Resonant states in double and triple quantum wells

The full set of resonant states in double and triple quantum well/barrier structures is investigated. This includes bound, anti-bound and normal resonant states which are all eigensolutions of Schrodinger's equation with generalized outgoing wave boundary conditions. The transformation of resonant states and their transitions between different subgroups as well as the role of each subgroup in observables, such as the quantum transmission, is analyzed. The quantum well potentials are modeled by Dirac delta functions; therefore, as part of this study, the well-known problem of bound states in delta-like potentials is also revisited.Comment: 10 pages, 11 figure

Dipolar polaritons in microcavity-embedded coupled quantum wells in electric and magnetic fields

We present a microscopic calculation of spatially indirect exciton states in semiconductor coupled quantum wells and polaritons formed from their coupling to the optical mode of a microcavity. We include the presence of electric and magnetic fields applied perpendicular to the quantum well plane. Our model predicts the existence of polaritons that are in the strong-coupling regime and at the same time possess a large static dipole moment. We demonstrate, in particular, that a magnetic field can compensate for the reduction in light-matter coupling that occurs when an electric field impresses a dipole moment on the polariton

Excitons and polaritons in planar heterostructures in external electric and magnetic fields: A multi-sub-level approach

Excitons and microcavity polaritons that possess a macroscopic dipole alignment are attractive systems to study. This is due to an enhancement of collective many body effects and an ability to electrostatically control their transport and internal structure. Here, we present an overview of a rigorous calculation of spatially-indirect exciton states in semiconductor coupled quantum wells in externally applied electric and magnetic fields. We also treat dipolaritons that form when such structures are positioned at the antinode of a resonant cavity mode. Our approach is general and can be applied to various planar solid state heterostructures inside optical resonators. It offers a thorough description of the properties of excitons and polaritons that are important for modelling their respective fluids. In particular, we calculate the exciton Bohr radius, binding energy, optical lifetime and magnetic field induced enhancement of the effective mass. We also describe electric and magnetic field control of the exciton and polariton dipole moment and brightness

Resonant states in double and triple quantum wells

The full set of resonant states in double and triple quantum well/barrier structures is investigated. This includes bound, anti-bound and normal resonant states which are all eigensolutions of Schrödinger's equation with generalized outgoing wave boundary conditions. The transformation of resonant states and their transitions between different subgroups as well as the role of each subgroup in observables, such as the quantum transmission, is analyzed. The quantum well potentials are modeled by Dirac delta functions; therefore, as part of this study, the well known problem of bound states in delta-like potentials is also revisited

Resonant-state expansion applied to one-dimensional quantum systems

The resonant state expansion, a rigorous perturbation theory, recently developed in electrodynamics, is applied to non-relativistic quantum mechanical systems in one dimension. The method is used here for finding the resonant states in various potentials approximated by combinations of Dirac delta functions. The resonant state expansion is first verified for a triple quantum well system, showing convergence to the available analytic solution as the number of resonant states in the basis increases. The method is then applied to multiple quantum well and barrier structures, including finite periodic systems. Results are compared with the eigenstates in triple quantum wells and infinite periodic potentials, revealing the nature of the resonant states in the studied systems.Comment: 10 pages, 7 figure

Accidental and symmetry-protected bound states in the continuum in planar photonic-crystal structures, studied by the resonant-state expansion

The resonant-state expansion (RSE) provides a precise and computationally cheap tool to find resonant states in complex systems using the optical modes of a simpler system as a basis. We apply the RSE to a photonic crystal slab in order to identify and analyze its bound states in the continuum (BICs). We show that the RSE is a useful and reliable method for not only finding the BICs but also for differentiating between accidental and symmetry-protected BICs, as well as for understanding their formation from the basis modes and evolution with structural and material parameters of the system. The high efficiency of the RSE allows us to track the properties of BICs and other high-quality optical modes, covering the full parameter space of the system in a reasonable time frame

Comment on "normalization of quasinormal modes in leaky optical cavities and plasmonic resonators"

Recently, Kristensen, Ge and Hughes have compared [Phys. Rev. A 92, 053810 (2015)] three di�erent methods for normalization of quasinormal modes in open optical systems, and concluded that they all provide the same result. We show here that this conclusion is incorrect and illustrate that the normalization of [Opt. Lett. 37, 1649 (2012)] is divergent for any optical mode having a �nite quality factor, and that the Silver-M�uller radiation condition is not ful�lled for quasinormal modes

Resonant-state expansion for planar photonic-crystal structures

We present a powerful concept in the field of photonic crystals and metamaterials, applying the resonant-state expansion (RSE) to planar photonic crystal structures. The RSE allows us to understand and quantify optical resonances in photonic crystal structures in terms of the analytic resonant states of a homogeneous planar waveguide. The RSE provides an efficient and reliable tool for accurate calculation of a complete set of the resonant states of a photonic crystal slab, which is required for the correct description and a better understanding of its optical spectra. For the proof of principle, numerical verification of the RSE, and demonstration of its unprecedented accuracy and convergence, an infinite planar photonic crystal slab periodic in one dimension is taken as an example. To illustrate the power of this approach, we consider the mode evolution with the amplitude of the periodic modulation, revealing the role of the guided modes in the formation of bound states in the continuum

Optimizing the Drude-Lorentz model for material permittivity: Examples for semiconductors

Approximating the frequency dispersion of the permittivity of materials with simple analytical functions is of fundamental importance for understanding and modeling their optical properties. Quite generally, the permittivity can be treated in the complex frequency plane as an analytic function having a countable number of simple poles which determine the dispersion of the permittivity, with the pole weights corresponding to generalized conductivities of the medium at these resonances. The resulting Drude-Lorentz model separates the poles at frequencies with zero real part (Ohm's law and Drude poles) from poles with finite real part (Lorentz poles). To find the parameters of such an analytic function, we minimize the error weighted deviation between the model and measured values of the permittivity. We show examples of such optimizations for various semiconductors (Si, GaAs and Ge), for different frequency ranges and up to five pairs of Lorentz poles accounted for in the model.Comment: arXiv admin note: substantial text overlap with arXiv:1612.0692

How to calculate the pole expansion of the optical scattering matrix from the resonant states

We present a formulation for the pole expansion of the scattering matrix of open optical resonators, in which the pole contributions are expressed solely in terms of the resonant states, their wave numbers, and their electromagnetic fields. Particularly, our approach provides an accurate description of the optical scattering matrix without the requirement of a fit for the pole contributions, or the restriction to geometries, or systems with low Ohmic losses. Hence, it is possible to derive the analytic dependence of the scattering matrix on the wave number with low computational effort, which allows for avoiding the artificial frequency discretization of conventional frequency-domain solvers of Maxwell's equations and for finding the optical far- and near-field response based on the physically meaningful resonant states. This is demonstrated for three test systems, including a chiral arrangement of nanoantennas, for which we calculate the absorption and the circular dichroism