Modeling of cavities using the analytic modal method and an open geometry formalism

Area of Science:

• Physics
• Optics
• Computational Electromagnetics

Background:

• Calculating properties of dipole emitters in microstructures is crucial for quantum optics and nanophotonics.
• Traditional simulation methods often suffer from artificial boundary reflections, limiting accuracy.
• Micropillars are key structures for controlling light-matter interactions.

Purpose of the Study:

• To present an eigenmode expansion technique for accurate calculation of dipole emitter properties within micropillars.
• To address the limitations of finite-sized simulation domains and parasitic reflections.
• To investigate discretization techniques for continuous radiation modes.

Main Methods:

• An eigenmode expansion technique is employed for an infinite solution domain.
• The electric field is expanded on analytic eigenmodes, avoiding outer boundary conditions.
• Two discretization techniques (equidistant and nonequidistant) for continuous radiation modes were explored.

Main Results:

• The proposed method successfully calculates the Purcell factor in a two-dimensional micropillar.
• Both equidistant and nonequidistant discretizations converge.
• Nonequidistant discretization demonstrates uniform convergence, unlike equidistant discretization.
• The technique yields more accurate results compared to existing simulation methods.

Conclusions:

• The eigenmode expansion technique provides a robust and accurate method for analyzing dipole emitters in micropillars.
• Avoiding artificial boundaries enhances the reliability of simulation results.
• This method serves as a promising foundation for future research in nanophotonics and quantum optics.