Parabolic Lenses Research Articles

Design and evaluation of a THz time domain imaging system using standard optical design software

A terahertz (THz) time domain imaging system is analyzed and optimized with standard optical design software (ZEMAX). Special requirements to the illumination optics and imaging optics are presented. In the optimized system, off-axis parabolic mirrors and lenses are combined. The system has a numerical aperture of 0.4 and is diffraction limited for field points up to 4 mm and wavelengths down to 750 microm. ZEONEX is used as the lens material. Higher aspherical coefficients are used for correction of spherical aberration and reduction of lens thickness. The lenses were manufactured by ultraprecision machining. For optimization of the system, ray tracing and wave-optical methods were combined. We show how the ZEMAX Gaussian beam analysis tool can be used to evaluate illumination optics. The resolution of the THz system was tested with a wire and a slit target, line gratings of different period, and a Siemens star. The behavior of the temporal line spread function can be modeled with the polychromatic coherent line spread function feature in ZEMAX. The spectral and temporal resolutions of the line gratings are compared with the respective modulation transfer function of ZEMAX. For maximum resolution, the system has to be diffraction limited down to the smallest wavelength of the spectrum of the THz pulse. Then, the resolution on time domain analysis of the pulse maximum can be estimated with the spectral resolution of the center of gravity wavelength. The system resolution near the optical axis on time domain analysis of the pulse maximum is 1 line pair/mm with an intensity contrast of 0.22. The Siemens star is used for estimation of the resolution of the whole system. An eight channel electro-optic sampling system was used for detection. The resolution on time domain analysis of the pulse maximum of all eight channels could be determined with the Siemens star to be 0.7 line pairs/mm.

Planoconcave lens by negative refraction of stacked subwavelength hole arrays

This work presents the design of a planoconcave parabolic negative index metamaterial lens operating at millimeter wavelengths fabricated by using stacked subwavelength hole arrays. A staircase approximation to the ideal parabola profile has been done by removing step by step one lattice in each dimension of the transversal section. Theory predicts power concentration at the focal point of the parabola when the refractive index equals -1. Both simulation and measurement results exhibit an excellent agreement and an asymmetrical focus has been observed. The possibility to design similar planoconcave devices in the terahertz and optical wavelengths could be a reality in the near future.

Overtone spectroscopy and thermal lens detection limit of methane in cryo-solutions

The overtone spectra of methane solutions from 5000 cm−1 to 17000 cm−1 in liquid nitrogen and liquid argon are presented. The region between 5000 and 15000 cm−1 has been measured using a Fourier transform spectrophotometer with methane concentrations between 0.41% and 37% in mole fraction. The thermal lens technique (TLS) was used to measure the fifth overtone, not observed with the Fourier transform spectrophotometer. For a fixed concentration, maximization of the TLS signal with low modulation frequency and high laser power of excitation is shown. Time-dependent signal profiles of single-beam thermal lens experiments are analysed with the parabolic and aberrant lens models. Fitting parameters are obtained from the time-dependent signals. The absorption coefficient of methane was calculated from the fitting parameters and thermo-optical properties of the solvent. The calculated absorption coefficient of the Δυ = 6 transition of methane is 1.7 × 10−3 cm−1, which is in good agreement with literature values. A limit of detection is calculated with measurements of the fifth overtone absorption of methane in liquid nitrogen for solutions of concentration from 0.012% to 0.36% in mole fraction. Calculated limits of detection are 54 ppm and 15 ppm according to two different definitions of limit of detection for the thermal lens technique.

Capillary μFocus X-ray lenses with parabolic and elliptic profile

The parameters of two elliptical poly-capillary lenses and one mono-capillary parabolic lens were characterized at the optical test bench of the BM05 ESRF beamline and at the BESSY μFocus beamline. The poly-capillary lenses with an input aperture of ∅ 5–6 mm have shown a focal spot size (FWHM) on the order of 6–20 μm with a gain factor of about 600–700 in a wide energy range. For the first time the parabolic mono-capillary lens has shown a focal spot size of <2 μm in the energy range of 10–15 keV. The gain factor reached 980.

