On the trade-off between mode volume and quality factor in dielectric nanocavities optimized for Purcell enhancement.

This study explores the effect of geometric limitations on the achievable Purcell factor for single emitters in dielectric structures by employing topology optimization as an inverse design tool to maximize the local density of states. Nanobeams of different lengths with varying fixed central bridge widths are considered to investigate the impact of footprint and geometric length-scale. In single-mode photonic cavities, the Purcell factor is known to be proportional to the ratio of the quality factor Q to the effective mode volume V. Analysis of the optimized nanocavities shows a trade-off between quality factor and mode volume as a function of geometric limitations. Crucially, the design exhibiting the largest Purcell enhancement does not have the highest Q nor the lowest V found in the design pool. On the contrary, it is found that Q consistently drops along with decreasing V as the minimum allowed geometric length-scale decreases while the Purcell factor increases. Finally, the study provides insight into the importance of Q and V for enhancing the Purcell factor under geometric limitations.

Modal properties of dielectric bowtie cavities with deep sub-wavelength confinement.

We present a design for an optical dielectric bowtie cavity which features deep sub-wavelength confinement of light. The cavity is derived via simplification of a complex geometry identified through inverse design by topology optimization, and it successfully retains the extreme properties of the original structure, including an effective mode volume of Veff = 0.083 ± 0.001 (λc/2nSi)3 at its center. Based on this design, we present a modal analysis to show that the Purcell factor can be well described by a single quasinormal mode in a wide bandwidth of interest. Owing to the small mode volume, moreover, the cavity exhibits a remarkable sensitivity to local shape deformations, which we show to be well described by perturbation theory. The intuitive simplification approach to inverse design geometries coupled with the quasinormal mode analysis demonstrated in this work provides a powerful modeling framework for the emerging field of dielectric cavities with deep sub-wavelength confinement.

Enhanced Faraday rotation by dielectric metasurfaces with Bayesian shape-optimized scatterers.

In this Letter, we demonstrate how to optimize the magneto-optic response of a Huygens metasurface composed of square arrays of all-dielectric nano-disk scatterers. We compare cylindrical and shape-modified disks. Both provide a strongly enhanced Faraday rotation that is accompanied by almost 100% transmittance. The shape modification obtained via a Bayesian optimization algorithm results in a 50% increase in the magneto-optic response compared to the best cylindrical disk, providing 15° of polarization rotation for a 260 nm thick metasurface.

Quantization of Quasinormal Modes for Open Cavities and Plasmonic Cavity Quantum Electrodynamics.

We introduce a second quantization scheme based on quasinormal modes, which are the dissipative modes of leaky optical cavities and plasmonic resonators with complex eigenfrequencies. The theory enables the construction of multiplasmon or multiphoton Fock states for arbitrary three-dimensional dissipative resonators and gives a solid understanding to the limits of phenomenological dissipative Jaynes-Cummings models. In the general case, we show how different quasinormal modes interfere through an off-diagonal mode coupling and demonstrate how these results affect cavity-modified spontaneous emission. To illustrate the practical application of the theory, we show examples using a gold nanorod dimer and a hybrid dielectric-metal cavity structure.

Semianalytical quasi-normal mode theory for the local density of states in coupled photonic crystal cavity-waveguide structures.

We present and validate a semianalytical quasi-normal mode (QNM) theory for the local density of states (LDOS) in coupled photonic crystal (PhC) cavity-waveguide structures. By means of an expansion of the Green's function on one or a few QNMs, a closed-form expression for the LDOS is obtained, and for two types of two-dimensional PhCs, with one and two cavities side-coupled to an extended waveguide, the theory is validated against numerically exact computations. For the single cavity, a slightly asymmetric spectrum is found, which the QNM theory reproduces, and for two cavities, a nontrivial spectrum with a peak and a dip is found, which is reproduced only when including both the two relevant QNMs in the theory. In both cases, we find relative errors below 1% in the bandwidth of interest.

Calculation, normalization, and perturbation of quasinormal modes in coupled cavity-waveguide systems.

We show how one can use a nonlocal boundary condition, which is compatible with standard frequency domain methods, for numerical calculation of quasinormal modes in optical cavities coupled to waveguides. In addition, we extend the definition of the quasinormal mode norm by use of the theory of divergent series to provide a framework for modeling of optical phenomena in such coupled cavity-waveguide systems. As example applications, we calculate the Purcell factor and study perturbative changes in the complex resonance frequency of a photonic crystal cavity coupled to a defect waveguide.

Roundtrip matrix method for calculating the leaky resonant modes of open nanophotonic structures.

We present a numerical method for calculating quasi-normal modes of open nanophotonic structures. The method is based on scattering matrices and a unity eigenvalue of the roundtrip matrix of an internal cavity, and we develop it in detail with electromagnetic fields expanded on Bloch modes of periodic structures. This procedure is simpler to implement numerically and more intuitive than previous scattering matrix methods, and any routine based on scattering matrices can benefit from the method. We demonstrate the calculation of quasi-normal modes for two-dimensional photonic crystals where cavities are side-coupled and in-line-coupled to an infinite W1 waveguide, and we show that the scattering spectrum of these types of cavities can be reconstructed from the complex quasi-normal mode frequency.

Dual-resonances approach to broadband cavity-assisted optical signal processing beyond the carrier relaxation rate.

We propose and analyze a differential control scheme for cavity-enhanced optical signal processing devices based on carrier nonlinearities. The scheme relies on two optical cavities to increase the bandwidth beyond the limit given by the slowest carrier relaxation rate of the medium. Practical implementations are envisioned using photonic crystal cavities, and the controls may be electrical or optical in nature.

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.

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.

Energy-bandwidth trade-off in all-optical photonic crystal microcavity switches.

The performance of all-optical switches is a compromise between the achievable bandwidth of the switched signal and the energy requirement of the switching operation. In this work we consider a system consisting of a photonic crystal cavity coupled to two input and two output waveguides. As a specific example of a switching application, we investigate the demultiplexing of an optical time division multiplexed signal. To quantify the energy-bandwidth trade-off, we introduce a figure of merit for the detection of the demultiplexed signal. In such investigations it is crucial to consider patterning effects, which occur on time scales that are longer than the bit period. Our analysis is based on a coupled mode theory, which allows for an extensive investigation of the influence of the system parameters on the switching dynamics. The analysis is shown to provide new insights into the ultrafast dynamics of the switching operation, and the results show optimum parameter ranges that may serve as design guidelines in device fabrication.