Contents
Source: Allelco
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The Q Factor in Resonators
Introduction
The Q factor (quality factor) of a resonator is a crucial parameter that characterizes the damping of its oscillations or the relative linewidth. Originally used in electronic circuits and microwave cavities, the concept of Q factor has also found significance in optical resonators.
Definitions of Q Factor
There are two common definitions of the Q factor:
- Definition via energy storage: Q = 2 * (stored energy / energy dissipated per cycle)
- Definition via resonance bandwidth: Q = (resonance frequency / FWHM bandwidth)
Q Factor of Optical Resonators
In optical resonators, the Q factor depends on the optical frequency, power loss per round trip, and round-trip time. The formula for calculating Q in optical resonators is Q = (2πν0 * Trt) / l.
Important Relations
The Q factor is related to various quantities:
- Q = 2 * (exponential decay time * optical frequency)
- Q = 2 * (number of periods for energy decay to ≈ 37% of initial value)
- Q = finesse * optical frequency / free spectral range
Intrinsic and Loaded Q Factor
The intrinsic Q factor is the value without external coupling, while the loaded Q factor includes coupling effects. In some resonators, coupling can be removed to achieve higher Q values.
High-Q Resonators
High-Q optical resonators have applications in quantum optics, telecommunications, and frequency metrology. Supermirrors and microcavities are used to achieve ultra-high Q factors.
The Q Factor of an Oscillator
The term Q factor is sometimes applied to lasers and oscillators, but it should be reserved for passive resonators. Q-switching, a method of pulse generation, is based on abrupt changes in the Q factor of a laser resonator.
Conclusion
The Q factor is a fundamental parameter in resonator physics, influencing various aspects of optical and electronic systems. Understanding and optimizing the Q factor is essential for a wide range of applications.
Source: Allelco
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