Related papers: Fundamental limits on $\chi^{(2)}$ second harmonic…
At the fundamental level, full description of light-matter interaction requires quantum treatment of both matter and light. However, for standard light sources generating intense laser pulses carrying quadrillions of photons in a coherent…
The power flow equations are fundamental to power system planning, analysis, and control. However, the inherent non-linearity and non-convexity of these equations present formidable obstacles in problem-solving processes. To mitigate these…
A finite element method for the evolution of a two-phase membrane in a sharp interface formulation is introduced. The evolution equations are given as an $L^2$--gradient flow of an energy involving an elastic bending energy and a line…
Highly resonant photonic structures, such as cavities and metasurfaces, can dramatically enhance the efficiency of nonlinear processes by utilizing strong optical field enhancement at the resonance. The latter, however, comes at the expense…
We study second harmonic generation in a planar dielectric waveguide having a low-index, polymer core layer, bounded by two multilayer stacks. This geometry allows exceptionally strong confinement of the light at the fundamental wavelength…
Conic programs arise broadly in physics, quantum information, machine learning, and engineering, many of which are defined over sparse graphs. Although such problems can be solved in polynomial time using classical interior-point solvers,…
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…
We observe enhanced second-harmonic generation in monolayer graphene in the presence of an ultra-strong terahertz field pulse with a peak amplitude of 250 kV/cm. This is a strongly nonperturbative regime of light-matter interaction in which…
A theory is developed and applied to the study of opportunities and specific features of coherent control of four-wave mixing as well as of the accompanying processes in the continuous-wave regime, which involve transitions between bound…
We study the weak universality of the two-dimensional fractional nonlinear wave equation. For a sequence of Hamiltonians of high-degree potentials scaling to the fractional $\Phi_2^4$, we first establish a \emph{sufficient and almost…
We present experimental and simulated results to quantify the impact of nonlinear noise in integrated photonic devices relying on spontaneous four-wave mixing. Our results highlight the need for design rule adaptations to mitigate the…
We introduce an accurate non-Hermitian Schr\"odinger-type approximation of Bloch optical equations for two-level systems. This approximation provides a complete description of the excitation, relaxation and decoherence dynamics in both weak…
The interpretation proposed in quant-ph/9812011 is extended to the general case of a non-relativistic particle moving in an arbitrary external potential. It is shown that, even in this general case, "particle" solutions exist which do not…
The optimal design for infrared second harmonic generation (SHG) is determined for a GaAs-based quantum device using a recently developed genetic approach. Both compositional parameters and electric field are simultaneously optimized, and…
Theoretical limits and physical bounds across many areas of science, mathematics, and technology -- including Shannon's information-capacity limits, Bennett and Landauer's thermodynamic limits on computation, and G\"odel's incompleteness…
Second-harmonic generation (SHG) is a fundamental nonlinear optical process widely used in photonics; however, it is strictly forbidden in the bulk of centrosymmetric materials due to their inversion symmetry. Nevertheless, applying an…
We derive, by means of variational techniques, a limiting description for a class of integral functionals under linear differential constraints. The functionals are designed to encode the energy of a high-contrast composite, that is, a…
This is the second step of a program to use anharmonic plane waves as basis set in non-perturbative quantum field theory. The general framework developed previously is applied to quantum electrodynamics. To test the compatibility with…
Second-order nonlinearity gives rise to many distinctive physical phenomena, e.g., second-harmonic generation, which plays an important role in fundamental science and various applications. Lithium niobate, one of the most widely used…
The motive of this work is to understand the complex spatial characteristics of finite-amplitude elastic wave propagation in periodic structures and leverage the unique opportunities offered by nonlinearity to activate complementary…