Focusing properties of surface plasmon polariton floating dielectric lenses

We have investigated the focusing properties of surface plasmon polariton floating dielectric lenses. An analysis of the scattering characteristics of surface plasmon polaritons using a floating dielectric block shows that the air-gap thickness between a floating dielectric block and a metal substrate can be an effective dynamic variable for modulating the amplitude and phase of the transmission coefficient of the surface plasmon polaritons. This property can be used to realize a variable-focusing surface plasmon dielectric lens with the air-gap thickness as the dynamic variable. The focusing properties of a Fresnel lens and a parabolic lens with respect to the air-gap thickness are compared and analyzed.

Supercritical Angle Fluorescence Correlation Spectroscopy

We explore the potential of a supercritical angle (SA) objective for fluorescence correlation spectroscopy (FCS). This novel microscope objective combines tight focusing by an aspheric lens with strong axial confinement of supercritical angle fluorescence collection by a parabolic mirror lens, resulting in a small detection volume. The tiny axial extent of the detection volume features an excellent surface sensitivity, as is demonstrated by diffusion measurements in model membranes with an excess of free dye in solution. All SA-FCS measurements are directly compared to standard confocal FCS, demonstrating a clear advantage of SA-FCS, especially for diffusion measurements in membranes. We present an extensive theoretical framework that allows for accurate and quantitative evaluation of the SA-FCS correlation curves.

New modules for the VITESS software package: Time-gradient magnetic fields and neutron refractive lenses

Neutron spin-handling devices that employ time-dependent magnetic fields are very frequently used in different polarized neutron instruments. We have developed a new VITESS module that allows us to calculate the neutron spin dynamics in a time-dependent magnetic field, time dependent both in direction and in magnitude. Neutron beam focusing by means of a neutron refractive optic principally allows for a very significant enhancement of neutron flux at the sample position of the small-angle scattering instruments. Presently, there is no possibility to simulate the performance of such neutron refractive optical elements. The new VITESS module for the simulation of spherical and parabolic neutron refractive lenses enables the inclusion of a sequence of neutron lenses (the compound lens), and it takes into account the gravity effects and is conveniently supplied with the trajectory visualization option.

Determination of the electron beam size at the Kurchatov synchrotron radiation source using an X-ray refractive lens

The electron beam size in the storage ring of the Kurchatov synchrotron radiation source at 2.5 GeV is determined using an x-ray two-dimensional parabolic refractive lens. The vertical size of the electron beam of the storage ring is found to be 270 μm, which exceeds the corresponding design value 140 μm (at a betatron coupling of 1%). The difference is explained by the imperfect geodetic arrangement of ring elements and the incomplete adjustment of the ring.

Investigation of phase contrast hard X‐ray microscopy using planar sets of refractive crossed linear parabolic lenses made from SU‐8 polymer

AbstractPlanar X‐ray refractive lenses with parabolic surface profile, and in crossed geometry to provide 2D focusing, are fabricated from SU‐8 polymer using the LIGA process and deep X‐ray lithography technology. A transmission X‐ray microscope (TXM) using a condenser and an objective lens based on this type of X‐ray optics was set up at the ESRF beamline BM 5, for photon energies of 17.1 and 18 keV. Test structures made of gold and SU‐8, with different thicknesses, were imaged with this TXM using in‐line phase‐contrast, with X‐ray magnification factors of 13–20, spatial resolution between 0.2 and 0.3 µm and exposure times around 1 s. The advantages of a TXM based on refractive SU‐8 planar crossed condenser and objective and the optimisation of the optical scheme and of the condenser focusing profile are discussed. (© 2007 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

The approximate ABCD matrix for a parabolic lens of revolution and its application in calculating the coupling efficiency

Using ray optics, we present an explicit formulation of the ABCD matrix for reflection and refraction of light beams at a parabolic interface separating media of different refractive indices under paraxial approximation. Based on the formulated ABCD matrix for refraction by a parabolic lens tip, we present a simple theoretical investigation of the coupling efficiency between a laser diode and a single-mode fiber with a parabolic lens formed on the fiber tip. The results show that this technique is effective and will be of benefit to designing suitable microlenses applying the laser-coupling technique.

