Search

Reconfigurable devices have garnered significant attention for alleviating the scaling requirements of conventional CMOS technology, as they require fewer components to construct circuits with similar function. Prior works required continuous voltage application for programming gate terminal(s) in addition to the primary gate terminal, which undermines the advantages of reconfigurable devices in realizing compact and power-efficient integrated circuits. Here, we realize reconfigurable devices based on a single-gate field-effect transistor (FET) architecture by integrating semiconducting channels consisting of a monolayer film of highly aligned SWCNTs with a ferroelectric AlScN gate dielectric, all compatible with CMOS back-end-of-line (BEOL) processing. We demonstrated these SWCNT ferroelectric FETs (FeFETs) in a centimeter-scale array (~1 cm^2) comprising ~735 devices, with high spatial uniformity in device characteristics across the array. The devices exhibited ambipolar transfer characteristics with high on-state currents and current on/off ratios exceeding 10^5, demonstrating an excellent balance between electron and hole conduction (~270 {\mu}A/{\mu}m at a drain voltage of 3 V. When functioning as a non-volatile memory, the SWCNT FeFETs demonstrated large memory windows of 0.26 V/nm and 0.08 V/nm in the hole and electron conduction regions, respectively, combined with excellent retention behavior for up to 10^4 s. Repeated reconfiguration between p-FET and n-FET modes was also enabled by switching the spontaneous polarization in AlScN and operating the transistor within a voltage range below the coercive voltage. We revealed through circuit simulations that reconfigurable SWCNT transistors can realize ternary content-addressable memory (TCAM) with far fewer devices compared to circuits based on silicon CMOS technology or based on resistive non-volatile devices., Comment: 37 pages, 16 figures (5 main and 11 supplementary figures)

Ferroelectric field-effect transistors (FeFET) with two-dimensional (2D) semiconductor channels are promising low-power, embedded non-volatile memory (NVM) candidates for next-generation in-memory computing. However, the performance of FeFETs can be limited by a charge imbalance between the ferroelectric layer and the channel, and for low-dimensional semiconductors, also by a high contact resistance between the metal electrodes and the channel. Here, we report a significant enhancement in performance of contact-engineered FeFETs with a 2D MoS2 channel and a ferroelectric Al0.68Sc0.32N (AlScN) gate dielectric. Replacing Ti with In contact electrodes results in a fivefold increase in on-state current (~120 uA/um at 1 V) and on-to-off ratio (~2*10^7) in the FeFETs. In addition, the high carrier concentration in the MoS2 channel during the on-state (> 10^14 cm^-2) facilitates the observation of a metal-to-insulator phase transition in monolayer MoS2 permitting observation of high field effect mobility (> 100 cm^2V^-1s^-1) at cryogenic temperatures. Our work and devices broaden the potential of FeFETs and provides a unique platform to implement high-carrier-density transport in a 2D channel., Comment: 42 pages, 5 main figures

Commercial production of integrated photonic devices is limited by scalability of desirable material platforms. We explore a relatively new photonic material, AlScN, for its use in electro-optic modulation. Its CMOS-compatibility could facilitate large-scale production of integrated photonic modulators, and it exhibits an enhanced second-order optical nonlinearity compared to intrinsic AlN, indicating the possibility for efficient modulation. Here, we measure the electro-optic effect in AlScN-based modulators, demonstrating $V_{\pi}L$ around 750 V$\cdot$cm. Since the electro-optic response is smaller than expected, we discuss potential causes for the reduced response and future outlook for AlScN-based photonics., Comment: 9 pages, 3 figures

