arXiv subjects

Kezheng Li

Publications and source records attributed to Kezheng Li.

4 recordsLinked to original sources

arXiv2022

Correction of aberrations via polarization in single layer metalenses

The correction of multiple aberrations in an optical system requires different optical elements, which increases its cost and complexity. Metasurfaces hold great promise to providing new functionality for miniaturized and low-cost optical systems. A key advantage over their bulk counterparts is the metasurface's ability to respond to the polarization of light, which adds a new degree of freedom to the optical design. Here, we show that polarization control enables a form-birefringent metalens to correct for both spherical and off-axis aberrations using a single element only, which is not possible with bulk optics. The metalens encodes two phase profiles onto the same surface, thus allowing switching from high resolution to wide field of view operation. Such ability to obtain both high resolution and wide field of view in a single layer is an important step towards integration of miniaturized optical systems, which may find many applications, e.g., in microscopy and endoscopy.

physics.optics↗

arXiv2016

Efficient silicon metasurfaces for visible light

Dielectric metasurfaces require high refractive index contrast materials for optimum performance. This requirement imposes a severe restraint; devices have either been demonstrated at wavelengths of 700nm and above using high-index semiconductors such as silicon, or they use lower index dielectric materials such as TiO$_{2}$ or Si$_{3}$N$_{4}$ and operate in the visible wavelength regime. Here, we show that the high refractive index of silicon can be exploited at wavelengths as short as 532 nm by demonstrating a silicon metasurface with a transmission efficiency of 47% at this wavelength. The metasurface consists of a graded array of silicon posts arranged in a square lattice on a quartz substrate. We show full 2π phase control and we experimentally demonstrate polarization-independent beam deflection at 532nm wavelength. The crystalline silicon is placed on a quartz substrate by a bespoke layer transfer technique and we note that an efficiency >70% may be achieved for a further optimized structure in the same material. Our results open a new way for realizing efficient metasurfaces based on silicon in the visible wavelength regime.

physics.optics↗

arXiv2012

A direct formulation of Dieudonné module theory

We define a Dieudonné module as the module of Dieudonné elements, and set up Dieudonné module theory in a simple way. Under this formulation we give explicit formulae for the duality and the corresponding differential operators.

math.AG↗

arXiv2007

A Geometric Proof of Mordell's Conjecture for Function Fields

Let $\Cal C,\Cal C'$ be curves over a base scheme $S$ with $g(\Cal C)\ge 2$. Then the functor $T\mapsto\{$generically smooth $T$-morphisms $T\times_S\Cal C'\to T\times_S\Cal C\}$ from $((S$-schemes)) to ((sets)) is represented by a quasi-finite unramified $S$-scheme. From this one can deduce that for any two integers $g\ge 2$ and $g'$, there is an integer $M(g,g')$ such that for any two curves $C,C'$ over any field $k$ with $g(C)=g$, $g(C')=g'$, there are at most $M(g,g')$ separable $k$-morphisms $C'\to C$. It is conjectured that the arithmetic function $M(g,g')$ is bounded by a linear function of $g'$.

math.AG↗