High-efficiency diffractive waveguide lenses by parametric optimization

The first-order diffraction efficiency of a waveguide diffraction grating is maximized, for a wide range of grating periods, by optimization of the effective-index modulation profile. Three different values of effective-index modulation in the range of 0.02-0.11 are considered. The analysis is performed with the thin-grating-decomposition method. The results are verified by electromagnetic grating theory and applied to the construction of diffractive waveguide lenses with an improved overall efficiency. In the neighborhood of the optical axis, the optimized lens structure is a close approximation of a gradient-thickness Fresnel lens. Significant deviations from this shape appear when the local grating period reduces below ~ 15-25λ, where ~ is the wavelength of the guided mode. Near the edges of a high-numerical-aperture lens, where the local period is ~ 3-6λ, an approximate Bragg grating structure is obtained.     

Integrated waveguide diffractive doublet for guided-wave manipulation

An integrated waveguide diffractive doublet consisting of a uniform grating coupler and a diffractive optical element is proposed. Design of this waveguide diffractive doublet for guided-wave manipulation is described in detail. Experimental results for a fabricated waveguide diffractive doublet are also presented to demonstrate the device principles. It was found that this waveguide diffractive doublet can enhance device functionality while remaining simple and compact and having a planar structure. Furthermore, this device can be fabricated by use of all-optical lithography.     

Focusing waveguide grating coupler using a diffractive doublet

A novel focusing waveguide grating coupler comprising an integrated uniform grating coupler and binary-phase-only diffractive lens is proposed, designed, and fabricated. Experimental results are also presented to demonstrate the device performance. This device is in direct competition with single-element focusing grating couplers defined by direct-write electron-beam lithography and its structure is attractive because the fabrication procedure is better suited for mass production.     

Comparative analysis of doublets versus single-layer diffractive optical elements in eyepiece or magnifier design

We quantify the impact of eye clearance requirement on the performance of eyepieces utilizing doublets versus diffractive optical elements on aspheric substrates. In this study, the doublets were designed to be cemented on-axis elements. Specifically, four different values of eye clearance were implemented: 17, 20, 23, and 26 mm. For each value, axial and lateral color, spherical aberration, coma, astigmatism, field curvature, and distortion were compared. Each system under comparison was optimized for the same focal length, a 9 mm exit pupil, photopic wavelengths (513-608 nm), and a 40 degrees full field of view. We demonstrate that the single-layer diffractive optical element supports an eye clearance value of approximately 80% of the effective focal length, while the doublet drops below desired specifications at approximately 65% of the effective focal length.     

Radiation characteristics of a coaxial waveguide with opposing dielectric filled grooves

The purpose of the present study is to provide a rigorous analysis to the coaxial waveguide with two opposing grooves in the outer and inner cylinders with different depths and filled with different dielectric materials. The representation of the solution to the three-part mixed boundary-value problem in terms of Fourier integrals leads to a couple of simultaneous modified Wiener-Hopf equations that are reduced to infinite systems of linear algebraic equations. These systems are solved numerically and the bandstop filter characteristics of the reflection coefficient are studied in terms of frequency, groove sizes and the parameters of the filling dielectric material.     

Application of holographic diffractive doublets as collimators for highly elliptical light beams edge emitted from diode lasers

Two schemes for collimation of diode laser light beams with high cross-sectional ellipticity by means of a doublet of holographic diffractive elements are proposed and designed; one of the schemes is realized and tested. In both the schemes the first element of the doublet collimates the beam in the plane of the longer axis of the ellipse, and the second element collimates it in the perpendicular plane. Each element simulates a cylindrical lens. The set-up with the focal line of the cylindrical beam oriented perpendicular to the meridional plane is realized experimentally. The elements are holographic surface-relief gratings recorded in photoresist. For recording, only homocentric diverging beams are used, which minimizes potential aberrations and optical dirt. The parameters of the elements are computed using four equations, including one equation for compensation of the aberration of the lowest order. The doublet is proposed for the He—Ne red wavelength. A collimated He—Ne laser beam is employed for quality testing of collimation in a reverse way, with this beam impinging upon the second element. Characteristics of an outgoing beam from the first element of the doublet are recorded with a charge-coupled device camera. Calculated spot diagrams are compared with cylindrical focal lines captured separately from both the elements.     

Radiation of sound waves from a rigid stepped cylindrical waveguide

The radiation of plane harmonic sound waves from a rigid stepped cylindrical waveguide is treated by using the mode-matching method in conjunction with theWiener-Hopf technique. The solution is exact, but formal, since infinite series of unknowns and some branch-cut integrals with unknown integrands are involved. Approximation procedures based on rigorous asymptotics are used and the approximate solution to the Wiener-Hopf equations is derived in terms of infinite series of unknowns, which are determined from infinite systems of linear algebraic equations. Numerical solutions of these systems are obtained for various values of the parameters of the problem and their effects on the directivity of the stepped waveguide is presented.     

