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We present a quantized quasinormal approach to rigorously describe coupled lossy resonators, and quantify the quantum coupling parameters as a function of distance between the resonators. We also make a direct connection between classical and quantum quasinormal modes parameters and theories, offering new and unique insights into coupled open cavity resonators. We present detailed calculations for coupled microdisk resonators and show striking interference effects that depend on the phase of the quasinormal modes, an effect that is also significant for high quality factor modes. Our results demonstrate that commonly adopted master equations for such systems are generally not applicable and we discuss the new physics that is captured using the quantized quasinormal mode coupling parameters and show how these relate to the classical mode parameters. Using these new insights, we also present several models to fix the failures of the dissipative Jaynes-Cummings type models for coupled cavity resonators. Additionally, we show how to improve the classical and quantum lossless mode models (i.e., using normal modes) by employing a non-diagonal mode expansion based on the knowledge of the quasinormal mode eigenfrequencies, and analytical coupled mode theory, to accurately capture the mode interference effects for high quality factors., 21 pages, 9 figures

Quantum emitters coupled to plasmonic resonators are known to allow enhanced broadband Purcell factors, and such systems have been recently suggested as possible candidates for on-demand single photon sources, with fast operation speeds. However, a true single photon source has strict requirements of high efficiency (brightness) and quantum indistinguishability of the emitted photons, which can be quantified through two-photon interference experiments. To help address this problem, we employ and extend a recently developed quantized quasinormal mode approach, which rigorously quantizes arbitrarily lossy open system modes, to compute the key parameters that accurately quantify the figures of merit for plasmon-based single photon sources. We also present a quantized input-output theory to quantify the radiative and nonradiative quantum efficiencies. We exemplify the theory using a nanoplasmonic dimer resonator made up of two gold nanorods, which yields large Purcell factors and good radiative output beta factors. Considering an optically pulsed excitation scheme, we explore the key roles of pulse duration and pure dephasing on the single photon properties, and show that ultrashort pulses (sub-ps) are generally required for such structures, even for low temperature operation. We also quantify the role of the nonradiative beta factor both for single photon and two-photon emission processes. Our general approach can be applied to a wide variety of plasmon systems, including metal-dielectrics, and cavity-waveguide systems, without recourse to phenomenological quantization schemes.

We demonstrate a fundamental breakdown of the photonic spontaneous emission (SE) formula derived from Fermi's golden rule, in absorptive and amplifying media, where one assumes the SE rate scales with the local photon density of states, an approach often used in more complex, semiclassical nanophotonics simulations. Using a rigorous quantization of the macroscopic Maxwell equations in the presence of arbitrary linear media, we derive a corrected Fermi's golden rule and master equation for a quantum two-level system (TLS) that yields a quantum pumping term and a modified decay rate that is net positive. We show rigorous numerical results of the temporal dynamics of the TLS for an example of two coupled microdisk resonators, forming a gain-loss medium, and demonstrate the clear failure of the commonly adopted formulas based solely on the local density of states., Comment: 6 pages, 3 figures

We provide theory and formal insight on the Green function quantization method for absorptive and dispersive spatial-inhomogeneous media in the context of dielectric media. We show that a fundamental Green function identity, which appears, e.g., in the fundamental commutation relation of the electromagnetic fields, is also valid in the limit of non-absorbing media. We also demonstrate how the zero-point field fluctuations yields a non-vanishing surface term in configurations without absorption, when using a more formal procedure of the Green function quantization method. We then apply the presented method to a recently developed theory of photon quantization using quasinormal modes [Franke et al., Phys. Rev. Lett. 122, 213901 (2019)] for finite nanostructures embedded in a lossless background medium. We discuss the strict dielectric limit of the commutation relations of the quasinormal mode operators and present different methods to obtain them, connected to the radiative loss for non-absorptive but open resonators. We show exemplary calculations of a fully three-dimensional photonic crystal beam cavity, including the lossless limit, which supports a single quasinormal mode and discuss the limits of the commutation relation for vanishing damping (no material loss and no radiative loss)., 20 pages, 4 figures

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.

The growth mechanism and the barrier performance of Al2O3, SiO2 and a binary Si-Al oxide (SiAlxOy) deposited by spatial atomic layer deposition (SALD) were investigated. Alumina and silica were deposited by TMA and BDEAS with growth-per-cycles (GPC) of 0.16 and 0.013 nm, respectively. Interestingly a significant higher GPC of 0.225 nm was found for SiAlxOy. Although alumina in principle has excellent barrier properties, the films easily degraded and lose their barrier performance if exposed to water vapor at elevated temperatures. Therefore, the barrier performances of these films were investigated under harsh environment conditions. We found that the barrier performance of 100 nm Al2O3 failed in less than one day at 70 °C with 70 % relative humidity, whereas 100 nm SiAlxOy sustained for approximately one week. However, the resistivity of those barrier systems was significantly improved by inserting a single 3.3 nm SiO2 layer into the barrier films. In this way the barrier system withstands up to 5 months and the intrinsic water vapor transition rate was reduced by two to three orders of magnitude to ∼10-4 g/m2/day at these tough aging conditions.

Alumina layers were grown from trimethylaluminum (TMA) and water, ozone as well as an oxygen plasma as co-reactants in low temperature spatial atomic layer deposition (ALD). The influence of the amount of precursor, the precursor exposure duration, and substrate temperature were investigated with respect to the growth rate while employing different oxygen sources. The TMA/water process provided alumina (AlOx) films with superb film quality as shown by infrared measurements. Ozone-based processes allowed lower substrate temperatures. Nevertheless, carbon residuals in different binding states were found within the bulk material. However, the carbon impurities have no impact on the barrier performance, since 50 nm AlOx grown by TMA either with water or ozone exhibited a water vapor transition rate in the range of 10−6 g/m2/day. However, when our home-built microwave plasma source was applied in a remote configuration, the water vapor transition rate was one order of magnitude higher due to a reduction in fil...

We describe an efficient near-field to far-field transformation for optical quasinormal modes, which are the dissipative modes of open cavities and plasmonic resonators with complex eigenfrequencies. As an application of the theory, we show how one can compute the reservoir modes (or regularized quasinormal modes) outside the resonator, which are essential to use in both classical and quantum optics. We subsequently demonstrate how to efficiently compute the quantum optical parameters necessary in the theory of quantized quasinormal modes [Franke et al., Phys. Rev. Lett. 122, 213901 (2019)]. To confirm the accuracy of our technique, we directly compare with a Dyson equation approach (in regimes where this is possible), and we demonstrate several order of magnitude improvement for the calculation runtimes. We also introduce an efficient pole approximation for computing the quantized quasinormal mode parameters. Using this approach, we show how to compute regularized quasinormal modes and quantum optical parameters for a full 3D metal dimer (with various material losses) in under one minute on a standard desktop computer. Our technique is exemplified by studying the quasinormal modes of metal dimers and a hybrid structure consisting of a gold dimer on top of a photonic crystal beam, designed to yield a Purcell factor in excess of 1 million. In the latter example, we show how to compute the quantized mode parameters that describe a pronounced Fano resonance, using structural geometries that cannot practically be solved using a Dyson equation approach. All calculations for the spontaneous emission rates are confirmed with full-dipole calculations in Maxwell's equations and are shown to be in excellent agreement.