All-dielectric reflection gratings: a study of the physical mechanism for achieving high efficiency

The physical mechanism for the all-dielectric reflection gratings to achieve high efficiency in the -1st-order Littrow mounting is studied. The all-dielectric gratings consist of two parts, a surface-relief grating and a highly reflecting dielectric stack. The surface-relief grating sits on top of the reflecting stack. A simple analytical expression for diffraction efficiency is obtained in terms of the S-matrix elements of the two parts. By analyzing the expression we show that the diffraction can be interpreted as the interference of a symmetric wave and an antisymmetric wave. The conditions for achieving high diffraction efficiency are also identified. The analytical results are illustrated by numerical computations.     

Pseudospectral modal method for conical diffraction of gratings

For lamellar gratings and other layered periodic structures, the modal methods (including both analytic and numerical ones) are often the most efficient, since they avoid the discretization of one spatial variable. The pseudospectral modal method (PSMM) previously developed for in-plane diffraction problems of one-dimensional gratings achieves high accuracy for a small number of discretization points, and it outperforms most other modal methods. In this paper, an extension of the PSMM to conical diffraction problems is presented and implemented. Numerical examples are used to demonstrate the high accuracy and excellent convergence property of this method for both dielectric and metallic gratings.     

White LED light coupling into light guides with diffraction gratings

Radial diffractive gratings are used to couple light of a white LED into a light guide. Theoretical coupling efficiencies are evaluated with rigorous diffraction theory in a pure conical mounting. It is shown that when the refractive index of the grating increases from 1.46 to 2.05 the incoupling efficiency increases from 42% to 63%. Also, with the increasing refractive index the incoupling efficiency is shown to become more nearly uniform over the visible spectrum. Experimental results for the incoupled efficiencies and the color coordinates of the incoupled spectra are introduced for refractive indices n=1.46 and n=1.56.     

Diffraction properties of volume holographic gratings for an ultrashort pulsed beam with different polarization states readout

The diffraction properties of volume holographic gratings are studied when the gratings are illuminated by an ultrashort pulsed beam with different polarization states. The developed coupled wave theory of Kogelnik is used. Considering the dispersion effect of the grating media, solutions for the diffracted and transmitted intensities, diffraction efficiencies and the bandwidths of the gratings are given in transmission volume holographic gratings and reflection volume holographic gratings. The bandwidths of the gratings are reduced by the dispersion effect of the grating media. They also have different influences on the diffraction of an ultrashort pulsed beam with different polarization states. For different values of the ratio of the spectral bandwidth of the input pulse to that of the grating, the changes of the spectral and temporal distributions of the diffracted intensities, as well as the diffraction efficiencies of the gratings are shown.     

Two-channel tunable monochromatic illuminator with a concave diffraction grating and an original scanning system

A two-channel monochromatic illuminator with only one diffraction grating and an original scanning system has been designed for multiple applications. This scanning system consists of two rotational plane mirrors that reflect light diffracted by a concave diffraction grating to the ?1 orders of the spectrum. The light reflected by the mirrors goes to two exit slits that correspond to two channels of the device. The positions of the centers of rotation of the mirrors are selected to produce minimal deviation of the direction of the light reflected during the scanning. The aberration characteristics of some variations in the optical mounting of the device made by use of spherical and toroidal holographic diffraction gratings recorded in stigmatic and astigmatic beams, the possibilities for application of the device for measuring the color sensitivity of the human eye, and the possibilities for measuring the efficiency of concave diffraction gratings, are also discussed.     

Near-normal-incidence extreme-ultraviolet efficiency of a flat crystalline anisotropically etched blazed grating

We have measured the extreme-ultraviolet (EUV) efficiency at an angle of incidence of 10 degrees of a flat crystalline anisotropically etched blazed grating. The measured efficiencies are high for uncoated gratings and agree well with a calculated model derived from a reasonable estimate of the groove profile. The highest groove efficiencies derived from the measurements are 48.8% at 19.07 nm and 64.1% at 16.53 nm for the -2 and -3 orders, respectively, which are comparable to the best values obtained yet from a holographic ion-etched blazed grating. This presents opportunities to instrument designs for high-resolution EUV spectroscopy in astrophysics where high efficiency in high orders is desirable.     

