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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...
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
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...
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...
Characteristics of Series Resonant Circuit01:24

Characteristics of Series Resonant Circuit

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:
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...

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Related Experiment Video

Updated: Jun 15, 2026

Microwave Photonics Systems Based on Whispering-gallery-mode Resonators
12:18

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Published on: August 5, 2013

Mode losses in unstable resonators with rounded edges.

C Santana, L B Felsen

    Applied Optics
    |March 6, 2010
    PubMed
    Summary

    Edge rounding in unstable resonators significantly impacts eigenmode losses. Rounding causes mode detachment at lower Fresnel numbers, improving loss behavior and mode separation, especially in cylindrical and circular mirror configurations.

    Area of Science:

    • Optics and Photonics
    • Laser Physics
    • Resonator Design

    Background:

    • Unstable resonators are crucial in laser design.
    • Understanding eigenmode losses is key to optimizing resonator performance.
    • The effect of mirror edge geometry on resonator stability is not fully understood.

    Purpose of the Study:

    • To investigate the impact of round-edged mirrors on eigenmode losses in unstable resonators.
    • To compare the behavior of round-edged versus sharp-edged mirrors in 2-D and 3-D configurations.
    • To analyze the influence of edge rounding on mode detachment and loss characteristics.

    Main Methods:

    • Utilizing the waveguide approach for analyzing unstable resonators.
    • Calculating eigenmode losses for 2-D and 3-D resonators with perfectly reflecting round-edged mirrors.

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  • Comparing results with sharp-edged mirror configurations.

    • Main Results:

    • Edge rounding in cylindrical resonators leads to mode detachment at lower Fresnel numbers compared to sharp edges.
    • Loss behavior in round-edged resonators more closely approximates the geometric optical limit for infinite mirrors.
    • In circular resonators, sharp edges prevent mode detachment, while rounding introduces it.
    • Edge rounding enhances the spectral separation between the fundamental detached mode and higher-order modes.

    Conclusions:

    • Mirror edge geometry, specifically rounding, plays a critical role in the stability and loss characteristics of unstable resonators.
    • The waveguide approach effectively models these effects, providing insights into resonator design.
    • Edge rounding offers a method to improve mode discrimination and potentially enhance laser performance.