Rigorous Diffraction Theory Research Articles

Optical activity in subwavelength-period arrays of chiral metallic particles

We report on a chirality-induced polarization effect in a planar subwavelength metallic nanograting. We demonstrate that the grating rotates the polarization at normal incidence. Because of the fourfold rotation symmetry, the effect does not depend on the incident beam polarization, but resembles optical activity in isotropic media. We use rigorous diffraction theory to show that polarization effects in the zeroth diffraction order take place in the presence of waveguide resonances with subwavelength-period arrays of chiral metallic particles.

22.2: Application and Optimized Design of Wire‐Grid Polarizers

AbstractThe properties of wire‐grid polarizers (WGP) are studied and optimized. Experimentally, the efficiency and the contrast ratio of the projection system using WGP are investigated as a function of the incident angle. It is confirmed that WGP can afford large extinction ratios and large numerical apertures (NA). However, WGP suffers from the drawback of large absorption by the metal grid. We calculated the properties of the WGP as a function of its physical parameters using rigorous diffraction theory. Optimal designs are obtained based on the criteria of best optical performances (high efficiency, large NA, large extinction ratio). With these optimal physical parameters the WGP can show very good performance with efficiency >85%, large NA, and high extinction ratio >1000.

Optical wire-grid polarizers at oblique angles of incidence

Nanotechnology enables the fabrication of wire-grid polarizers (WGP) in the visible optical region. At oblique angles of incidence, WGP can be used as polarizing beam splitters (PBS). As such, they have the advantages of large numerical aperture and high-extinction ratios in both transmission and reflection. Because of these properties, WGP is being explored as PBS replacement in projectors. In this article, we present a complete theoretical investigation of the WGP. Rigorous diffraction theory, exact lowest-order eigenmode effective-media theory, and form birefringence theory are discussed. These theories are compared with experimental measurement of T(θ) and R(θ) as a function of the polarization state of the input light and as a function of the incident angle θ. It is shown that only the rigorous diffraction theory can fit the data for all incident angles. Using diffraction theory we provide a calculation relating the optical properties of the WGP to the physical dimensions of the wire grids. Thus, a framework for optimizing the optical properties of the WGP for various applications and requirements is provided.

Optical Diffraction in Close Proximity to Plane Apertures. II. Comparison of Half-Plane Diffraction Theories.

The accuracy and physical significance of the classical Rayleigh-Sommerfeld and Kirchhoff diffraction integrals are assessed in the context of Sommerfeld’s rigorous theory of half-plane diffraction and Maxwell’s equations. It is shown that the Rayleigh-Sommerfeld integrals are in satisfactory agreement with Sommerfeld’s theory in most of the positive near zone, except at sub-wavelength distances from the screen. On account of the bidirectional nature of diffraction by metallic screens the Rayleigh-Sommerfeld integrals themselves cannot be used for irradiance calculations, but must first be resolved into their forward and reverse components and it is found that Kirchhoff’s integral is the appropriate measure of the forward irradiance. Because of the inadequate boundary conditions assumed in their derivation the Rayleigh-Sommerfeld and Kirchhoff integrals do not correctly describe the flow of energy through the aperture.

Step-transition perturbation approach for pixel-structured nonparaxial diffractive elements.

An extension of an approximate step-transition perturbation method is presented that permits numerically efficient diffraction analysis of pixel-structured surface profiles in the nonparaxial domain. Comparison with the rigorous diffraction theory of gratings shows that the method is reasonably accurate provided that the pixel size exceeds approximately two wavelengths even if the structure contains isolated pixels.

Nano-structured anti-reflective surfaces replicated by hot embossing

We developed a fabrication technique of anti-reflective structures for applications in the visible spectral range. The depth and duty cycle of the grating structures optimised for wavelengths around 500 nm were calculated using rigorous diffraction theory. We used electron-beam lithography for the manufacturing of linear and crossed grating patterns with pitches of 200 nm and various duty cycles over areas of several square millimeters. The structures are transferred to a quartz master, which is then replicated by Ni electroforming into a stamper for the hot embossing into polycarbonate (PC) sheets. The optical properties of the replicated PC gratings were measured over a wide wavelength range. The general shapes of the curves are in good agreement with the calculations, and for both polarizations, the reflectivity has been reduced significantly.

Reflection of infrared radiation from lamellar gratings on a silicon wafer: Spectroscopy of nonspecular orders

Spectral efficiencies in the wavelength range from 1.5 to 14 μm of nonspecular orders reflected by grating-on-silicon structures with periods comparable to the wavelengths have been measured. The measurements were carried out at varying incident and scattered angles while keeping their sum fixed. The spectra consist of broadened peaks at wavelengths close to those predicted by the grating equation. A mechanism of the broadening due to finite incident beam width has been discussed. Simulations using rigorous diffraction theory and wavelet analysis have been performed. The results obtained agree well with the experimental data.

