Many photonic design problems are sparse QCQPs.

Photonic design is a process of mathematical optimization of a desired objective (beam formation, mode conversion, etc.) subject to the constraint of Maxwell's equations. Finding the optimal design is challenging: Generically, these problems are highly nonconvex and finding global optima is NP hard.

Fundamental limits to multi-functional and tunable nanophotonic response.

Tunable and multi-functional nanophotonic devices are used for applications from beam steering to sensing. Yet little is understood about fundamental limits to their functionality. The difficulty lies with the fact that it is a single structure that must exhibit optimal response over multiple scenarios.

Assessing base-resolution DNA mechanics on the genome scale.

Intrinsic DNA properties including bending play a crucial role in diverse biological systems. A recent advance in a high-throughput technology called loop-seq makes it possible to determine the bendability of hundred thousand 50-bp DNA duplexes in one experiment. However, it's still challenging to assess base-resolution sequence bendability in large genomes such as human, which requires thousands of such experiments.

Conservation-Law-Based Global Bounds to Quantum Optimal Control.

Active control of quantum systems enables diverse applications ranging from quantum computation to manipulation of molecular processes. Maximum speeds and related bounds have been identified from uncertainty principles and related inequalities, but such bounds utilize only coarse system information and loosen significantly in the presence of constraints and complex interaction dynamics. We show that an integral-equation-based formulation of conservation laws in quantum dynamics leads to a systematic framework for identifying fundamental limits to any quantum control scenario.

Computational Bounds to Light-Matter Interactions via Local Conservation Laws.

We develop a computational framework for identifying bounds to light-matter interactions, originating from polarization-current-based formulations of local conservation laws embedded in Maxwell's equations. We propose an iterative method for imposing only the maximally violated constraints, enabling rapid convergence to global bounds. Our framework can identify bounds to the minimum size of any scatterer that encodes a specific linear operator, given only its material properties, as we demonstrate for the optical computation of a discrete Fourier transform.

Broadband Variable Meta-Axicons Based on Nano-Aperture Arrays in a Metallic Film.

Metasurfaces are two-dimensional metamaterials composed of a carefully designed series of subwavelength meta-atom (antenna or aperture) arrays. These surfaces can manipulate the phase, amplitude and polarization of output light by changing the shapes and orientations of the meta-atoms on a subwavelength scale. Using these properties, we experimentally demonstrate variable meta-axicons composed of rectangular nano-apertures arranged in several concentric rings that can focus left circularly polarized (LCP) light into a real Bessel beam and defocus right circular polarized (RCP) light to form a virtual beam.

Electrochromic-Tuned Plasmonics for Photothermal Sterile Window.

Electrochromic materials are widely used in smart windows. An ideal future electrochromic window would be able to control visible light transmission, tune building's heat conversion of near-infrared (NIR) solar radiation, and reduce attacks by microorganisms. To date, most of the reports have primarily focused on visible-light transmission modulation using electrochromic materials.

Next Generation of Phonon Tests of Lorentz Invariance Using Quartz BAW Resonators.

We demonstrate technological improvements in phonon sector tests of the Lorentz invariance that implement quartz bulk acoustic wave oscillators. In this experiment, room temperature oscillators with state-of-the-art phase noise are continuously compared on a platform that rotates at a rate of order of a cycle per second. The discussion is focused on improvements in noise measurement techniques, data acquisition, and data processing.

Examining second-harmonic generation of high-order Laguerre-Gaussian modes through a single cylindrical lens.

We experimentally investigate the second-harmonic generation of a high-order Laguerre-Gaussian (LG) mode under the quasi-phase-matching (QPM) configuration. First, we introduce a simple method to observe the azimuthal (l) and radial (p) indices of the high-order LG modes. Based on the astigmatic transformation technique, l and p are revealed in the number of dark stripes of the converted pattern in the focal plane.

On-chip generation of broadband high-order Laguerre-Gaussian modes in a metasurface.

With experimental results, we demonstrate the generation of high-order Laguerre-Gaussian modes with non-zero radial indices using a metal meta-surface, which is composed of a series of rectangle nanoholes with different orientation angles. The phase shift after transmission through the metasurface is determined by the orientation angle of the nanohole. This device works over a broad wavelength band ranging from 700 to 1000 nm.