Alexander Cerjan
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View article: Topological photonic crystal fiber
Topological photonic crystal fiber Open
Photonic crystal fibers (PCFs) provide a versatile platform for various applications, thanks to the flexibility with which light guiding can be customized by modifying the fiber geometry. We realize a PCF with guided modes produced by phot…
View article: Semiconductor Meta-Graphene and Valleytronics
Semiconductor Meta-Graphene and Valleytronics Open
Nano-patterned semiconductor interfaces offer a versatile platform for creating quantum metamaterials and exploring novel electronic phenomena. In this study, we illustrate this concept using artificial graphene--a metamaterial featuring d…
View article: Dynamically reconfigurable topological routing in nonlinear photonic systems
Dynamically reconfigurable topological routing in nonlinear photonic systems Open
The propagation path of topologically protected states is bound to the interface between regions with different topology, and as such, the functionality of linear photonic devices leveraging these states is fixed during fabrication. Here, …
View article: Classification of fragile topology enabled by matrix homotopy
Classification of fragile topology enabled by matrix homotopy Open
Flat bands in twisted materials have attracted considerable attention due to the emergence of correlated phases that can be associated with the non-Wannier-representable nature of its single-particle states. Specifically, these bands can e…
View article: Efficient first-principles inverse design of nanolasers
Efficient first-principles inverse design of nanolasers Open
We develop and demonstrate a first-principles approach, based on the nonlinear Maxwell-Bloch equations and steady-state ab-initio laser theory (SALT), for inverse design of nanostructured lasers, incorporating spatial hole-burning correcti…
View article: Detecting local topology with the spectral localizer
Detecting local topology with the spectral localizer Open
The spectral localizer is a predictive framework for the computation of topological invariants of natural and artificial materials. Here, three crucial improvements on the criterion for the validity of the framework are reported: first, me…
View article: Bi-stability and period-doubling cascade of frequency combs in exceptional-point lasers
Bi-stability and period-doubling cascade of frequency combs in exceptional-point lasers Open
Recent studies have demonstrated that a laser can self-generate frequency combs when tuned near an exceptional point (EP), where two cavity modes coalesce. These EP combs induce periodic modulation of the population inversion in the gain m…
View article: Dimensional crossover of class D real-space topological invariants
Dimensional crossover of class D real-space topological invariants Open
The topological properties of a material depend on its symmetries, parameters, and spatial dimension. Changes in these properties due to parameter and symmetry variations can be understood by computing the corresponding topological invaria…
View article: Nonlinear Topological Photonics: Capturing Nonlinear Dynamics and Optical Thermodynamics
Nonlinear Topological Photonics: Capturing Nonlinear Dynamics and Optical Thermodynamics Open
Combining multiple optical resonators or engineering dispersion of complex media has provided an effective method for demonstrating topological physics controlling photons in unprecedented ways such as unidirectional light propagation and …
View article: Topological Phenomena in Artificial Quantum Materials Revealed by Local Chern Markers
Topological Phenomena in Artificial Quantum Materials Revealed by Local Chern Markers Open
A striking example of frustration in physics is Hofstadter's butterfly, a fractal structure that emerges from the competition between a crystal's lattice periodicity and the magnetic length of an applied field. Current methods for predicti…
View article: Imaging Photonic Resonances within an All‐Dielectric Metasurface via Photoelectron Emission Microscopy
Imaging Photonic Resonances within an All‐Dielectric Metasurface via Photoelectron Emission Microscopy Open
Dielectric metasurfaces, through volume‐type photonic resonances, enable precise control of light‐matter interactions for applications including imaging, holography, and sensing. The application space of dielectric metasurfaces has extende…
View article: Classification of Fragile Topology Enabled by Matrix Homotopy
Classification of Fragile Topology Enabled by Matrix Homotopy Open
The moire flat bands in twisted bilayer graphene have attracted considerable attention not only because of the emergence of correlated phases but also due to their nontrivial topology. Specifically, they exhibit a new class of topology tha…
View article: Topological phenomena in artificial quantum materials revealed by local Chern markers
Topological phenomena in artificial quantum materials revealed by local Chern markers Open