Extreme-ultraviolet radiation filtering by freestanding transmission gratings

Measurement of energetic neutral atoms fluxes in space requires efficient suppression of exceptionally strong background extreme-ultraviolet (EUV) and UV radiation. Diffraction filters make it possible to separate (transmit) charged and neutral particles from the background radiation (which would be suppressed). Recently developed freestanding transmission gratings look especially promising for implementation in a new family of diffraction EUV/UV filters. The first results of our experimental study of filtering properties of freestanding transmission gratings with a period of 200 nm are presented. The grating transmission was measured in the 52-131-nm wavelength range, and grating polarization properties were determined at 58.4 nm. It is shown that transmission gratings can be used efficiently as filters and polarizers in the EUV/UV spectral range.     

Sub-10 nm patterning using EUV interference lithography

Extreme ultraviolet (EUV) lithography is currently considered as the leading technology for high-volume manufacturing below sub-20 nm feature sizes. In parallel, EUV interference lithography based on interference transmission gratings has emerged as a powerful tool for industrial and academic research. In this paper, we demonstrate nanopatterning with sub-10 nm resolution using this technique. Highly efficient and optimized molybdenum gratings result in resolved line/space patterns down to 8 nm half-pitch and show modulation down to 6 nm half-pitch. These results show the performance of optical nanopatterning in the sub-10 nm range and currently mark the record for photon-based lithography. Moreover, an efficient phase mask completely suppressing the zeroth-order diffraction and providing 50 nm line/space patterns over large areas is evaluated. Such efficient phase masks pave the way towards table-top EUV interference lithography systems.     

Beam separator for high-order harmonic radiation in the 3-10 nm spectral region

We present the scheme of a beam separator for ultrashort high-order harmonic radiation below 10 nm. The system consists of a collimating mirror and two plane grazing-incidence gratings in compensated configuration. The first grating acts as the beam separator: it diffracts the extreme ultraviolet (XUV) light into the first order while reflecting the fundamental laser beam into the zero order. The diffracted light goes to a second grating that compensates both for the spectral dispersion and for the temporal broadening of the XUV ultrashort pulse caused by the diffraction at the first grating. The system can be designed for any wavelength in the 3-40 nm region. Since the gratings are operated at extreme grazing incidence, the area of the optical surface illuminated by the fundamental laser pulse is large, and therefore there is no risk of damage of the optical surfaces. The effects on the phase of the ultrashort pulse for narrowband applications are discussed.     

Compensation of optical path lengths in extreme-ultraviolet and soft-x-ray monochromators for ultrafast pulses

The extraction of the spectrum corresponding to a single extreme-ultraviolet ultrashort pulse embedded in an extended spectrum may alter the duration of the pulse itself. This is due to the spectral filtering of optics and the differences in the optical path of the rays caused by ordinary diffraction when a grating is used. The basic mechanism that leads to the latter effect is the difference of one wavelength of the path length of two rays diffracted at the first order by nearby grating grooves. A study of these effects and some possible solutions obtained from using a pair of diffraction gratings is presented. The aim of this study is the selection without dispersion of one or more high-order laser harmonics produced by a pulse lasting a few femtoseconds and interacting with a gas jet.     

Diffractive optical isolator made of high-efficiency dielectric gratings only

The working principle of an optical isolator made of two corrugated dielectric gratings is introduced. One grating acts as a polarizer, and the other acts as a quarter-wave plate used in conical incidence converting linearly polarized light into circularly polarized light. Global maxima of diffraction efficiency for surface-corrugated gratings with binary, sinusoidal, and pyramidal ridge shapes with dependence on the material index are identified. Regarding technological feasibility for use in the visible wavelength range, high-frequency gratings with a binary shape were realized. With these gratings, an extinction ratio of more than 40 dB for the polarizer is theoretically possible, and more than 20 dB was experimentally achieved. A good correlation between theoretically calculated efficiencies and birefringences based on rigorous methods and the experimental results is demonstrated.     

