Rigorous Diffraction Theory Research Articles

The numerical analysis of low diffraction efficiency phenomenon at the blaze wavelength for echelle gratings

In this paper, we explain and unify the low diffraction efficiency behavior of echelle gratings at blaze wavelengths under Littrow mount in terms of the metal refractive index (RI). The similarity in the diffraction efficiency (DE) behavior (e.g., efficiency decline and valley-like diffraction curves for low-efficiency orders) of echelle gratings with different metals at TM polarization points the research line of sight to the RIs. Further, the numerical calculations based on the rigorous vector diffraction theory show that the efficiency behavior of the echelle grating at TM polarization is extremely sensitive to the imaginary part of the RI. This is because there is a series of low light-collecting ability (LCA) regions as the imaginary part of the RI changes in the echelle grating, resulting in several disturbed DE zones. In addition, the increase in groove depth improves the LCA at both polarizations, which moves away from the low LCA region at the TM polarization. This leads to low polarization sensitivity and higher DE for echelle gratings, further revealing the essence of the efficiency improvement by increasing the groove depth. From the RI to the LCA, these results will give new concepts to designing and fabricating broadband high-efficiency echelle gratings.

Comparative analysis estimates for two-relief microstructure diffraction efficiency in the visible and dual-infrared ranges in the framework of scalar and rigorous diffraction theories

Comparative analysis estimates for two-relief microstructure diffraction efficiency in the visible and dual-infrared ranges in the framework of scalar and rigorous diffraction theories

Diffractive microstructures of zoom lenses for visible and near-infrared ranges based on novel optical plastics

Subject of study. The possibilities of minimizing the negative effect of the secondary diffraction orders of diffractive microstructures included in structurally simple zoom lenses on the formed image are considered. Objective. The study aims at demonstrating the effectiveness of novel optical plastics in the design of diffractive microstructures for the correction of chromatism and the extension of the operating spectral range of the objectives using three-component eight- and four-lens refractive–diffractive zoom lenses for the visible and near-infrared ranges as an example. Method. Combined mathematical modeling within geometrical optics approximation and rigorous diffraction theory is used. Main results. We demonstrate that, even in structurally simple objectives, new optical plastics allow bilayer diffractive microstructures to be assembled ensuring the absence of halo and any other visually observable negative effect of secondary diffraction orders on the quality of the formed image in all the specified ranges of focal length variation both under daylight and scotopic illumination. Practical significance. The reported results demonstrate the effectiveness of diversification of advanced commercially available optical plastics using the diffractive microstructures of zoom lenses as an example. These results are aimed at stimulating further efforts toward the development and mass production of optical plastics.

Highly Efficient Double-Layer Diffraction Microstructures Based on New Plastics and Molded Glasses

Within the framework of rigorous diffraction theory, the maximum possible incidence angles of radiation on two-layer sawtooth relief-phase microstructures in the visible (0.4 ≤ λ ≤ 0.7 μm) spectral range are compared. Optical materials for the layers of these microstructures are selected from a database of 47 plastics and 165 molded glasses. It is shown that when the ratio of the spatial period of the microstructure to the effective depth of the relief is greater than 20, the achievable angles within which the diffraction efficiency exceeds 0.95 lie in a wide range from 18.5° to 40.5° for single-relief structures and 7.5° to 22.3° for structures with two internal reliefs. The best results for purely plastic microstructures are obtained when the plastic CMT and the indium tin oxide nanocomposite in polymethylmethacrylate are used.

Limiting spectral and angular characteristics of sawtooth dual-relief two-layer diffraction microstructures

Sawtooth two-layer microstructures with internal and external, as well as with two internal reliefs, composed of technological and commercially available optical plastics or an optical plastic and nanocomposite material are investigated. By using the corresponding model microstructures in the frameworks of the rigorous diffraction theory, the limiting spectral and angular characteristics are estimated for sawtooth two-layer dual-relief diffraction microstructures of both types.

Diffraction Focusing of Electromagnetic Radiation by Transmission through Sub-Wavelength Nanoapertures

It is shown theoretically, that the phenomenon of radiation focusing in a small region of the near zone inside a dielectric film can present due to electromagnetic wave transmission through sub-wavelength nanoapertures. The confirmation is based on the rigorous theory of plane wave diffraction by a slot in a perfectly conducting screen of finite thickness in the presence of a plane dielectric film on a substrate, which plays the role of a radiation detector.

Potential opportunities of sawtooth diffraction microstructure with two layers and single relief

We present the estimated parameter (Q factor) derived from scalar diffraction theory for a two-layer single-relief sawtooth diffraction microstructure comprising a pair of optical materials. The Q factor allows the negative effects that arise due to the nonlinearity of the difference in the refractive indices of optical materials to be evaluated. This parameter enables pairs of optical materials to be easily compared and the most promising ones to be selected. Using the mathematical model based on microstructures with the minimum and maximum Q factor values, the best possible angular characteristics in framework of the rigorous theory of diffraction are estimated for a two-layer single-relief microstructure. It is shown that the angular characteristics of a microstructure composed of two nanocomposite materials are very close to the maximum possible characteristics.

