Husimi functions at gradient index cavities designed by conformal transformation optics.

Area of Science:

• Optics and Photonics
• Materials Science
• Computational Physics

Background:

• Traditional dielectric cavity systems feature uniform refractive indices.
• Husimi functions are standard for representing optical modes in homogeneous cavities.
• Gradient index dielectric cavities offer advanced optical properties but lack phase space analysis methods.

Purpose of the Study:

• To develop a phase space analysis method for resonant modes in gradient index dielectric cavities.
• To adapt conventional Husimi functions for transformation cavities.
• To visualize and understand the behavior of optical modes in novel cavity designs.

Main Methods:

• Constructing a reciprocal virtual space to map gradient index cavities.
• Applying conventional Husimi functions within this virtual space.
• Obtaining Husimi plots for specific modes in a limaçon-shaped transformation cavity.

Main Results:

• Successfully revealed the phase space structure of resonant modes in gradient index cavities.
• Generated Husimi plots for anisotropic whispering gallery modes (WGMs) and short-lived modes.
• Demonstrated compatibility between the virtual space phase description and physical space far-field directionality.

Conclusions:

• The reciprocal virtual space method effectively extends Husimi function analysis to gradient index dielectric cavities.
• This approach provides crucial insights into the phase space dynamics of transformation cavities.
• The findings support the design and application of advanced optical devices utilizing gradient index materials.