Antireflection structures with use of multilevel subwavelength zero-order gratings

It is known that the zero-order two-phase-level gratings with a period much smaller and a thickness much larger than the wavelength may have antireflection properties the same as appropriate dielectric layers under normal incidence. On the basis of the rigorous coupled-wave analysis method formulation, it is shown that multilevel unidimensional phase gratings, for both TE and TM polarization, are functionally equivalent to antireflection structures of multilevel dielectric layers, even if the period is close to the wavelength.     

On the effective medium theory of subwavelength periodic structures

Abstract

The effective medium theory of one-dimensional and two-dimensional periodic structures are investigated. A method based on a Fourier decomposition of the wave propagating along the direction perpendicular to the periodic structures allows one to determine the zeroth-, first- and second-order effective indices. For one-dimensional problems, we derive closed-form expressions of the effective indices for both TE and TM polarization. Our result can be applied to arbitrary periodic structure with symmetric or non-symmetric lamellar or continuously varying index profiles. The theoretical predictions are carefully validated using rigorous coupled-wave analysis. For the two-dimensional case, only symmetric structures are discussed and the computation of the zeroth-, first-, and second-order effective indices requires the inversion of an infinite matrix which can be truncated and simply solved numerically. The EMT prediction is qualitatively validated using rigorous computation for small period-to-wavelength ratios. It is shown that for large period-to-wavelength ratios near the cutoff value, no analogy between 2-D periodic structures and homogeneous media holds for highly modulated lamellar gratings.     

Edge localization of subwavelength structures by use of polarization interferometry and extreme-value criteria

A polarization interferometric method is presented for the quantitative microscopy of topographical structures with subwavelength linewidths. A liquid-crystal phase shifter is inserted into the imaging optics of a reflected-light microscope, and the principles of phase-shifting interferometry are applied to measuring the phase and the contrast of the TE-polarized image (E parallel edge) with the TM-polarized image (E perpendicular edge) as the reference. This common-path interferometric method provides selective edge detection for line structures because the polarization difference is localized at the structure edges. Two different threshold criteria for linewidth determination are discussed: distance of the contrast minima and distance of the points of the steepest phase change. Linewidths as small as 300 nm were measured at a 635-nm wavelength. The dependence on the illumination numerical aperture, as well as on the material, the width, and the depth of the structure, is investigated both experimentally and by rigorous numerical simulations.     

Optical propagator in a graded-index medium with a hyperbolic secant refractive-index profile

Light transmission through a gradient-index medium, whose refractive-index profile can be represented by a one-dimensional hyperbolic secant function, is analyzed by a wave-optics approach. An asymptotic expression of the corresponding optical propagator (the Green's function) in this medium is evaluated in a such a way that nonparaxial propagation can be studied. Thus optical transformations such as focusing and collimation are obtained, and the pupil effect (diffractive effect) is shown.     

Polarization-multiplexed diffractive optical elements fabricated by subwavelength structures

Polarization-multiplexed phase-only diffractive optical elements with subwavelength structures are proposed and fabricated. The differences among the phase modulations result from the differences among the effective indices exhibited in the subwavelength structures with various filling factors and surface profiles, and the phase retardations are obtained by the relief depth of the structures. The polarization-selective property is achieved by the polarization dependence of the effective indices exhibited in the one-dimensional subwavelength structures and the polarization independence exhibited in the two-dimensional structures. Additionally, the polarization contrast of our polarization-multiplexed elements, defined as the cross talk between the two polarization incidences, is independent of the relief depth. The principle of the polarization multiplexing by use of the subwavelength structures is described, and the fabrication results for the polarization-multiplexed computer-generated holograms are demonstrated.     

Guided waves in graded-index planar waveguides with nonlinear cover medium

Dispersion relations for TE modes in a planar exponentially graded-index waveguide with self-focusing nonlinear cover material have been solved numerically. It is shown that the threshold power required to pull the field maximum out of the film region into the cover is lower compared with that for the step-index waveguide and agrees well with the experimental results. Empirical relations to calculate the corresponding minimum film thickness and the minimum threshold power are given for the lowest-order mode.     

Improvement of viewing angle in integral imaging by use of moving lenslet arrays with low fill factor

Lenslet arrays with a low fill factor can improve the viewing angle in integral imaging. However, the viewing resolution is degraded by low fill-factor lenslets because the spatial sampling rate of the ray information is reduced. We show that both the viewing resolution and the viewing angle of integral imaging can be improved by adopting a moving array-lenslet technique.     

Near-field Fourier transform polarimetry by use of a discrete space-variant subwavelength grating

We present a unique method for real-time polarization measurement by use of a discrete space-variant subwavelength grating. The formation of the grating is done by discrete orientation of the local subwavelength grooves. The complete polarization analysis of the incident beam is determined by spatial Fourier transform of the near-field intensity distribution transmitted through the discrete subwavelength dielectric grating followed by a subwavelength metal polarizer. We discuss a theoretical analysis based on Stokes-Mueller formalism, as well as on Jones calculus, and experimentally demonstrate our approach with polarization measurements of infrared radiation at a wavelength of 10.6 microm.     