Silicon microelectronics, consisting of complementary metal oxide semiconductor (CMOS) technology, have changed nearly all aspects of human life from communication to transportation, entertainment, and healthcare. Despite the widespread and mainstream use, current silicon-based devices suffer significant reliability issues at temperatures exceeding 125 C. The emergent technological frontiers of space exploration, geothermal energy harvesting, nuclear energy, unmanned avionic systems, and autonomous driving will rely on control systems, sensors, and communication devices which operate at temperatures as high as 500 C and beyond. At these extreme temperatures, active (heat exchanger, phase change cooling) or passive (fins and thermal interface materials) cooling strategies add significant mass and complication which is often infeasible. Thus, new material solutions beyond conventional silicon CMOS devices are necessary for high temperature, resilient electronic systems. Accomplishing this will require a united effort to explore development, integration, and ultimately manufacturing of non-silicon-based logic and memory technologies, non-traditional metals for interconnects, and ceramic packaging technology., Comment: 6 Figures

The growth in data generation necessitates efficient data processing technologies to address the von Neumann bottleneck in conventional computer architecture. Memory-driven computing, which integrates non-volatile memory (NVM) devices in a 3D stack, is gaining attention, with CMOS back-end-of-line (BEOL) compatible ferroelectric (FE) diodes being ideal due to their two-terminal design and inherently selector-free nature, facilitating high-density crossbar arrays. Here, we demonstrate BEOL-compatible, high-performance FE-diodes scaled to 5, 10, and 20 nm FE Al0.72Sc0.28N/Al0.64Sc0.36N films. Through interlayer (IL) engineering, we show substantial improvements in the ON/OFF ratios (>166 times) and rectification ratios (>176 times) in these scaled devices. The superlative characteristics also enables 5-bit multi-state operation with a stable retention. We also experimentally and theoretically demonstrate the counterintuitive result that the inclusion of an IL can lead to a decrease in the ferroelectric switching voltage of the device. An in-depth analysis into the device transport mechanisms is performed, and our compact model aligns seamlessly with the experimental results. Our results suggest the possibility of using scaled AlxSc1-xN FE-diodes for high performance, low-power, embedded NVM.

We introduce a new reduction of the motion of three point vortices in a two-dimensional ideal fluid. This proceeds in two stages: a change of variables to Jacobi coordinates and then a Nambu reduction. The new coordinates demonstrate that the dynamics evolve on a two-dimensional manifold whose topology depends on the sign of a parameter $\kappa_2$ that arises in the reduction. For $\kappa_2>0$, the phase space is spherical, while for $\kappa_2<0$, the dynamics are confined to the upper sheet of a two-sheeted hyperboloid. We contrast this reduction with earlier reduced systems derived by Gr\"obli, Aref, and others in which the dynamics are determined from the pairwise distances between the vortices. The new coordinate system overcomes two related shortcomings of Gr\"obli's reduction that have made understanding the dynamics difficult: their lack of a standard phase plane and their singularity at all configurations in which the vortices are collinear. We apply this to two canonical problems. We first discuss the dynamics of three identical vortices and then consider the scattering of a propagating dipole by a stationary vortex. We show that the points dividing direct and exchange scattering solutions correspond to the locations of the invariant manifolds of equilibria of the reduced equations and relate changes in the scattering diagram as the circulation of one vortex is varied to bifurcations of these equilibria., Comment: This is a major restructuring on the paper. Whereas the initial submission focused on the scattering problem, the revision focuses on the method of the reduction, its mathematical structure, and its advantages. It treats the scattering problem as an application of the method and adds a second application: the problem of three identical vortices. The title has been changed to reflect this

Here we provide a complete English translation of Walter Gr\"obli's 1877 Ph.D. Thesis, together with some notes on the process. The work considers the dynamics of point vortices in a two-dimensional inviscid incompressible fluid and derives a number of exact solutions in the cases of three, four and $2n$ vortices with certain restriction on the vortices' circulation and the symmetry of the initial configuration.

