Light-emitting transistor (LET) and transistor laser (TL) can provide the high-speed electrical and optical modulations simultaneously, advancing light-emitting diodes and diode lasers. Still, between experimental data and rate-equation modeling, there are two-order-of-magnitude uncertainties on the carrier lifetimes of quantum wells (QWs) inserted in heavily p-doped bases of these devices. In view of the importance of this timescale on the modulation speed, we provide a comprehensive approach to calculate carrier lifetimes under such circumstances. We model the Hartree potential energy with self-consistent solutions of the Schrodinger’s and Poisson’s equations. The hole distribution is obtained from real-space density of states through multiband retarded Green functions, taking the outgoing-wave features of hole quasi-bound states into account. We then estimate the carrier lifetimes based on a multiband source-radiation approach including both bound-to-bound and bound-to-continuum components of spontaneous (SP) emissions. Under low surface carrier injections, a large Hartree potential is formed, and the valence band around the QW is strongly tilted. Both bound and quasi-bound valence states are present, and quasi-bound holes may tunnel out of QW and reemerge in the base. The SP spectrum from the QW in the heavily doped base is significantly larger than that from an undoped one due to preexisting holes. At the high injection level, the screening effect significantly reduces the Hartree potential and band bending. We also include the nonradiative Auger recombination to evaluate the total carrier lifetime. Overall carrier lifetimes and small-signal ones are estimated as hundred picoseconds at a doping density of 1019 cm−3 and might be even shorter in the case of heavier doping.
In this work, we present the model of plasmonic chrial nanolasers composed of aluminum-coated gallium-nitride (GaN) gammadions, which may lase with a high degree of circular polarization at room temperatures. Using the finite-element method, we examine resonant modes of the four-fold rotationally symmetric cavities of gammadions whose resonant frequencies lie in the gain spectrum of GaN. We find a degenerate doublet of resonant modes which can couple to plane waves in the far-field zone above gammadions. Their near-field profiles exhibit localized distribution in the arms of gammadions and a Fabry-Perot standing-wave pattern along the post. In practice, fabrication imperfections would inevitably spoil the four-fold rotation symmetry of gammadions. Typical perturbation could lift the degeneracy of doublet and leads to mixing of the two degenerate modes which may still output signals with observable handedness above gammadions. Considering a gammadion cavity with a single elongated arm, we show that the magnitude of dissymmetry factor of its resonant mode can be larger than unity. Our calculations are consistent with the experimental results, indicating that the right-handed gammadion cavities lase with a magnitude of dissymmetry factors near 1 at a wavelength of 364 nm. The dimensionless effective mode volume scaled by the cube of effective wavelength is 2.62, reflecting a modal distribution remarkably confined in the plasmonic structures and the capability of enhancing the spontaneous-emission rate noticeably. These chiral nanolasers with an ultrasmall footprint could be potentially utilized as future circularly-polarized photon source at the chip level.
We develop a method based on the reciprocity and Green function to efficiently obtain the far-field pattern of dipole emitters around plasmonic nanostructures. Applying this method to air hole arrays fabricated on metal films, we reveal their plasmonic characteristics in the near-field scanning optical microscopy. Modeling scanning-probe tips as surface plasmon launchers, we clarify the orientation effect of their equivalent dipoles and also how these effective dipoles contribute to the excitation of different plasmonic modes, resulting in distinguishable characteristics in the far-field imaging. The outcomes of our calculations are validated with the experimental data from a high-resolution raster scanning nano-focusing plasmonic tip. Satisfactory agreements between the model and measurements are demonstrated.