Development, production, and investigation of PMMA-based X-ray compound refractive lenses

Equipment and technology for producing X-ray refractive lenses from polymethyl methacrylate are described. Each single lens has a spherical profile with a radius of 2.38 mm. A compound lens is composed of 235 single lenses. The focal length of the compound lens for 14-keV X-ray photons is 4.8 m. The lenses developed thereby have been tested on the synchrotron radiation source of the Scientific and Engineering Complex at the Kurchatov Centre of Synchrotron Radiation and Nanotechnologies. The advantages and the drawbacks of the parabolic and spherical lenses are discussed.

Simulations of Bragg diffraction of a focused x-ray beam by a single crystal with an epitaxial layer

The Bragg case diffraction of a narrow x-ray beam in a multilayer crystal is studied theoretically. The beam produced by a parabolic refractive lens is Bragg reflected by a crystalline sample and a spatial distribution of the intensity is recorded by a detector placed at the focus of the lens. This x-ray optical scheme represents a topographic technique which is extremely sensitive to a depth variation of a crystalline structure. Simulations of the intensity pattern were performed by using a computational technique based on a convolution of individual propagators by performing a double fast Fourier transform procedure. It was shown that each interface in a multilayer crystal can be observed on the intensity pattern with a contrast depending on the incident angle. Thus, by recording a series of images at different angles, valuable depth sensitive structural information can be obtained.

High resolution x-ray microscope

The authors present x-ray images of grid meshes and biological material obtained using a microspot x-ray tube with a multilayer optic and a 92-element parabolic compound refractive lens (CRL) made of a plastic containing only hydrogen and carbon. Images obtained using this apparatus are compared with those using an area source with a spherical lens and a spherical lens with multilayer condenser. The authors found the best image quality using the multilayer condenser with a parabolic lens, compared to images with a spherical lens and without the multilayer optics. The resolution was measured using a 155-element parabolic CRL and a multilayer condenser with the microspot tube. The experiment demonstrates about 1.1μm resolution.

Ray-tracing simulation of parabolic compound refractive lenses

X-ray compound refractive lenses (CRL) are becoming a widespread tool for the generation of microfocus spot sizes at synchrotron beamlines. The calculation of their performance by means of ray-tracing is useful for a rapid estimation of flux, resolution and focusing properties achievable in a beamline, when other optics are present, or simply to study the lens acceptance and focusing in the presence of a particular bending magnet, wiggler or undulator X-ray source. The ray-tracing method presented in this paper has been used to calculate the efficiency of beryllium CRL's using, for the instrument layout, realistic source size and divergence, and usual optics like perfect crystal monochromators. It is shown that the intensity transmitted by the lens, the effective aperture and the gain are in good agreement with analytical formulas. Additional information provided when running the program are the precise shape of beam at the focus, and at any position along the optical axis. For instance the intensity distribution at the CRL entrance and exit planes allows a comparison between the effective and the geometrical apertures. Finally, the method provides a precise value for the lens focal distance, which depends on the CRL length.

A Novel Intracavity Lens Design for Compact and High Efficiency Tapered Laser Diode

An integrated parabolic lens capable of introducing a diverging effect to the optical mode propagating within the cavity of a tapered laser is proposed and demonstrated. This idea allows broader high-power beams to be generated by shorter cavities. Diverging lenses with etch depths of 0.13 and 0.27 mum are implemented, with 12 (9.5%) and 16.8 mum (13.3%) overall broadening of the near-fields widths measured at 1/e <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> intensity. The peak output power as well as the threshold current is found to increase following the lens etching process, confirming the beneficial broadening effect introduced by the diverging lens

Efficient FDTD method for analysis of mushroom-structure based left-handed materials

