arXiv subjects

Songyan Hou

Publications and source records attributed to Songyan Hou.

17 recordsLinked to original sources

arXiv2026

Broadband temporal localization and delocalized temporal edge states in time photonic crystals

Time photonic crystals have attracted growing attention in recent years owing to their abilities to enable broadband field enhancements, e.g., free-space electromagnetic waves, dipolar emissions, free-electron radiation, etc. While the non-Hermitian nature of time photonic crystals is primarily attributed to their dependence on external temporal modulations, the constituent materials are oftentimes assumed to be Hermitian. How the material-induced non-Hermiticity interplays with the intrinsic non-Hermitian dynamics of time photonic crystals remains rarely explored. In this work, we demonstrate that the non-Hermiticity arising from the bi-anisotropic electromagnetic response of materials introduces a new mechanism to manipulate the localization of temporal bulk and edge states in time photonic crystals. To be specific, the temporal bulk states in our configurations exhibit remarkable attenuation or amplification, which is theoretically predicted by extending the generalized Brillouin zone framework to the temporal domain. Our analysis reveals that the attenuation or amplification strength, quantified by the temporal penetration depth, is directly governed by electromagnetic constitutive parameters. By appropriately tuning these parameters, we uncover new phenomena including broadband temporal localization, i.e. the collective concentration of energy towards a certain time moment, and delocalized temporal edge states.

physics.optics↗

arXiv2026

The geometry of the adapted Bures--Wasserstein space

The adapted Bures--Wasserstein space consists of Gaussian processes endowed with the adapted Wasserstein distance. It can be viewed as the analogue of the classical Bures--Wasserstein space in optimal transport for the setting of stochastic processes, where the standard Wasserstein distance is inadequate and has to be replaced by its adapted counterpart. We develop a comprehensive geometric theory for the adapted Bures--Wasserstein space, thereby also providing the first results on the fine geometric structure of adapted optimal transport. In particular, we show that the adapted Bures--Wasserstein space is an Alexandrov space with non-negative curvature and provide explicit descriptions of tangent cones and exponential maps. Moreover, we show that Gaussian processes satisfying a natural non-degeneracy condition form a geodesically convex subspace. This subspace is characterized precisely by the property that its tangent cones are linear and hence coincide with the tangent space.

math.PR↗

arXiv2025

Nested Optimal Transport Distances

Simulating realistic financial time series is essential for stress testing, scenario generation, and decision-making under uncertainty. Despite advances in deep generative models, there is no consensus metric for their evaluation. We focus on generative AI for financial time series in decision-making applications and employ the nested optimal transport distance, a time-causal variant of optimal transport distance, which is robust to tasks such as hedging, optimal stopping, and reinforcement learning. Moreover, we propose a statistically consistent, naturally parallelizable algorithm for its computation, achieving substantial speedups over existing approaches.

cs.LG↗

arXiv2025

Estimating causal distances with non-causal ones

The adapted Wasserstein ($AW$) distance refines the classical Wasserstein ($W$) distance by incorporating the temporal structure of stochastic processes. This makes the $AW$-distance well-suited as a robust distance for many dynamic stochastic optimization problems where the classical $W$-distance fails. However, estimating the $AW$-distance is a notably challenging task, compared to the classical $W$-distance. In the present work, we build a sharp estimate for the $AW$-distance in terms of the $W$-distance, for smooth measures. This reduces estimating the $AW$-distance to estimating the $W$-distance, where many well-established classical results can be leveraged. As an application, we prove a fast convergence rate of the kernel-based empirical estimator under the $AW$-distance, which approaches the Monte-Carlo rate ($n^{-1/2}$) in the regime of highly regular densities. These results are accomplished by deriving a sharp bi-Lipschitz estimate of the adapted total variation distance by the classical total variation distance.

