Search

Strain deformations and piezoelectric effects greatly modify the band edge potential profile and the symmetry of the semiconductor self-assembled quantum dot system, playing a critical role in determining the material optical and electronic properties. In this paper, based on the continuum elasticity model, we develop an easily implementable finite element method approach to calculate the material displacement, strain, stress, piezoelectric effect, and their impacts on the band edges of quantum dots. No matter the intrinsic symmetric level of the quantum dot geometric shape, we show the maximum symmetry group of the Hamiltonian for an III-V group quantum dot system is C2v. Orientation changes of the quantum dot in the crystal will lead to different Hamiltonian symmetry even though the geometric symmetry groups are the same. We also notice that for a symmetric quantum dot, such as a pyramid, its smallest band gap is normally not at the geometric center, but at the base or near the top. Aspect ratio changes of quantum dots will lead to apparent bandgap variations; however, conformal size changes of the quantum dots will not result in visible bandgap modifications.

Efficient theoretical modeling of metasurface is highly desired for designing metasurfaces. However, most of current modeling of metasurfaces relies on full-wave numerical simulation methods that solve the Maxwell’s equations. As a metasurface typically consists of many meta-units, solving Maxwell’s equations is computationally expensive and thus inefficient for designing metasurface. Here, we develop a general theoretical framework for modeling metasurface based on the coupled mode theory (CMT), which fully describes the interaction between the meta-units and light by a simple set of coupled-mode equations. Consequently, the CMT formulism is far less computationally demanding than the Maxwell’s equations. We show that our CMT approach allows us to quickly and efficiently optimize the design of a beam-steering metagrating. The optimal design obtained from our CMT model is further validated by numerical simulation. The proposed CMT model provides an efficient tool to model and design optical devices based on multiple optical resonators.

—Radiation detection often requires several detectors to be employed at once. Normally, each detector outputs a signal that must be transported, digitized, and stored. One common format for these signals is a finite, aperiodic pulse. Since the detector and data acquisition system are not necessarily physically close, transporting signals from several detectors to a central data acquisition system often requires the use of many cables. The technique presented here allows for the combination and later recovery of a number of analog detector signals using a single cable, by shifting their content to narrow bands in the frequency domain and summing them together into a single channel for transmission. The output is a linear combination of decaying sinusoids, whose peak frequencies and bandwidths in the frequency domain are controlled by inductor, resistor, and capacitor values in the circuit. By separating the outputs by several megahertz, and lowering the bandwidth to about 1 MHz, we can isolate each signal. The timing of the original input can be recovered by taking the inverse Fourier transform of the isolated peak and identifying the start time of the resulting single decaying sinusoid. The energy of the input signal is proportional to the square root of the integral of the corresponding power spectrum peak. We show that energy spectra can be reconstructed with minimal additions to energy resolution. We also show that coincidence timing measurements can be performed with an uncertainty smaller than 2 ns. The result is an N to 1 reduction in cabling, with obvious cost and complexity gains. Since most of the signal content exists only in a band around each peak frequency, noise outside of these bands does not impact the performance.

Self-assembled semiconductor quantum dots possess an intrinsic geometric symmetry due to the crystal periodic structure. In order to systematically analyze the symmetric properties of quantum dots' bound states resulting only from geometric confinement, we apply group representation theory. We label each bound state for two kinds of popular quantum dot shapes: pyramid and half ellipsoid with the irreducible representation of the corresponding symmetric groups, i.e., C 4v and C 2v , respectively. Our study completes all the possible irreducible representation cases of groups C 4v and C 2v . Using the character theory of point groups, we predict the selection rule for electric dipole induced transitions. We also investigate the impact of quantum dot aspect ratio on the symmetric properties of the state wavefunction. This research provides a solid foundation to continue exploring quantum dot symmetry reduction or broken phenomena because of strain, band-mixing and shape irregularity. The results will benefit the researchers who are interested in quantum dot symmetry related effects such as absorption or emission spectra, or those who are studying quantum dots using analytical or numerical simulation approaches.

Self-assembled quantum dots possess an intrinsic geometric symmetry. Applying group representation theory, we systematically analyze the symmetric properties of the bound states for ideal pyramid quantum dots, which neglect band mixing and strain effects. We label each bound state by its symmetry group's corresponding irreducible representation and define a concept called the quantum dots' symmetry category. A class of quantum dots with the same irreducible representation sequence of bound states are characterized as belonging to a specific symmetry category. This category concept generally describes the symmetric order of Hilbert space or wavefunction space. We clearly identify the connection between the symmetry category and the geometry of quantum dots by the symmetry category graph or map. The symmetry category change or transition corresponds to an accidental degeneracy of the bound states. The symmetry category and category transition are observable from the photocurrent spectroscopy or optical spectrum. For simplicity's sake, in this paper, we only focus on inter-subband transition spectra, but the methodology can be extended to the inter-band transition cases. We predict that from the spectral measurements, the quantum dots' geometric information may be inversely extracted.