A finite-difference time-domain method, combined with thin-wire and thin-slot algorithms, which is used to analyse a metamaterial based on periodic mushroom structures, is proposed. This proposed method is suitable for analysing problems involving large structures with fine structural details. Several composite right/left handed (CRLH) metamaterial mushroom-based structures are investigated. A 19 × 8 flat lens and a parabolic lens structure composed of 410 unit mushroom cells are investigated and they demonstrate negative-refractive-index characteristics while operating in the LH region. The simulation and measurement results of one- and two-dimensional CRLH mushroom-based structures are compared. The periodic analysis for mushroom structures is also introduced. Only a single unit mushroom cell is required to present the phenomena of infinite periodicity with periodic boundary conditions.

Small-angle options of the upgraded ultrasmall-angle x-ray scattering beamline BW4 at HASYLAB

We present the upgrade and present status of the ultrasmall-angle x-ray scattering (USAXS) beamline BW4 at the Hamburg Synchrotronstrahlungslabor. In order to extend the accessible scattering vector range, new small-angle setups have been established, making use of the high flux and small divergence of BW4. In standard transmission geometry using a beam size of B=400×400μm2 (horizontal×vertical), typical small-angle resolution ranges from dmax=90to650nm, depending on sample-to-detector distance. Additionally a new microfocus option has been established. This microfocus option allows reducing the sample size by one order of magnitude. Using parabolic beryllium compound refractive lenses, a new standard beam size of B=65×35μm2 (horizontal×vertical) can be provided. The μ-SAXS resolution is as high as dmax=150nm. Using μ-SAXS in combination with grazing incidence (μ-GISAXS) on a standard noble metal gradient multilayer, we prove the feasibility of μ-GISAXS experiments at a second generation source.

Diffraction reflection of a focused X-ray wave by a multilayer crystal

The Bragg diffraction of a narrow X-ray beam in a multilayer crystal is studied in the reflection geometry. It is shown by computer simulation of the experiment that strong integrated kinematic reflection occurs at any boundary of a multilayer crystal at the point of intersection of a narrow beam with the boundary. In contrast to the dynamic diffraction of a plane wave, attenuation of a narrow incident beam due to the reflection is small in comparison with the conventional absorption. As an example of a multilayer crystal, a Fabry-Perot interferometer is considered, which consists of two 70-μm-thick crystal Si layers separated by a 100-μm-thick air layer. The 12 4 0 reflection is studied at a photon energy of 15 keV. Three methods of formation of a narrow beam are considered: wavefront limitation by a slit, focusing with a parabolic lens, and focusing with a zone plate. It is shown that, for a local analysis of the thickness of layers and scattering parameters, the method of parabolic lens focusing has some advantages in comparison with the other methods.

X-ray parabolic lenses made from glassy carbon by means of laser

Parabolic planar compound refractive lenses (CRLs) made from glassy carbon by means of laser ablation are presented. They have radii of curvatures of 5 and 200μm and geometric apertures of 40 and 900μm, respectively. The numbers of biconcave elements in the CRLs were 4, 7, and 200. The planar lenses allow formation of a linear focus of length comparable with the depths of their profiles. Usage of two CRLs in a crossed geometry provides formation of two-dimensional focus. The lenses were tested at the European Synchrotron Radiation Facility at the bending magnet beam line BM-5. The minimum experimental size of the focus has been achieved as 1.4μm.

Design of diffractive optical elements for the fractional Fourier transform domain: phase-space approach

Phase-space optics is used to relate the problem of designing diffractive optical elements for any first-order optical system to the corresponding design problem in the Fraunhofer diffraction regime. This, in particular, provides a novel approach for the fractional Fourier transform domain. For fractional Fourier transforms of arbitrary order, the diffractive element is determined as the optimum design computed for a generic Fourier transform system, scaled and modulated with a parabolic lens function. The phase-space description also identifies critical system parameters that limit the performance and applicability of this method. Numerical simulations of paraxial wave propagation are used to validate the method.