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Eigenvalue-accelerated LDOS optimization of high-Q optical resonances.

George Shaker, Beñat Martinez de Aguirre Jokisch, Pengning Chao

|March 18, 2026

Summary

This summary is machine-generated.

We developed a new inverse design method for high-Q resonant cavities. This approach accelerates optimization of the local density of states (LDOS) by using a shift-invert eigensolver, enabling designs with Q > 10^6.

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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.