Efficiencies of master, replica, and multilayer gratings for the soft-x-ray-extreme-ultraviolet range: modeling based on the modified integral method and comparisons with measurements

The near-normal-incidence efficiencies of a 2400-groove/mm holographic master grating, a replica grating, and a multilayer grating are modeled in the soft-x-ray-extreme-ultraviolet (EUV) regions and are compared with efficiencies that are measured with synchrotron radiation. The efficiencies are calculated by the computer program PCGrate, which is based on a rigorous modified integral method. The theory of our integral method is described both for monolayer and multilayer gratings designated for the soft-x-ray-EUV-wavelength range. The calculations account for the groove profile as determined from atomic force microscopy with a depth scaling in the case of the multilayer grating and an average random microroughness (0.7 nm) for the short wavelengths. The refractive indices of the grating substrate and coatings have been taken from different sources because of the wide range of the wavelengths (4.5-50 nm). The measured peak absolute efficiency of 10.4% in the second diffraction order at a wavelength of 11.4 nm is achieved for the multilayer grating and is in good agreement with a computed value of approximately 11.5%. Rigorous modeling of the efficiencies of three similar gratings is in good overall agreement with the measured efficiency over a wide wavelength region. Additional calculations have indicated that relatively high normal incidence efficiency (of at least several percent) and large angular dispersion in the higher orders can be achieved in the 4.5-10.5-nm range by application of various multilayer coatings.     

High-efficiency x-ray gratings with asymmetric-cut multilayers

We present the fabrication and analysis of efficient and highly dispersive gratings for the x-ray and extreme ultraviolet (EUV) regime. We show that an asymmetric-cut multilayer structure can act as a near-perfect blazed grating. The precision and high line density are achieved by layer deposition of materials, which can be controlled to the angstrom level. We demonstrate this in the EUV regime with two structures made by cutting and polishing magnetron-sputtered multilayer mirrors of over 2000 bilayers thick, each with a period of 6.88 nm. These were cut at angles of 2.9° and 7.8° to the surface. Within the 3% bandwidth rocking curve of the multilayer, the angular dispersion of the diffracted wave was in agreement with the grating equation for elements with 7250 and 19,700 line pairs/mm, respectively. The dependence of the measured efficiency was in excellent agreement with a formulation of dynamical diffraction theory for multilayered structures. At a wavelength of 13.2 nm, the efficiency of the first-order diffraction was over 95% of the reflectivity of the uncut multilayer. We predict that such structures should also be effective at shorter x-ray wavelengths. Both the Laue (transmitting) and Bragg (reflecting) geometries are incorporated in our formalism, which is applied to the analysis of multilayer Laue lenses and focusing and dispersing Bragg optics.     

Wadsworth mount redux: paraboloidal versus spherical gratings

Spherical and paraboloidal diffraction gratings are considered for use on an experiment involving a collection of satelliteborne spectrographs that will investigate astrophysical plasmas in the spectral region from approximately 100 to 300 A. We shall use eight spectrographs: Wadsworth mounts in near-normal incidence with effective focal lengths of 3 m, each centered on a chosen wavelength in this spectral range. Ray tracings show that paraboloidal gratings used in the Wadsworth mount have a significant increase in resolution over spherical gratings of the same effective focal length, used in the same mounting, as long as the spectral ranges are small (approximately 10% of the central wavelength). This increase in resolution is due to the spatial extent of coma for a paraboloidal grating that is less than the circle of least confusion of spherical gratings.     

Formation of anisotropic diffraction gratings in a polymer-dispersed liquid crystal by polarization modulation using a spatial light modulator

Anisotropic diffraction gratings based on a holographic polymer-dispersed liquid crystal (HPDLC) are realized by interferometric exposure using a spatial light modulator (SLM). The SLM is used in the HPDLC grating formation for anisotropic holographic recordings of two-dimensional polarization states for an incident light beam. The diffraction efficiency for P-polarization and the distinctive ratio of diffraction efficiency in P-polarization to that in S-polarization increases with the signal level applied to the SLM. The resulting volume gratings exhibit diffraction efficiency of more than 60% and a distinctive ratio of diffraction over 100. The microscopic origin of the anisotropic property is investigated by an optical polarizing microscope. The novel characteristics of the anisotropic diffraction properties of HPDLC are applied to an image reconstruction technique.     

