Varied Line-space Grating Research Articles

Wide-range angle sensing based on mixed variable line spacing gratings

Variable line spacing (VLS) gratings are core components in spatial spectrum and synchrotron radiation facilities due to their merits of self-focusing, aberration correction, and flat focal field. However, optimal design and fabrication of VLS gratings are still required for matching various applications. Scratch-induced selective wet etching has been proven as a robust way for fabricating various nanostructures because of its simplicity, flexibility, and controllability. In this paper, we proposed convenient and maskless methods to fabricate VLS grating based on scratch-induced selective wet etching. During the etching, key factors, including normal load for the scratching, etching time, and types of etchants, were investigated systematically toward optimizing the process. The shapes including sidewall angle and the bottom curvature of the grating elements can be controlled by adjusting the normal load, etching time and/or etching etchants. It is found that the VLS gratings present a wide-range sensing for angle detection based on the reflection spectrum. Furthermore, combining transferring process, the VLS master gratings could be replicated on polydimethylsiloxane (PDMS) surface, which showed great optical performance. This work opened new light to some extent for the application of angle sensing and structural color showing.

Design of soft x-ray varied-line-spacing (VLS) high-dispersion laminar-type grating coated with super-mirror-type (SMT) multilayer for flat-field spectrograph in a region of 2-4 keV.

A soft x-ray varied-line-spacing (VLS) laminar-type spherical grating with a super-mirror-type (SMT) multilayer was designed for a soft x-ray high resolution flat-field spectrograph in a region of 2-4keV. The effective groove density of the designed VLS grating is 3200 lines/mm, and the local groove density varies from 2700 to 3866 lines/mm. The geometrical imaging property was evaluated by numerical calculations. The resolving power estimated by means of ray tracing was up to ∼103. For the evaluation of diffraction efficiency, the SMT multilayer structure designed for 3200 lines/mm in our previous work, Koike etal., Rev. Sci. Instrum. 94, 045109 (2023), was employed, and the numerical calculation was performed considering the local groove density of VLS grooves and the local incidence angle being affected by the curvature of the spherical surface and the geometrical relation between the source and incidence point on the grating. The results showed that the SMT multilayer-coated grating exhibited about an order of magnitude higher diffraction efficiency compared with an Au-coated grating.

Highly efficient and aberration-free off-plane grating spectrometer and monochromator for EUV—soft X-ray applications

We demonstrate a novel flat-field, dual-optic imaging EUV—soft X-ray spectrometer and monochromator that attains an unprecedented throughput efficiency exceeding 60% by design, along with a superb spectral resolution of λ/Δλ > 200 accomplished without employing variable line spacing gratings. Exploiting the benefits of the conical diffraction geometry, the optical system is globally optimized in multidimensional parameter space to guarantee optimal imaging performance over a broad spectral range while maintaining circular and elliptical polarization states at the first, second, and third diffraction orders. Moreover, our analysis indicates minimal temporal dispersion, with pulse broadening confined within 80 fs tail-to-tail and an FWHM value of 29 fs, which enables ultrafast spectroscopic and pump-probe studies with femtosecond accuracy. Furthermore, the spectrometer can be effortlessly transformed into a monochromator spanning the EUV—soft X-ray spectral region using a single grating with an aberration-free spatial profile. Such capability allows coherent diffractive imaging applications to be conducted with highly monochromatic light in a broad spectral range and extended to the soft X-ray region with minimal photon loss, thus facilitating state-of-the-art imaging of intricate nano- and bio-systems, with a significantly enhanced spatiotemporal resolution, down to the nanometer–femtosecond level.

Spatiotemporal response of concave VLS grating to ultra-short X-ray pulses.

