shielding effects for improved optical resonator analysis.

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    Microwave Photonics Systems Based on Whispering-gallery-mode Resonators
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    Area of Science:

    • Optics and Photonics
    • Laser Physics
    • Computational Electromagnetics

    Background:

    • Unstable resonators are critical components in high-power laser systems.
    • Existing ray-optical methods face limitations with complex geometries and edge effects.
    • Analysis of resonators with non-axial elements like axicons requires advanced modeling techniques.

    Purpose of the Study:

    • To review and extend a previously developed ray-optical method for analyzing unstable, symmetric, bare resonators.
    • To demonstrate the method's adaptability to various edge configurations and non-axial structures, including resonators with internal axicons.
    • To investigate the physical implications and canonical diffraction problems associated with axicon elements in resonators.

    Main Methods:

    • A deductive, stepwise procedure based on a ray-optical approach is presented.
    • The method is adapted to accommodate rounded edges and non-axial configurations.
    • Ray categorization and identification of canonical diffraction problems are employed for axicon analysis.

    Main Results:

    • The ray-optical method is shown to be applicable to resonators with rounded edges and internal axicons.
    • The approach effectively categorizes rays and identifies critical diffraction phenomena like shadowing and scattering.
    • Approximate calculations demonstrate the impact of axicon tip shielding and spacing on resonator eigenvalues.

    Conclusions:

    • The generalized ray-optical method provides a robust framework for analyzing complex unstable resonator designs.
    • The study highlights the importance of considering edge effects and non-axial elements for accurate resonator modeling.
    • The findings offer insights into optimizing resonator performance by managing axicon tip geometry and placement.