Related papers: Eigenfunction and eigenmode-spacing statistics in …
We present a systematic numerical approach to compute the eigenmodes and the related eigenfrequencies of a disordered photonic crystal, characterized by small fluctuations of the otherwise periodic dielectric profile. The field eigenmodes…
We study wave function structure for quantum graphs in the chaotic and disordered regime, using measures such as the wave function intensity distribution and the inverse participation ratio. The result is much less ergodicity than expected…
We propose a new class of one-dimensional (1D) photonic waveguides: the fractal photonic crystal waveguides (FPCWs). These structures are photonic crystal waveguides (PCWs) etched with fratal distribution of grooves such as Cantor bars. The…
Distributions of eigenmodes are widely concerned in both bounded and open systems. In the realm of chaos, counting resonances can characterize the underlying dynamics (regular vs. chaotic), and is often instrumental to identify…
Photonic crystal waveguides (PCWs) allow for the engineering of photonic modes and band structures to control the flow of light and light-matter interactions within the waveguide. They have shown potential for enhancing optical…
The great interest to the two and three dimensionally periodic structures, called photonic crystals (PCs), has begun with the pioneer works of Yablonovitch and John as one can efficiently control the propagation of the electromagnetic (EM)…
In studies on complex network systems using graph theory, eigen-analysis is typically performed on an undirected graph model of the network. However, when analyzing cascading failures in a power system, the interactions among failures…
Topological photonic crystals (PCs) can support robust edge modes to transport electromagnetic energy in an efficient manner. Such edge modes are the eigenmodes of the PDE operator for a joint optical structure formed by connecting together…
The eigenfunctions of quantized chaotic systems cannot be described by explicit formulas, even approximate ones. This survey summarizes (selected) analytical approaches used to describe these eigenstates, in the semiclassical limit. The…
A gas of interacting particles is a paradigmatic example of chaotic systems. It is shown here that even if all but one particle are fixed in generic positions, the excited states of the moving particle are chaotic. They are characterized by…
We introduce a theory to describe disorder-induced scattering in photonic crystal waveguides, specifically addressing the influence of local field effects and scattering within high-index-contrast perturbations. Local field effects are…
Photonic crystal (PC) coupled cavity waveguides (CCWs) with \textit{completely separated eigenfrequencies} (or supermodes) are investigated. Using a coupled mode theory, the properties of the supermodes, such as the electric field profiles,…
We study the distribution of eigenfrequency spacings (the so-called level spacing statistics) for light in a two-dimensional (2D) disordered photonic crystal composed of circular dielectric (silicon) rods in air. Disorder introduces…
The phonon propagation dynamics in a phononic crystal waveguide, realized via a suspended one-dimensional membrane array with periodic air holes, is investigated as function of its geometry. The bandstructure of the phononic crystal can be…
We provide a versatile plateform to investigate wave-particle duality. This photonic waveguide network implements quantum (wave) graphs as proposed in the seminal paper by Kottos \& Smilansky [PRL \textbf{85} 968 (2000)]. We experimentally…
Traditionally, one can construct a waveguide by introduce defects into surface-wave photonic crystals (SPCs). Here we propose a new structure named closed SPC that can introduce waveguide modes out of photonic bandgap of surface-wave…
We describe analytical and numerical results on the statistical properties of complex eigenvalues and the corresponding non-orthogonal eigenvectors for non-Hermitian random matrices modeling one-channel quantum-chaotic scattering in systems…
We present a semi-analytic method to calculate the dispersion curves and the group velocity of photonic crystal waveguide modes in two-dimensional geometries. We model the waveguide as a homogenous strip, surrounded by photonic crystal…
We present experimental results on eigenfunctions of a wave chaotic system in the continuous crossover regime between time-reversal symmetric and time-reversal symmetry-broken states. The statistical properties of the eigenfunctions of a…
Phononic crystals (PnCs) are periodic engineered media that can customize the spatio-temporal characteristics of mechanical energy propagation. PnCs that additionally leverage precisely embedded defects can achieve robust energy…