In soft X-ray free-electron laser (FEL) beamlines, variable-line-spacing (VLS) gratings are often used as dispersive components of monochromators and spectrometers due to their combined dispersion and focusing properties. X-ray FEL pulses passing through the VLS grating can result in not only transverse focusing but also spatiotemporal coupling effects, such as pulse front tilt, pulse front rotation, and pulse stretching. In this paper, we present a theoretical study of the spatiotemporal response of concave VLS gratings to ultra-short X-ray pulses. The theoretical analysis indicates that the tilt angle of the non-zero diffraction orders varies with the propagation distance, and disappears at the focus, where the focal lengths and pulse stretching differ for different diffraction orders. The model demonstrates the pulse duration after the concave VLS grating is the convolution of the initial pulse duration and the stretching term induced by dispersion, while the beam size at the focus in x dimension is the convolution of the geometric scaling beam size and the dispersion term. This work provides a mathematical explanation for the spatiotemporal response of concave VLS grating to ultra-short X-ray pulses and offers valuable insights into the design of FEL grating monochromators, spectrometers, pulse compressors, and pulse stretchers.

Self-Calibration of a Large-Scale Variable-Line-Spacing Grating for an Absolute Optical Encoder by Differencing Spatially Shifted Phase Maps from a Fizeau Interferometer

A new method based on the interferometric pseudo-lateral-shearing method is proposed to evaluate the pitch variation of a large-scale planar variable-line-spacing (VLS) grating. In the method, wavefronts of the first-order diffracted beams from a planar VLS grating are measured by a commercial Fizeau form interferometer. By utilizing the differential wavefront of the first-order diffracted beam before and after the small lateral shift of the VLS grating, the pitch variation of the VLS grating can be evaluated. Meanwhile, additional positioning errors of the grating in the lateral shifting process could degrade the measurement accuracy of the pitch variation. To address the issue, the technique referred to as the reference plane technique is also introduced, where the least squares planes in the wavefronts of the first-order diffracted beams are employed to reduce the influences of the additional positioning errors of the VLS grating. The proposed method can also reduce the influence of the out-of-flatness of the reference flat in the Fizeau interferometer by taking the difference between the measured positive and negative diffracted wavefronts; namely, self-calibration can be accomplished. After the theoretical analysis and simulations, experiments are carried out with a large-scale VLS grating to verify the feasibility of the proposed methods. Furthermore, the evaluated VLS parameters are verified by comparing them with the readout signal of an absolute surface encoder employing the evaluated VLS grating as the scale for measurement.

Reconstruction design method of an aspherical recording optical system for the varied line-space grating.

A reconstruction design method for an aspherical recording system for varied line-space gratings is introduced. This method converts the recording system design from achieving specific groove distribution coefficients within the expansion model into reconstruction of the auxiliary mirror surface via the ray-tracing method. The effects of higher-order expansion terms in the expansion model are investigated and more accurate design of the varied line-space grating recording structure is achieved. By varying the surface reconstruction target, this method can be used to design aspherical recording structures with any auxiliary mirror surface shapes.

Theoretical Exposure Dose Modeling and Phase Modulation to Pattern a VLS Plane Grating with Variable-Period Scanning Beam Interference Lithography

Variable-period scanning beam interference lithography (VP-SBIL) can be used to fabricate varied-line-spacing (VLS) plane gratings. The exposure phase modulation method to pattern a VLS grating with a desired groove density must be carefully devised. In this paper, a mathematical model of the total exposure dose for VLS plane grating fabrication is established. With model-based numerical calculations, the phase modulation effects of the parameters, including the fringe locked phase, fringe density, and step size, are analyzed. The parameter combinations for the phase modulation are compared and chosen, and the optimal coordinate for phase compensation is selected. The calculation results show that the theoretical errors of the groove density coefficients can be controlled within 1e-8. The mathematical model can represent the deposited exposure dose for patterning VLS gratings during the lithography process, and the chosen parameters and proposed phase modulation method are appropriate for patterning VLS gratings with VP-SBIL.

Conception of a single-component broadband high-resolution plane-VLS-grating monochromator.

