Absolute Diffraction Efficiencies Research Articles

Electrically Tunable Reflective Metasurfaces with Continuous and Full-Phase Modulation for High-Efficiency Wavefront Control at Visible Frequencies.

All-dielectric optical metasurfaces can locally control the amplitude and phase of light at the nanoscale, enabling arbitrary wavefront shaping. However, lack of postfabrication tunability has limited the true potential of metasurfaces for many applications. Here, we utilize a thin liquid crystal (LC) layer as a tunable medium surrounding the metasurface to achieve a phase-only spatial light modulator (SLM) with high reflection in the visible frequency, exhibiting active and continuous resonance tuning with associated 2π phase control and uncoupled amplitude. Dynamic wavefront shaping is demonstrated by programming 96 individually addressable electrodes with a small pixel pitch of ∼1 μm. The small pixel size is facilitated by the reduced LC thickness, strongly suppressing cross-talk among pixels. This device is used to demonstrate dynamic beam steering with a wide field-of-view and high absolute diffraction efficiencies. We believe that our demonstration may help realize next-generation, high-resolution SLMs, with wide applications in dynamic holography, tunable optics, and light detection and ranging (LiDAR), to mention a few.

Nonlinear continual growth model of nonuniformly scaled reliefs as applied to the rigorous analysis of the X-ray scattering intensity of multilayer mirrors and gratings

It is revealed that certain terms entering into the nonlinear continual equation describing thin-film growth enable its application to the simulation of the surfaces of multilayer mirrors and gratings with a large height and/or jumps of boundary-profile gradients. The proposed model characterizes both variations in the power spectral-density function of the surface of Al/Zr multilayer mirrors and the smoothing and shift of the boundaries of Mo/Si and Al/Zr gratings grown on Si substrates with triangular groove profiles by means of magnetron and ion-beam deposition. Rigorous calculations indicate that the intensities of diffuse X-ray scattering by Au mirrors, which have similar boundary profiles with Gaussian and exponential autocorrelation functions, differ substantially from each other. Computer simulation of the growth of Mo/Si and Al/Zr multilayer gratings is performed. On the basis of the calculated boundary profiles, the absolute diffraction efficiencies of the Mo/Si and Al/Zr gratings are found via the integral equation method in the extreme UV region. It is demonstrated that the proposed comprehensive approach to calculations of the boundary profiles and the intensities of short-wavelength scattering from multilayer mirrors and gratings makes it possible to carry out studies comparable in accuracy to measurements based on synchrotron radiation.

Nonlinear continuum growth model of multiscale reliefs as applied to rigorous analysis of multilayer short-wave scattering intensity. I. Gratings

It is shown that taking into proper account certain terms in the nonlinear continuum equation of thin-film growth makes it applicable to the simulation of the surface of multilayer gratings with large boundary profile heights and/or gradient jumps. The proposed model describes smoothing and displacement of Mo/Si and Al/Zr boundaries of gratings grown on Si substrates with a blazed groove profile by magnetron sputtering and ion-beam deposition. Computer simulation of the growth of multilayer Mo/Si and Al/Zr gratings has been conducted. Absolute diffraction efficiencies of Mo/Si and Al/Zr gratings in the extreme UV range have been found within the framework of boundary integral equations applied to the calculated boundary profiles. It has been demonstrated that the integrated approach to the calculation of boundary profiles and of the intensity of short-wave scattering by multilayer gratings developed here opens up a way to perform studies comparable in accuracy to measurements with synchrotron radiation, at least for known materials and growth techniques.

Laminar and blazed type holographic gratings for a versatile soft x-ray spectrograph attached to an electron microscope and their evaluation in the 50–200 eV range

Laminar and blazed type holographic varied-line-spacing spherical gratings for use in a versatile soft x-ray flat-field spectrograph attached to an electron microscope are designed, fabricated, and evaluated. The absolute diffraction efficiencies of laminar (or blazed) master and replica gratings at 86.00° incidence evaluated by synchrotron radiation show over 5% (or 8%) in the 50-200 eV range with the maxima of 22% (or 26%-27%). Also the resolving power evaluated by a laser produced plasma source is in excess of 700 at the energy near the K emission spectrum of lithium (~55 eV) for all gratings. Moreover, the K emission spectrum of metallic Li with high spectral resolution is successfully observed with the spectrograph attached to a transmission electron microscope.

