Related papers: Universal threshold and Arnold tongues in Kerr rin…
In the recent experiments the unusual oscillatory magnetoresistance in superconductors was discovered with a periodicity essentially independent on magnetic field direction and even material parameters. The nearly universal period points to…
We study the solutions to the wave equation in a two-dimensional tube of unit width comprised of two straight regions connected by a region of constant curvature. We introduce a numerical method which permits high accuracy at high…
Ultrashort pulses from Kerr-lens mode-locked oscillators have inspired a variety of applications. The design and alignment of these laser resonators have thus far been theoretically supported by the conventional analysis of beam…
We analyze dark pulse Kerr frequency combs in optical resonators with normal group-velocity dispersion using the Lugiato-Lefever model. We show that in the time domain these correspond to interlocked switching waves between the upper and…
Gap modes in a modified Mathieu equation, perturbed by a Dirac delta potential, are investigated. It is proved that the modified Mathieu equation admits stable isolated gap modes with topological origins in the unstable regions of the…
Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary…
We use numerical simulations based on an extended Lugiato-Lefever equation (LLE) to investigate the stability properties of Kerr frequency combs generated in microresonators. In particular, we show that an ensemble average calculated over…
We obtain a bound on the expectation of the spectral shift function for alloy-type random Schr\"odinger operators on $\mathbb{R}^d$ in the region of localisation, corresponding to a change from Dirichlet to Neumann boundary conditions along…
The Katz-Sarnak density conjecture states that, as the analytic conductor $R \to \infty$, the distribution of the normalized low-lying zeros (those near the central point $s = 1/2$) converges to the scaling limits of eigenvalues clustered…
An optical ring resonator with third-order, or Kerr, nonlinearity will exhibit symmetry breaking between the two counterpropagating circulating powers when pumped with sufficient power in both the clockwise and counterclockwise directions.…
We consider interaction of counter-propagating waves in a bi-directionally pumped ring microresonator with Kerr nonlinearity. We introduce a hierarchy of the mode expansions and envelope functions evolving on different time scales set by…
Expander (Tanner) codes combine sparse graphs with local constraints, enabling linear-time decoding and asymptotically good distance--rate tradeoffs. A standard constraint-counting argument yields the global-rate lower bound $R\ge 2r-1$ for…
The recent demonstration of dissipative Kerr solitons in microresonators has opened a new pathway for the generation of ultrashort pulses and low-noise frequency combs with gigahertz to terahertz repetition rates, enabling applications in…
We predict the existence of a novel type of temporal localized structure in injected Kerr--Gires--Tournois interferometers (KGTI). These bright pulses exist in the normal dispersion regime, yet they do not correspond to the usual scenario…
We consider a two dimensional magnetic Schroedinger operator with a spatially stationary random magnetic field. We assume that the magnetic field has a positive lower bound and that it has Fourier modes on arbitrarily short scales. We prove…
Parametric nonlinear optical processes allow for the generation of new wavelengths of coherent electromagnetic radiation. Their ability to create radiation that is widely tunable in wavelength is particularly appealing, with applications…
We propose an Ansatz for Universal conductance fluctuations in continuous dimensions from 0 up to 4. The Ansatz agrees with known formulas for integer dimensions 1, 2 and 3, both for hard wall and periodic boundary conditions. The method is…
We study systems with a crossover parameter lambda, such as the temperature T, which has a threshold value lambda* across which the correlation function changes from exhibiting fixed wavelength (or time period) modulations to continuously…
We show that introducing quenched disorder into a circle map leads to the suppression of quasiperiodic behavior in the limit of large system sizes. Specifically, for most parameters the fraction of disorder realizations showing…
Optical frequency combs generated in normally dispersive Kerr microresonators have been observed to correspond to dark temporal structures, and theoretically explained as interlocked switching waves (also known as domain walls or fronts).…