Nonparaxial diffraction-limited propagation of light in a graded-index planar medium with a hyperbolic secant refractive-index profile

Nonparaxial diffraction-limited propagation of light with amplitude distribution in hyperbolic functions through an inhomogeneous planar medium with a hyperbolic secant refractive-index profile is studied by means of the stationary phase method. The irradiance distribution at geometrical shadow, edge of shadow, and a geometrically illuminated region is analyzed for a particular case.     

Polarization quadrature measurement of subwavelength diffracting structures

The amplitude and the phase of the diffracted far field depends on polarization when the diffracting structure is comparable to or less than the wavelength. When the far-field amplitude and the phase of one polarization with respect to the orthogonal polarization is measured, small changes in the structure can be measured. To make the far-field polarization measurements, we design a detector that measures the relative polarization amplitude and the phase in quadrature. We predict numerically and verify experimentally the polarization amplitude and the phase for an optical disc and a set of gratings with varying depth. Our results show that this measurement technique is sensitive to small variations in the diffracting structure and that it can be useful in applications such as critical dimension and overlay metrology in microelectronics fabrication.     

Improvement of transmittance by fabricating broadband subwavelength anti-reflection structures for polycarbonate

We report on how to increase transmittance of a 0.2 mm thick polycarbonate (PC) film by periodic subwavelength anti-reflection structures in the visible spectral range. Subwavelength anti-reflection structures like moth-eyes are fabricated into the polycarbonate substrate itself by thermal nano-imprinting lithography (TH-NIL), which uses silicon stamps that have periodic structures such as gratings (lines and spaces) and pillared dots, and are fabricated by laser interference lithography (LIL) and transformer coupled plasma etching. To increase transmittance of a polycarbonate film, we control the periods and shapes of patterns, the number of patterned surfaces, and the overlapping direction of patterns that are fabricated into its surfaces. As a result of this, we show that average transmittance improves as the pattern period gets shorter and as both surfaces of the film are patterned. We also show that the spectrum range gets larger as the pattern period gets shorter and is determined by the longer pattern period in the case of designing a film to have different pattern period on its surfaces. The maximum average transmittance of a polycarbonate film increases up to approximately 6% compared to a bare sample in the 470-800 nm spectral range.     

同轴纳米柱对亚波长金属牛眼结构EOT的调控

牛眼结构是一种典型的纳米光学结构。本文设计了一种带有同轴纳米柱的牛眼结构,利用时域有限差分法(FDTD)研究了该结构的增强透射效应。研究发现,柱的半径和高度对透射特性具有显著的影响,恰当选择柱的半径和高度会得到最大的透射强度。另外,牛眼结构对环境折射率有较高的灵敏度。理论分析表明,该种结构的透射增强效应是由局域表面等离激元与表面极化等离激元相互作用产生。这为纳米光学元件的研发与应用提供一个新的思路。     

Broadband antireflective glasses with subwavelength structures using randomly distributed Ag nanoparticles

We demonstrate broadband antireflective glasses with subwavelength structures (SWSs) using randomly distributed Ag nanoparticles. Ag nanoparticles formed by a thermal dewetting process were used as an etch mask for dry etching to fabricate antireflective SWSs on the glass surface. The size and shape of Ag nanoparticles are changed by the different thickness of the Ag thin film. The morphology of SWSs fabricated by using the Ag thin films is well consistent with that of the Ag nanoparticles. The single-side SWS integrated glass exhibits improved transmittance of approximately 96% at 750 nm due to the graded refractive index profiles, while the transmittance is only approximately 92.5% for the flat surface. To reduce Fresnel reflection at the other side of the glass substrate, the SWSs with optimized Ag film thickness and dry etching conditions are formed on both sides of the glass. The dual-side SWS integrated glass show an average transmittance of approximately 97.5% in a wavelength range of 350-750 nm. Transmission band shrinkage effects of the SWS integrated glass are also observed with increased average size of the Ag nanoparticles.     

锗表面二维亚波长结构的反应离子刻蚀制备

为了获得具有金字塔结构的二维亚波长结构表面,提高其高宽比,用掩模曝光光刻及反应离子刻蚀技术,以SF6和O2为反应气体,在Ge衬底上制备了二维亚波长结构.用扫描电镜对刻蚀图形的形貌进行了观察,研究了功率、气压、气体流量及掩模图形对刻蚀图形的影响.结果表明:刻蚀图形腰部被优先刻蚀,形成凹陷的侧壁轮廓;O2流量增大有利于在侧壁形成保护层,从而减小腰部刻蚀、增大顶部及根部刻蚀;功率及气压过大或过小均会使侧壁刻蚀较大;方形图案比圆形图案掩模更有利于刻蚀出深度较大的亚波长结构.     