We describe QGLAB, a new MATLAB package for analyzing partial differential equations on quantum graphs. The software is built on the existing, object-oriented MATLAB directed-graph class, inheriting its structure and adding additional easy-to-use features. The package allows one to construct a quantum graph and accurately compute the spectrum of elliptic operators, solutions to Poisson problems, the linear and nonlinear time evolution of a variety of PDEs, the continuation of branches of steady states (including locating and switching branches at bifurcations) and more. It overcomes the major challenge of discretizing quantum graphs -- the enforcement of vertex conditions -- using non-square differentiation matrices. It uses a unified framework to implement finite-difference and Chebyshev discretizations of differential operators on a quantum graph. For simplicity, the package overloads many built-in MATLAB functions to work on the class., Comment: 41 pages, 18 figures. Major rewrite. Examples moved from appendix to body. Comments Welcome! Code associated with this publication available at https://github.com/manroygood/Quantum-Graphs/tree/master

FRB 20220912A is a repeating Fast Radio Burst (FRB) that was discovered in Fall 2022 and remained highly active for several months. We report the detection of 35 FRBs from 541 hours of follow-up observations of this source using the recently refurbished Allen Telescope Array, covering 1344 MHz of bandwidth primarily centered at 1572 MHz. All 35 FRBs were detected in the lower half of the band with non-detections in the upper half and covered fluences from 4-431 Jy-ms (median$=$48.27 Jy-ms). We find consistency with previous repeater studies for a range of spectrotemporal features including: bursts with downward frequency drifting over time; a positive correlation between bandwidth and center frequency; and a decrease in sub-burst duration over time. We report an apparent decrease in the center frequency of observed bursts over the 2 months of the observing campaign (corresponding to a drop of $6.21\pm 0.76$ MHz per day). We predict a cut-off fluence for FRB 20220912A of $F_\textrm{max}\lesssim 10^4$ Jy-ms, for this source to be consistent with the all-sky rate, and find that FRB 20220912A significantly contributed to the all-sky FRB rate at a level of a few percent for fluences of $\sim$100 Jy-ms. Finally, we investigate characteristic timescales and sub-burst periodicities and find a) a median inter-subburst timescale of 5.82$\pm$1.16 ms in the multi-component bursts and b) no evidence of strict periodicity even in the most evenly-spaced multi-component burst in the sample. Our results demonstrate the importance of wideband observations of FRBs, and provide an important set of observational parameters against which to compare FRB progenitor and emission mechanism models., Comment: 17 pages, 8 figures, 2 tables, accepted to MNRAS

Surface Acoustic Wave (SAW) devices featuring Aluminum Scandium Nitride (AlScN) on a 4H-Silicon Carbide (SiC) substrate, offer a unique blend of high sound velocity, low thermal resistance, substantial piezoelectric response, simplified fabrication, as well as suitability for high-temperature and harsh environment operation. This study presents high-frequency SAW resonators employing AlScN thin films on SiC substrates, utilizing the second SAW mode (referred to as the Sezawa mode). The resonators achieve remarkable performance, boasting a K2 value of 5.5% and a maximum Q-factor (Qmax) of 1048 at 4.7 GHz, outperforming previous benchmarks. Additionally, a SAW resonator with a 960 nm wavelength attains 5.9 GHz frequency with record K2 (4.0%) and Qmax (887). Our study underscores the potential of the AlScN on SiC platform for advanced radio-frequency applications., Comment: 19 pages, 5 figures in main text and 3 figures in supplementary

Achieving robust and electrically controlled valley polarization in monolayer transition metal dichalcogenides (ML-TMDs) is a frontier challenge for realistic valleytronic applications. Theoretical investigations show that integration of 2D materials with ferroelectrics is a promising strategy; however, its experimental demonstration has remained elusive. Here, we fabricate ferroelectric field-effect transistors using a ML-WSe2 channel and a AlScN ferroelectric dielectric, and experimentally demonstrate efficient tuning as well as non-volatile control of valley polarization. We measured a large array of transistors and obtained a maximum valley polarization of ~27% at 80 K with stable retention up to 5400 secs. The enhancement in the valley polarization was ascribed to the efficient exciton-to-trion (X-T) conversion and its coupling with an out-of-plane electric field, viz. the quantum-confined Stark effect. This changes the valley depolarization pathway from strong exchange interactions to slow spin-flip intervalley scattering. Our research demonstrates a promising approach for achieving non-volatile control over valley polarization and suggests new design principles for practical valleytronic devices., Comment: Manuscript (22 pages and 5 figures), supporting information