The spontaneous emission of an excited molecule can be tailored by its environment. Modifications of the spontaneous emission rate using plasmonic structures are widely investigated for applications ranging from the near-field optics, nanophotonics, to biomedical imaging. It is possible to track the spontaneous emission rate of a dipole emitter which responds to spatial changes of the environment and therefore reflect the morphology of surface of interest. In this work, we model the fluorescence lifetime imaging of gold nanorod dimers by utilizing a single dipole emitter as a sensitive probe scanning along one dimension above the metallic nanostructures. The fluorescence lifetime is spatially mapped out as an attempt to reconstruct the corresponding images. However, it is found that the lifetime imaging is not always consistent with the real morphology of nanostructure. Artifacts in lifetime imaging may arise due to the strong coupling fields in the resonance structures. The sharpness of nanorod dimers could make spontaneous emission rate of a dipole emitter change dramatically and play a key role in artifacts. The operation frequency of a dipole emitter can also influence the lifetime and contribute to artifacts. Here, we will investigate the relation between orientations of dipole emitters and spatial profile of the image. In addition, we will address strategies to distinguish these artifacts from the real morphology and present a theoretical model based on the waveguide geometry to examine possible origins of artifacts.
Optical isolators are important devices in photonic circuits. To reduce the unwanted reflection in a robust manner, several setups have been realized using nonreciprocal schemes. In this study, we show that the propagating modes in a strongly-guided chiral photonic crystal (no breaking of the reciprocity) are not backscattering-immune even though they are indeed insensitive to many types of scatters. Without the protection from the nonreciprocity, the backscattering occurs under certain circumstances. We present a perturbative method to calculate the backscattering of chiral photonic crystals in the presence of chiral/achiral scatters. The model is, essentially, a simplified analogy to the first–order Born approximation. Under reasonable assumptions based on the behaviors of chiral photonic modes, we obtained the expression of reflection coefficients which provides criteria for the prominent backscattering in such chiral structures. Numerical examinations using the finite-element method were also performed and the results agree well with the theoretical prediction. From both our theory and numerical calculations, we find that the amount of backscattering critically depends on the symmetry of scatter cross sections. Strong reflection takes place when the azimuthal Fourier components of scatter cross sections have an order l of 2. Chiral scatters without these Fourier components would not efficiently reflect the chiral photonic modes. In addition, for these chiral propagating modes, disturbances at the most significant parts of field profiles do not necessarily result in the most effective backscattering. The observation also reveals what types of scatters or defects should be avoided in one-way applications of chiral structures in order to minimize the backscattering.
We have analyzed a hybrid photonic-plasmonic crystal nanocavity consisting of a silicon grating nanowire adjacent to a metal surface with a gain gap between. The hybrid plasmonic cavity modes are highly confined in the gap due to the coupling of photonic crystal cavity modes and surface plasmonic gap modes. Using the finite-element method, we numerically solve guided modes of the hybrid plasmonic waveguide at a wavelength of 1.55 μm. The modal characteristics such as waveguide confinement factors and modal losses of the fundamental hybrid plasmonic modes are explored as a function of the groove depth at various gap heights. After that, we show the band structure of the hybrid crystal modes, corresponding to a wide band gap of 17.8 THz. To effectively trap the optical modes, we introduce a single defect into the hybrid crystal. At a deep sub-wavelength defect length as small as 180 nm, the resonant mode exhibits a high quality factor of 566.5 and an ultrasmall mode volume of 0.00186 (λ/n) 3 at the resonance wavelength of 1.55 μm. In comparison to the conventional photonic crystal nanowire cavity in the absence of metal surface, the figure of merit Q/Vm is enormously enhanced around 15 times. The proposed nanocavities open up the opportunities for various applications with strong light-matter interaction such as nanolasers and biosensors.
We analyze a plasmonic gap-mode Fabry-Perot nanocavity containing a metallic nanowire. The proper choice of the cladding layer brings about a decent confinement inside the active region for the fundamental and first-order plasmonic gap modes. We numerically extract the reflectivity of the fundamental and first-order mode and obtain the optical field inside the cavity. We also study the dependence of the reflectivity on the thickness of Ag reflectors and show that a decent reflectivity above 90 % is achievable. For such cavities with a cavity length approaching 1.5 μm, a quality factor near 150 and threshold gain lower than 1500 cm−1 are achievable.