Subwavelength High-contrast Gratings Research Articles

Vectorial far-field method for subwavelength grating based VCSELs

We proposed in detail a procedure for the vectorial far-field analysis of high-contrast subwavelength gratings (HCGs) for vertical cavity surface emitting lasers (VCSELs). The vectorial far-field analysis method (VFM) is based on the vectorial angular spectrum method. The transmission and reflection coefficients of the HCG are used to modulate the polarized far-field components, and the modulated far-field components are vectorially composited to obtain the final transmitted and reflected far-field distribution. The reflectance and transmittance of the HCG to a two-dimensional finite-size beam can be solved by the integral of the output beam. The near field of the transmitted and reflected beam can be solved by an inverse Fourier transform of the far-field distribution. The VFM can be effectively applied in the transmit and reflect far-field beam shaping design and polarization analysis of HCG-VCSELs. The near field reconstructed by VFM can be applied to the calculation of coupling efficiency and lens design. The results of VFM are verified by a three-dimensional finite-difference time domain based on the licensed RSoft FullWAVE tool. VFM only needs to calculate a single-period structure, and the response of HCG to various near-field distributions can be obtained by one calculation, which provides an efficient and accurate method for the design of polarized HCG-VCSELs. The VFM reveals the underlying physics of the shaping effect of subwavelength grating on polarized beams and can be easily extended to the far-field analysis of arbitrary periodical meta-surfaces.

Surface-Impedance Formulation for Hollow-Core Waveguides Based on Subwavelength Gratings

A rigorous Surface Impedance (SI) formulation for planar waveguides is presented. This modal technique splits the modal analysis of the waveguide in two steps. First, we obtain the modes characteristic equations as a function of the SI and, second, we need to obtain the surface impedance values using either analytical or numerical methods. We validate the technique by comparison with well-known analytical cases: the parallel-plate waveguide with losses and the dielectric slab waveguide. Then, we analyze an optical hollow-core waveguide defined by two high-contrast subwavelength gratings validating our results by comparison with reported values. Finally, we show the potential of our formulation with the analysis of a THz hollow-core waveguide defined by two surface-relief subwavelength gratings, including material losses in our formulation.

Dispersion Engineering for a Metastructure Composed of a High‐Contrast Subwavelength Grating and a Distributed Bragg Reflector

High‐contrast subwavelength grating (HCG) and distributed Bragg reflector (DBR) are demonstrated to be able to tailor the dispersion independently. Herein, it is found that multiple‐shape dispersions can be realized by a metastructure, which consists of an HCG on the DBR. Such a simple structure exhibits the linear dispersions with band‐edge modes, the M‐shaped dispersion with a cavity mode, and the W‐shaped dispersion with a bound state in the continuum. The origins of these dispersions and the mode characteristics (field distribution and quality factor) in the dispersions are studied. This study is helpful to realize single‐mode high‐efficiency surface‐emitting lasers, optical sensors, and quantum electrodynamics.

Comprehensive design and simulation of a composite reflector for mode control and thermal management of a high-power VCSEL

We propose a composite top reflector composed of a distributed Bragg reflector (DBR) and a subwavelength high-contrast grating (HCG) for a high-power 808-nm vertical-cavity surface-emitting laser (VCSEL). The DBR and HCG in the reflector are connected by an indium tin oxide (ITO) surrounding layer, which makes it possible for the reflector to improve current injection uniformity and reduce heat generation while providing high reflectivity. The angle-dependent reflectivity of the composite reflector is optimized to suppress the high-order transverse modes of VCSEL while ensuring sufficient fundamental mode feedback. The number of top DBR periods and the thickness of the ITO surrounding layer are optimized to reduce the loss and provide high out-coupling efficiency. The double resonator coupled by top DBR is designed to provide optimal resonant wavelength stability, longitudinal optical confinement factor, and thermoelectric characteristics. Optical simulation results demonstrate that the well-designed configuration can provide a highest fundamental mode reflectivity of 99.7%, an out-coupling efficiency of 65%, a wavelength stability rate of 0.011 with the thickness of the ITO layer, and a confinement factor of 0.05. The transverse modes with order greater than 2 are effectively suppressed. The result of the thermoelectric model shows that the composite reflector-based VCSEL has low operating temperature and uniform current injection; thermal resistance of 0.87 K/mW is realized. In this context, devices with high emission efficiency and beam quality can be expected.