Here we report on an acoustoelectric slab waveguide heterostructure for phonon amplification using a thin Al$_{0.58}$Sc$_{0.42}$N film grown directly on a 4H-SiC substrate with an ultra-thin In$_{0.53}$Ga$_{0.47}$As epitaxial film heterogeneously integrated onto the surface of the Al$_{0.58}$Sc$_{0.42}$N. The aluminum scandium nitride film grown directly on silicon carbide enables a thin (1 micron thick) piezoelectric film to be deposited on a thermally conductive bulk substrate (370 W/m-K for 4H-SiC), enabling negligible self-heating when combined with the In$_{0.53}$Ga$_{0.47}$As semiconductor parameters of large mobility (~7000 cm$^2$/V-s) and low concentration of charge carriers (~5x10$^{15}$ cm$^{-3}$). A Sezawa mode with optimal overlap between the peak of its evanescent electric field and the semiconductor charge carriers is supported. The high velocity of the heterostructure materials allows us to operate the Sezawa mode amplifier at 3.05 GHz, demonstrating a gain of 500 dB/cm (40 dB in 800 microns). Additionally, a terminal end-to-end radio frequency gain of 7.7 dB and a nonreciprocal transmission of 52.6 dB are achieved with a dissipated DC power of 2.3 mW. The power added efficiency and acoustic noise figure are also characterized.

Non-volatile memory (NVM) devices that reliably operate at temperatures above 300 $^\circ$C are currently non-existent and remains a critically unmet challenge in the development of high-temperature (T) resilient electronics, necessary for many emerging, complex computing and sensing in harsh environments. Ferroelectric Al$_x$Sc$_{1-x}$N exhibits strong potential for utilization in NVM devices operating at very high temperatures (> 500 $^\circ$C) given its stable and high remnant polarization (PR) above 100 $\mu$C/cm$^2$ with demonstrated ferroelectric transition temperature (TC) > 1000 $^\circ$C. Here, we demonstrate an Al$_{0.68}$Sc$_{0.32}$N ferroelectric diode based NVM device that can reliably operate with clear ferroelectric switching up to 600 $^\circ$C with distinguishable On and Off states. The coercive field (EC) from the Pulsed I-V measurements is found to be -5.84 (EC-) and +5.98 (EC+) (+/- 0.1) MV/cm at room temperature (RT) and found to decrease with increasing temperature up to 600 $^\circ$C. The devices exhibit high remnant polarizations (> 100 $\mu$C/cm$^2$) which are stable at high temperatures. At 500 $^\circ$C, our devices show 1 million read cycles and stable On-Off ratio above 1 for > 6 hours. Finally, the operating voltages of our AlScN ferrodiodes are < 15 V at 600 $^\circ$C which is well matched and compatible with Silicon Carbide (SiC) based high temperature logic technology, thereby making our demonstration a major step towards commercialization of NVM integrated high-T computers., Comment: MS and SI

In this paper, we explore potential uses of generative AI models, such as ChatGPT, for investment portfolio selection. Trusting investment advice from Generative Pre-Trained Transformer (GPT) models is a challenge due to model "hallucinations", necessitating careful verification and validation of the output. Therefore, we take an alternative approach. We use ChatGPT to obtain a universe of stocks from S&P500 market index that are potentially attractive for investing. Subsequently, we compared various portfolio optimization strategies that utilized this AI-generated trading universe, evaluating those against quantitative portfolio optimization models as well as comparing to some of the popular investment funds. Our findings indicate that ChatGPT is effective in stock selection but may not perform as well in assigning optimal weights to stocks within the portfolio. But when stocks selection by ChatGPT is combined with established portfolio optimization models, we achieve even better results. By blending strengths of AI-generated stock selection with advanced quantitative optimization techniques, we observed the potential for more robust and favorable investment outcomes, suggesting a hybrid approach for more effective and reliable investment decision-making in the future.

