Philip Trøst Kristensen

Size dependence of the wavefunction of self-assembled InAs quantum dots from time-resolved optical measurements

Jeppe Johansen, Søren Stobbe, Ivan S. Nikolaev, Toke Lund-Hansen, Philip T. Kristensen, Jørn M. Hvam, Willem L. Vos, and Peter Lodahl COM · DTU, Department of Communications, Optics, and Materials, Nano · DTU, Technical University of Denmark, DTU Building 345V, DK-2800 Kgs. Lyngby, Denmark Center for Nanophotonics, FOM Institute for Atomic and Molecular Physics (AMOLF), Amsterdam, The Netherlands Complex Photonics Systems, MESA+ Institute for Nanotechnology, University of Twente, The Netherlands

Generalized effective mode volume for leaky optical cavities

We show explicitly how the commonly adopted prescription for calculating effective mode volumes is wrong and leads to uncontrolled errors. Instead, we introduce a generalized mode volume that can be easily evaluated based on the mode calculation methods typically applied in the literature, and which allows one to compute the Purcell effect and other interesting optical phenomena in a rigorous and unambiguous way.We show that for optical cavities with any finite dissipation, the term “cavity mode” should be understood as a solution to the Helmholtz equation with outgoing wave boundary conditions. This choice of boundary condition renders the problem non-Hermitian, and we demonstrate that the common definition of an effective mode volume is ambiguous and not applicable. Instead, we propose an alternative effective mode volume which can be easily evaluated based on the mode calculation methods typically applied in the literature. This corrected mode volume is directly applicable to a much wider range of physical systems, allowing one to compute the Purcell effect and other interesting optical phenomena in a rigorous and unambiguous way.

Spontaneous emission spectra and quantum light-matter interactions from a strongly coupled quantum dot metal-nanoparticle system

We investigate the quantum optical properties of a quantum-dot dipole emitter coupled to a finite-size metal nanoparticle using a photon Green-function technique that rigorously quantizes the electromagnetic fields. We first obtain pronounced Purcell factors and photonic Lamb shifts for both a 7- and 20-nm-radius metal nanoparticle, without adopting a dipole approximation. We then consider a quantum-dot photon emitter positioned sufficiently near the metal nanoparticle so that the strong-coupling regime is possible. Accounting for nondipole interactions, quenching, and photon transport from the dot to the detector, we demonstrate that the strong-coupling regime should be observable in the far-field spontaneous emission spectrum, even at room temperature. The vacuum-induced emission spectra show that the usual vacuum Rabi doublet becomes a rich spectral triplet or quartet with two of the four peaks anticrossing, which survives in spite of significant nonradiative decays. We discuss the emitted light spectrum and the effects of quenching for two different dipole polarizations.

Improved switching using Fano resonances in photonic crystal structures

We present a simple and robust structure for realizing asymmetric Fano transmission characteristics in photonic crystal waveguide-cavity structures. The use of Fano resonances for optical switching is analyzed using temporal coupled mode theory in combination with three-dimensional finite difference time domain simulations taking into account the signal bandwidth. The results suggest a significant energy reduction by employing Fano resonances compared to more well established Lorentzian resonance structures. A specific example of a Kerr nonlinearity shows an order of magnitude energy reduction.

Influence of pure dephasing on emission spectra from single photon sources

We investigate the light-matter interaction of a quantum dot with the electromagnetic field in a lossy microcavity and calculate emission spectra for non-zero detuning and dephasing. It is found that dephasing shifts the intensity of the emission peaks for non-zero detuning. We investigate the characteristics of this intensity shifting effect and offer it as an explanation for the non-vanishing emission peaks at the cavity frequency found in recent experimental work.

Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics

We describe a powerful and intuitive theoretical technique for modeling light–matter interactions in classical and quantum nanoplasmonics. Our approach uses a quasinormal mode (QNM) expansion of the photon Green function within a metal nanoresonator of arbitrary shape, together with a Dyson equation, to derive an expression for the spontaneous decay rate and far field propagator from dipole oscillators outside resonators. For a single QNM, at field positions outside the quasi-static coupling regime, we give a closed form solution for the Purcell factor and generalized effective mode volume. We augment this with an analytic expression for the divergent local density of optical states very near the metal surface, which allows us to derive a simple and highly accurate expression for the electric field outside the metal resonator at distances from a few nanometers to infinity. This intuitive formalism provides an enormous simplification over full numerical calculations and fixes several pending problems in QNM theory.

Normalization of quasinormal modes in leaky optical cavities and plasmonic resonators

We discuss three formally different formulas for normalization of quasinormal modes currently in use for modeling optical cavities and plasmonic resonators and show that they are complementary and provide the same result. Regardless of the formula used for normalization, one can use the norm to define an effective mode volume for use in Purcell factor calculations.

Frequency dependence of the radiative decay rate of excitons in self-assembled quantum dots: Experiment and theory

We analyze time-resolved spontaneous emission from excitons confined in self-assembled InAs quantum dots placed at various distances to a semiconductor-air interface. The modification of the local density of optical states due to the proximity of the interface enables unambiguous determination of the radiative and nonradiative decay rates of the excitons. From measurements at various emission energies, we obtain the frequency dependence of the radiative decay rate, which is only revealed due to the separation of the radiative and nonradiative parts. It contains detailed information about the dependence of the exciton wave function on quantum dot size. We derive the quantum optics theory of a solid-state emitter in an inhomogeneous environment and compare this theory to our experimental results. Using this model, we extract the frequency dependence of the overlap between the electron and hole wave functions. We furthermore discuss three models of quantum dot strain and compare the measured wave-function overlap to these models. The observed frequency dependence of the wave-function overlap can be understood qualitatively in terms of the different compressibility of electrons and holes originating from their different effective masses and binding energies.

Switching characteristics of an InP photonic crystal nanocavity: Experiment and theory

The dynamical properties of an InP photonic crystal nanocavity are experimentally investigated using pump-probe techniques and compared to simulations based on coupled-mode theory. Excellent agreement between experimental results and simulations is obtained when employing a rate equation model containing three time constants, that we interpret as the effects of fast carrier diffusion from an initially localized carrier distribution and the slower effects of surface recombination and bulk recombination. The variation of the time constants with parameters characterizing the nanocavity structure is investigated. The model is further extended to evaluate the importance of the fast and slow carrier relaxation processes in relation to patterning effects in the device, as exemplified by the case of all-optical wavelength conversion.

Heterodyne pump probe measurements of nonlinear dynamics in an indium phosphide photonic crystal cavity

Using a sensitive two-color heterodyne pump-probe technique, we investigate the carrier dynamics of an InP photonic crystal nanocavity. The heterodyne technique provides unambiguous results for all wavelength configurations, including the degenerate case, which cannot be investigated with the widely used homodyne technique. A model based on coupled mode theory including two carrier distributions is introduced to account for the relaxation dynamics, which is assumed to be governed by both diffusion and recombination.