Ultra-broadband reflector using double-layer subwavelength gratings

Double-layer high-contrast subwavelength gratings that are separated by a dielectric space layer are investigated to achieve ultra-broadband reflection. The reflection phase of subwavelength gratings and the propagation phase shift between two gratings are manipulated to expand reflection bandwidth by properly stacking two reflective gratings. A reflector exhibiting a 99% reflectance bandwidth of ∼ 1080 nm in the near-infrared is designed. Then this reflector is prepared using laser interference lithography and ion beam planarization, and an ultra-broadband reflection is achieved with reflectance exceeding 97% over a wavelength range of 955 nm in the near-infrared region.

Design and fabrication of 1[formula omitted]N polarization-insensitive beam splitters based on 2D subwavelength gratings

Based upon the wave front control of transmitted light using 2D high index contrast subwavelength gratings, a kind of 1×N polarization-insensitive beam splitters are proposed and demonstrated, which could redistribute the incident light into N beams while each of them converges to a spot respectively in the relevant subregion. 1×3 and 1×4 beam splitters as typical instances are designed applying the rigorous coupled-wave analysis (RCWA) results, of which the characterizations are tested by numerical simulation and the samples are fabricated on a silicon-on-insulator (SOI) wafer. Both numerical and experimental results demonstrate that good splitting ability without polarization sensitivity can be achieved while simultaneously maintaining high transmissivity under normal incidence at a wavelength of 1.55μm.

Broadband, Multiband, and Multifunctional All-Dielectric Metasurfaces

Bianisotropic all-dielectric metasurfaces offer a broad range of functionalities in optics, but so far have been designed case by case, and their generalization to different forms of polarization control is not straightforward. Moreover, their demonstrated range of bianisotropic properties has been limited, due to the single-layer topologies used. The authors propose multilayered metasurfaces built from high-contrast subwavelength gratings of varying orientations. Such multilayered all-dielectric metasurfaces can yield polarization conversion with broadband, multiband, and multifunctional responses, and can be designed in a systematic manner to realize all three types of responses.

A two-thickness subwavelength grating focusing lens for TE polarization light

A focusing lens for TE-polarization light based on silicon high-contrast subwavelength gratings (HCGs) with two different thicknesses is proposed. The key point in designing this structure is to obtain a total phase shift of 2π rad continuously by changing the period, duty cycle, and thickness of each grating bar simultaneously for TE polarization light. Meanwhile, a novel two-thickness method is presented to provide more suitable grating bars for the design of HCGs. The properties are numerically studied by the finite element method (FEM). The results show that the focal length is 7.2 µm, the total transmissivity is 72%, and the full-width at half-maximum (FWHM) at the focal plane is 0.8 µm at a wavelength of 1.55 µm. This structure will be potentially integrated into optical devices, such as vertical cavity surface emitting lasers (VCSELs), photodetectors, CCDs, and CMOSs. We also estimate the two-thickness method to be a trade-off between high performances and fabricating accuracy. This lens as an example provides guides for the design of one-dimensional (1D) HCGs and provides suggestions for the design of 2D or 3D HCGs.

Optical spatial differentiator based on subwavelength high-contrast gratings

An optical spatial differentiator based on subwavelength high-contrast gratings (HCGs) is proposed experimentally. The spatial differentiation property of the subwavelength HCG is analyzed by calculating its spatial spectral transfer function based on the periodic waveguide theory. By employing the FDTD solutions, the performance of the subwavelength HCG spatial differentiator was investigated numerically. The subwavelength HCG differentiator with the thickness at the nanoscale was fabricated on the quartz substrate by electron beam lithography and Bosch deep silicon etching. Observed under an optical microscope with a CCD camera, the spatial differentiation of the incident field profile was obtained by the subwavelength HCG differentiator in transmission without Fourier lens. By projecting the images of slits, letter “X,” and a cross on the subwavelength HCG differentiator, edge detections of images were obtained in transmission. With the nanoscale HCG structure and simple optical implementation, the proposed optical spatial differentiator provides the prospects for applications in optical computing systems and parallel data processing.