We propose a broadband single-element monochromator with a constant deviation angle and fixed slits for the wavelength range of 3-60 nm, which uses a grazing incidence plane varied line-space (VLS) grating with exponential dependence of line frequency across the aperture. Wavelength scanning is performed by translating the VLS grating along its surface. The deviation angle is constant, and the source, input, and output slits are stationary. With an exit slit (or CCD pixel size) of 6 µm, the practical resolving power λ/δλ=6000 remains constant throughout the operating range. The proposed scheme is compared with a narrowband specialized monochromator (135±4Å) with the same acceptance angle, in which wavelength scanning is performed by rotating a plane VLS grating, as well as with a Rowland monochromator with a similar acceptance.

Active control technology of a diffraction grating wavefront by scanning beam interference lithography.

To fabricate plain holographic gratings with high wavefront quality and to obtain the wavefront required in varied line-space grating, an active control technology of a diffraction grating wavefront by modulating the phase distribution of the scanning-beam interference lithography system was proposed. Sinusoidal wavefront control is simulated, and the controlled wavefront being almost the same as the target wavefront. A photoresist grating was fabricated whose surface is uniform and the wavefront is ideally sinusoidal. The theoretical analysis and experimental results confirmed that the wavefront of the diffraction grating can be actively controlled by modulating the phase distribution of the scanning-beam interference lithography system.

Self-assembly of wedge-shaped PDMS substrate for the fabrication of variable line-space gratings

A low-cost and high-efficiency method for fabricating variable line-space gratings is reported. Specifically, oxygen plasma was used to process the stretched wedge polydimethylsiloxane substrate. After slowly releasing the stress, a gradient grating with a continuous change in line spacing was formed via self-assembly. The period of the self-assembly grating was 2.96 to 3.25 μm, from thick to thin, when the sample was stretched transversely. In longitudinal stretching, the period was 3.71 to 5.20 μm from thick to thin. The period variation range of the gratings obtained by the two types of stretching was 15% and 45%, respectively. Diffraction tests of the two samples showed that the diffraction spots were evident. The diffraction angles varied in the range of 11.31 deg to 12.41 deg and 7.12 deg to 9.93 deg. The gratings prepared using this method can compensate for the shortcomings of the traditional process and have a wide range of application prospects.

Imaging spectrometer with single component of freeform concave grating.

In this Letter, an imaging spectrometer in which a freeform concave grating is the only optical component in the system is introduced. The degrees of freedom of optical freeform surfaces and a variable line-spacing (VLS) grating are used to realize imaging spectrometers. A point-by-point system design method is proposed that can generate a good initial solution rapidly. By exploring the limitations of the system specifications, it is demonstrated that the spectral dispersion, spectral resolving power, and system length can be improved significantly by using the freeform VLS concave grating. It is also found that freeform surfaces with higher degrees of freedom than a toroid can further improve system performance when using a VLS grating.

Highly efficient soft x-ray spectrometer for transient absorption spectroscopy with broadband table-top high harmonic sources.

We present a novel soft x-ray spectrometer for ultrafast absorption spectroscopy utilizing table-top femtosecond high-order harmonic sources. Where most commercially available spectrometers rely on spherical variable line space gratings with a typical efficiency on the order of 3% in the first diffractive order, this spectrometer, based on a Hettrick–Underwood design, includes a reflective zone plate as a dispersive element. An improved efficiency of 12% at the N K-edge is achieved, accompanied by a resolving power of 890. The high performance of the soft x-ray spectrometer is further demonstrated by comparing nitrogen K-edge absorption spectra from calcium nitrate in aqueous solution obtained with our high-order harmonic source to previous measurements performed at the electron storage ring facility BESSY II.

