Far-field imaging of optical second-harmonic generation in single GaN nanowires

Means for assessing the nonlinear optical properties of nanoscale materials are of key importance for the advancement of active nanophotonics. By correlating second-harmonic generation (SHG) with electron backscattered diffraction from single GaN nanowires (NWs), we demonstrate that far-field microscopic imaging of SHG offers an approach for distinguishing crystallographic orientations of NWs lying on a substrate. The quasi-static approximation, which should prove useful in describing many nanophotonic behaviors, is shown to satisfactorily account for the SHG data.     

远场合成孔径计算光学成像技术：文献综述与最新进展

传统光学成像实质上是目标场景的光强信号在空间维度上的直接均匀采样记录与再现的过程。因此,其成像分辨率与信息量不可避免地受到光学衍射极限、成像系统空间带宽积等若干物理条件制约。如何突破这些物理制约,获得更高分辨率、更宽广的图像信息,一直是该领域的永恒课题。计算光学成像通过前端光学调控与后端信号处理相结合,为突破成像系统的衍射极限限制,实现超分辨成像提供了新思路。本文综述了基于计算光学合成孔径成像实现成像分辨率的提升以及空间带宽积拓展的相关研究工作,主要包括基于相干主动合成孔径成像与非相干被动合成孔径成像的基础理论及关键技术。本文进一步揭示了当前“非相干、无源被动、超衍射极限”成像的迫切需求及其现阶段存在的瓶颈问题,并展望了今后的研究方向以及解决这些问题可能的技术途径。

     

Far-field optical degradation due to near-field transmission through a turbulent heated jet

When a laser beam traverses an optically active, turbulent flow field, the laser wave front is aberrated by the flow. Density variations in a heated two-dimensional jet, for example, correspond to index-of-refraction variations, and this modulation of the index in the fluid can imprint an optical phase disturbance, or phase error, onto the laser wave front. Adaptive-optic systems seek to correct the phase error of the wave front, and thus restore the integrity of the far-field irradiance pattern. Given a near-field spatial mapping of a phase disturbance, the far-field irradiance pattern of the affected wave front can be calculated with Fourier-optics techniques. A Fourier-optics computer code was used to study the far-field irradiance patterns arising from actual time-varying measurements of a fluid-induced phase error. The time-averaged Strehl ratio was studied to provide insight into the spatial and temporal design requirements for adaptive-optic systems applied to the time series of near-field spatial phase-error maps.     

Subwavelength imaging in a superlens of plasmon nanospheres

A structure comprising two lattices of silver or gold nanospheres is considered. It is shown that this structure can be used as a superlens capable of providing subwavelength imaging of a point source and a sub-wavelength spatial resolution of two sources at a distance within one wavelength.     

High aspect subdiffraction-limit photolithography via a silver superlens

Photolithography is the technology of choice for mass patterning in semiconductor and data storage industries. Superlenses have demonstrated the capability of subdiffraction-limit imaging and been envisioned as a promising technology for potential nanophotolithography. Unfortunately, subdiffraction-limit patterns generated by current superlenses exhibited poor profile depth far below the requirement for photolithography. Here, we report an experimental demonstration of sub-50 nm resolution nanophotolithography via a smooth silver superlens with a high aspect profile of ~45 nm, as well as grayscale subdiffraction-limit three-dimensional nanopatterning. Theoretical analysis and simulation show that smooth interfaces play a critical role. Superlens-based lithography can be integrated with conventional UV photolithography systems to endow them with the capability of nanophotolithography, which could provide a cost-effective approach for large scale and rapid nanopatterning.     

Two-dimensional imaging by far-field superlens at visible wavelengths

We report that two-dimensional (2D) sub-diffraction-limited images can be theoretically reconstructed by a new metamaterial far-field superlens. The metamaterial far-field superlens, composed of a metal-dielectric multilayer and a one-dimensional (1D) subwavelength grating, can work over a broad range of visible wavelengths intrinsically. The imaging principle and the reconstruction process are described in detail. The 2D sub-diffraction-limited imaging ability enables more applications of the far-field superlens in optical nanoimaging and sensing.     

Far-field Diffraction Patterns of Two Slits

The diffraction of a scalar wave by two parallel slits in a plane screen is examined by a new method which uses an orthogonal set of functions and Fourier transformations. The far field is obtained for the case of normal incidence and numerical results are given for k = 0·2 ? 5 and D =3 ? 10, where k is the wavenumber and D is the slit separation.     

Subwavelength imaging of a multilayered superlens with layers of nonequal thickness

We propose a multilayered superlens comprising alternately layered metal and dielectric films with layers of nonequal thickness to realize subwavelength imaging, even when permittivities of the metal and dielectric are mismatched. Based on ideal imaging conditions, the exact constraint relations about the thickness of each dielectric layer and the permittivity of the surrounding medium of the multilayered superlens are first acquired when the superlens is modeled by the effective medium theory. Theoretical analysis and numerical simulations indicate that a multilayered superlens with constraint relations can realize subwavelength imaging at wavelengths of 335 to 385 nm.     

Far-field propagation of an off-axis Gaussian wave

Based on a far-field asymptotic solution of the Helmholtz equation a vector theory to describe the propagation of an off-axis Gaussian wave is developed, the accurate formulas represented in terms of elementary functions are derived, and the propagation properties such as wave spot size and divergence angle are discussed in detail. The applicable range of scalar theory is also presented. A relative error criterion of optical intensity is given by epsilon = sin(2) alpha.     