Single- and multilayer kinoform elements for compact mid-infrared objectives

It is shown that the introduction of a kinoform element into the optical layout of a refractive triplet makes it possible to reduce both chromatic and monochromatic aberrations to an acceptable level, thereby obtaining a high-aperture infrared objective capable of forming an image with a high resolution over a fairly wide angular field. In this case, the diffraction efficiency of the kinoform element, predicted through rigorous diffraction theory, will not fall below 0.8 over the entire operating spectral range. The possibilities of increasing the diffraction efficiency to 0.9 or 0.95 owing to the use of two- or three-layer kinoform microstructures are demonstrated.

Improved optical imaging of high aspect ratio nanostructures using dark-field microscopy

Improvements to white light optical imaging of widely spaced, high aspect ratio nanostructures are demonstrated using dark-field field microscopy. 1D models of bright- and dark-field imaging are developed from rigorous modal diffraction theory by assuming that features are periodic. A simple model is developed to explain dark field results and simulated line images obtained using the two modalities are compared for different dimensions and materials. Increased contrast between etched features and the substrate is demonstrated in dark field, due to its reduced sensitivity to scattering from flat areas. The results are verified using silicon nanostructures fabricated by sidewall transfer lithography, and feature separation with improved tolerance to apparent substrate brightness is demonstrated during image segmentation using the Otsu method.

Spectral and Angular Dependences of the Efficiency of Three-Layer Relief-Phase Diffraction Elements of the IR Range

Within the framework of the scalar and rigorous diffraction theory based on solving a system of Maxwell equations, saw-tooth relief-phase three-layer microstructures designed for the work with polychromatic radiation of the mid-IR range (3 ≤ λ ≤ 5 μm) are studied. The series of effective microstructures composed of different optical materials is extended, and the depths of their reliefs are minimized. The series is extended, in particular, owing to microstructures in which Fresnel losses for reflection from both reliefs do not exceed 10%. This factor, in combination with the relatively low total relief depth, can turn out to be decisive when choosing one or another microstructure for solving a specific scientific or technological problem.

ANALYSIS OF A TWO-CRYSTAL DELAY LINE FOR FEMTOSECOND PULSES OF THE X-RAY FREE ELECTRON LASER

Using the methods of statistical optics the formation of delayed X-ray pulses in the diffraction reflection of an incident pulse with an arbitrary degree of temporal coherence from a system of parallel crystals with different lattice periods is considered. The results are of interest for constructing delay lines in experiments with a time resolution of the pump-and-probe type and realizing of the self-seeding mode to increase the degree of temporal coherence of the X-ray free-electron laser radiation.
 A rigorous theory of dynamic diffraction in Bragg geometry is applied to the diffraction reflection of short X-ray pulses from a system of two parallel crystals with arbitrary thicknesses, and also, for a system of two pairs of parallel crystals. The dependence of the delay time and the intensity of the delayed pulses on the thickness of the crystals and the distances between them are analyzed. Since the pulses from the X-ray free electron laser have high spatial coherence, i.e. a small angular divergence, but very poor temporal coherence, special attention is paid to the effect of the degree of temporal coherence on the width of the energy spectrum of the incident pulses and on the influence of this width on the intensity of the delayed pulses.

ANALYSIS OF A TWO-CRYSTAL DELAY LINE FOR FEMTOSECOND PULSES OF THE X-RAY FREE ELECTRON LASER

Using the methods of statistical optics the formation of delayed X-ray pulses in the diffraction reflection of an incident pulse with an arbitrary degree of temporal coherence from a system of parallel crystals with different lattice periods is considered. The results are of interest for constructing delay lines in experiments with a time resolution of the pump-and-probe type and realizing of the self-seeding mode to increase the degree of temporal coherence of the X-ray free-electron laser radiation.
 A rigorous theory of dynamic diffraction in Bragg geometry is applied to the diffraction reflection of short X-ray pulses from a system of two parallel crystals with arbitrary thicknesses, and also, for a system of two pairs of parallel crystals. The dependence of the delay time and the intensity of the delayed pulses on the thickness of the crystals and the distances between them are analyzed. Since the pulses from the X-ray free electron laser have high spatial coherence, i.e. a small angular divergence, but very poor temporal coherence, special attention is paid to the effect of the degree of temporal coherence on the width of the energy spectrum of the incident pulses and on the influence of this width on the intensity of the delayed pulses.

A high-diffraction-efficiency subwavelength silica Dammann grating

In this paper, a large scale and highly efficient 1×9 Dammann beam splitter operating in 1.064μm wavelength for TE polarization is designed and fabricated under normal incidence. This element consisting of a triple-groove fused silica grating layer is designed using the inverse mathematical method and rigorous vector diffraction theory. The beam splitter is fabricated by using the self-developed blue light laser writing system and dry etching technique. The fabricated beam splitter presents excellent beam splitter ability for TE polarization light with the average diffraction efficiencies is more than 85% at 1.064μm wavelength (96.4% in theory), which is over 20% higher than the traditional one.