Research on the Displacement Sensing Structure with Varied Line-space Grating and Its Error Analysis

Research on the Displacement Sensing Structure with Varied Line-space Grating and Its Error Analysis

Wide-range displacement sensor based on variable line-spacing grating and Y-type twin-core fibre

In the paper, a wide range displacement sensor based on the variable line-spacing (VLS) grating was proposed and its displacement characteristics at different temperature environments were measured. The VLS grating was inscribed by electron beam lithography method, and the sensor mechanical structure was designed and fabricated. A broadband light was irradiated to the VLS grating though a twin-core Y-type fibre, and an aluminizing reflector mirror was used to adjust light spot positions to change the displacement. In the experiment, the temperature stabilities of sensor were tested when the temperature rose from −20°C to 60°C, and the maximum drift of diffraction peak was less than 1.01 nm. In 30 mm length displacements, the diffraction wavelength was shifted simultaneously, the sensitivity was 15.941 and 15.917 nm/mm at 20°C and 50°C respectively, and the linearity was 0.994 both at 20°C and 50°C.

Electron beam lithography inscribed varied-line-spacing and uniform integrated reflective plane grating fabricated through line-by-line method

A varied-line-spacing (VLS) and uniform integrated reflective plane grating was inscribed by electron beam lithography (EBL) and reactive ion etching method, and its displacement sensing characteristics was tested. For the VLS grating, the groove density was varied from 868 to 442 L/mm over the device, according to the designed linear density function, and the device was coated with an aluminized surface to reflect light. For the uniform grating, the groove density was 655 L/mm. A Y-type twin-core fiber with a collimator head was used to input light from a broadband source and collect reflected light from the integrated grating for analysis by an optical spectrum analyzer. The inscribed integrated grating length and width were 50 × 10 mm, and the input light angle was fixed at 23°.The integrated grating displacement characteristics was varied, when the light spot was irradiated at VLS and uniform grating simultaneously, with the result that as the light spot moved to different grating positions, two peaks of diffracted light were collected. For 0–35 mm displacement changes in 5 mm increments, for the VLS grating, the diffracted light wavelength changed from 945.3 to 1612.2 nm with sensitivity of 18.68 nm/mm, and linearity of 0.975; for the uniform grating, the wavelength shift was less than 3.2 nm.

Soft X-ray spectrometers based on aperiodic reflection gratings and their application

This paper is concerned with the history, properties, development, application, and prospects of soft X-ray (2 – 300 Å) VLS spectrometers, i.e., spectrometers with reflection diffraction gratings whose spacing varies monotonically across the aperture according to a prescribed law (so-called Varied Line-Space (VLS) gratings). An important feature of grazing-incidence VLS spectrometers is that the spectrum is formed on a nearly flat surface perpendicular (or slightly inclined) to the diffracted beams, making them perfectly compatible with modern CCD detectors. VLS spectrometers are employed for the spectroscopy of laboratory and astrophysical plasmas, including the diagnostics of relativistic laser-produced plasmas, for measuring the linewidth of an X-ray laser, for recording the high-order harmonics of laser radiation, and for recording the emission of fast electric discharges and other laboratory X-ray sources. Instruments with VLS gratings are employed to advantage in reflectometry/metrology, X-ray fluorescence analysis, and microscopy with the use of synchrotron, free-electron laser, and laser-produced plasma radiation, as well as in SXR emission spectroscopy, combined with an electron microscope (SXES). Recent years have seen the active development of VLS spectrometers dedicated to the investigation of the electronic structure of different materials and molecules by resonant inelastic X-ray scattering (RIXS) spectroscopy with synchrotron radiation. Among recent trends is the development of VLS gratings with a multilayer reflective coating and extension of the operating spectral range towards ‘tender’ X-rays (ℏω ∼ 1.5 – 6 keV), some projects aiming to achieve a resolving power λ/δ λ ∼ 105 in the region ℏω ∼ 1 keV.

