Ting Mei | Searcharxiv

arXiv2025

Linear and nonlinear optical tuning with Sb$_2$S$_3$-based metasurfaces

Here, we experimentally demonstrate the unique properties of Sb$_2$S$_3$ metasurfaces on monolithic and hybridised Sb$_2$S$_3$-Si platforms. Their advantages are particularly pronounced in the telecommunication spectral range, where both phases remain nearly lossless together with a large and stable refractive index contrast compared to other counterparts. The monolithic metasurface enables transmission modulation depths of up to 92\% and resonance shifts as large as $\sim$150~nm at the telecommunication wavelengths through laser-induced phase transitions from amorphous to $\sim$ 50\% polycrystalline states. Furthermore, we demonstrate that integrating a silicon overlayer introduces high-Q hybrid resonances with enhanced near-field confinement, enabling comparable modulation, experimentally, with nearly half the laser switching power required as compared to the monolithic structure. Beyond linear optical switching, the broad resonance tunability of the Sb$_2$S$_3$ metasurface, together with the strong third-order nonlinearity of these materials, provides a promising platform for tunable nonlinear light generation. By exciting the Sb$_2$S$_3$ metasurfaces with a fixed broadband pump, we experimentally demonstrate tunable third-harmonic generation emission over a $\sim$40~nm spectral range through phase-change transition. Such tunability provides a versatile route for integrating Sb$_2$S$_3$ with intrinsically highly nonlinear materials to enable the combination of large optical tunability and efficient nonlinear light generation. We have proven this concept via our hybrid Sb$_2$S$_3$-Si platform, which shows a threefold enhancement in tunable THG emission arising from the combined nonlinear responses of Sb$_2$S$_3$ and silicon, and benefiting from enhanced electromagnetic field confinement enabled by the metasurface's high-Q resonances.

physics.optics↗

arXiv2013

Compactness of commutators of bilinear maximal Calderón-Zygmund singular integral operators

Let $T$ be a bilinear Calderón-Zygmund singular integral operator and $T_*$ be its corresponding truncated maximal operator. The commutators in the $i$-$th$ entry and the iterated commutators of $T_*$ are defined by $$ T_{\ast,b,1}(f,g)(x)=\sup_{δ>0}\bigg|\iint_{|x-y|+|x-z|>δ}K(x,y,z)(b(y)-b(x))f(y)g(z)dydz\bigg|, $$ $$T_{\ast,b,2}(f,g)(x)=\sup_{δ>0}\bigg|\iint_{|x-y|+|x-z|>δ}K(x,y,z)(b(z)-b(x))f(y)g(z)dydz\bigg|,$$ \begin{align*} T_{\ast,(b_1,b_2)}(f,g)(x)=\sup\limits_{δ>0}\bigg|\iint_{|x-y|+|x-z|>δ} K(x,y,z)(b_1(y)-b_1(x))(b_2(z)-b_2(x))f(y)g(z)dydz\bigg|. \end{align*} In this paper, the compactness of the commutators $T_{\ast,b,1}$, $T_{\ast,b,2}$ and $T_{\ast,(b_1,b_2)}$ on $L^r(\mathbb{R}^n))$ is established.

math.CA↗

arXiv2013

Sharp Weighted Bounds for Multilinear fractional Maximal type Operators with Rough Kernels

In this paper, we will give the weighted bounds for multilinear fractional maximal type operators $\mathcal{M}_{Ω,α}$ with rough homogeneous kernels. We obtain a mixed $A_{(\vec{P},q)}-A_\infty$ bound and a $A_{\vec{P}}$ type estimate for $\mathcal{M}_{Ω,α}$. As an application, we give an almost sharp estimate for the multilinear fractional integral operator with rough kernels $\mathcal{I}_{Ω,α}$.

math.CA↗