Related papers: Scalable numerical approach for the steady-state a…
We review our recent work leading to steady-state solutions of the semiclassical (Maxwell-Bloch) equations of a laser. These are coupled non-linear partial differential equations in space and time which have previously been solved either by…
We show that Steady-state Ab initio Laser Theory (SALT) can be applied to find the stationary multimode lasing properties of an N-level laser. This is achieved by mapping the N-level rate equations to an effective two-level model of the…
We improve the steady-state ab initio laser theory (SALT) of Tureci et al. by expressing its fundamental self-consistent equation in a basis set of threshold constant flux states that contains the exact threshold lasing mode. For cavities…
We investigate the range of validity of the recently developed steady-state ab-initio laser theory (SALT). While very efficient in describing various microlasers, SALT is conventionally believed not to be applicable to lasers featuring…
Studying time-dependent behavior in lasers is analytically difficult due to the saturating non-linearity inherent in the Maxwell-Bloch equations and numerically demanding because of the computational resources needed to discretize both time…
A linear scaling method for calculation of the static {\em ab inito} response within self-consistent field theory is developed and applied to calculation of the static electric polarizability. The method is based on density matrix…
We present a general method to obtain the stable lasing solutions for the steady-state ab-initio lasing theory (SALT) for the case of a degenerate symmetric laser in two dimensions (2d). We find that under most regimes (with one…
We propose a scalable method for implementing linear optics quantum computation using the ``linked-state'' approach. Our method avoids the two-dimensional spread of errors occurring in the preparation of the linked-state. Consequently, a…
A self-consistent integral equation is formulated and solved iteratively which determines the steady-state lasing modes of open multi-mode lasers. These modes are naturally decomposed in terms of frequency dependent biorthogonal modes of a…
We present a perturbative technique for modeling the scattering of light by a nonlinear material. This approach eliminates the need for an iterative algorithm to solve the fully coupled nonlinear problem. We demonstrate its effectiveness in…
We investigate the scattering of light by a nonlinear, anisotropic slab under conical incidence and arbitrary polarization, within the framework of Maxwell's equations, where the nonlinearities are described by nonlinear susceptibility…
We present an ab-initio treatment of the steady-state of lasers with injected signals that describes a regime, valid for micro lasers, in which the locking transition is dominated by cross-saturation and spatial hole-burning. The theory…
We derive and test a generalization of Steady-State Ab Initio Laser Theory (SALT) to treat complex gain media. The generalized theory (C-SALT) is able to treat atomic and molecular gain media with diffusion and multiple lasing transitions,…
We present a method to determine the equilibrium geometry of large atomistic systems with linear scaling. It is based on a separate treatment of long and short wavelength components of the forces. While the rapidly varying part is handled…
Iterative multiscale methods for electronic structure calculations offer several advantages for large-scale problems. Here we examine a nonlinear full approximation scheme (FAS) multigrid method for solving fixed potential and…
We propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a $p$-adic lifting technique combined with the use of block matrices with structured blocks. It achieves a sub-cubic…
We numerically examine the exterior solution of spherically symmetric and static configuration in scalar-tensor theories by using the nonminimally coupled scalar field with zero potential as our sample model. Our main purpose in this work…
It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the…
The construction of stochastic solutions for nonlinear partial differential equations is a powerful method to obtain new exact results and to develop efficient numerical algorithms, in particular when domain decomposition techniques are…
We propose a principled method for projecting an arbitrary square matrix to the non-convex set of asymptotically stable matrices. Leveraging ideas from large deviations theory, we show that this projection is optimal in an…