Angular sensing system based on Y-type twin-core fiber and reflective varied-line spacing grating fabricated by electron beam lithography

A varied-line spacing grating (VLSG) inscribed by electron beam lithography was proposed and used for an experimental demonstration of angular sensing. The designed VLSG central groove density was 655 L/mm, and it had an aluminized surface to reflect light. A Y-type twin-core fiber of 600 μm diameter cores connected with a collimator lens was used to input and collect reflected light from the VLSG. The Y-type fiber input and output paths were connected to a white light source and an optical spectrum analyzer, respectively. The fabricated quasi-continuous VLSG size was 70 × 30 mm, with a fixed 23° input angle. The reflected wavelength changed from 917.3 to 1656.9 nm as the incident light spot moved to different grating positions, with a displacement sensitivity of 14.812 nm/mm. As the input angle was adjusted from 23° to 35° in 1° increments, the spot location on the VLSG changed simultaneously, and the reflection wavelength peak positions changed from 917.3 to 1584.5 nm, with a sensitivity of 57.544 nm/° and linearity of 0.993.

Flat-field VLS spectrometer for a wavelength range of 50 – 275 Å

A flat-field VLS spectrograph for a wavelength range ∼50 – 275 Å with an average linear dispersion of 0.18 mm Å−1, which makes use of a grazing-incidence varied line-space (VLS) grating, was calculated and implemented (a spectrograph of Harada class). To fabricate the VLS grating by interference lithography technique, an algorithm was developed for calculating the writing configuration with an auxiliary aberrating mirror (the solution of the inverse problem of interference lithography). The spectrograph was put to a test and line spectra were recorded from the laser-produced plasma of lithium fluoride and teflon targets, which were excited by a focused laser beam (0.5 J, 8 ns, 1.06 μm). A resolving power λ/d l = 800 was demonstrated in a wavelength region of 135 Å.

Switchable pupil expansion propagation using orthogonal superposition varied-line-spacing H-PDLC gratings in a holographic waveguide system.

To solve the problem of small field of view in traditional holographic waveguides, this paper proposes a waveguide-coupling technique using orthogonal superposition varied-line-spacing (VLS) gratings. These gratings expand the x and y directions and orthogonally superimpose to achieve transmission in a waveguide and enlarge the pupil field of view. At the optical coupling input end and the coupling output end of a waveguide, one-dimensional VLS gratings are used to realize horizontal expansion of the image. Then a vertical VLS grating is orthogonally superimposed at the exit end to realize vertical expansion of the image. Finally, the waveguide transmission and expansion of the image are completed. In the experiment, holographic polymer dispersed liquid crystal one-dimensional VLS gratings in the x and y directions are fabricated and coupled with a waveguide. An image source with a diameter of 0.5cm is waveguide-transferred and coupled out, and then passed through the vertical grating. Amplification is performed to obtain an expanded image of a diameter of 2.28cm. In this study, the diffraction characteristics of the grating used to realize pupil expansion in the holographic waveguide system are analyzed and simulated. It is calculated that the diffraction efficiency of the VLS gratings can reach 80% or more in the 532nm band. Additionally, the characteristics of an electronically controlled switch are studied. Experimental results show that the method can be used for expanding the field of view and can be applied to waveguide systems for image transmission and expansion.

Soft X-ray varied-line-spacing gratings fabricated bynear-field holography using an electron beam lithography-written phase mask.

A fabrication method comprising near-field holography (NFH) with an electron beam lithography (EBL)-written phase mask was developed to fabricate soft X-ray varied-line-spacing gratings (VLSGs). An EBL-written phase mask with an area of 52 mm × 30 mm and a central line density greater than 3000 lines mm-1 was used. The introduction of the EBL-written phase mask substantially simplified the NFH optics for pattern transfer. The characterization of the groove density distribution and diffraction efficiency of the fabricated VLSGs indicates that the EBL-NFH method is feasible and promising for achieving high-accuracy groove density distributions with corresponding image properties. Vertical stray light is suppressed in the soft X-ray spectral range.