Spatial Frequency Multiplication Research Articles

Population difference gratings created on vibrational transitions by nonoverlapping subcycle THz pulses

We study theoretically a possibility of creation and ultrafast control (erasing, spatial frequency multiplication) of population density gratings in a multi-level resonant medium having a resonance transition frequency in the THz range. These gratings are produced by subcycle THz pulses coherently interacting with a nonlinear medium, without any need for pulses to overlap, thereby utilizing an indirect pulse interaction via an induced coherent polarization grating. High values of dipole moments of the transitions in the THz range facilitate low field strength of the needed THz excitation. Our results clearly show this possibility in multi-level resonant media. Our theoretical approach is based on an approximate analytical solution of time-dependent Schrödinger equation (TDSE) using perturbation theory. Remarkably, as we show here, quasi-unipolar subcycle pulses allow more efficient excitation of higher quantum levels, leading to gratings with a stronger modulation depth. Numerical simulations, performed for THz resonances of the H_20 molecule using Bloch equations for density matrix elements, are in agreement with analytical results in the perturbative regime. In the strong-field non-perturbative regime, the spatial shape of the gratings becomes non-harmonic. A possibility of THz radiation control using such gratings is discussed. The predicted phenomena open novel avenues in THz spectroscopy of molecules with unipolar and quasi-unipolar THz light bursts and allow for better control of ultra-short THz pulses.

Influence of symmetry and duty cycles on the pattern generation in achromatic Talbot lithography

Achromatic Talbot lithography has been proved as a robust and high throughput technique for large area nanopatterning with controllable feature sizes and duty cycles. In this work, the influence of symmetry and duty cycles on the pattern generation has been investigated in detail. Compared with square lattice case, no lattice rotation and spatial frequency multiplication can be observed in hexagonal nanopattern generation. Uniform pattern distribution with a 20 nm feature size has been obtained in square and hexagonal lattices by the masks with 144 nm period and ∼50% duty cycle. For the exposure of mask with a smaller duty cycle, nonuniform dot size distribution has been obtained in the square lattice. While, by using a smaller duty cycle hexagonal lattice mask, a highly uniform periodic hexagonal nanopattern with a 10% duty cycle has been obtained. All the experimental results were consistent with the simulation work.

Optical properties of 2D fractional Talbot patterns under coherent EUV illumination

We investigate optical properties of (2D) fractional Talbot patterns under illumination with EUV laser light. The fractional Talbot effect, due to spatial frequency multiplication, can enable patterning of micro and nano-structures with various feature sizes using a micro-scale pitch mask. The experiment is performed with a free-standing mask fabricated by focused ion beam milling and a highly coherent illumination at 46.9 nm wavelength generated by a compact capillary discharge Ne-like Argon laser. As a result of spatial frequency multiplication, structure density of a square array of apertures in the mask was increased by a factor of up to 9 at the recording plane. The depth of field of the fractional Talbot images has been investigated using Fresnel diffraction analysis. Added field distribution complexity caused by asymmetry of the 2D arrays was observed both in simulation and in the experiment. This approach could be useful for sub-micron structuring of 2D patterns for various applications including among others the fabrication of photonic crystals, quantum dots, and also of submicron-electronic devices.

High-resolution nanopatterning by achromatic spatial frequency multiplication with electroplated grating structures

The authors demonstrate generation of high-resolution nanostructures using achromatic spatial frequency multiplication in the extreme ultraviolet wavelength region. The technique based on the achromatic Talbot effect is used for periodic transmission gratings under wideband illumination, enabling one- and two-dimensional nanopatterns with sub-20 nm feature sizes. The transmission masks with desired properties are fabricated with electron-beam lithography followed by electroplating of gold. Features sizes down to 12 nm are obtained. The presented technique provides high-throughput and large-area nanopatterning with great flexibility in tuning pattern parameters such as linewidth and dot size.

High-resolution Fresnel zone plate fabrication by achromatic spatial frequency multiplication with extreme ultraviolet radiation

We used an approach based on the self-imaging property of gratings to fabricate high-resolution Fresnel zone plates (FZPs). Under certain conditions, the illumination of a parent ZP with a wideband EUV beam produces a radially oscillating intensity distribution with double the spatial frequency of the ZP. This intensity distribution is observed in a certain distance range, given by the local zone width, the focal length of the ZP, and the spectral bandwidth of the illuminating beam. This phenomenon has been used to lithographically record daughter ZPs that have approximately half the zone width, thus twice the resolution, of the parent ZP. FZPs with zone widths as low as 30 nm have been fabricated in this way. Use of this technique in the extreme ultraviolet (EUV) region has the potential for high throughput production of FZPs and similar high-resolution diffraction optics with variable spatial frequency for the EUV and x-ray regions.

