### Abstract

We investigate theoretically the confinement of light in a three-dimensional (3D) superlattice of cavities that is embedded in a 3D photonic band gap crystal. Such a superlattice serves to trap photons and manipulate their behavior, which is relevant in applications like photovoltaic absorp¬tion enhancement, Anderson localization of light [And58], or photonic computing [Har08].
As a host of the 3D superlattice we choose the so-called inverse woodpile structure that consists of two perpendicular sets of pores in a high-refractive-index backbone. Inverse woodpile crystals made from silicon, as realized in our group, have a broad 3D photonic band gap [Lei11], ideal for cavity confinement. Cavities are defined in the inverse woodpile structure by introducing two proximate defect pores to have smaller radius than the other pores [Wol14]. Near the intersection of the de¬fect pores, excess silicon traps light. Indeed, band structure calculations reveal flat defect bands in the band gap, typical of cavity resonances. For the optimal pore size for the band gap, the single-cavity resonances are identified to have quadrupolar symmetry [Dev19]. When the band gap cavities are weakly coupled in a superlattice, light effectively hops from cavity to cavity, along main Cartesian (x,y,z) directions, hence the name “Cartesian light” [Hac19].
It seems that resonances (and the band gap) are strong functions of the crystal pore radius and the defect pore radius. But this behavior has to date not been mapped, whereas such a map is crucial to interpret ongoing experiments, where real crystals have pore radii that differ from the design, or pore radii that depend on the location where the crystal is probed. Here, we set out to obtain such a map, and study whether the resonances remain quadrupolar. We use the plane-wave expansion with supercells to assess the open questions. In certain parts of parameter space, the number of resonances changes drastically compared to the known behavior: there are sometimes just a few (perhaps displaying dipolar behavior) and in other ranges 11 to 13 resonances that are attributed to higher order multipoles. At the same time our results show good agreement with available experimental data and offer new insights into the physics of light confinement and propagation through 3D nanostructures.
REFERENCES
[And58] P.W. Anderson, Phys. Rev. 109, 1492 (1958)
[Dev19] D. Devashish, et al., Phys. Rev. B 99, 075112 (2019)
[Hac19] S.A. Hack, J.J.W. van der Vegt, and W.L. Vos, Phys. Rev. B 99, 115308 (2019)
[Ho94] K. Ho, C. Chan, C. Soukoulis, R. Biswas, M. Sigalas, Solid State Commun. 89, 413 (1994)
[Har08] M.J. Hartmann, F.G.S.L. Brandao, and M.B. Plenio, Laser & Photon. Rev. 2, 527 (2008)
[Lei11] M.D. Leistikow, et al., Phys. Rev. Lett. 107, 193903 (2011)
[Wol14] L.A. Woldering, A.P. Mosk, and W.L. Vos, Phys. Rev. B. 90, 115140 (2014)

Original language | English |
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Publication status | Published - 10 Oct 2019 |

Event | 44th Woudschoten Conference 2019 - Woudschoten Conference Center, Zeist, Netherlands Duration: 9 Oct 2019 → 11 Oct 2019 Conference number: 44 https://wsc.project.cwi.nl/woudschoten-conferences/2019-woudschoten-conference |

### Conference

Conference | 44th Woudschoten Conference 2019 |
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Country | Netherlands |

City | Zeist |

Period | 9/10/19 → 11/10/19 |

Internet address |

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## Cite this

Kozon, M., Hack, S. A., van der Vegt, J. J. W., Schlottbom, M., Lagendijk, A., & Vos, W. L. (2019).

*Numerical computation of light confinement in realistic 3D cavity superlattices*. Poster session presented at 44th Woudschoten Conference 2019, Zeist, Netherlands.