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1. Rapid acquisition of broadband two-dimensional electronic spectra by continuous scanning with conventional delay lines

   https://doi.org/10.1364/OL.391360  

   Spencer, Austin_P; Chen, Lin_X (May 2020, Optics Letters)

   A passively phase-stable, broadband ( $\sim <\#comment/>7\mathrm{f}\mathrm{s}$, $><\#comment/>2000{\mathrm{c}\mathrm{m}}^{-<\#comment/>1}$) two-dimensional (2D) electronic spectroscopy apparatus that achieves rapid acquisition rates by continuously—rather than step-wise—scanning the Fourier-transform dimension is demonstrated for the first time, to the best of our knowledge. This is made possible through use of a partially common path interferometer design in which the coherence time $\mathrm{\tau <\#comment/>}$is sampled in a “rotating frame.” Rapid, continuous scanning of $\mathrm{\tau <\#comment/>}$increases the duty cycle of signal collection, rejects the majority of excitation pulse scatter, and enables the measurement of a complete 2D spectrum in 92 ms, which minimizes the influence of pulse intensity and delay fluctuations on the 2D spectrum. In practice, these improvements make possible the acquisition of hundreds of 2D spectra in tens of minutes, which opens the door to dense sampling of ultrafast relaxation dynamics and to generating extremely broadband 3D Fourier-transform spectra. 

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2. Size dependence- and induced transformations- of fractional quantum Hall effects under tilted magnetic fields

   https://doi.org/10.1038/s41598-022-22812-x  

   Wijewardena, U. Kushan; Nanayakkara, Tharanga R.; Kriisa, Annika; Reichl, Christian; Wegscheider, Werner; Mani, Ramesh G. (November 2022, Scientific Reports)

   Abstract Two-dimensional electron systems subjected to high transverse magnetic fields can exhibit Fractional Quantum Hall Effects (FQHE). In the GaAs/AlGaAs 2D electron system, a double degeneracy of Landau levels due to electron-spin, is removed by a small Zeeman spin splitting,$$g \mu _B B$$ $g{\mu }_{B}B$, comparable to the correlation energy. Then, a change of the Zeeman splitting relative to the correlation energy can lead to a re-ordering between spin polarized, partially polarized, and unpolarized many body ground states at a constant filling factor. We show here that tuning the spin energy can produce fractionally quantized Hall effect transitions that include both a change in$$\nu$$ $\nu$for the$$R_{xx}$$ $R_{\mathrm{xx}}$minimum, e.g., from$$\nu = 11/7$$ $\nu =11/7$to$$\nu = 8/5$$ $\nu =8/5$, and a corresponding change in the$$R_{xy}$$ $R_{\mathrm{xy}}$, e.g., from$$R_{xy}/R_{K} = (11/7)^{-1}$$ $R_{\mathrm{xy}}/R_K={(11/7)}^{-1}$to$$R_{xy}/R_{K} = (8/5)^{-1}$$ $R_{\mathrm{xy}}/R_K={(8/5)}^{-1}$, with increasing tilt angle. Further, we exhibit a striking size dependence in the tilt angle interval for the vanishing of the$$\nu = 4/3$$ $\nu =4/3$and$$\nu = 7/5$$ $\nu =7/5$resistance minima, including “avoided crossing” type lineshape characteristics, and observable shifts of$$R_{xy}$$ $R_{\mathrm{xy}}$at the$$R_{xx}$$ $R_{\mathrm{xx}}$minima- the latter occurring for$$\nu = 4/3, 7/5$$ $\nu =4/3,7/5$and the 10/7. The results demonstrate both size dependence and the possibility, not just of competition between different spin polarized states at the same$$\nu$$ $\nu$and$$R_{xy}$$ $R_{\mathrm{xy}}$, but also the tilt- or Zeeman-energy-dependent- crossover between distinct FQHE associated with different Hall resistances. 

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3. High-resolution and compact serpentine integrated grating spectrometer

   https://doi.org/10.1364/JOSAB.423968  

   Brand, Michael; Zhang, Bohan; Onural, Deniz; Al_Qubaisi, Kenaish; Popović, Miloš; Dostart, Nathan; Wagner, Kelvin (June 2021, Journal of the Optical Society of America B)