Diffraction efficiency of 200-nm-period critical-angle transmission gratings in the soft x-ray and extreme ultraviolet wavelength bands

We report on measurements of the diffraction efficiency of 200-nm-period freestanding blazed transmission gratings for wavelengths in the 0.96 to 19.4 nm range. These critical-angle transmission (CAT) gratings achieve highly efficient blazing over a broad band via total external reflection off the sidewalls of smooth, tens of nanometer thin ultrahigh aspect-ratio silicon grating bars and thus combine the advantages of blazed x-ray reflection gratings with those of more conventional x-ray transmission gratings. Prototype gratings with maximum depths of 3.2 and 6 μm were investigated at two different blaze angles. In these initial CAT gratings the grating bars are monolithically connected to a cross support mesh that only leaves less than half of the grating area unobstructed. Because of our initial fabrication approach, the support mesh bars feature a strongly trapezoidal cross section that leads to varying CAT grating depths and partial absorption of diffracted orders. While theory predicts broadband absolute diffraction efficiencies as high as 60% for ideal CAT gratings without a support mesh, experimental results show efficiencies in the range of ∼50-100% of theoretical predictions when taking the effects of the support mesh into account. Future minimization of the support mesh therefore promises broadband CAT grating absolute diffraction efficiencies of 50% or higher.

Performance of laminar-type holographic grating for a soft x-ray flat-field spectrograph in the 0.7–6 nm region

A laminar-type holographic grating having a groove density of 2400 lines/mm was designed and fabricated for use with a soft x-ray flat-field spectrograph covering the 0.7–6 nm region. The varied-line-spaced grating pattern was generated by use of an aspheric wave front recording system and the laminar-type grooves were formed by a reactive ion-etching method. The performance of the grating was evaluated by using a molybdenum K x-ray generator and a spectrograph with a charge coupled device imaging detector. Also, the absolute diffraction efficiencies of the zeroth, first, second, and third, spectral orders were measured by use of the reflectometers installed at Synchrotron Radiation Beamlines. The experimental results showed that the holographic grating indicated comparable spectral resolution and maximum first-order diffraction efficiency (>2%) at ∼2 nm with a replica grating made from a mechanically ruled varied-line-spacing grating. It also showed higher efficiency in the <1.0 nm region and lower level higher-order light over the whole wavelength range than the replica grating.

STUDY OF TRANSMISSION GRATING DIFFRACTION EFFICIENCIES FOR SOFT X-RAYS

Absolute diffraction efficiencies of a transmission grating at a photon energy of 844eV have been calibrated on synchrotron radiation source.With the aid of grating model,all structure parameters of the grating are obtained and absolute diffraction efficiencies for soft X-rays in the range of 100—2000eV are calculated and discussed.

Measurement of the diffraction efficiency of individual images in multiplexed holography

It is important in multiplex holography to measure the relative and absolute diffraction efficiencies of the individual images because of the phenomenon of holographic reciprocity law failure (HRLF). Existing techniques based on diffraction grating images cannot be used for realistic multiplex holograms. This paper describes a simple and rapid technique, based on a charge-coupled device (CCD) camera and digital oscilloscope, that can be applied to all multiplex holograms where the images are spatially separated. Both absolute and relative diffraction efficiencies can be measured, and by using an image area comparison technique some insensitivity to focusing errors is obtained.

Recent Developments in National Physical Laboratory X-Ray Gratings and Spectrometers

X-ray gratings have been developed for use in the wavelength region of 0.01 to 20 nm, where it is required to employ a grazing incidence configuration. Both laminar and blazed gratings have been produced by conversion of a ruled or photo-fabricated grating, using various etching procedures. The X-ray gratings are formed in a vitreous silica substrate and are relatively robust. Absolute diffraction efficiencies in the first order range from about 5% in the 0.15 to 0.3 nm region to nearly 20% for wavelengths greater than 1 nm. A new precision focusing spectrometer for use in the wavelength range 0.05 to 0.5 nm has been developed. The spectrometer design is based on the polar coordinate principle and the spectrometer can cater for concave gratings of various radii between 5 and 15 m.