Topological optimization aims to find a material distribution (typically solid) that optimizes a
given response. For example, in structural mechanics, the objective is to determine the density
distribution of a beam to support a given load [1]. At the same time, one may also aim to use
the least amount of material to reduce manufacturing costs. In nanophotonics, there are several
examples of devices designed to control and modify the propagation and properties of light, such
as mode converters [2], wavelength demultiplexers [3], and nonlinear port switchers [4]. In these
cases, the minimum feature sizes are often subwavelength scale [5], that is, smaller than the oper-
ating wavelength. Topological optimization typically employs gradient descent algorithms to op-
timize an objective function, which represents the device’s intended functionality. Concurrently,
the adjoint problem must be solved, enabling the computation of the sensitivity or dependence of
the objective function with respect to the design variables [6]. This method has attracted signif-
icant interest in both mechanics and photonics due to its strong algorithmic performance and its
ability to discover devices with non-intuitive geometries. In this work, we aim to present a new
model for designing optomechanical cavities, initially focused on enhancing the optomechanical
coupling rate in the dispersive regime because of its significant implications for microwave signal
conversion, quantum information processing [7] and others.

[1] Boyan Stefanov Lazarov and Ole Sigmund. Filters in topology optimization based on
helmholtz-type differential equations. International journal for numerical methods in en-
gineering, 86(6):765–781, 2011.
[2] Rasmus E Christiansen. Inverse design of optical mode converters by topology optimization:
tutorial. Journal of Optics, 25(8):083501, 2023.
[3] Logan Su, Dries Vercruysse, Jinhie Skarda, Neil V Sapra, Jan A Petykiewicz, and Jelena
Vuˇckovi´c. Nanophotonic inverse design with spins: Software architecture and practical con-
siderations. Applied Physics Reviews, 7(1), 2020.
[4] Tyler W Hughes, Momchil Minkov, Ian AD Williamson, and Shanhui Fan. Adjoint method
and inverse design for nonlinear nanophotonic devices. ACS Photonics, 5(12):4781–4787,
2018.
[5] Sean Molesky, Zin Lin, Alexander Y Piggott, Weiliang Jin, Jelena Vuckovi´c, and Alejan-
dro W Rodriguez. Inverse design in nanophotonics. Nature Photonics, 12(11):659–670,
2018.
[6] Paolo Luchini and Alessandro Bottaro. An introduction to adjoint problems. arXiv preprint
arXiv:2404.17304, 2024.
[7] K. Stannigel, P. Komar, S. J.M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl.
Optomechanical quantum information processing with photons and phonons.