A single tunable filter simplifies complexity, reduces insertion loss, and minimizes size compared to frequency switchable filter banks commonly used for radio frequency (RF) band selection. Magnetostatic wave (MSW) filters stand out for their wide, continuous frequency tuning and high-quality factor. However, MSW filters employing electromagnets for tuning consume excessive power and space, unsuitable for consumer wireless applications. Here, we demonstrate miniature and high selectivity MSW tunable filters with zero static power consumption, occupying less than 2 cc. The center frequency is continuously tunable from 3.4 GHz to 11.1 GHz via current pulses of sub-millisecond duration applied to a small and nonvolatile magnetic bias assembly. This assembly is limited in the area over which it can achieve a large and uniform magnetic field, necessitating filters realized from small resonant cavities micromachined in thin films of Yttrium Iron Garnet. Filter insertion loss of 3.2 dB to 5.1 dB and out-of-band third order input intercept point greater than 41 dBm are achieved. The filter's broad frequency range, compact size, low insertion loss, high out-of-band linearity, and zero static power consumption are essential for protecting RF transceivers and antennas from interference, thus facilitating their use in mobile applications like IoT and 6G networks., Comment: 65 pages, PDF; one supplementary note added, Revised spelling error in acknowledgement, results unchanged

Al$_{0.68}$Sc$_{0.32}$N (AlScN) has gained attention for its outstanding ferroelectric properties, including a high coercive field and high remnant polarization. Although AlScN-based ferroelectric field-effect transistors (FETs) for memory applications have been demonstrated, a device for logic applications with minimal hysteresis has not been reported. This study reports on the transport characteristics of a MoS$_{2}$ negative capacitance FET (NCFET) based on an AlScN ferroelectric material. We experimentally demonstrate the effect of a dielectric layer in the gate stack on the memory window and subthreshold swing (SS) of the NCFET. We show that the hysteresis behavior of transfer characteristics in the NCFET can be minimized with the inclusion of a non-ferroelectric dielectric layer, which fulfills the capacitance-matching condition. Remarkably, we also observe the NC effect in MoS$_{2}$/AlScN NCFETs arrays based on large-area monolayer MoS$_{2}$ synthesized by chemical vapor deposition, showing the SS values smaller than its thermionic limit (~36-60 mV/dec) and minimal variation in threshold voltages (< 20 mV)., Comment: MS + SI

Two-dimensional (2D) indium monoselenide (InSe) has attracted significant attention as a III-VI two-dimensional semiconductor (2D) with a combination of favorable attributes from III-V semiconductors as well as van der Waals 2D transition metal dichalcogenides. Nevertheless, the large-area synthesis of phase-pure 2D InSe remains unattained due to the complexity of the binary In-Se system and the difficulties in promoting lateral growth. Here, we report the first polymorph-selective synthesis of epitaxial 2D InSe by metal-organic chemical deposition (MOCVD) over 2 inch diameter sapphire wafers. We achieve thickness-controlled, layer-by-layer epitaxial growth of InSe on c-plane sapphire via dynamic pulse control of Se/In flux ratio. The layer-by-layer growth allows thickness control over wafer scale with tunable optical properties comparable to bulk crystals. Finally, the gate-tunable electrical transport suggests that MOCVD-grown InSe could be a potential channel material for back-end-of-line integration in logic transistors with field-effect mobility comparable to single-crystalline flakes., Comment: MS + SI