Analysis of free-space optical interconnects for the three-dimensional optoelectronic stacked processor

Performance of free-space optical interconnect for the three-dimensional optoelectronic stacked processor (3DOESP) has been analyzed. The wave propagation in the optical interconnection system has been investigated by utilizing rigorous scalar diffraction theory. The effects of ghost talk caused by the superposition of the delayed reflections of the original signal due to the multiple propagation of the wave between the vertical-cavity surface-emitting laser (VCSEL) and metal-semiconductor-metal (MSM) detector have been analyzed. The conducted study indicates that even in the presence of significant amount of ghost talk a high performance free-space optical interconnect can be realized in this system by employing a receiver architecture that allows for DC level adjustment of the signal at the input of the transimpedance amplifier stage.

Efficient optimization of diffractive optical elements based on rigorous diffraction models.

An efficient optimization strategy for the design of diffractive optical elements that is based on rigorous diffraction theory is described. The optimization algorithm combines diffraction models of different degrees of accuracy and computational complexity. A fast design algorithm for diffractive optical elements is used to yield estimates of the optimum surface profile based on paraxial diffraction theory. These estimates are subsequently evaluated with a rigorous diffraction model. This scheme allows one to minimize the need to compute diffraction effects rigorously, while providing accurate design. We discuss potential applications of this scheme as well as details of an implementation based on a modified Gerchberg-Saxton algorithm and the finite-difference time-domain method. Illustrative examples are provided in which we use the algorithm to design Fourier array illuminators.

Wavenumber-modulated patterns of transmission through one- and two-dimensional gratings on a silicon substrate

The phenomenon of filtering in zero-diffraction order is studied for transmission through one- and two-dimensional periodic structures on a silicon wafer. Our study combines FTIR spectrometry in the range 2.5 to 25 µm, a theoretical insight using scalar diffraction theory and a rigorous full-vector simulation. The phenomenon exhibits itself as `bright' and `dark' bands in the spectra of normal transmission through grating samples, which replace each other quasi-periodically with respect to wavenumber, at wavelengths smaller than the grating period. The transmission modulation ratio is high for two-side polished samples, while it drastically degrades in samples with an unpolished backside. It is shown that the scalar theory, which satisfactorily describes the periodicity of the transmission, is incapable of calculating correctly the transmission modulation depth. To fully account for the experimental data numerical simulations using rigorous electromagnetic diffraction theory are carried out. Good agreement between the rigorous theory and experiment, both in the range of the transmission oscillations and in the region of enhanced absorption, is obtained.

Efficient Bragg waveguide-grating analysis by quasi-rigorous approach based on Redheffer's star product

We introduce a computationally efficient quasi-rigorous method for the analysis of corrugated planar waveguide structures. The method is based on rigorous diffraction theory of gratings. The computational efficiency is achieved by using Redheffer's star product and the so-called binary method for the involution of the transfer matrix. The developed method enables efficient rigorous analysis of corrugated waveguide structures without any limitations for the corrugation depth. Comparison with the thin-film stack method shows that the proposed method gives similar results for Bragg grating for the fundamental mode when the corrugations are shallow, but the results differ significantly when the corrugations are deep. Furthermore, the quasi-rigorous method also facilities the analysis of the coupling of light from the fundamental mode into the higher waveguide modes.

Analysis of Near-Field Intensity Distributions of High-Compression Talbot Array Illuminators Using Rigorous Diffraction Theory

The technology nowadays employed in the field of binary optics allows a relatively easy fabrication of grating structures down to the wavelength region. The analysis of light propagation through such grating structures requires the use of rigorous diffraction theories such as the rigorous coupled-wave analysis (RCWA), in order to take proper account of polarization effects in the electric and magnetic field and the thickness of the grating. In this paper, we examine the near-field intensity distributions and associated illumination efficiencies of Talbot array illuminators (TAIL#x0027;s) with compression ratios of 8 and 16 using RCWA. The high illumination efficiency observed close to the grating surface is expected to bring about new applications of TAIL#x0027;s in the field of super-resolution and near-field optics.

