Dielectric square resonator investigated with microwave experiments

Area of Science:

• Physics
• Materials Science
• Wave Phenomena

Background:

• Dielectric resonators are crucial in microwave and optical applications.
• Understanding field distributions and symmetry is key to resonator design.
• Semiclassical models offer insights into quantum-like behavior in classical systems.

Purpose of the Study:

• To experimentally investigate the symmetry properties and momentum space representation of field distributions in a dielectric square resonator.
• To compare experimental findings with a semiclassical model.
• To explore the relationship between resonant states and classical tori.

Main Methods:

• Experimental measurements of resonance spectra and field distributions using a flat ceramic microwave resonator.
• Analysis of momentum space representations of field distributions.
• Investigation of antenna arrangements to study symmetry properties.
• Comparison with a semiclassical model and trace formula.

Main Results:

• Resonant states were found to correspond to specific classical tori, explaining the regular spectrum structure.
• Momentum space representations enabled precise determination of the refractive index.
• Specific symmetries of resonances could be purposefully selected by adjusting antenna arrangements.
• The length spectrum and trace formula were discussed within the semiclassical framework.

Conclusions:

• The study establishes a link between resonant states, classical tori, and the regular spectrum of dielectric square resonators.
• Experimental methods allow for precise refractive index determination and controlled selection of resonance symmetries.
• The findings validate the utility of semiclassical models in understanding complex resonator behavior.