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

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

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

Exciton dephasing in quantum dots due to LO-phonon coupling: an exactly solvable model

It is widely believed that, due to its discrete nature, excitonic states in a quantum dot coupled to dispersionless longitudinal-optical (LO) phonons form everlasting mixed states (exciton polarons) showing no line broadening in the spectrum. This is indeed true if the model is restricted to a limited number of excitonic states in a quantum dot. We show, however, that extending the model to a large number of states results in LO phonon-induced spectral broadening and complete decoherence of the optical response

Extended frequency range of transverse-electric surface plasmon polaritons in graphene

The dispersion relation of surface plasmon polaritons in graphene that includes optical losses is often obtained for complex wave vectors while the frequencies are assumed to be real. This approach, however, is not suitable for describing the temporal dynamics of optical excitations and the spectral properties of graphene. Here, we propose an alternative approach that calculates the dispersion relation in the complex frequency and real wave vector space. This approach provides a clearer insight into the optical properties of a graphene layer and allows us to find the surface plasmon modes of a graphene sheet in the full frequency range, thus removing the earlier reported limitation (1.667 < $\hbar\omega/\mu$ < 2) for the transverse-electric mode. We further develop a simple analytic approximation which accurately describes the dispersion of the surface plasmon polariton modes in graphene. Using this approximation, we show that transverse-electric surface plasmon polaritons propagate along the graphene sheet without losses even at finite temperature.Comment: 13 pages, 7 figure

Scattering solution to the problem of additional boundary conditions

Maxwell's boundary conditions (MBCs) were long known to be insufficient to determine the optical responses of spatially dispersive medium. Supplementing MBCs with additional boundary conditions (ABCs) has become a normal yet controversial practice. Here, the problem of ABCs is solved by analyzing some subtle aspects of a physical surface. A generic theory is presented for handling the interaction of light with the surfaces of an arbitrary medium and applied to study the traditional problem of exciton polaritons. We show that ABCs can always be adjusted to fit the theory in the examples studied here but they can by no means be construed as intrinsic surface characteristics, which are instead captured by a surface scattering amplitude. Methods for experimentally extracting the spatial profile of this quantity are proposed

Transverse-electric surface plasmon polaritons in periodically modulated graphene

Transverse-electric (TE) surface plasmon polaritons are unique eigenmodes of a homogeneous graphene layer that are tunable with the chemical potential and temperature. However, as their dispersion curve spectrally lies just below the light line, they cannot be resonantly excited by an externally incident wave. Here, we propose a way of exciting the TE modes and tuning their peaks in the transmission by introducing a one-dimensional graphene grating. Using the scattering-matrix formalism, we show that periodic modulations of graphene make the transmission more pronounced, potentially allowing for experimental observation of the TE modes. Furthermore, we propose the use of turbostratic graphene to enhance the role of the surface plasmon polaritons in optical spectra.Comment: 15 pages, 13 figure

Exceptional points in optical systems: A resonant-state expansion study

Exceptional points (EPs) in open optical systems are rigorously studied using the resonant-state expansion (RSE). A spherical resonator, specifically a homogeneous dielectric sphere in a vacuum, perturbed by two point-like defects which break the spherical symmetry and bring the optical modes to EPs, is used as a worked example. The RSE is a non-perturbative approach encoding the information about an open optical system in matrix form in a rigorous way, and thus offering a suitable tool for studying its EPs. These are simultaneous degeneracies of the eigenvalues and corresponding eigenfunctions of the system, which are rigorously described by the RSE and illustrated for perturbed whispering-gallery modes (WGMs). An exceptional arc, which is a line of adjacent EPs, is obtained analytically for perturbed dipolar WGMs. Perturbation of high-quality WGMs with large angular momentum and their EPs are found by reducing the RSE equation to a two-state problem by means of an orthogonal transformation of a large RSE matrix. WGM pairs of opposite chirality away from EPs are shown to have the same chirality at EPs. This chirality can be observed in circular dichroism measurements, as it manifested itself in a squared-Lorentzian part of the optical spectra, which we demonstrate here analytically and numerically in the Purcell enhancement factor for the perturbed dipolar WGMs.Comment: 24 pages. 13 figures (3 in Appendix). To be submitted in Physical Review A. Authors: K S Netherwood (primary author), H Riley (initial concept work), E A Muljarov (theme leader

Analytical normalization of resonant states in photonic crystal slabs and periodic arrays of nanoantennas at oblique incidence

We present an analytical formulation for the normalization of resonant states at oblique incidence in one- and two-dimensional periodic structures with top and bottom boundaries to homogeneous space, such as photonic crystal slabs and arrays of nanoantennas. The normalization is validated by comparing the resonant state expansion using one and two resonant states with numerically exact results. The predicted changes of resonance frequency and linewidth due to perturbations of refractive index or geometry can be used to study resonantly enhanced refractive index sensing as well as the influence of disorder. In addition, the normalization is essential for the calculation of the Purcell factor

Surface scattering amplitude for a spatially dispersive model dielectric

Recently, it was shown [H.-Y. Deng and E. A. Muljarov, Phys. Rev. B 106, 195301 (2022)] that the so-called additional boundary conditions (ABCs) had significant issues when describing the surface properties of spatially dispersive media and an alternative ABC-free theory was developed introducing the surface scattering amplitude (SSA), which determines how polarization waves are scattered by a surface. Here we analytically calculate the SSA for a spatially dispersive model dielectric using wave-scattering theory and discuss some emerging generic properties independent of the model. The model consists of a lattice of interacting harmonic oscillators which had historically been used to mimic local excitons. It was shown that for short-range interactions the SSA is a constant independent of where the polarization waves were originated, which is not the case for long-range interaction. The calculated optical properties of a slab verify the general ABC-free theory