Optical scatterometry evaluation of groove depth in lamellar silicon grating structures

Shlomo HavaMark AuslenderBen-Gurion University of the NegevDepartment of Electrical and ComputerEngineeringPOB 653Beer-Sheva 84105, IsraelE-mail: marka@ee.bgu.ac.ilAbstract. A simple nondestructive method of measuring groove depthin lamellar gratings is presented. The method is based on processingscatterometry data for a wavelength much smaller than the grating pitchusing formulas derived by means of scalar diffraction theory. The methodhas structural and optical limitations that are specified. The intensities ofthe 0th and 61st orders reflected from silicon grating samples irradiatedby a He-Ne laser, as functions of the incident angle, are measured andprocessed to determine the groove depths. The diffraction efficienciescalculated using the thus determined groove depths by means of rigor-ous diffraction theory agree with the experimental data. For the ex-amples studied in this paper the uncertainty in the determined groovedepths is as small as 10 nm.

Step-discontinuity approach for non-paraxial diffractive optics

Abstract An approximate method based on local field perturbations caused by abrupt transitions of the surface profile is described, which enables rapid approximate calculation of diffraction patterns of diffractive elements in the non-paraxial domain of diffractive optics. In this domain the simple complex-amplitude transmittance model based on scalar diffraction theory is no longer valid and rigorous computations are exceedingly time-consuming. Comparisons with rigorous diffraction theory show that the method is accurate for binary and multilevel profiles provided that the minimum feature size is larger than approximately one optical wavelength. The method is applied to the evaluation of the uniformity error of binary, four-level, and analogue array illuminators.

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.

Step-discontinuity approach for non-paraxial diffractive optics

An approximate method based on local field perturbations caused by abrupt transitions of the surface profile is described, which enables rapid approximate calculation of diffraction patterns of diffractive elements in the non-paraxial domain of diffractive optics. In this domain the simple complex-amplitude transmittance model based on scalar diffraction theory is no longer valid and rigorous computations are exceedingly time-consuming. Comparisons with rigorous diffraction theory show that the method is accurate for binary and multilevel profiles provided that the minimum feature size is larger than approximately one optical wavelength. The method is applied to the evaluation of the uniformity error of binary, four-level, and analogue array illuminators.

Photonic crystal diffraction gratings

It is shown from numerical results deduced from a rigorous theory of diffraction that diffraction gratings made with two-dimensional dielectric photonic crystals may present blazing effects. Since these structures are lossless, efficiencies of 100% in the -1st order can be obtained in polarized light. Efficiency curves in Littrow mount are shown.

Radiation filters and emitters for the NIR based on periodically structured metal surfaces

Abstract The spectrally selective optical properties of wavelength selective radiation emitters and filters based on periodically microstructured metal surfaces were investigated. Metal surfaces were structured by the use of a holographic mask and subsequent etching processes. Due to the microstructure, thermally excited surface plasmons couple to electromagnetic radiation. Therefore a structured tungsten surface can act as a selective radiation emitter. The calculation of the absorptance by a rigorous diffraction theory allows the prediction of the emissivity of such structures. The angle dependent emissivity of tungsten gratings with periods of 1.4 μm and 2.0 μm was measured. A peak emissivity of 70% at a wavelength of 1.6 μm was achieved. Band pass filters for the near infrared spectral range based on perforated metal films were investigated theoretically and experimentally. Filters with a grating period of 2.0 μm were produced. A peak transmittance of 80% at a wavelength 2.9 μm was achieved. The optical properties of the diffractive elements described partly show a strong angle dependence

Radiation filters and emitters for the NIR based on periodically structured metal surfaces

The spectrally selective optical properties of wavelength selective radiation emitters and filters based on periodically microstructured metal surfaces were investigated. Metal surfaces were structured by the use of a holographic mask and subsequent etching processes. Due to the microstructure, thermally excited surface plasmons couple to electromagnetic radiation. Therefore a structured tungsten surface can act as a selective radiation emitter. The calculation of the absorptance by a rigorous diffraction theory allows the prediction of the emissivity of such structures. The angle dependent emissivity of tungsten gratings with periods of 1.4 μm and 2.0 μm was measured. A peak emissivity of 70% at a wavelength of 1.6 μm was achieved. Band pass filters for the near infrared spectral range based on perforated metal films were investigated theoretically and experimentally. Filters with a grating period of 2.0 μm were produced. A peak transmittance of 80% at a wavelength 2.9 μm was achieved. The optical properties of the diffractive elements described partly show a strong angle dependence

Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light

Historical introduction 1. Basic properties of the electromagnetic field 2. Electromagnetic potentials and polarization 3. Foundations of geometrical optics 4. Geometrical theory of optical imaging 5. Geometrical theory of aberrations 6. Image-forming instruments 7. Elements of the theory of interference and interferometers 8. Elements of the theory of diffraction 9. The diffraction theory of aberrations 10. Interference and diffraction with partially coherent light 11. Rigorous diffraction theory 12. Diffraction of light by ultrasonic waves 13. Scattering from inhomogeneous media 14. Optics of metals 15. Optics of crystals 16. Appendices Author index Subject index.