阵列波导光栅解复用器光谱响应特性分析

基于单模光波导本征模场及其端面衍射场分布的高斯近似表达,推导出两个端面非接触光波导耦合的耦合系数的函数表达式,并基于此推导出阵列波导光栅解复用器的简单光谱响应效率的函数表达式。建立了分析阵列波导光栅解复用器光谱响应特性的简洁数学模型,阐明了阵列波导光栅解复用器对通道中心频率的响应度和相邻信号通道间的串扰与基本参数的关系,为设计和分析阵列波导光栅解复用器提供了理论基础。     

Near-field and far-field characteristics of a MQW waveguide

Definitions of beam half-width and divergence half-angle according to different kinds of methods were investigated. Results of these definitions are given for the fundamental mode and numerical calculation proves that some of them are more appropriate for describing the propagation characteristics of a multiple quantum well (MQW) planar waveguide.     

Blazed diffractive optics

Diffractive optical elements with blazed profiles can, in theory, have 100% relative efficiency. We review several methods for making such elements and compare their advantages and limitations. Our emphasis is on processes to produce elements other than those with approximate, stepped surfaces, such as binary optical elements. For optical methods, we offer an expression relating the maximum numerical aperture of a diffractive lens with a given maximum efficiency to the numerical aperture of the recording system.     

Radiation of a charge moving in a waveguide with a resonantly dispersive dielectric layer

The radiation of an ultrarelativistic point charged particle moving along the axis of a cylindrical waveguide containing a layer of resonantly dispersive dielectric medium is studied theoretically. It is shown that, in the case of a sufficiently thin waveguide, the dispersion leads to a significant contraction of the radiation, a decrease in the energy of harmonics, and an increase in the relative contribution due to the first mode as compared to the higher harmonics. These effects are less pronounced in waveguides with relatively large radii; still, they have to be taken into account, especially in determining the frequencies of harmonics. The role of the resonance dispersion is most significant in cases where the dielectric layer thickness is small compared to the waveguide radius.     

Harmonic diffractive lenses

The harmonic diffractive lens is a diffractive imaging lens for which the optical path-length transition between adjacent facets is an integer multiple m of the design wavelength λ(o). The total lens thickness in air is mλ(o)/(n - 1), which is m times thicker than the so-called modulo 2π diffractive lens. Lenses constructed in this way have hybrid properties of both refractive and diffractive lenses. Such a lens will have a diffraction-limited, common focus for a number of discrete wavelengths across the visible spectrum. A 34.75-diopter, 6-mm-diameter lens is diamond turned in aluminum and replicated in optical materials. The sag of the lens is 23 μm. Modulation transfer function measurements in both monochromatic and white light verify the performance of the lens. The lens approaches the diffraction limit for 10 discrete wavelengths across the visible spectrum.     

Coplanar refractive-diffractive doublets for optoelectronic integrated systems

A coplanar refractive-diffractive doublet array employing surface-relief diffractive phase elements embedded within poly(methyl methacrylate) microlenses is introduced as an optomechanical building block for optoelectronic integrated systems. The design method, fabrication technology, and results are described. Coplanarity of the quadratic- and linear-phase elements constituting the doublet can reduce optomechanical complexity in applications to unguided optical interconnects.     

Electrical modulation of diffractive structures

We present an experimental demonstration of two new methods for electronically modulating diffractive structures. The first involves the creation of periodic displacement of a liquid-air interface by application of a spatially modulated electric field produced by an array of electrodes. The second method also uses an electrode array but creates a diffraction grating by selectively attracting and repelling electrophoretic particles in a dielectric fluid. Potential areas of application of these techniques include controllable holography and wavelength division multiplexing.     

Ellipsometry of diffractive insect reflectors

Scales on the wings of certain insects, such as Trichoplusia orichalcea, exhibit a surface micro structure resembling a fine diffraction grating. Diffraction of incident light by this structure is responsible for many of the optical properties of the wings of this moth, such as the metallic yellow color and the almost-specular reflection and polarization properties of the scattered radiation. It is shown that by the use of null ellipsometry the polarization characteristics can be used to obtain the optical constants of the scale material. Theoretical considerations and suitable experimental conditions are discussed and evaluated.     

Efficiency analysis of diffractive lenses

Multilevel diffractive optical elements are necessary for achieving high-efficiency performance. Here the diffraction efficiency of a multilevel phase-only diffractive lens is analyzed. Approximate, as well as more accurate, approaches are presented. Both plane-wave and Gaussian illumination are discussed. It is shown that for many practical cases the diffraction efficiency can be determined by only a single parameter that takes into account the spatial bandwidth product as well as the focal length of the lens and the illumination wavelength. The analysis is based on the scalar theory and the thin-element approximation. Justification for doing this is presented. The results are valid for lenses with at least F/5.     

二维声子晶体异质结声波导特性研究

以二维铝圆柱／空气正方格子声子晶体为研究对象，通过用两列正方散射柱替换原型散射柱构造了异质结，采用平面波法结合超元胞的方法研究了该异质结的声波导特性。结果表明，当f=0．7、fd=0．5，旋转散射柱时，缺陷带出现在-45°〈θ〈45°范围内，数量、位置随旋转角变化，且缺陷带的分布关于（01）方向对称；对于给定的f=0．7，只要方形散射柱对角线在（10）方向的投影小于2．118R时，带隙中就有缺陷带出现，带隙中缺陷带的数量随fd的增加而减少；当fd很小时，缺陷柱的方位、横加面形状对声波导没有影响。