Effects of abrupt surface-profile transitions in nonparaxial diffractive optics

It is shown that the failure of the thin-element approximation of diffractive optics may, in the first approximation, be attributed to local diffraction effects caused by the abrupt vertical transitions in binary surface-relief profiles. We determine the field disturbance caused by a single-step transition (of given height) by rigorous diffraction theory. Associating such a disturbance with each individual transition point in the profile, we obtain a computationally efficient refinement of the thin-element approximation for the analysis and design of diffractive elements in the nonparaxial domain. The results agree well with those obtained by global application of rigorous diffraction theory, provided that the smallest features in the binary profile are larger than approximately one optical wavelength.     

Wave-optical structure design with the local plane-interface approximation

Abstract

The design of an optical element profile with specified transmission function for a given incident wave is of fundamental concern in optical design. A well-known example is the design of an aspherical surface in order to realize a spherical phase-only transmission. Various wave-optical system design methods lead to transmission functions as a first step. Then, often the thin-element approximation is applied in a second step to obtain an element structure with the desired transmission. However, if the refraction at the optical interface cannot be neglected, the thin-element approximation is not valid. In this case, a higher version of the local plane-interface approximation can be used for the element structure design. An algorithm for this model is introduced and its characteristics are discussed for the example of a non-paraxial Gaussian-to-tophat beam shaping element.     

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.     

Analysis of optical elements with the local plane-interface approximation

The local plane-interface approximation (LPIA) is a method for propagating electromagnetic fields through the inhomogeneous regions (e.g., elements) of an optical system. The LPIA is the superclass of all approximations that replace the usually curved optical interfaces with local tangential planes. Therefore the LPIA is restricted to smooth optical surfaces. A maximum radius of curvature of the optical interface of the order of a few wavelengths is a rough estimate for the validity of the LPIA. Two important approximation levels of the LPIA are the thin-element approximation (TEA) and a geometric-optical version of the LPIA (LPIA(ray)). The latter combines the wave-optical propagation of an electromagnetic field in the homogeneous region of an optical system with a ray-tracing step in the inhomogeneous region. We discuss the regions of validity of the LPIA in general and the approximation levels LPIA(ray) and TEA in detail.     

Simulation of light propagation by local spherical interface approximation

A new local elementary interface approximation is introduced for the modeling of wave propagation through interfaces between homogeneous media. The incident wave and the surface profile are approximated locally by a spherical wave and a spherical surface, respectively. The wave field travels through the modulated structure according to the laws of geometrical optics, being refracted by the surface and propagating to the output plane locally as a geometric spherical wave. Diffraction theory is applied to propagate the field from the output plane onwards. We provide comparisons of the method with the thin-element approximation, the local plane-wave and interface approach, and rigorous diffraction theory using a sinusoidal surface-relief grating as an example. We illustrate the power of the new method by applying it to the analysis of a diffractive beam splitter.     

Vectorial thin-element approximation: a semirigorous determination of Kirchhoff's boundary conditions

A semirigorous model is presented that bridges the gap between classical scalar diffraction theory on the one hand and fully rigorous simulation models on the other. It falls back on the basic ideas of scalar diffraction theory, especially the Kirchhoff approximation. In contrast to classical techniques, however, the boundary values are determined by rigorous methods of the stratified medium theory in the scope of a fully vectorial formulation. By this means the proposed approach takes vertical rigorous coupling effects inside the grating into account while neglecting the lateral ones. We therefore call this method semirigorous and use the name vectorial thin-element approximation. A direct comparison with rigorous coupled-wave analysis as a fully rigorous simulation model allows a detailed discussion of its range of validity and demonstrates a reduction of computation time of the order of 3 magnitudes. In addition, it also reveals deeper insight into the details of the electrodynamics inside diffracting structures. Some examples will demonstrate this benefit.     