平面全息光栅刻线密度的倍频式调整方法

平面全息光栅刻线密度的倍频式调整方法

Formation of Stripe Domain Structures by Pulse Laser Irradiation of LiNbO3 Crystals

The formation of quasi-regular stripe nanodomain structure induced by ultraviolet pulse laser irradiation was studied in single crystalline congruent lithium niobate LiNbO3. It has been shown that the domain structure with average period about 4 μm consists of “straight” and “wave-like” nanodomain rays. The scanning electron microscopy allows us to reveal that the rays represent quasi-periodic arrays of individual nanodomains with average size 50–200 nm and period 100–500 nm. The spatial frequency multiplication of quasi-regular structures has been revealed.

Spatial-frequency multiplication with multilevel interference lithography

The authors present a large-area spatial-frequency multiplication fabrication process for patterning one-dimensional periodic structures using multilevel interference lithography. In this process, multiple grating levels with different phase offsets are overlaid by aligning to a reference grating. Each grating level is pattern transfered into a single hard mask layer, effectively reducing the grating period. The linewidth of the grating lines is controlled with nanometer repeatability by plasma etching and an image-reversal process. The authors demonstrate overlay accuracy of 0.6±1.9nm over 16×12mm2 for two levels of 200nm period gratings. Using this process, a subdiffraction-limited resolution grating with 100nm period is fabricated using light with λ=351.1nm. This process can also be used to fabricate more complex periodic geometries.

Fabrication of 50 nm period gratings with multilevel interference lithography

We have developed a multilevel interference lithography process to fabricate 50 nm period gratings using light with a 351.1 nm wavelength. In this process multiple grating levels patterned by interference lithography are overlaid and spatial-phase aligned to a common reference grating using interferometry. Each grating level is patterned with offset phase shifts and etched into a single layer to achieve spatial-frequency multiplication. The effect of the multilayer periodic structure on interference lithography is examined to optimize the fabrication process. This process presents a general scheme for overlaying periodic structures and can be used to fabricate more complex periodic structures.

Phase control in multiexposure spatial frequency multiplication

Multiexposure spatial frequency multiplication is a technique that allows the spatial frequency of grating patterns to be increased by integer factors 2,3,4,… by applying a nonlinear development process between patterning steps. One of the main technical issues with this technique is how to accurately place subsequent patterns on a substrate with respect to previously established patterns, which is referred to as phase control of the overlay. The authors report a technique that achieves accurate phase control over large areas during spatial frequency multiplication by utilizing a surrounding alignment grating. Three key factors—the angle, period, and phase of the alignment grating—have been accurately measured and utilized to position subsequent patterns with respect to previous patterns. Some factors that can dramatically diminish the accuracy of phase control, such as particle-induced substrate distortion and nonlinear distortion of the alignment grating, have also been considered and minimized in order to improve the accuracy of phase control. For spatial frequency doubling with a 574 nm principal pitch, the authors achieved overlay phase errors with a mean of −1.0 nm±2.8 nm(1σ) between level 1 and level 2 grating patterns over a 25×32.5 mm2 area.

Spatial-frequency multiplication via absorbance modulation

The absorbance of a thin film of photochromic material can be reversibly modified by exposure to two different wavelengths, λ1 and λ2. When such a film is illuminated by both wavelengths simultaneously, and the longer wavelength λ2 possesses a node in its intensity distribution, then the absorbance of the layer can be made high except at an arbitrarily small region near the node. By exploiting the large nonlinearity introduced by this mechanism, combined with the reversibility of the absorbance of the photochromic layer, the authors demonstrate that spatial frequencies larger than those present in incident intensity distributions may be generated. They show photoresist exposures to demonstrate this technique.

Achromatic spatial frequency multiplication: A method for production of nanometer-scale periodic structures

Fabrication of periodic structures with resolution below 100nm is required in many emerging applications such as subwavelength optical components, self-assembly templates, or patterned magnetic media. The achromatic spatial frequency multiplication technique that we have developed uses wideband illumination and self-imaging property (Talbot effect) of gratings to create periodic structures. The depth of field is practically unlimited, unlike the Talbot images obtained with monochromatic illumination. The technique requires limited spatial coherence making it suitable for use with sources other than lasers or synchrotrons which are normally used in interference lithography. We demonstrated the feasibility of the method using simulations and exposures in the extreme ultraviolet (EUV) region. One- and two-dimensional patterns with 50nm feature sizes were obtained. The technique is especially suitable for use with EUV light where the newly developed sources (laser or discharge produced plasma) have a rather wide bandwidth and limited spatial coherence. The technique is extendible to the production of much higher-resolution structures with the fundamental limit for the pattern period being equal to one-half of the wavelength.

