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Updated: Jun 22, 2026

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Microwave Photonics Systems Based on Whispering-gallery-mode Resonators
Published on: August 5, 2013
Planar glass waveguide ring resonators with gain.
1Department of Electrical Engineering and Computer Science, University of Michigan, 1301 Beal Avenue, Ann Arbor, MI 48109-2122, USA.
Optics Express
|June 25, 2009
Summary
This study derives a resolution limit for active waveguide ring resonator spectrometers, crucial for improving gyroscope accuracy. Researchers achieved a record low propagation loss in a neodymium-doped glass resonator.
Area of Science:
- Optics and Photonics
- Optical Sensing
- Inertial Navigation
Background:
- Spontaneous emission noise limits the frequency resolution of active waveguide ring resonator spectrometers.
- This noise impacts the performance of active ring resonator gyroscopes.
Purpose of the Study:
- To derive a closed-form expression for the frequency resolution limit.
- To determine the minimum achievable angular rotation rate random walk error for active ring resonator gyroscopes.
- To demonstrate a low-loss active waveguide ring resonator.
Main Methods:
- Derivation of a closed-form expression for frequency resolution.
- Experimental demonstration of an active waveguide ring resonator in neodymium-doped glass.
- Laser diode pumping and characterization of resonator finesse and propagation loss.
Main Results:
- A closed-form expression for frequency resolution was derived.
- The minimum rms angular rotation rate random walk error was determined.
- A finesse of 250 was achieved at 1060 nm in a 1.6 cm diameter ring.
- An effective propagation loss of ~0.013 dB/cm was measured, the lowest reported for this ring size.
Conclusions:
- The derived resolution limit provides a benchmark for spectrometer and gyroscope design.
- The demonstrated low-loss resonator is a significant advancement for optical gyroscopes.
- Further improvements in finesse and reduced loss are key for enhanced gyroscope performance.
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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:
Gain
Gain and phase shift are properties of linear circuits that describe the effect a circuit has on a sinusoidal input voltage or current. The circuit's behavior that contains reactive elements will depend on the frequency of the input sinusoid. As a result, it is observed that the gain and phase shift will all be frequency functions.
Gain:
Suppose Vin is the input and Vout is the output signal to a circuit.
Gain:
Suppose Vin is the input and Vout is the output signal to a circuit.