Propagation dynamics of off-axis symmetrical and asymmetrical vortices embedded in flat-topped beams

In this paper, propagation dynamics of off-axis symmetrical and asymmetrical optical vortices(OVs) embedded in flat-topped beams have been explored numerically based on rigorous scalar diffraction theory. The distribution properties of phase and intensity play an important role in driving the propagation dynamics of OVs. Numerical results show that the single off-axis vortex moves in a straight line. The displacement of the single off-axis vortex becomes smaller, when either the order of flatness N and the beam size ω0are increased or the off-axis displacement d is decreased. In addition, the phase singularities of high order vortex beams can be split after propagating a certain distance. It is also demonstrated that the movement of OVs are closely related with the spatial symmetrical or asymmetrical distribution of vortex singularities field. Multiple symmetrical and asymmetrical optical vortices(OVs) embedded in flat-topped beams can interact and rotate. The investment of the propagation dynamics of OVs may have many applications in optical micro-manipulation and optical tweezers.

Dielectric V-ridge gratings: transition from antireflection to retroreflection.

We present a systematic study of the optical properties of dielectric gratings with symmetric V-shaped ridges having a 90 degree apex angle and refractive index n. Such structures exhibit completely different optical properties if the dimensions are scaled with respect to the vacuum wavelength λ0 of light. In the subwavelength domain, where the grating period d is less than λ0/n, the grating behaves as an antireflection layer. In the large-period domain d≫λ0 (with normal incidence from the dielectric side), the grating turns into a micro-retroreflector array. The transition between these well-known domains is studied using rigorous diffraction theory. The results are verified experimentally by fabricating and characterizing V-profile gratings with the aid of wet etching of silicon using a process that defines a 90 degree apex angle and replication into a polymer.

Probing surface plasmons by bare V-shaped tips: modeling by geometrical optics and rigorous diffraction theory

We consider probing inhomogeneous waves in the near fields of metallic nanostructures with the aid of a dielectric V-shaped wedge connected to a waveguide. A geometrical model based on the local plane interface approach is proposed to describe the interaction of the wedge with the inhomogeneous field. The fundamental ideas behind the geometrical model are validated by comparison with the results given by rigorous diffraction analysis, and applied to probing plasmonic interference patterns generated by metallic gratings with very narrow slits. The model explains intuitively why a bare wedge with a large apex angle is capable of subwavelength resolution in the spirit of scanning near-field microscopy.

Diffractive optics based on modulated subwavelength-domain V-ridge gratings

We study the properties of reflection-type V-ridge gratings in the subwavelength domain and describe a method to realize diffractive optical elements by using such gratings as signal carriers. In particular, we utilize a coding scheme based on position modulation of a high-frequency V-ridge carrier grating. We design and demonstrate beam splitting elements using this coding scheme, electron-beam lithography, anisotropic wet etching of silicon, hot embossing of polymer, and metal deposition. These elements have the outstanding property of operating over a large spectral range from 406 to 520 nm. The measured diffraction patterns show excellent agreement with theoretical results given by rigorous diffraction theory.

Propagation dynamics of vortices in helico-conical optical beams

We present the dynamics of optical vortices (OVs) that came from the propagation of helico-conical optical beam. This dynamics is investigated numerically by tracking the OVs at several distances using rigorous scalar diffraction theory. To ensure that our numerical calculations are correct, we compare the intensity profiles and their corresponding interferograms taken at different propagation distances between simulations and experiments. We observe that the peripheral isopolar vortices transport radially inward, toward the optical axis along the transverse spatial space as the beam propagates. When the beam has a central vortex, these vortices have significant induced angular rates of motion about the optical axis. These propagation dynamics of vortices influence the internal energy flow and the wave profile reconstruction of the beam, which can be important when deciding their applications.

Diffraction at a straight edge

The simplest problem in diffraction — light passing a straight edge — did not receive a rigorous solution till Sommerfeld’s work of 1896. The earlier theories, their successes and their limitations are recounted. They led upto Sommerfeld’s final solution which had eluded many great contemporaries. This solution was a landmark of rigorous diffraction theory.

A quasi-rigorous solution for focusing radially polarized vector beams by an arbitrary opening paraboloid mirror

For focusing of radially polarized vector beams using an arbitrary opening paraboloid mirror, a quasi-rigorous integral representation of light field is derived based on a rigorous vectorial diffraction theory of electromagnetic waves. Under far-field approximation conditions, the derived integrals reduce to the results from vectorial Debye-Wolf diffraction integral. Numerical calculations show that a marked deviation, as represented by evident focal shift, appears for low-aperture paraboloid mirrors, e.g. the maximum focusing semi-angle α below π/9 with the focal length f being 103λ, or below π/6 when f reduces to 102λ. The radial light spot sharpens to be 0.39λ (FWHM) and purely longitudinally polarized when α is close to 115°, while the axial light spot continuously sharpens to be about half wavelength with α approaching π. For an annular paraboloid mirror, it is possible to further compress the radial light spot down to 0.36λ (FWHM).