math.PR↗

arXiv2024

Entropic adapted Wasserstein distance on Gaussians

The adapted Wasserstein distance is a metric for quantifying distributional uncertainty and assessing the sensitivity of stochastic optimization problems on time series data. A computationally efficient alternative to it, is provided by the entropically regularized adapted Wasserstein distance. Suffering from similar shortcomings as classical optimal transport, there are only few explicitly known solutions to those distances. Recently, Gunasingam--Wong provided a closed-form representation of the adapted Wasserstein distance between real-valued stochastic processes with Gaussian laws. In this paper, we extend their work in two directions, by considering multidimensional ($\mathbb{R}^d$-valued) stochastic processes with Gaussian laws and including the entropic regularization. In both settings, we provide closed-form solutions.

math.OC↗

arXiv2024

Time-Causal VAE: Robust Financial Time Series Generator

We build a time-causal variational autoencoder (TC-VAE) for robust generation of financial time series data. Our approach imposes a causality constraint on the encoder and decoder networks, ensuring a causal transport from the real market time series to the fake generated time series. Specifically, we prove that the TC-VAE loss provides an upper bound on the causal Wasserstein distance between market distributions and generated distributions. Consequently, the TC-VAE loss controls the discrepancy between optimal values of various dynamic stochastic optimization problems under real and generated distributions. To further enhance the model's ability to approximate the latent representation of the real market distribution, we integrate a RealNVP prior into the TC-VAE framework. Finally, extensive numerical experiments show that TC-VAE achieves promising results on both synthetic and real market data. This is done by comparing real and generated distributions according to various statistical distances, demonstrating the effectiveness of the generated data for downstream financial optimization tasks, as well as showcasing that the generated data reproduces stylized facts of real financial market data.

cs.LG↗

arXiv2024

Generalized coherent wave control at dynamic interfaces

Coherent wave control is of key importance across a broad range of fields such as electromagnetics, photonics, and acoustics. It enables us to amplify or suppress the outgoing waves via engineering amplitudes and phases of multiple incidences. However, within a purely spatially (temporally) engineered medium, coherent wave control requires the frequency of the associated incidences to be identical (opposite). In this work, we break this conventional constraint by generalizing coherent wave control into a spatiotemporally engineered medium, i.e., the system featuring a dynamic interface. Owing to the broken translational symmetry in space and time, both the subluminal and superluminal interfaces allow interference between scattered waves regardless of their different frequencies and wavevectors. Hence, one can flexibly eliminate the backward- or forward-propagating waves scattered from the dynamic interfaces by controlling the incident amplitudes and phases. Our work not only presents a generalized way for reshaping arbitrary waveforms but also provides a promising paradigm to generate ultrafast pulses using low-frequency signals. We have also implemented suppression of forward-propagating waves in microstrip transmission lines with fast photodiode switches.

physics.optics↗

arXiv2024

Broadband transmissive polarization rotator by gradiently-twisted $\alpha$-MoO$_3$

Polarization engineering has been proven to enhance the capabilities of light manipulation and thus facilitate the development of integrated photonic devices. In this study, we introduce a polarization rotator based on gradiently-twisted $\alpha$-MoO$_3$ thin film, that works for the mid infrared range and functions in a transmission mode. To be specific, the proposed device is constructed by gradiently-twisted $\alpha$-MoO$_3$ multilayers with a subwavelength thickness of only 5 microns, namely, one-third of the working wavelength. Our analytical calculation demonstrates the efficacy of this subwavelength thin film rotator in converting a linearly polarized wave into its orthogonal counterpart, thanks to its chiral nature. The twisted $\alpha$-MoO$_3$ multilayers exhibit the capability to significantly manipulate dispersion characteristics while maintaining low optical losses, thereby enabling a wide bandwidth exceeding 2.5 THz with a polarization ratio surpassing 17 dB. Moreover, the operational frequency can be adjusted across a 3.4 THz range by altering the incident angle of the incident waves. This adaptable design, characterized by its polarization versatility, can be customized to suit practical applications within wireless communication, radar systems, optical switching, and imaging technologies.