Ultra-Low-Loss High-Contrast Gratings Based Spoof Surface Plasmonic Waveguide

Large metallic losses and short propagation lengths associated with surface plasmons (SPs) have long been considered as the obstacles which severely limit the practical applications of surface plasmonic waveguides. In this paper, we introduce the concept of dielectric spoof SPs (SSPs) and show that subwavelength high-contrast gratings (HCGs) offer a route to effectively suppress the losses and hence dramatically increase the propagation length of surface electromagnetic waves. We experimentally realized a wideband ultra-low-loss high-confinement plasmonic waveguide constructed by a high refractive-index dielectric array with deep-subwavelength periodicity on a metal substrate. Simulation and measurement results on the near-field distributions and S-parameters at microwave frequencies provide explicit evidences of strong field localization and show excellent transmission efficiency of HCGs-based SSPs across a broad frequency band. More importantly, the propagation length of the HCGs-based SSPs is proved to be at least more than one order of magnitude larger than that of metallic gratings-based SSPs at the same or even higher level of field confinement. Thus, the SSPs as experimentally realized in this paper hold great promise for numerous practical applications in ultra-low-loss and long-range transmission SP devices and circuits and may open up new vistas in SP optics.

Monolithic High-Contrast Gratings: Why Do They Not Scatter Light?

Monolithic high-contrast gratings (MHCGs) are able to reflect light as well as can classical subwavelength high-contrast gratings (HCGs), without requiring, as do classical HCGs, to be sandwiched between low-refractive-index layers. Although the replacement of low-index cladding on the input side with high-index material should cause strong scattering of the incident wave into higher diffractive orders, this effect can be suppressed so that MHCGs reflect only the zero-order plane wave. This paper describes a numerical investigation of the reflectivity maxima for both classical and monolithic gratings, and conducts a formal mathematical analysis of the plane wave reflection. It shows that the absence of scattering in MHCGs is attributed to a particular structure of the impedance/admittance matrix, which makes the reflectivity of the grating independent of the substrate refractive index. By carefully choosing the grating parameters, this structure of the impedance/admittance matrix can be found for any value of the grating refractive index, allowing MHCGs to be designed in any material wavelength.

基于亚波长高对比度光栅的波前调控器设计

基于亚波长高对比度光栅的波前调控器设计

Localized Spoof Surface Plasmons based on Closed Subwavelength High Contrast Gratings: Concept and Microwave-Regime Realizations.

In this work, we report the existence of spoof localized surface plasmons (spoof-LSPs) arising with closed high contrast gratings (HCGs) at deep subwavelength scales, another platform for field localization at microwave frequencies. The HCGs are in the form of a periodic array of radial dielectric blocks with high permittivity around a metal core supporting spoof-LSPs of transverse magnetic (TM) form. Simulation results validate the phenomenon and a metamaterial approach is also given to capture all the resonant features of this kind of spoof-LSPs. In addition, experimental verification of the existence of spoof-LSPs supported by a three dimensional (3D) HCGs resonance structure in the microwave regime is presented. This work expands the original spoof-LSPs theory and opens up a new avenue for obtaining resonance devices in the microwave frequencies.

Silicon-on-sapphire mid-IR wavefront engineering by using subwavelength grating metasurfaces

Subwavelength high-contrast gratings (sub-λ HCGs) were pursued to design mid-IR optical devices based on wavefront engineering. Unlike metallic counterparts, dielectric and semiconductors offer low-loss operation over a wide spectral range. Silicon gratings on sapphire substrate are proposed here as the device platform due to their transparency at near-IR to mid-IR wavelengths. The proposed generic methodology manipulates the wavefront of the reflected wave based on the phase and magnitude of reflectivity for unit cells with different dimensions. To demonstrate the capability of generating an arbitrary wavefront profile, several design examples are shown: (1) a reflective mirror with ∼100% power efficiency and broad bandwidth of >1 μm as reflectivity >90%; (2) a blazed grating with a reflection peak automatically aligned with its +1st diffraction order at 19.5°; (3) a focusing mirror with a focal length of 35 μm and diffraction-limited focus; (4) a sinusoidal phase profile with a periodicity of 8860 nm.

