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Goos-Hänchen induced vector eigenmodes in a dome cavity.
David H Foster1, Andrew K Cook, Jens U Nöckel
1Deep Photonics Corporation, Corvallis, Oregon 97333, USA. noeckel@darkwing.uoregon.edu
Optics Letters
|June 19, 2007
Summary
The Goos-Hänchen effect shapes electromagnetic eigenmodes in 3D dome cavities, creating unique V-shaped modes. These modes are accurately modeled by a 2D billiard map incorporating the Goos-Hänchen shift.
Area of Science:
- Physics
- Optics
- Electromagnetism
Background:
- Cavity resonators are crucial in various optical and electromagnetic applications.
- Understanding electromagnetic eigenmodes is key to designing efficient resonators.
- The Goos-Hänchen effect, a transverse shift of a reflected light beam, can influence mode formation.
Purpose of the Study:
- To numerically calculate and characterize electromagnetic eigenmodes in a 3D dome cavity resonator.
- To investigate the role of the Goos-Hänchen effect in dictating eigenmode shapes.
- To establish a connection between theoretical models and numerical simulations of these modes.
Main Methods:
- Numerical calculation of electromagnetic eigenmodes in a 3D dome cavity.
- Modeling eigenmode behavior using a 2D billiard map augmented with the Goos-Hänchen shift.
- Analysis of phase space plots to identify bifurcations and stable orbits.
Main Results:
- Demonstration of V-shaped electromagnetic eigenmodes in a 3D dome cavity resonator.
- These V-shaped modes (purely TE or TM polarization) are entirely shaped by the Goos-Hänchen effect.
- A saddle-node bifurcation in the augmented billiard map corresponds to the numerically calculated V modes, determining their 'V' angle.
- Observed transition from a Gaussian to a TM V mode as cavity approaches hemispherical shape.
Conclusions:
- The Goos-Hänchen effect is the primary determinant of V-shaped eigenmodes in 3D dome cavities.
- A 2D billiard map with the Goos-Hänchen shift accurately predicts these complex mode structures.
- Bifurcation analysis provides a theoretical framework for understanding the formation and properties of these unique eigenmodes.
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