Rigorous and approximate analysis of metallic gratings in soft X-ray and EUV regions

Abstract

In deep ultraviolet and soft X-ray regions the complex refractive indices of metals differ substantially from their values in the visible region of the spectrum. The implications of this fact are analysed for metallic gratings illuminated by electromagnetic fields with wavelengths ranging from soft X‐rays to near infrared, concentrating on short wavelengths. In particular, we study metal-stripe gratings (linear polarizers for visible light) by rigorous diffraction theory to determine the short-wavelength region in which a combination of the geometrical thin-element approximation and the theory of single-layer films can be applied. Then we study inductive grid filters for protection of X-ray detectors from infrared radiation in space applications.     

Born approximation for the nonparaxial scalar treatment of thick phase gratings

The conventional design of phase gratings or kinoforms with a paraxial transmission function is restricted to the paraxial domain and thin elements. Therefore, the design and analysis of thick phase-relief structures require a nonparaxial theory, as given by the Born approximation. The Born approximation is derived as an extension of the scalar thin-element theory, which is applicable for thick elements with large propagation angles. As an example, general prism gratings on curved surfaces are treated.     

SAW diffraction using the thin-element decomposition method

We adapt the angular spectrum of plane waves (ASPW) decomposition to numerical simulations of the diffraction of surface-acoustic waves (SAWs) on anisotropic model substrate, such as YZ lithium niobate. We utilize the thin-element decomposition (TED) method, appropriately modified for an anisotropic substrate; we also introduce a novel "average-wavenumber" variation of this scheme; these are numerically found to be mutually consistent. We apply the TED method to simulate wave propagation both in infinite periodic structures of metallized gratings and also in finite gratings. We demonstrate that the ASPW provides a convenient and numerically fast tool for precise diffraction calculations in practical SAW devices which also display structural variations in the lateral direction, perpendicular to the principal direction of wave propagation. Additionally, we compare the present TED method to waveguide theory in an analysis of the role of SAW reflections from the electrodes.     

Focusing of ultrashort laser pulses by the combination of diffractive and refractive elements

Hybrid elements, containing optical power with both diffractive (holographic) and refractive components, are shown to be able to eliminate the effect of propagation time difference. The consideration is provided through a paraxial approximation of diffraction theory.     

Guided light and diffraction model of human-eye photoreceptors

The photoreceptors of the living human eye are known to exhibit waveguide-characteristic features. This is evidenced by the Stiles-Crawford effect observed for light incident near the pupil rim, and by the directional component of light reflected off the retina in the related optical Stiles-Crawford effect. We describe a model for the coupling of light to/from photoreceptors on the basis of waveguide theory that includes diffraction between the eye pupil and the photoreceptor apertures, and we show that valuable insight can be gained from a Gaussian approximation to the mode field. We apply this knowledge to a detailed study of the relationship between the Stiles-Crawford effect and its optical counterpart.     

反射式近场光学显微镜样品近场光分布特性

建立了一种反射式近场光学显微镜中样品近场光分布特性的模型,应用矢量衍射理论,得到了系统的场方程。在弱波动条件下,采用微扰法对场方程进行了求解,能方便地得到样品表面的各阶近场光反射和透射模复振幅表达式。计算结果表明,一级场分布要比零级场小一个量级,各阶近场信号的强弱完全由面形函数的傅里叶变换决定。通过与零级结果的比较,证明了计算结果的正确性。提供了一种计算样品表面近场分布简便方法,对反射式近场光学显微镜中调制检测技术具有指导意义。     

Achromatic optical fourier transformer with planar-integrated free-space optics

We address the problem of achromatization of an optical system for the realization of planar-integrated, free-space optics. In particular we demonstrate an integrated optical Fourier transformation module that was achromatized for the visible spectrum by means of a diffractive lens doublet. The optical system design is studied by using the parabolic approximation of the scalar diffraction theory, including terms related to astigmatism. Based on the method of ABCD ray matrices, the optical specifications of the lens doublet are derived and the chromatic correction effect is quantified. For experimental confirmation the diffraction patterns of various grating structures are evaluated.     