一种亚波长高折射率差光栅滤波器的设计与分析

一种亚波长高折射率差光栅滤波器的设计与分析

Polarization-Insensitive Focusing Lens Using 2D Blocky High-Contrast Gratings

We propose a high-transmissivity, polarization-insensitive focusing lens (PIFL) using 2D blocky sub-wavelength high-contrast gratings (2D-BSW-HCGs). Simultaneously, a design method for 2D-BSW-HCGs PIFL is put forward. A PIFL with high transmissivity can be constructed by designing the transmissivity and phase shift profile of nonperiodic 2D-BSW-HCGs. Properties of focusing and transmission are numerically studied with the finite-element method. The numerical simulation results show that, when the incident wavelength is 1550 nm, the transmissivity is 0.8659, and the numerical aperture (NA) is 0.535. At the focal plane, the field distribution of the average full width at half maximum is 1.7515 μm. Moreover, the design approach also can be expended to a high-NA PIFL and a polarization-insensitive focusing reflector.

High-numerical-aperture high-reflectivity focusing reflectors using concentric circular high-contrast gratings.

We present a concise approach to design focusing reflectors using concentric circular subwavelength high-contrast gratings (CCSW-HCGs). With this method, we design a high-numerical-aperture, high-reflectivity CCSW-HCG focusing reflector. By designing the CCSW-HCG structure, the grating can give the target phase front of reflected light while maintaining a high reflectivity. The properties of focusing and reflection are numerically studied with the finite element method. Simulation results show that, when the incident wavelength is 1550nm, the reflectivity is 0.8538, and the numerical aperture is up to 0.9213. At the reflection focal plane, the full width at half-maximum of the field distribution is 0.9845μm. Furthermore, the CCSW-HCG can simultaneously focus the reflected and transmitted light and has a strong robustness.

Broadband filter using multi-layer sub-wavelength high-contrast grating structure

This paper proposed a novel broadband filter using multi-layer sub-wavelength high-contrast grating (HCG) structure. This filter has wide bandwidth and good sideband suppression. We simulated and analyzed the effects of different numbers of layers and different grating indexes on filtering performance of the broadband filter. According to the simulated results, we designed a multilayer HCG broadband filter, which has bandwidth of 843 nm and center wavelength of 1550 nm.

Cavity-enhanced measurements for determining dielectric-membrane thickness and complex index of refraction.

The material properties of silicon nitride (SiN) play an important role in the performance of SiN membranes used in optomechanical applications. An optimum design of a subwavelength high-contrast grating requires accurate knowledge of the membrane thickness and index of refraction, and its performance is ultimately limited by material absorption. Here we describe a cavity-enhanced method to measure the thickness and complex index of refraction of dielectric membranes with small, but nonzero, absorption coefficients. By determining Brewster's angle and an angle at which reflection is minimized by means of destructive interference, both the real part of the index of refraction and the sample thickness can be measured. A comparison of the losses in the empty cavity and the cavity containing the dielectric sample provides a measurement of the absorption.

Sub-Wavelength Grating Lenses With a Twist

Dielectric high-contrast sub-wavelength grating (SWG) structures have received much attention in recent years, offering a new paradigm for the integration of optical systems. Their nanoscale resonant properties can result in a complex and unintuitive far-field behavior that, if carefully crafted, allows the full control of the optical phase front from a thin sub-wavelength planar layer. To date, experimental demonstrations of these new devices have only been realized with polarized light in a reflective mode, greatly limiting their use for practical systems. In this letter, we demonstrate a highly efficient, sub-wavelength thick, transmissive grating lens configuration using symmetrical resonant posts to achieve polarization-independent operation. Our transmissive SWG lenses are easily fabricated using low-cost scalable semiconductor process technology. To illustrate their performance, we demonstrate the generation of high-order orbital angular momentum beams and their use in an optical mode-isolator application that achieves a suppression ratio of over 25 dB.