We propose an open-boundary method for the simulation of the modes of confining dielectric structures. The technique is inclusive of normal modes, but is especially advantageous for the simulation of quasi-normal, or leaky, modes. The central idea is to utilize the asymptotic form of targeted solutions to eliminate the outer part of the computational domain and bring the numerical boundary close to the simulated structure. While a similar approach was previously demonstrated for scalar quantum models, here we put forward a generalization for fully vectorial fields. Accuracy in this new context is validated using step-index and tube-type hollow core fiber geometries. The method has broad applicability, as quasi-bound modes are intrinsic to many systems of interest in optics and photonics.

We investigate novel transparent boundary conditions that reduce the size of quasi-bound state simulations in open systems. This method has applications in many areas, including tunneling ionization rates and leaky modes in fibers.

We numerically investigate the nonlinear propagation of long-wavelength, higher order Bessel pulses in the atmosphere. We show that 10 micron higher order Bessel beams can generate more homogeneous plasma channels than their 800 nm counterparts. We utilize 4th-order 10.23 μm Bessel wavepackets to create tunable transient plasma tubes in air, and show that they are well suited for the guiding of THz radiation with exceptionally low losses.

A method is presented for transparent, energy-dependent boundary conditions for open, non-Hermitian systems, and is illustrated on an example of Stark resonances in a single-particle quantum system. The approach provides an alternative to external complex scaling, and is applicable when asymptotic solutions can be characterized at large distances from the origin. Its main benefit consists in a drastic reduction of the dimesnionality of the underlying eigenvalue problem. Besides application to quantum mechanics, the method can be used in other contexts such as in systems involving unstable optical cavities and lossy waveguides.