A striking example of frustration in physics is Hofstadter's butterfly, a fractal structure that emerges from the competition between a crystal's lattice periodicity and the magnetic length of an applied field. Current methods for predicti…
View article: Robust multiresonant nonlocal metasurfaces by rational design
Robust multiresonant nonlocal metasurfaces by rational design Open
Dielectric metasurfaces supporting optical resonances have become a promising platform for quantum and nonlinear optics. However, resonant metasurfaces remain limited in their capacity to independently control the behavior of many distinct…
View article: Bi-stability and period-doubling cascade of frequency combs in exceptional-point lasers
Bi-stability and period-doubling cascade of frequency combs in exceptional-point lasers Open
Recent studies have demonstrated that a laser can self-generate frequency combs when tuned near an exceptional point (EP), where two cavity modes coalesce. These EP combs induce periodic modulation of the population inversion in the gain m…
View article: Quasinormal coupled-mode analysis of dynamic gain in exceptional-point lasers
Quasinormal coupled-mode analysis of dynamic gain in exceptional-point lasers Open
One of the key features of lasers operating near exceptional points (EPs) is that the gain medium can support an oscillating population inversion above a pump threshold, leading to self-modulated laser dynamics. This unusual behavior opens…
View article: Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory Open
Recently, the spectral localizer framework has emerged as an efficient approach to classifying topology in photonic systems featuring local nonlinearities and radiative environments. In nonlinear systems, this framework provides rigorous d…
View article: Classifying photonic topology using the spectral localizer and numerical <i>K</i>-theory
Classifying photonic topology using the spectral localizer and numerical <i>K</i>-theory Open
Recently, the spectral localizer framework has emerged as an efficient approach for classifying topology in photonic systems featuring local nonlinearities and radiative environments. In nonlinear systems, this framework provides rigorous …
View article: Quantitative measure of topological protection in Floquet systems through the spectral localizer
Quantitative measure of topological protection in Floquet systems through the spectral localizer Open
The standard understanding of topological protection from band theory is that a system's topology cannot change without first closing the bulk band gap. However, in Floquet systems, this typical definition of topological protection is one …
View article: Clifford and quadratic composite operators with applications to non-Hermitian physics
Clifford and quadratic composite operators with applications to non-Hermitian physics Open
A variety of physical phenomena, such as amplification, absorption, and radiation, can be effectively described using non-Hermitian operators. However, the introduction of non-uniform non-Hermiticity can lead to the formation of exceptiona…
View article: Classifying topology in photonic crystal slabs with radiative environments
Classifying topology in photonic crystal slabs with radiative environments Open
In the recent years, photonic Chern materials have attracted substantial interest as they feature topological edge states that are robust against disorder, promising to realize defect-agnostic integrated photonic crystal slab devices. Howe…
View article: Multivariable pseudospectrum in $C^*$-algebras
Multivariable pseudospectrum in $C^*$-algebras Open
We look at various forms of spectrum and associated pseudospectrum that can be defined for noncommuting $d$-tuples of Hermitian elements of a $C^*$-algebra. The emphasis is on theoretical calculations of examples, in particular for noncomm…
View article: Local Markers for Crystalline Topology
Local Markers for Crystalline Topology Open
Over the last few years, crystalline topology has been used in photonic crystals to realize edge- and corner-localized states that enhance light-matter interactions for potential device applications. However, the band-theoretic approaches …
View article: Classifying topology in photonic crystal slabs with radiative environments
Classifying topology in photonic crystal slabs with radiative environments Open
In the recent years, photonic Chern materials have attracted substantial interest as they feature topological edge states that are robust against disorder, promising to realize defect-agnostic integrated photonic crystal slab devices. Howe…
View article: Generating and processing optical waveforms using spectral singularities
Generating and processing optical waveforms using spectral singularities Open
Here, we show that a laser at threshold can be utilized to generate the class of coherent and transform-limited waveforms (vt — z)mei(kz—ωt) at optical frequencies. We derive these properties analytically and demonstrate them in semiclassi…