Eigenvalue-accelerated LDOS optimization of high-Q optical resonances

Area of Science:

• Computational physics
• Electromagnetism
• Materials science

Background:

• Inverse design is crucial for optimizing resonant cavities.
• Maximizing local density of states (LDOS) is a key application.
• High-Q cavities present optimization challenges due to ill-conditioning.

Purpose of the Study:

• To introduce a novel, accelerated inverse design method for high-Q resonant cavities.
• To enhance the optimization of local density of states (LDOS).
• To demonstrate the method's applicability to other resonant-response metrics.

Main Methods:

• Utilizing a fast shift-invert eigensolver for optimization.
• Centering LDOS optimization around a strong resonance peak.
• Overcoming ill-conditioning issues in sharp resonance optimization.

Main Results:

• Achieved orders-of-magnitude acceleration in inverse design.
• Successfully designed 1D and 2D dielectric resonant cavities with Q > 10^6.
• Demonstrated robustness for Q >> 100, overcoming previous limitations.

Conclusions:

• The new method significantly speeds up inverse design for high-Q cavities.
• This approach is broadly applicable to various resonant-response optimization problems.
• Enables the design of ultra-high-Q cavities previously intractable.