Source-free domain adaptation (SFDA) aims to transfer knowledge learned from a source domain to an unlabeled target domain, where the source data is unavailable during adaptation. Existing approaches for SFDA focus on self-training usually including well-established entropy minimization techniques. One of the main challenges in SFDA is to reduce accumulation of errors caused by domain misalignment. A recent strategy successfully managed to reduce error accumulation by pseudo-labeling the target samples based on class-wise prototypes (centroids) generated by their clustering in the representation space. However, this strategy also creates cases for which the cross-entropy of a pseudo-label and the minimum entropy have a conflict in their objectives. We call this conflict the centroid-hypothesis conflict. We propose to reconcile this conflict by aligning the entropy minimization objective with that of the pseudo labels' cross entropy. We demonstrate the effectiveness of aligning the two loss objectives on three domain adaptation datasets. In addition, we provide state-of-the-art results using up-to-date architectures also showing the consistency of our method across these architectures.

The point vortex system is a system of longstanding interest in nonlinear dynamics, describing the motion of a two-dimensional inviscid fluid that is irrotational except at a discrete set of moving point vortices, at which the vorticity diverges. The leapfrogging orbit consists of two rotating pairs of like-signed vortices which, taken as a quartet, propagate at constant velocity. It is known that if the two pairs are initially widely separated, the motion is stable, while if they are closer together it becomes unstable, with this relation represented by a dimensionless parameter $\alpha$ defined in the text. We here demonstrate analytically that the transition from stability to instability happens at a critical value $\alpha = \phi^{-2}$, where $\phi$ is the golden ratio. This value had been hypothesized based on careful numerics by Toph{\o}j and Aref, and by the present authors using a semi-analytic argument but not previously demonstrated through exact analysis., Comment: 13 pages, 3 figures

Prediction models are typically optimized independently from decision optimization. A smart predict then optimize (SPO) framework optimizes prediction models to minimize downstream decision regret. In this paper we present dboost, the first general purpose implementation of smart gradient boosting for `predict, then optimize' problems. The framework supports convex quadratic cone programming and gradient boosting is performed by implicit differentiation of a custom fixed-point mapping. Experiments comparing with state-of-the-art SPO methods show that dboost can further reduce out-of-sample decision regret.

The deluge of sensors and data generating devices has driven a paradigm shift in modern computing from arithmetic-logic centric to data-centric processing. Data-centric processing require innovations at device level to enable novel compute-in-memory (CIM) operations. A key challenge in construction of CIM architectures is the conflicting trade-off between the performance and their flexibility for various essential data operations. Here, we present a transistor-free CIM architecture that permits storage, search and neural network operations on sub-50nm thick Aluminum Scandium Nitride ferroelectric diodes (FeDs). Our circuit designs and devices can be directly integrated on top of Silicon microprocessors in a scalable process. By leveraging the field-programmability, non-volatility and non-linearity of FeDs, search operations are demonstrated with a cell footprint < 0.12 um2 when projected onto 45-nm node technology. We further demonstrate neural network operations with 4-bit operation using FeDs. Our results highlight FeDs as candidates for efficient and multifunctional CIM platforms.

TIC137608661/TYC4544-2658-1/FBS0938+788 is a new sdBV+dM reflection-effect binary discovered by the TESS space mission with an orbital period of 7.21 hours. In addition to the orbital frequency and its harmonics, the Fourier transform of TIC137608661 shows many g-mode pulsation frequencies from the sdB star. The amplitude spectrum is particularly simple to interpret as we immediately see several rotational triplets of equally spaced frequencies. The central frequencies of these triplets are equally spaced in period with a mean period spacing of 270.12 s, corresponding to consecutive l=1 modes. From the mean frequency spacing of 1.25 {\mu}Hz we derive a rotation period of 4.6 days in the deep layers of the sdB star, significantly longer than the orbital period. Among the handful of sdB+dM binaries for which the sdB rotation was measured through asteroseismology, TIC137608661 is the non-synchronized system with both the shortest orbital period and the shortest core rotation period. Only NY Vir has a shorter orbital period but it is synchronized. From a spectroscopic follow-up of TIC137608661 we measure the radial velocities of the sdB star, determine its atmospheric parameters, and estimate the rotation rate at the surface of the star. This measurement allows us to exclude synchronized rotation also in the outer layers and suggests a differential rotation, with the surface rotating faster than the core, as found in few other similar systems. Furthermore, an analysis of the spectral energy distribution of TIC137608661, together with a comparison between sdB pulsation properties and asteroseismic models, gives us further elements to constrain the system., Comment: Accepted for publication in MNRAS Main Journal

