Closed-form exact solutions for periodic motions of a nonlinear oscillator, which contains a quadratic mixed-parity restoring force, are derived analytically. This oscillator is characterised by two ...real parameters, which are the coefficients of the linear and the quadratic terms, and has single-well potential. All possible combinations of positive and negative values of these coefficients providing periodic motions are considered, and two families of exact solutions are obtained in terms of Jacobi elliptic functions. The periods are given in terms of the complete elliptic integral of the first kind, the behaviour of these periods as a function of the initial amplitude is analysed, and the exact solutions for certain values of these parameters are plotted.
A low-toxicity photopolymer was employed to prepare holographic solar concentrators (HSCs). The main aim of this study is to obtain a versatile holographic element to concentrate the sunlight from ...different relative positions of the Sun during the day, avoiding the need of expensive tracking systems. Multiplexed holographic elements that combine symmetric and asymmetric holographic lenses of low frequency (545 l/mm) have been recorded in the same plate to concentrate the sunlight from sunrise to sunset. The holographic behavior of HSCs has been studied by measuring the angular diffraction efficiency at 633 nm (close to the maximum response of silicon cells). The efficiency of the complete system “HSC-solar cell” has been evaluated by measuring the short-circuit current (
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) under solar illumination at different incident angles. This study overcomes the trade-off between good efficiency and high incident acceptance angle, showing an important breakthrough to obtain wide acceptance angle systems.
In this paper, we have shown that parabolic motion from a critical launch angle has an unexpected property related to the distance between the object and the launcher. This distance decreases in a ...time interval that occurs between two moments: one, in which distance has a maximum and another in which it has a minimum. As it will be shown, this only happens in launch angles greater than cosθc=1/3, that is θc≅70.53°. The launch we have studied occurs from the ground and we have not taken into account air friction. We have not considered the possible variations in the acceleration of gravity, that is, we have taken it as a constant throughout the movement of the projectile. We have used dimensionless coordinates so that the focus is on the angular variable. In addition, at the end of the study, we have used polar variables to visualize what happened. This is a very didactic approach, which can be used in the first year of STEM university degrees. It will also prove useful for teachers that wish to explain parabolic motion in their classes.
This work presents recent results derived from the rigorous modelling of holographic polymer-dispersed liquid crystal (H-PDLC) gratings. More precisely, the diffractive properties of transmission ...gratings are the focus of this research. This work extends previous analysis performed by the authors but includes new features and approaches. More precisely, full 3D numerical modelling was carried out in all analyses. Each H-PDLC sample was generated randomly by a set of ellipsoid geometry-based LC droplets. The liquid crystal (LC) director inside each droplet was computed by the minimisation of the Frank elastic free energy as a function of the applied electric field. The analysis carried out considered the effects of Frank elastic constants K11, K22 and K33; the anchoring strength W0; and even the saddle-splay constant K24. The external electric field induced an orientation of the LC director, modifying the optical anisotropy of the optical media. This effect was analysed using the 3D split-field finite-difference time-domain (SF-FDTD) method. In order to reduce the computational costs due to a full 3D tensorial analysis, a highly optimised method for high-performance computing solutions (HPC) was developed. The influences of the anchoring and voltage on the diffraction efficiencies were investigated, showing the potential of this approach.
Diffraction gratings are recorded in a holographic photopolymer containing nematic liquid crystal and peppermint oil. The presence of the oil modifies the polymerization and the holographic response. ...The composite containing oil adulterated with triethyl citrate obtains a diffraction efficiency related to the oil's purity. The results obtained suggest the possibility of developing a holographic chemical analysis method for quality control of raw materials.
In this work, we study the imaging characteristics of an optical see-through display based on a holographic waveguide. To fabricate this device, two transmission holograms are recorded on a ...photopolymer material attached to a glass substrate. The role of the holograms is to couple the incident light between air and the glass substrate, accomplishing total internal reflection. The role of noise reflection gratings and shrinkage on the imaging characteristics of the device will be also explored. The holograms (slanted transmission gratings with a spatial frequency of 1690 lines/mm) were recorded on a polyvinyl alcohol acrylamide holographic polymer dispersed liquid crystal (HPDLC) material. We will show that sufficient refractive index modulation is achieved in the material, in order to obtain high diffraction efficiencies. We will demonstrate that the final device acts as an image formation system.
The similarity between object and image of negative asymmetrical holographic lenses (HLs) stored in a low-toxicity photopolymer has been evaluated theoretically and experimentally. Asymmetrical ...experimental setups with negative focal lengths have been used to obtain HLs. For this purpose, the resolution of the HLs was calculated using the convolution theorem. A USAF 1951 test was used as an object and the impulse responses of the HLs, which in this case was the amplitude spread function (ASF), were obtained with two different methods: using a CCD sensor and a Hartmann Shack (HS) wavefront sensor. For a negative asymmetrically recorded HL a maximum resolution of 11.31 lp/mm was obtained. It was evaluated at 473 nm wavelength. A theoretical study of object-image similarity had carried out using the MSE (mean squared error) metric to evaluate the experimental results obtained quantitatively.
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•The finite pixel grid pattern influences Stokes parameters.•The performance of PA-LCoS tends to be higher as the fill factor is increased.•The out-of-plane LC director distribution ...is asymmetrically produced between pixels.•Fringing fields and diffraction influence on Stokes parameters are coupled.•The pixel size and the fill factor are relevant for evaluating PA-LCoS devices.
Liquid crystal on silicon (LCoS) microdisplays are an element commonly found in advanced photonic applications. Phase-only modulation and spatial light modulators (SLMs) use parallel-aligned LCoS (PA-LCoS) microdisplays due to their large resolution and small pixel size. However, the crosstalk between neighbouring pixels induces several phenomena, i.e. the smoothing of the electric field in the interpixel region known as fringing fields, out-of-plane reorientation of the liquid crystal director, and diffraction effects due to the finite pixel grid pattern. These effects degrade the performance in SLM applications. Therefore, a rigorous numerical analysis is carried out based on a full 3D model that estimates the LC director distribution of the PA-LCoS microdisplay through uniform applied voltages. Once the LC director distribution is known, a numerical finite-difference scheme simulates light propagation across the structure. Here, the impact of crosstalk is analysed from the polarimetric point of view for different pixel and interpixel sizes. It has been found that the finite-patterned pixel scheme induces the phenomena previously addressed, degrading the responses of the Stokes vector components S0, and S1 and also the degree of polarization (DOP). Furthermore, the impact over these parameters is generally inversely proportional to the fill factor. To isolate the influence of diffraction, out-of-plane, and fringing fields effects is challenging since all phenomena are mixed in both time and space, however we have found some useful trends.
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