physics.optics↗

arXiv2024

Tunable double notch filter on thin-film lithium niobate platform

Tunable optical filter at the chip scale plays a crucial role in fulfilling the need for the reconfigurability in channel routing, optical switching, and wavelength division multiplexing systems. In this letter, we propose a tunable double notch filter on thin-film lithium niobate using dual micro-ring architecture. This unique integrated filter is essential for complex photonic integrated circuits, along with multiple channels and various frequency spacing. With only one loaded voltage, the device demonstrates a wide frequency spacing tunability from 16.1 GHz to 89.9 GHz by reversely tunning the resonances of the two micro-rings while the center wavelength between the two resonances remains unaltered. Moreover, by utilizing the pronounced electro-optic properties of lithium niobate, associated with the tight light confinement nanophotonic waveguides, the device demonstrates a spacing tunability of 0.82 GHz/V and a contrast of 10~16 dB. In addition, the device has an ultracompact footprint of 0.0248 mm2.

physics.optics↗

arXiv2024

Convergence of the Adapted Smoothed Empirical Measures

The adapted Wasserstein distance controls the calibration errors of optimal values in various stochastic optimization problems, pricing and hedging problems, optimal stopping problems, etc. However, statistical aspects of the adapted Wasserstein distance are bottlenecked by the failure of empirical measures to converge under this distance. Kernel smoothing and adapted projection have been introduced to construct converging substitutes of empirical measures, known respectively as smoothed empirical measures and adapted empirical measures. However, both approaches have limitations. Specifically, smoothed empirical measures lack comprehensive convergence results, whereas adapted empirical measures in practical applications lead to fewer distinct samples compared to standard empirical measures. In this work, we address both of the aforementioned issues. First, we develop comprehensive convergence results of smoothed empirical measures. We then introduce a smoothed version for adapted empirical measures, which provide as many distinct samples as desired. We refer them as adapted smoothed empirical measures and establish their convergence in mean, deviation, and almost sure convergence. The convergence estimation incorporates two results: the empirical analysis of the smoothed adapted Wasserstein distance and its bandwidth effects. Both results are novel and their proof techniques could be of independent interest.

math.PR↗

arXiv2023

Instance-Dependent Generalization Bounds via Optimal Transport

Existing generalization bounds fail to explain crucial factors that drive the generalization of modern neural networks. Since such bounds often hold uniformly over all parameters, they suffer from over-parametrization and fail to account for the strong inductive bias of initialization and stochastic gradient descent. As an alternative, we propose a novel optimal transport interpretation of the generalization problem. This allows us to derive instance-dependent generalization bounds that depend on the local Lipschitz regularity of the learned prediction function in the data space. Therefore, our bounds are agnostic to the parametrization of the model and work well when the number of training samples is much smaller than the number of parameters. With small modifications, our approach yields accelerated rates for data on low-dimensional manifolds and guarantees under distribution shifts. We empirically analyze our generalization bounds for neural networks, showing that the bound values are meaningful and capture the effect of popular regularization methods during training.

stat.ML↗

arXiv2023

Convergence of Adapted Empirical Measures on $\mathbb{R}^{d}$

We consider empirical measures of $\R^{d}$-valued stochastic process in finite discrete-time. We show that the adapted empirical measure introduced in the recent work \cite{backhoff2022estimating} by Backhoff et al. in compact spaces can be defined analogously on $\R^{d}$, and that it converges almost surely to the underlying measure under the adapted Wasserstein distance. Moreover, we quantitatively analyze the convergence of the adapted Wasserstein \add{distance} between those two measures. We establish convergence rates of the expected error as well as the deviation error under different moment conditions. \add{Under suitable integrability and kernel assumptions, we recover the optimal convergence rates of both expected error and deviation error.} Furthermore, we propose a modification of the adapted empirical measure with \add{projection} on a non-uniform grid, which obtains the same convergence rate but under weaker assumptions.

math.PR↗

arXiv2023

Improving Linewidth and Extinction Ratio Performances of Lithium Niobate Ring Modulator Using Ring-pair Structure