Phase and Amplitude Behaviour in Conical Diffraction Near the Resonant Excitation of Surface Plasmons

Abstract

The efficiencies and phase shifts of light specularly reflected by corrugated metallic gratings in conical mounting are studied by means of rigorous formalisms based on conformal and non-conformal transformations. The reflected field is separated into components co- and cross-polarized with respect to p- and s-polarized incident waves. The efficiency of these components and their relative phase shifts are calculated as functions of the angles of incidence in regions where coupling between light and surface plasmons occurs. The sensitivity of the efficiency of p–s conversion to changes in grating geometry is tested by comparing results obtained for cycloidal, sinusoidal and triangular profiles with different groove heights.     

Study of broadband polarization conversion with metallic surface-relief gratings by rigorous coupled-wave analysis

The conical rigorous coupled-wave analysis (RCWA) is employed to calculate the polarization conversion through the excitation of surface plasmons on metallic gratings. Various examples are examined with this numerical scheme. Our calculated results are consistent with those obtained from experiment and from other numerical methods. Three types of subwavelength surface-relief gratings are studied for the capability of broadband polarization conversion in the visible region. For wide-angle applications, various incident angles are studied and high polarization conversion efficiency is achieved.     

Propagation of longitudinal leaky surface waves under periodic metal grating structure on lithium tetraborate

The dispersion properties of longitudinal leaky surface waves propagating under the periodic Al strip grating on lithium tetraborate (Li(2)B(4)O(7); LBO) are described theoretically and experimentally for applications of the mode to high frequency SAW devices. A theoretical method developed here is based on Floquet's theorem using space harmonics as an orthogonal function set and real boundary integral equations derived from the method of weighted residuals for a period of each region, i.e., substrate, metal, and free space. The boundary integral equations are solved by using the Galerkin procedure. The periodic strip gratings with both single-electrodes and double-electrodes are investigated, considering the convergency of the numerical computation for the number of the space harmonics. As a result, the propagation loss for shorted gratings was found to be relatively low in the thickness range of the Al strip below about 1% for the single-electrodes and 2% for the double-electrodes, although it greatly increases for a thickness over 2% for the single-electrodes and 3% for the double-electrodes.     

Time-delay compensated monochromator in the off-plane mount for extreme-ultraviolet ultrashort pulses

The design of ultrafast monochromators using grazing-incidence gratings in the off-plane mount for the spectral selection of extreme-ultraviolet femtosecond pulses in a broad spectral region is presented. Their application in the selection of high-order laser harmonics is analyzed in detail. The main advantage of the off-plane mount is a much higher efficiency than that of the classical mount. It is shown that two-grating configurations preserve the length of the optical paths of different diffracted rays, maintaining the extremely short time duration of the pulse. Configurations with plane or toroidal gratings are discussed. As a test case, the design of a monochromator for the 17-61 nm region with a time compensation better than 1 fs is presented.     

Boundary integral equation Neumann-to-Dirichlet map method for gratings in conical diffraction

Boundary integral equation methods for diffraction gratings are particularly suitable for gratings with complicated material interfaces but are difficult to implement due to the quasi-periodic Green's function and the singular integrals at the corners. In this paper, the boundary integral equation Neumann-to-Dirichlet map method for in-plane diffraction problems of gratings [Y. Wu and Y. Y. Lu, J. Opt. Soc. Am. A26, 2444 (2009)] is extended to conical diffraction problems. The method uses boundary integral equations to calculate the so-called Neumann-to-Dirichlet maps for homogeneous subdomains of the grating, so that the quasi-periodic Green's functions can be avoided. Since wave field components are coupled on material interfaces with the involvement of tangential derivatives, a least squares polynomial approximation technique is developed to evaluate tangential derivatives along these interfaces for conical diffraction problems. Numerical examples indicate that the method performs equally well for dielectric or metallic gratings.