Quantum Optics Seminar: Ole Sigmund and Rasmus Ellebæk Christiansen, DTU

Topology Optimization of Nanophotonic Device for Extreme Light Manipulation

Topology Optimization (TO) [1-2] is an inverse design tool originally developed for mechanical design which has developed tremendously over the last decades. This progress has, a.o., been fueled by the developments in additive manufacturing (AM). The fundamental concept of freely distributing material in a design domain to optimize some physical figure of merit is general and is being applied in multiple physics settings including fluids, acoustics, and photonics.

TO as an inverse design tool for photonic devices and periodic media [3] has especially experienced a rapidly growing attention in recent years [4,5]. The method has demonstrated its capacity for designing structures with novel capabilities, better performance and/or reduced device footprints compared to existing structures, as-well-as for solving complex design problems where intuition and well-established design-strategies struggle.

The talk provides a general overview of the topology optimization method as a general design tool and then delves into its specifics within the realm of electromagnetics. It further explores the method’s capability to design nano photonic structures, which adhere directly to fabrication limitations by enforcing feature-size and connectivity constraints.

Illustrative examples include inverse design and experimental exploration of a range of photonic devices such as beam splitters, optical cloaks, optical metasurfaces and plasmonic nanoparticles. Finally, we discuss the use of the method for a demonstration of light confinement to a volume significantly below an eighth of a cubic wavelength [6] (in terms of the single-emitter mode volume).

[1] M. P. Bendsøe and N. Kikuchi, “Generating optimal topologies in structural design using a homogenization method,” Comput. Methods Appl. Mech. Eng. 71, 197–224 (1988).

[2] M. P. Bendsøe and O. Sigmund “Topology Optimization - Theory, Methods and Applications” Springer-verlag Berlin And Heidelberg Gmbh & Co. K (2003).

[3] R. E. Christiansen and O. Sigmund, “Inverse design in photonics by topology optimization: tutorial,” J. Opt. Soc. 350 Am. B 38, 496–509 (2021)

[4] J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser & Photonics Rev. 5, 308–321 (2011).

[5] S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vuckovic, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12, 659–670 (2018).

[6] M. Albrechtsen, B. V. Lahijani, R. E. Christiansen, V. T. H. Nguyen, L. N. Casses, S. E. Hansen, N. Stenger, O. Sigmund, H. Jansen, J. Mørk, and S. Stobbe, “Nanometer-scale photon confinement in topology-optimized dielectric cavities,” Nat. Commun. 13, 6281 (2022).