Topological Photonics in 3D Photonic Structures
Open Access
- Author:
- Noh, Jiho
- Graduate Program:
- Physics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 30, 2020
- Committee Members:
- Mikael Caleb Rechtsman, Dissertation Advisor/Co-Advisor
Mikael Caleb Rechtsman, Committee Chair/Co-Chair
Chaoxing Liu, Committee Member
Cuizu Chang, Committee Member
Noel Christopher Giebink, Outside Member
Richard Wallace Robinett, Program Head/Chair - Keywords:
- Topological Photonics
Higher-Order Topological Insulators
Weyl Points - Abstract:
- Topological insulators are materials that have an insulating bulk but robust conducting states on their edges. These states are topologically protected in the sense that they are inherently robust to defects and disorders that are unavoidable in all materials platforms. The growing interest on this topic has been highlighted by the 2016 Nobel Prize in Physics, which was awarded “for theoretical discoveries of topological phase transitions and topological phases of matter” to David J. Thouless, F. Duncan M. Haldane, and J. Michael Kosterlitz. Recently, it was experimentally demonstrated that photonic edge states could be “topologically protected” in diverse artificial dielectric structures called photonic topological insulators. This implies both new opportunities to study more exotic topological models due to the diversity and flexibility of the photonic platforms, and potential technological applications for robust photonic devices even in the presence of fabrication imperfections. From these realization of photonic topological insulators started a research field of topological photonics, which is a rapidly emerging field in which ideas from topological physics are incorporated to design and control the behavior of light. In this dissertation, we present a collection of studies on topological photonics using lattices of directly-written evanescently-coupled single-mode waveguides and three-dimensional photonic crystals. In the first part, we present our studies on higher-order topological insulators. Higher-order topological insulator is a new phase of matter, in which states being topologically protected are two or more dimensions lower than the system dimension, in contrast to the conventional topological insulators which possess states being protected that are only a single dimension lower than the system dimension. For the first time in any experimental platform, we experimentally demonstrated the higher-order topological insulator by observing the presence of a topologically protected zero-dimensional state localized at the corners of a femtosecond-laser-written waveguide array, and we have shown that this system can be used to topologically protect the mode frequency at mid-gap and to minimize mode volume. In addition, we studied a higher-order topological pumping using femtosecond-laser-written waveguide array, where we observe corner-to-corner transport through nontrivial adiabatic pumping cycles in 2D crystals with vanishing dipole moments. This observation of higher-order topological pumping is equivalent to studying chiral hinge states in a 3D topological system, since mapping the dynamical phenomenon demonstrated here from two spatial and one temporal to three spatial dimensions, this transport is equivalent to the observation of the chiral nature of the gapless hinge states in a 3D second-order topological insulator. In the second part, we present two different experimental demonstrations of photonic Weyl points. A Weyl point is a point degeneracy between two bands in a three-dimensional bandstructure, with linear dispersion in all three dimensions in its vicinity, which is the simplest topological degeneracy that can exist in the three-dimensional space. First, we realized a type-II Weyl point at optical wavelengths using femtosecond-laser-written waveguide array, where we observed two different signatures of a type-II Weyl point: conical diffraction at the Weyl-point wavelength and Fermi-arc surface states above the Weyl-point wavelength. This work is the first demonstration of a Weyl-point in the optical wavelength regime, which opened up the possibilities of studying complex phenomena as a result of an interplay between the Weyl dispersion and non-Hermitian, nonlinear, and quantum optics, etc. Also, we realized a charge 2 Weyl point in a low-contrast PhC fabricated by direct laser writing using Nanoscribe, where we experimentally observed the Weyl point from a reflection spectrum obtained by Fourier-transform infrared spectroscopy. This work also shows that the wavelength of Weyl points in such a 3D structure can be tuned between near-IR and mid-IR wavelength range by simply changing the lattice constant and that it is possible to observe the topological phenomenon in 3D PhCs even without high-contrast materials. In the third part, we present our experimental realization of a time-reversal invariant photonic topological insulator by incorporating the idea of the ‘valley-Hall effect’ from solid-state physics into analogous photonic structures using the femtosecond-laser-written waveguide array. Here, we observed the existence of valley-Hall topological edge states at the boundaries between two different inversion-symmetry-broken honeycomb photonic lattices. This study shows the possibility to open very large band gaps, which allows us to study in a regime that was not possible in solid-state 2D materials, and has the technological application as a straightforward route to realizing time-reversal invariant topological edge states, which can directly be applied to nanoscale on-chip photonics. In the fourth part, we present our work on a non-Abelian braiding of photonic topological zero modes. In this work, we directly realized the braiding of photonic topological zero modes localized at the vortices of an order parameter using the femtosecond-laser-written waveguide arrays, and we measured the non-Abelian Berry phase that varies according to the direction of the braiding process using an interferometer constructed using waveguides. This study of non-Abelian braiding in a classical system of optical waveguide arrays will be a good platform to be further developed for quantum systems, where the non-Abelian braiding can be used as a basis for robust quantum information processing.