Electro-optic modulators lie at the heart of complex integration and high density electro-optic systems. One of the representative electro-optic modulators is thin film lithium niobate based microring modulator which has demonstrated advantages of compact footprint, low optical loss and high modulation efficiency. However, the linewidth and extinction ratio of ring modulators are fundamentally limited by the ring losses and coupling, respectively. To this end, we propose a novel type of electro-optic modulators with ring-pair structure on thin film lithium niobate platform, which brings substantially improvement of linewidth and extinction ratio. The ring-pair modulator exhibits a larger linewidth up to 22 GHz, 1.74-time larger than that of single ring resonator with same design parameters. Moreover, the experimental results also reveal that the added-up extinction ratio of ring-pair resonator goes beyond 30 dB, much larger than that in an individual ring resonator. These advantages of ring-pair modulator pave a new way for the application of compact ring-based modulators with large working wavelength window and high extinction ratio, to be exploited in quantum optics, programmable nanophotonics and optical sensors, etc.

physics.optics↗

arXiv2022

Visible-telecom broadband optical isolator based on dynamic modulation in thin-film lithium niobate

Optical isolators are an essential component of photonic systems. Current integrated optical isolators have limited bandwidths due to stringent phase-matching conditions, resonant structures, or material absorption. Here, we demonstrate an ultra-broadband integrated optical isolator in thin-film lithium niobate photonics. We use dynamic standing-wave modulation in a tandem configuration to break Lorentz reciprocity and achieve isolation. We measure an isolation ratio of 15 dB and insertion loss below 0.5 dB for a design wavelength of 1550 nm. In addition, we experimentally show that this isolator can simultaneously operate at visible and telecom wavelengths with comparable performance. Isolation bandwidths ~100 nm can be achieved simultaneously at both visible and telecom wavelengths. Our device's large bandwidth, high flexibility, and real-time tunability can enable novel non-reciprocal functionality on integrated photonic platforms.

physics.optics↗

arXiv2021

Deep Partial Hedging

Using techniques from deep learning (cf. [Büh+19]), we show that neural networks can be trained successfully to replicate the modified payoff functions that were first derived in the context of partial hedging by [FL00]. Not only does this approach better accommodate the realistic setting of hedging in discrete time, it also allows for the inclusion of transaction costs as well as general market dynamics.

q-fin.MF↗

arXiv2021

Ultra-broadband quadrature squeezing with thin-film lithium niobate nanophotonics

Squeezed light is a key quantum resource that enables quantum advantages for sensing, networking, and computing applications. The scalable generation and manipulation of squeezed light with integrated platforms are highly desired for the development of quantum technology with continuous variables. In this letter, we demonstrate squeezed light generation with thin-film lithium niobate integrated photonics. Para-metric down-conversion is realized with quasi-phase matching using ferroelectric domain engineering. With sub-wavelength mode confinement, efficient nonlinear processes can be observed with single-pass configuration. We measure0.56+-0.09dB quadrature squeezing(~3 dB inferred on-chip). The single-pass configuration further enables the generation of squeezed light with large spectral bandwidth up to 7 THz. This work represents a significant step towards the on-chip implementation of continuous-variable quantum information processing

physics.optics↗

arXiv2019

Manipulating Coherent Light Matter Interaction: Continuous Transition between Strong Coupling and Weak Coupling in MoS2 Monolayer Coupled with Plasmonic Nanocavities

Strong interactions between surface plasmons in ultra-compact nanocavities and excitons in two dimensional materials have attracted wide interests for its prospective realization of polariton devices at room temperature. Here, we propose a continuous transition from weak coupling to strong coupling between excitons in MoS2 monolayer and highly localized plasmons in ultra-compact nanoantenna. The nanoantenna is assembled by a silver nanocube positioned over a gold film and separated by a dielectric spacer layer. We observed a 1570-fold enhancement in the photoluminescence at weak coupling regime in hybrid nanocavities with thick spacer layers. The interaction between excitons and plasmons is then directly prompted to strong coupling regime by shrinking down the thickness of spacer layer. Room temperature formation of polaritons with Rabi splitting up to 190 meV was observed, which is the largest plasmon-exciton Rabi splitting reported in two dimensional materials. Numerical calculations quantified the relation between coupling strength, local density of states and spacer thickness, and revealed the transition between weak coupling and strong coupling in nanocavities. The findings in this work offer a guideline for feasible designs of plasmon-exciton interaction systems with gap plasmonic cavities.

cond-mat.mes-hall↗