Advanced functionally graded plate-type structures impacted by blast loading

The foundation of the theory of functionally graded plates with simply supported edges, under a Friedlander explosive air-blast are developed within the classical plate theory (CPT). Within the development of the theory, the two constituent phases, ceramic and metal, vary across the wall thickness according to a prescribed power law. The theory includes the geometrical non-linearities, the dynamic effects, compressive tensile edge loadings, the damping effects, and thermal effects. The static and dynamic solutions are developed leveraging the use of a stress potential with the Extended Galerkin method and the Runge-Kutta method. Validations with simpler cases within the specialized literature are shown. The analysis focuses on how to alleviate the unwanted effects of large deformations through proper material selection and the proper gradation of the constituent phases or materials.     

Compressive imaging of subwavelength structures: periodic rough surfaces

A compressed sensing scheme for near-field imaging of corrugations of relative sparse Fourier components is proposed. The scheme employs random sparse measurement of near field to recover the angular spectrum of the scattered field. Surprisingly, it can be shown heuristically and numerically that under the Rayleigh hypothesis the angular spectrum is compressible and amenable to compressed sensing techniques. Iteration schemes are developed for recovering the surface profile from the angular spectrum. The proposed nonlinear least squares in the Fourier basis produces accurate reconstructions even when the Rayleigh hypothesis is known to be false.     

Reduction of the stress concentration factor in a homogeneous panel with hole by using a functionally graded layer

This work aims at understanding the effect of a radially heterogeneous layer around the hole in a homogeneous plate on the stress concentration factor. The problem concerns a single hole in a plate under different far-field in-plane loading conditions. By assuming a radial power law variation of Young’s modulus and constant value for Poisson’s ratio, the governing differential equations for plane stress conditions, and general in-plane loading conditions are studied. The elastic solutions are obtained in closed form and, in order to describe localized interface damage between the ring and the plate, two different interface conditions (perfectly bonded and frictionless contact) are studied. The formulae for the stress concentration factors are explicitly given for uniaxial, biaxial and shear in-plane loading conditions and comparisons with interface hoop stress values are performed. The solutions are investigated to understand the role played by the geometric and graded constitutive parameters. The results are validated with numerical finite element simulations in which some simplified hypotheses assumed in the analytical model, are relaxed to explore the range of validity of the elastic solution presented. In this way the results obtained are useful in tailoring the parameters for specific applications.     

Antireflective subwavelength structures on microlens arrays-comparison of various manufacturing techniques

Antireflective subwavelength structures (ARS) resembling nanostructures found on the cornea of night-active insects reduce the reflection of light by providing a gradual change in the refractive index at the interface. These artificial ARS have mainly been fabricated by a combination of conventional lithography and reactive ion etching, which constrains their application to planar substrates. We report on the fabrication of ARS using three different techniques including bottom-up and top-down methods as well as their combination on microlens arrays (MLAs) made of fused silica. The optical performance of the resulting ARS on the MLAs is as good as ARS fabricated on planar substrates with increased transmission of up to 96% at certain wavelengths.     

Large-scale assembly of colloidal nanoparticles and fabrication of periodic subwavelength structures

This paper reports a simple and scalable spin-coating technique for assembling 70?nm silica nanoparticles into non-close-packed colloidal crystals over a large area. The thickness of the shear-aligned colloidal crystals can be controlled from hundreds of layers to a single monolayer by adjusting the spin-coating conditions. We further demonstrate that the spin-coated colloidal monolayers can be used as structural templates to pattern sub-100?nm pillar arrays directly on silicon substrates. The resulting subwavelength-structured pillar arrays exhibit excellent broadband antireflective and superhydrophobic properties, which are promising for developing self-cleaning antireflection coatings for crystalline silicon solar cells. This bottom-up approach enables large-scale production of periodic nanostructures with resolution beyond the optical diffraction limit that have important technological applications ranging from high-density data storage and optoelectronics to biological sensing and subwavelength optics.     

Detection of subwavelength slit-width variation with measurements in the far field by use of an embedded-aperture interferometer configuration

The dynamic signature of the subwavelength variation of a rectangular aperture has recently been shown to be determinable from far-field irradiance with a precision better than 1 nm [Opt. Lett. 29, 1045 (2004)]. We have proposed, and have theoretically shown, that detection sensitivity can be greatly enhanced with an embedded-aperture Mach-Zehnder interferometer configuration, after parameter optimization. The sensitivity, in terms of derivative intensity of observed subwavelength variations, could be enhanced approximately 2.7 times, compared with the directly detected method. Another method of detection of subwavelength variation from pattern measurement of far-field diffraction has also been proposed. The associated shifting of the dark line of the diffraction pattern had a good linear correlation to subwavelength variation, which was magnified approximately 150 times, and gave good contrast for measurement.