Monochromatic electromagnetic wavelets and the huygens principle

For the first time, to our knowledge, optical diffraction is shown to be a wavelet transform with the electromagnetic wavelets. We show that the optical wavelets proposed by Onural [Opt. Lett. 18, 846 (1993)] are the Huygens wavelets under a Fresnel approximation, and the electromagnetic wavelets proposed by Kaiser [A Friendly Guide to Wavelets (Birkhauser, Boston, Mass., 1994)] reduce to Hyugens wavelets in the case of a monochromatic field.     

The relation between light diffraction and the fractional fourier transform

Abstract

The relation between the diffraction integral and the fractional Fourier transform is analysed in detail from the geometrical and energy points of view. It is shown that the optical matrices associated with the two transformations in the geometrical approximation, although very different, are consistent with the simple relation between the respective integral transforms. Moreover, the meaning of the complex degree of fractionality of the fractional Fourier transform is found to be related to the energy variation of the beam. Its influence on the phase-space representation of the optical beam is shown to be different compared with the diffraction through an energy variant system.     

Asymptotic analysis and design of diffractive optical elements

The problem of light diffraction by a micro-optical diffractive element is investigated. The method of stationary phase is applied to obtain approximate values of the integrals in the Kirchhoff approximation. The accuracy of the asymptotic approximation is studied in detail. As an application, the obtained approximate formulas are used to solve a design problem of constructing a diffractive optical element with a desired intensity distribution.     

Vector diffraction analysis by discrete-dipole approximation.

The discrete-dipole approximation is applied to vector diffraction analysis in a system with large-numerical-aperture (NA) optics and subwavelength targets. Distributions of light diffracted by subwavelength dielectric targets are calculated in a solid angle that corresponds to a NA of 0.9, and their dependence on incident polarization, target shape, and target size is studied. Electric field distributions inside the target are also shown. Basic features of the vector diffraction are clearly demonstrated. This technique facilitates understanding of the vectorial effects in systems that are expected to be applied in the future to optical data storage.     

Optical generation of focus wave modes

Localized wave solutions of free-space wave equation can be used in numerous applications where the localized transmission of electromagnetic energy is of major importance. However, an optical implementation of localized wave fields has not been accomplished yet, except for an ultrashort version of the Bessel beams or the so called Bessel-X pulses. We propose an approach to constructing realizable optical schemes for generation of localized wave fields. We show that wavelength dispersion of the cone angle of axicons and circular diffraction gratings can be used to generate good approximation to focus wave modes.     

Nonlinear optical beam propagation for optical limiting

We implement numerical modeling of high-energy laser-pulse propagation through bulk nonlinear optical materials using focused beams. An executable program with a graphical user interface is made available to researchers for modeling the propagation of beams through materials much thicker than the diffraction length (up to 10(3) times longer). Ultrafast nonlinearities of the bound-electronic Kerr effect and two-photon absorption as well as time-dependent excited-state and thermal nonlinearities are taken into account. The hydrodynamic equations describing the rarefaction of the medium that is due to heating are solved to determine thermal index changes for nanosecond laser pulses. We also show how this effect can be simplified in some cases by an approximation that assumes instantaneous expansion (so-called thermal lensing approximation). Comparisons of numerical results with several Z-scan, optical limiting and beam distortion experiments are presented. Possible application to optimization of a passive optical limiter design is discussed.     

Cubic CdS thin films studied by spectroscopic ellipsometry

CdS polycrystalline films were grown onto glass substrates by chemical bath deposition (CBD) and characterized by spectroellipsometry, X-ray diffraction and transmission electron microscopy. The X-ray diffraction patterns of the samples showed the presence of a CdS cubic phase (β-CdS) and of Cd2SiO4 as interfacial material. Using electron diffraction it was possible to index the films as cubic CdS. From effective dielectric function measurements and from reported optical data for the dielectric function of cubic CdS crystals, grown by vapour phase epitaxy, it was possible to fit the experimental data to an effective medium approximation, and to deduce the film thickness, the void fraction and the field screening. This revised version was published online in August 2006 with corrections to the Cover Date.