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The department's graduate programs include a PhD program in mathematics and MA programs in mathematics and in computer science. The research emphasis at Wesleyan at the doctoral level is in pure mathematics and theoretical computer science. One of the distinctive features of our department is the close interaction between the computer science faculty and the mathematics faculty, particularly those in logic and discrete mathematics.

Mathematics and computer science

Non-Hermitian systems with their spectral degeneracies known as exceptional points (EPs) have been explored for lasing, controlling light transport, and enhancing a sensor s response. A ring resonator can be brought to an EP by controlling the coupling between its frequency degenerate clockwise and counterclockwise traveling modes. This has been typically achieved by introducing two or more nanotips into the resonator s mode volume. While this method provides a route to study EP physics, the basic understanding of how the nanotips shape and size symmetry impact the system s non-Hermicity is missing, along with additional loss from both in-plane and out-of-plane scattering. The limited resonance stability poses a challenge for leveraging EP effects for switches or modulators, which requires stable cavity resonance and fixed laser-cavity detuning. Here we use lithographically defined asymmetric and symmetric Mie scatterers, which enable subwavelength control of wave transmission and reflections without deflecting to additional radiation channels. We show that those pre-defined Mie scatterers can bring the system to an EP without post tuning, as well as enable chiral light transport within the resonator. Counterintuitively, the Mie scatterer results in enhanced quality factor measured on the transmission port, through coherently suppressing the backscattering from the waveguide surface roughness. The proposed device platform enables pre-defined chiral light propagation and backscattering-free resonances, needed for various applications such as frequency combs, solitons, sensing, and other nonlinear optical processes such as photon blockade, and regenerative oscillators. 

pdf/chiral-exceptional-point-and-coherent-suppression-of-o11j28gp.pdf

Chiral exceptional point and coherent suppression of backscattering in silicon microring with low loss Mie scatterer

The application of artificial intelligence in everyday life is becoming all-pervasive and unavoidable. Within that vast field, a special place belongs to biomimetic/bio-inspired algorithms for multiparameter optimization, which find their use in a large number of areas. Novel methods and advances are being published at an accelerated pace. Because of that, in spite of the fact that there are a lot of surveys and reviews in the field, they quickly become dated. Thus, it is of importance to keep pace with the current developments. In this review, we first consider a possible classification of bio-inspired multiparameter optimization methods because papers dedicated to that area are relatively scarce and often contradictory. We proceed by describing in some detail some more prominent approaches, as well as those most recently published. Finally, we consider the use of biomimetic algorithms in two related wide fields, namely microelectronics (including circuit design optimization) and nanophotonics (including inverse design of structures such as photonic crystals, nanoplasmonic configurations and metamaterials). We attempted to keep this broad survey self-contained so it can be of use not only to scholars in the related fields, but also to all those interested in the latest developments in this attractive area.

/pdf/a-comprehensive-review-of-bio-inspired-optimization-1jnalpim.pdf

A Comprehensive Review of Bio-Inspired Optimization Algorithms Including Applications in Microelectronics and Nanophotonics

The tight focusing of an optical vortex with an integer topological charge (TC) and linear polarization was considered. We showed that the longitudinal components of the spin angular momentum (SAM) (it was equal to zero) and orbital angular momentum (OAM) (it was equal to the product of the beam power and the TC) vectors averaged over the beam cross-section were separately preserved during the beam propagation. This conservation led to the spin and orbital Hall effects. The spin Hall effect was expressed in the fact that the areas with different signs of the SAM longitudinal component were separated from each other. The orbital Hall effect was marked by the separation of the regions with different rotation directions of the transverse energy flow (clockwise and counterclockwise). There were only four such local regions near the optical axis for any TC. We showed that the total energy flux crossing the focus plane was less than the total beam power since part of the power propagated along the focus surface, while the other part crossed the focus plane in the opposite direction. We also showed that the longitudinal component of the angular momentum (AM) vector was not equal to the sum of the SAM and the OAM. Moreover, there was no summand SAM in the expression for the density of the AM. These quantities were independent of each other. The distributions of the AM and the SAM longitudinal components characterized the orbital and spin Hall effects at the focus, respectively.