Intimate integration of memory devices with logic transistors is a frontier challenge in computer hardware. This integration is essential for augmenting computational power concurrently with enhanced energy efficiency in big-data applications such as artificial intelligence. Despite decades of efforts, reliable, compact, energy efficient and scalable memory devices are elusive. Ferroelectric Field Effect Transistors (FE-FETs) are a promising candidate but their scalability and performance in a back-end-of-line (BEOL) process remain unattained. Here, we present scalable BEOL compatible FE-FETs using two-dimensional (2D) MoS2 channel and AlScN ferroelectric dielectric. We have fabricated a large array of FE-FETs with memory windows larger than 7.8 V, ON/OFF ratios of greater than 10^7, and ON current density greater than 250 uA/um, all at ~80 nm channel lengths. Our devices show stable retention up to 20000 secs and endurance up to 20000 cycles in addition to 4-bit pulse programmable memory features thereby opening a path towards scalable 3D hetero-integration of 2D semiconductor memory with Si CMOS logic.

Mean-variance optimization (MVO) is known to be sensitive to estimation error in its inputs. Norm penalization of MVO programs is a regularization technique that can mitigate the adverse effects of estimation error. We augment the standard MVO program with a convex combination of parameterized $L_1$ and $L_2$-norm penalty functions. The resulting program is a parameterized quadratic program (QP) whose dual is a box-constrained QP. We make use of recent advances in neural network architecture for differentiable QPs and present a data-driven framework for optimizing parameterized norm-penalties to minimize the downstream MVO objective. We present a novel technique for computing the derivative of the optimal primal solution with respect to the parameterized $L_1$-norm penalty by implicit differentiation of the dual program. The primal solution is then recovered from the optimal dual variables. Historical simulations using US stocks and global futures data demonstrate the benefit of the data-driven optimization approach.

We address the problem of reshaping light in the Schr\"odinger optics regime from the perspective of optimal control theory. In technological applications, Schr\"odinger optics is often used to model a slowly-varying amplitude of a para-axially propagating electric field where the square of the waveguide's index of refraction is treated as the potential. The objective of the optimal control problem is to find the controlling potential which, together with the constraining Schr\"odinger dynamics, optimally reshape the intensity distribution of Schr\"odinger eigenfunctions from one end of the waveguide to the other. This work considers reshaping problems found in work due to Kunkel and Leger, and addresses computational needs by adopting tools from the quantum control literature. The success of the optimal control approach is demonstrated numerically.

Applications of Bose-Einstein Condensates (BEC) often require that the condensate be prepared in a specific complex state. Optimal control is a reliable framework to prepare such a state while avoiding undesirable excitations, and, when applied to the time-dependent Gross-Pitaevskii Equation (GPE) model of BEC in multiple space dimensions, results in a large computational problem. We propose a control method based on first reducing the problem, using a Galerkin expansion, from a PDE to a low-dimensional Hamiltonian ODE system. We then apply a two-stage hybrid control strategy. At the first stage, we approximate the control using a second Galerkin-like method known as CRAB to derive a finite-dimensional nonlinear programming problem, which we solve with a differential evolution (DE) algorithm. This search method then yields a candidate local minimum which we further refine using a variant of gradient descent. This hybrid strategy allows us to greatly reduce excitations both in the reduced model and the full GPE system.