Optical and Interferometric Lithography - Nanotechnology Enablers

Interferometric lithography (IL), the interference of a small number of coherent optical beams, is a powerful technique for the fabrication of a wide array of samples of interest for nanoscience and nanotechnology. The techniques and limits of IL are discussed with particular attention to the smallest scales achievable. With immersion techniques, the smallest pattern size for a single exposure is a half-pitch of /spl lambda//4n where /spl lambda/ is the optical wavelength and n is the refractive index of the immersion material. Currently with a 193-nm excimer laser source and H/sub 2/O immersion, this limiting dimension is /spl sim/34 nm. With nonlinear spatial frequency multiplication techniques, this limit is extended by factors of 1/2, 1/3, etc.-extending well into the nanoscale regime. IL provides an inexpensive, large-area capability as a result of its parallelism. Multiple exposures, multiple beams, and mix-and-match with other lithographies extend the range of applicability. Imaging IL provides an approach to arbitrary structures with comparable resolution. Numerous application areas, including nanoscale epitaxial growth for semiconductor heterostructures; nanofluidics for biological separations; nanomagnetics for increased storage density; nanophotonics including distributed feedback and distributed Bragg reflectors, two- and three-dimensional photonic crystals, metamaterials, and negative refractive index materials for enhanced optical interactions are briefly reviewed.

Patterning a 50-nm period grating using soft x-ray spatial frequency multiplication

Soft x-ray spatial frequency multiplication is a technique that has the capability of reducing by a factor of 2 or more the finest period grating that can be written by other methods. We describe two geometries for this technique: a single-grating geometry that requires spatially coherent illumination, and a two-grating geometry that can be used with incoherent illumination. Starting with a parent grating of period p and area A, gratings of period p/2, p/4, p/6 over an area A/3, A/5, A/7, respectively, can be printed in the single-grating geometry. The two-grating geometry produces the same final grating periods for parent gratings of period p, but the final grating area is limited only by the sizes of the parent gratings. As an initial demonstration of this technique, we have used the single-grating geometry to pattern a 50-nm period grating in polymethylmethacrylate over an area of 30 μm×100 μm, starting with a 100-nm period parent grating with an area of 90 μm×100 μm. The x-ray source was a synchrotron undulator at λ=18 Å and required a 5-min exposure time. Recent developments in coherent radiation from x-ray undulator sources will give shorter exposure times and permit larger areas to be patterned in the single-grating geometry.

High-resolution Fresnel zone plates for x-ray applications by spatial-frequency multiplication

We propose a scheme for deriving a high-resolution zone plate from a coarser one by interfering the light from two positive-order foci. We give a theorteical analysis of the process, which we call spatial-frequency multiplication. The analysis requires calculation of diffracted intensities far off axis, and we derive validity conditions for the application of approximate methods to this calculation. Specifically, we show that the Fresnel approximation is useful in many cases, whereas the method of stationary phase is valid for all cases of technological interest. Some practically useful parameter choices are considered for implementation of the zone-plate fabrication method. An example calculation suggests that a zone plate with smallest zone spacing of 13.8 nm may be possible.

Diphasic and polyphasic temporal modulations multiply apparent spatial frequency.

The effects of diphasic and polyphasic flicker on apparent spatial frequency were studied in several experiments through simultaneous spatial-frequency matches. In diphasic flicker the spatial phase of a sinusoidal grating alternated between two values in a counterphase fashion, and in polyphasic flicker the spatial phases of gratings were varied discretely in time in a variable number of steps. Both forms of flicker increased the apparent spatial frequency at low temporal frequencies, in the same manner as low-frequency monophasic flicker has been found to do. At high temporal frequencies, diphasic flicker doubled the apparent spatial frequency, as reported by Kelly (1966). We found that through high-frequency polyphasic flicker the spatial effect that Kelly mentions can be generalised to spatial frequency multiplication: polyphasic flicker produces not only the apparent second harmonic but also the third and the fourth harmonic, depending on the phase parameters. A numerical analysis showed that the spatial high-frequency effects can be explained through temporal integration of nonlinearly filtered input signals if a value of 200 td(1) is assumed for the nonlinearity constant in [Formula: see text] where B( I) is the brightness, I is the retinal illuminance, K is a scale constant, and I½ is the constant of nonlinearity. A minimum value of 60 ms had to be estimated for integration time. An investigation of the integration time with diphasic flicker indicated that spatial integration time decreases when the level of light adaptation increases, and that the integration time for spatial effects is longer than for flicker fusion. The spatial effects of low-frequency and high-frequency flicker differ in so many respects that different neural processes have to be postulated for their explanation.