# Euler–Lagrange equations for full topology optimization of the Q-factor in leaky cavities

@article{Eller2019EulerLagrangeEF, title={Euler–Lagrange equations for full topology optimization of the Q-factor in leaky cavities}, author={Matthias Eller and Illya M. Karabash}, journal={2021 Days on Diffraction (DD)}, year={2019}, pages={29-35} }

We derive Euler–Lagrange equations for the structural optimization of exponential decay rate of standing waves in 3-D leaky optical cavities. This leads to a new class of time-harmonic differential or integro-differential equations, which can be written as nonlinear Maxwell equations with switching functions of special types. Our approach is based on the notion of Pareto optimal frontier and on the multi-parameter perturbation theory for eigenvalues.

## One Citation

### M-dissipative boundary conditions and boundary tuples for Maxwell operators

- MathematicsJournal of Differential Equations
- 2022

## References

SHOWING 1-10 OF 42 REFERENCES

### Formulation for scalable optimization of microcavities via the frequency-averaged local density of states.

- PhysicsOptics express
- 2013

We present a technique for large-scale optimization of optical microcavities based on the frequency-averaged local density of states (LDOS), which circumvents computational difficulties posed by…

### Optimization of scattering resonances

- Physics
- 2008

The increasing use of micro- and nano-scale components in optical, electrical, and mechanical systems makes the understanding of loss mechanisms and their quantification issues of fundamental…

### Optimization of quasi-normal eigenvalues for 1-D wave equations in inhomogeneous media; description of optimal structures

- MathematicsAsymptot. Anal.
- 2013

It is proved that optimal structures are piecewise constant functions taking only two extreme possible values $b_1$ and $b-2$ and this result explains an effect recently observed in numerical experiments.

### Optimization of the Q factor in photonic crystal microcavities

- Physics
- 2002

We express the quality factor of a mode in terms of the Fourier transforms of its field components and prove that the reduction in radiation loss can be achieved by suppressing the mode's wavevector…

### Optimization of resonances in photonic crystal slabs

- PhysicsSPIE Optics + Photonics
- 2003

Variational methods are applied to the design of a two-dimensional lossless photonic crystal slab to optimize resonant scattering phenomena. The method is based on varying properties of the…

### On the strong unique continuation principle for inequalities of Maxwell type

- Mathematics
- 1991

Our goal of this paper is to prove Carleman-type inequalities for solutions a of Maxwell type inequalities |curl a|+|div(αa)|≤cre −1 |a| assuming α ij eC 0.1 in a neighborhood of 0. Such inequalities…

### Resonance free regions and non-Hermitian spectral optimization for Schrödinger point interactions

- Physics
- 2017

Resonances of Schrodinger Hamiltonians with point interactions are considered. The main object under the study is the resonance free region under the assumption that the centers, where the point…

### Long-Lived Scattering Resonances and Bragg Structures

- MathematicsSIAM J. Appl. Math.
- 2013

The structural design problem: Find a refractive index profile $n_\star({\bf x})$ within an admissible class which has a scattering frequency with minimal imaginary part is studied, defined in terms of the compact suppo...