Far-field expression of a high-power laser diode

Based on the off-axis theory, a model for describing the far field with the bipeak structure of a high-power laser diode is proposed. The computed results agree well with the measured far-field data of practical devices. A minimum overall error criterion for fitting the theoretical model with the measured data is also given. The results show that the overall error of this model is less than 5% for popular laser diodes. This model has a simple mathematical structure and can be easily used to design the beam-shaping system and to analyze the propagation properties when the laser beam passes through an optic system.     

Far-field reflectometry for characterization of active antennas

Testing active antennas or polarimetric radar calibrators in the far field (plane wave excitation) is complicated by imperfect isolation between transmit and receive channels. We describe a far-field reflectometry setup which overcomes this problem. A large dynamic range is achieved by modulating the active element bias and using a quadrature receiver and lock-in detection scheme. A calibration method and a novel mixer phase-error correction scheme are described. The system is capable of full polarimetric characterization of active scatterers     

Far-field interference from a sphere and its applications

A theoretical model of far-field interference from a sphere has been established, and its applications have been investigated. When two coherent parallel laser beams shine on a smooth sphere surface from opposite directions, the reflected lights form interference fringes at far field. The fringes have hyperbolic shapes and are not uniformly distributed. This paper derives a method for calculating the path-length difference between two parallel reflected lights, analyzes the interference field, and discusses reasons that cause the fringe density variations. A formula for calculating the highest orders of interference fringes is also provided. A method for using a spectrometer, CCD camera, and computer to measure the sphere diameter is demonstrated. The results agree with those from an Abbe comparator. The theory and methods are also suitable for measuring diameters of smooth cylinders.     

Far-field vectorial structure of a higher-order cosh-Gaussian beam

Based on the vector angular spectrum representation and the method of stationary phase, the vectorial structural characteristics of a higher-order cosh-Gaussian (HOCG) beam in the far field are investigated. Analytical expressions for the energy flux distributions of the TE term, TM term and the whole beam are derived and illustrated by numerical examples. Influences of beam orders and cosh parameters on energy flux distributions are analyzed, respectively. Furthermore, the discrepancy for the total energy flux distributions between the non-paraxial and paraxial cases is presented and analytical explanations for the phenomenon are also given.     

Far-field theory of wave power capture by oscillating systems

A new derivation is given of an equation, relating the capture width of a wave power converter to the polar diagram of the waves generated by the device. The pattern of waves in the lee of the device is calculated in detail.     

Far-field diffraction patterns of circular sectors and related apertures

In studies of scalar diffraction theory and experimental practice, the basic geometric shape of a circle is widely used as an aperture. Its Fraunhofer diffraction pattern has a simple mathematical expression easily determined by use of the Fourier-Bessel transform. However, it may require considerable mathematical effort to determine the far-field diffraction patterns of aperture shapes related to the circular geometry. From a computational point of view, the mathematical difficulties posed by other aperture geometries as well as more-general apertures with irregular shapes can be surpassed by means of optical setups or fast numerical algorithms. Unfortunately, no additional insight or information can be obtained from their exclusive application, as would be the case if mathematical formulas were available. The research presented here describes the far-field diffraction patterns of single-sector apertures as well as their extension to double symmetrical sectors and to sector wheels formed by interleaved transparent sectors of equal angular size; in each case, full or annular sectors are considered. The analytic solutions of their far-field amplitude distribution are given here in terms of a series of Bessel functions, some interesting properties are deduced from these solutions, and several examples are provided to illustrate graphically the results obtained from approximate numerical computations. Our results have been verified numerically with the fast-Fourier-transform algorithm and experimentally by means of a spherical wavefront-single-lens Fourier-transform architecture.     

Analysis of Far-field Diffraction Characteristics of Wavelength-sized Surface Relief Gratings

The rigorous boundary matching technique was used to analyse the far-field diffraction from wavelength-sized surface relief gratings for TE polarization. Diffraction characteristics of such surface relief gratings were studied as functions of complex refractive index, groove depth and the angle of incidence. The surface field at the bottom of the grooves is more severely influenced by the edges and walls for metallic material than dielectric ones. The reflectivities of gold gratings show significant fluctuation for different incident wavelengths. This can be clearly seen from the fact that the zeroth-order diffraction efficiency DE ₀ of gold is lower than that of aluminium at u = 0·4 wm but higher at u = 1·0 wm. It is also shown that the depth of the grooves has significant influences on the diffraction efficiencies, an optimum depth can be chosen to minimize the specular component. However, this optimum depth value is found to be different for the gratings of different materials, e.g. aluminium and gold, although the gratings have exactly the same size and shape. The effect of the incident angle, particularly at critical angles when certain diffracted waves are just about to be cut off was discussed. The zeroth-order diffraction efficiencies are found to change noticeably at the critical angles.     

Far-field radiation of a vibrating point source in anisotropic media

In this paper, Lamb's technique,⁽¹⁾ which was used to study acoustic radiation due to an external force acting in an infinite isotropic solid or over the surface of an isotropic solid, has been extended to the case of general anisotropic media. The far-field radiation is numerically calculated for a vibrating point source in an infinite anisotropic solid or on the free surface of a semi-infinite anisotropic solid. The directivity patterns of a point source are obtained for the three different elastic modes, and a brief discussion of the main features of the numerical results is presented.     

Far-field intensity distribution and M2 factor of hollow Gaussian beams

The far-field intensity distribution of hollow Gaussian beams was investigated based on scalar diffraction theory. An analytical expression of the M2 factor of the beams was derived on the basis of the second-order moments. Moreover, numerical examples to illustrate our analytical results are given.