https://www.mdpi.com/2072-666X/14/4/788/pdf?version=1680250992

Hall Effect at the Focus of an Optical Vortex with Linear Polarization

Spatial self-phase modulation (SSPM) effect is widely used in the characterization of 2D nanomaterials because of its terse principle and intuitive experimental setup, although the understanding of its physical mechanism is still incomplete so far. Herein, we use the truncated Gaussian beam (TGB) along the horizontal direction to investigate the SSPM effect in solution dispersions of black phosphorus (BP) nanosheets. By means of the gravity-promoted thermal convection effect, we observe the spatial separation of the circular symmetric narrow rings and the distorted wide rings in the upper half of the SSPM patterns at 532 nm and 1064 nm when the laser beam propagates horizontally through the vertically placed sample. Based on the theory of local and nonlocal optical nonlinearities and the experiment of the TGB SSPM, we confirm that the narrow and wide rings originate from the optical Kerr nonlinearity (OKN) and the thermally induced nonlinearity (TIN), respectively. This work provides an efficient approach to distinguish the OKN from the TIN in 2D nanomaterial dispersions, to separate their contributions, and to extract nonlinear optical parameters. 

Broadband third-order nonlinear optical responses of black phosphorus nanosheets via spatial self-phase modulation using truncated Gaussian beams

We propose a machine-learning-based method for grating waveguides and augmented reality, significantly reducing the computation time compared with existing finite-element-based numerical simulation methods. Among the slanted, coated, interlayer, twin-pillar, U-shaped, and hybrid structure gratings, we exploit structural parameters such as grating slanted angle, grating depth, duty cycle, coating ratio, and interlayer thickness to construct the gratings. The multi-layer perceptron algorithm based on the Keras framework was used with a dataset comprised of 3000-14,000 samples. The training accuracy reached a coefficient of determination of more than 99.9% and an average absolute percentage error of 0.5%-2%. At the same time, the hybrid structure grating we built achieved a diffraction efficiency of 94.21% and a uniformity of 93.99%. This hybrid structure grating also achieved the best results in tolerance analysis. The high-efficiency artificial intelligence waveguide method proposed in this paper realizes the optimal design of a high-efficiency grating waveguide structure. It can provide theoretical guidance and technical reference for optical design based on artificial intelligence.

Grating waveguides by machine learning for augmented reality.

In this paper, based on the low loss double strip silicon nitride platform, we designed and fabricated an ultra-low loss 1×4 microwave photonic beamforming chip, which contains a 1×4 beam splitter and four 5-bit optical delay lines. Each optical delay line can achieve 32 delay states varying from 0 ps to about 130 ps, which can support 21 different beamforming angles covers from -56.42° to 56.68° for 10 GHz RF signal. A low on-chip insertion loss of about 4 dB is achieved for each 5-bit optical delay line. Furthermore, a very low loss delay ratio of about 0.0016 dB/ps is achieved and a recorded low loss fluctuation of about 0.3 dB is obtained during the 32 states delay switching. In addition, the switching speed and driving power consumptions of the proposed beamforming chip were investigated. The proposed beamforming chip could have great potential in optical controlled phased antenna arrays systems.

Low loss silicon nitride 1×4 microwave photonic beamforming chip.

Performance comparison of integrated optical switching delay lines on three typical photonic integration pilot lines

Microwave frequency combs (MFCs) have important applications in communication and sensing owing to their characteristics of large number of comb lines, wide frequency range, and high precision of comb spacing. In many applications, MFCs are required to emit signals with tunable center frequency and variable comb spacing to accommodate different operating frequency bands and accuracies. Here, we demonstrate a tunable MFC by injecting a low-frequency electrical signal into a tunable optoelectronic oscillator (OEO). Tuning of MFC's center frequency and comb spacing are realized, allowing a frequency tuning range from 1 to 22 GHz and 50 comb lines within a 5 MHz bandwidth obtained in the MFC generator. In addition, the introduction of the silicon nitride micro-disk resonator (Si3N4-MDR) in the system paves the way for the integration of MFC generator.

Tunable microwave frequency comb generation using a Si3N4-MDR based actively mode-locked OEO.

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