   Integrated astrophotonic spectrometers are integrated variants of conventional free-space spectrometers that offer significantly reduced size, weight, and cost and immunity to alignment errors, and can be readily integrated with other astrophotonic instruments such as nulling interferometers. Current integrated dispersive astrophotonic spectrometers are one-dimensional devices such as arrayed waveguide gratings or planar echelle gratings. These devices have been limited to ${10}^4$resolving powers and $<<\#comment/>1000$spectral bins due to having limited total optical delay paths and 1D detector array pixel densities. In this paper, we propose and demonstrate a high-resolution and compact astrophotonic serpentine integrated grating (SIG) spectrometer design based on a 2D dispersive serpentine optical phased array. The SIG device combines a 5.2 cm long folded delay line with grating couplers to create a large optical delay path along two dimensions in a compact integrated device footprint. Analogous to free-space crossed-dispersion high-resolution spectrometers, the SIG spectrometer maps spectral content to a 2D wavelength-beam-steered folded-raster emission pattern focused onto a 2D detector array. We demonstrate a SIG spectrometer with $\sim <\#comment/>100\mathrm{k}$resolving power and $\sim <\#comment/>6750$spectral bins, which are approximately an order of magnitude higher than previous integrated photonic designs that operate over a wide bandwidth, in a $0.4{\mathrm{m}\mathrm{m}}^2$footprint. We measure a Rayleigh resolution of $1.93\pm <\#comment/>0.07\mathrm{G}\mathrm{H}\mathrm{z}$and an operational bandwidth from 1540 nm to 1650 nm. Finally, we discuss refinements of the SIG spectrometer that improve its resolution, bandwidth, and throughput. These results show that SIG spectrometer technology provides a path towards miniaturized, high-resolution spectrometers for applications in astronomy and beyond. 

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4. Fast Barycentric-Based Evaluation Over Spectral/hp Elements

   https://doi.org/10.1007/s10915-021-01750-2  

   Laughton, Edward; Zala, Vidhi; Narayan, Akil; Kirby, Robert M.; Moxey, David (January 2022, Journal of Scientific Computing)

   Abstract As the use of spectral/hpelement methods, and high-order finite element methods in general, continues to spread, community efforts to create efficient, optimized algorithms associated with fundamental high-order operations have grown. Core tasks such as solution expansion evaluation at quadrature points, stiffness and mass matrix generation, and matrix assembly have received tremendous attention. With the expansion of the types of problems to which high-order methods are applied, and correspondingly the growth in types of numerical tasks accomplished through high-order methods, the number and types of these core operations broaden. This work focuses on solution expansion evaluation at arbitrary points within an element. This operation is core to many postprocessing applications such as evaluation of streamlines and pathlines, as well as to field projection techniques such as mortaring. We expand barycentric interpolation techniques developed on an interval to 2D (triangles and quadrilaterals) and 3D (tetrahedra, prisms, pyramids, and hexahedra) spectral/hpelement methods. We provide efficient algorithms for their implementations, and demonstrate their effectiveness using the spectral/hpelement libraryNektar++by running a series of baseline evaluations against the ‘standard’ Lagrangian method, where an interpolation matrix is generated and matrix-multiplication applied to evaluate a point at a given location. We present results from a rigorous series of benchmarking tests for a variety of element shapes, polynomial orders and dimensions. We show that when the point of interest is to be repeatedly evaluated, the barycentric method performs at worst$$50\%$$ $50\%$slower, when compared to a cached matrix evaluation. However, when the point of interest changes repeatedly so that the interpolation matrix must be regenerated in the ‘standard’ approach, the barycentric method yields far greater performance, with a minimum speedup factor of$$7\times $$ $7\times$. Furthermore, when derivatives of the solution evaluation are also required, the barycentric method in general slightly outperforms the cached interpolation matrix method across all elements and orders, with an up to$$30\%$$ $30\%$speedup. Finally we investigate a real-world example of scalar transport using a non-conformal discontinuous Galerkin simulation, in which we observe around$$6\times $$ $6\times$speedup in computational time for the barycentric method compared to the matrix-based approach. We also explore the complexity of both interpolation methods and show that the barycentric interpolation method requires$${\mathcal {O}}(k)$$ $O\left(k\right)$storage compared to a best case space complexity of$${\mathcal {O}}(k^2)$$ $O\left(k^2\right)$for the Lagrangian interpolation matrix method. 

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5. Deep-learning-based image reconstruction for compressed ultrafast photography

   https://doi.org/10.1364/OL.397717  

   Ma, Yayao; Feng, Xiaohua; Gao, Liang (August 2020, Optics Letters)

   Compressed ultrafast photography (CUP) is a computational optical imaging technique that can capture transient dynamics at an unprecedented speed. Currently, the image reconstruction of CUP relies on iterative algorithms, which are time-consuming and often yield nonoptimal image quality. To solve this problem, we develop a deep-learning-based method for CUP reconstruction that substantially improves the image quality and reconstruction speed. A key innovation toward efficient deep learning reconstruction of a large three-dimensional (3D) event datacube ( $x,y,t$) ( $x,y$, spatial coordinate; $t$, time) is that we decompose the original datacube into massively parallel two-dimensional (2D) imaging subproblems, which are much simpler to solve by a deep neural network. We validated our approach on simulated and experimental data. 

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