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Keywords = wavefront shaping

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18 pages, 3360 KiB  
Article
On the Modelling of Asymptotic Wavefronts in Long Ducts with Chambers
by Alan E. Vardy
Fluids 2024, 9(10), 240; https://doi.org/10.3390/fluids9100240 - 14 Oct 2024
Viewed by 550
Abstract
A novel method of determining the possible shapes of pressure wavefronts in ducts after they have travelled sufficient distances to evolve to asymptotic states is introduced. Although it is possible in principle to achieve the same outcome by simulating complete flow histories from [...] Read more.
A novel method of determining the possible shapes of pressure wavefronts in ducts after they have travelled sufficient distances to evolve to asymptotic states is introduced. Although it is possible in principle to achieve the same outcome by simulating complete flow histories from the time of the creation of the wavefronts, this can be impracticable. It is especially unsuitable to use such methods when extremely small grid lengths are needed to represent the final outcome adequately. The new method does not simulate the propagation phase at all. Instead, it explores what final end states are possible, but gives no information about the initiating disturbance or the wavefront evolution towards the assessed asymptotic state. Accordingly, the two methods do not overlap, but instead are complementary to each other. A typical case in which the new capability has high potential is described and used to illustrate the purpose and use of the methodology. However, the primary focus is on the presentation and assessment of the method, not on any particular phenomenon. It is shown that the required computational resources are far smaller than those needed for conventional unsteady flow simulations of propagating wavefronts. The potential numerical limitations of the method are highlighted and, with one exception, are shown to be either of no consequence or easily reduced to acceptable levels. Special attention is paid to the one exception because it cannot be proven to be unimportant and, indeed, it would be unsafe to use it in general analyses of wave propagation. However, strong evidence is presented of its acceptability for the study of asymptotic wavefronts. Full article
(This article belongs to the Special Issue Modelling Flows in Pipes and Channels)
Show Figures

Figure 1

Figure 1
<p>Wavefront shortening/steepening during propagation along a 7.7 km long railway tunnel. (Reproduced with kind permission of Deutsche Bahn AG, DB Systemtechnik). NB: The graphs are offset in time to compensate for times of travel between successive measurement locations. The ‘time’ axis should be used only to infer the scales of individual graphs.</p>
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<p>Wavefront propagating in a duct with air chambers.</p>
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<p>Alternative, nominally possible initial wavefront shapes.</p>
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<p>Using the asymptotic behaviour to tailor the numerical grid structure.</p>
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<p>Indicative form of an asymptotic wavefront in a duct with air chambers (<span class="html-italic">Pressures in tunnel and chambers</span>).</p>
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<p>Paths of asymptotic wavefront and natural grid characteristics (<span class="html-italic">Shaded zone = domain of dependence at solution point A</span>).</p>
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<p>Asymptotic wavefront in a tunnel with lateral air chambers.</p>
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<p>Numerical sensitivity of the solution methodology. The parameter α in the legend of (<b>c</b>) is a numerical amplifier of linear extrapolation (see Equation (3)).</p>
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<p>Relationship between the wavefront speed and pressure amplitude.</p>
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10 pages, 1635 KiB  
Article
Effect of Small Angle Misalignments on Ocular Wavefront Zernike Coefficients
by Ebrahim Safarian Baloujeh, Francisco J. Ávila and José M. González-Méijome
Photonics 2024, 11(9), 795; https://doi.org/10.3390/photonics11090795 - 27 Aug 2024
Viewed by 562
Abstract
Purpose: To assess the possible impact of minor changes in fixation on wavefront measurements as a potential constraint in detecting subtle temporal variations in ocular wavefront error. Methods: Twelve healthy subjects with an average age of 36.3 ± 8.8 were instructed to put [...] Read more.
Purpose: To assess the possible impact of minor changes in fixation on wavefront measurements as a potential constraint in detecting subtle temporal variations in ocular wavefront error. Methods: Twelve healthy subjects with an average age of 36.3 ± 8.8 were instructed to put their heads in the aberrometer’s chin-rest and look at a fixation target that was embedded in the device. The fixation targets were readily observable to the participants without accommodation, thanks to the aberrometer’s Badal system. When each eye was staring at the target, its wavefront aberration was recorded three times and then averaged for further analysis. The averaged Zernike coefficients were rescaled to the smallest value of the maximum round pupil found among all eyes (4.41 mm), and this procedure was repeated for each target. Results: Alteration of the fixation targets caused changes to the Zernike coefficients of defocus (C(2,0)), vertical trefoil (C(3,–3)), vertical coma (C(3,–1)), horizontal coma (C(3,1)), oblique trefoil (C(3,3)), primary spherical aberration (C(4,0)), and secondary spherical aberration (C(6,0)), but the changes were not statistically significant. Nevertheless, an alteration in the target’s size and shape exhibited a significant correlation across all of the aforementioned coefficients in both eyes (p < 0.05). The total RMS of aberrations and the RMS of the spherical-like aberrations were both lowest while choosing the larger Maltese cross, and the bigger E-letter minimized the RMS of HOA and comatic aberrations. Conclusion: The aberrometric changes occur as a consequence of altering the fixational gaze and are within the range of the changes found after performing a near-vision task, so they might potentially act as a confounding factor when attempting to identify such small variations in the ocular wavefront. Using a smaller E-letter (5 arcmin) as an internal fixation target resulted in the least standard deviation of measurements, fixational stability, and higher accuracy in ocular wavefront measurements. Full article
(This article belongs to the Special Issue Technologies and Applications of Biophotonics)
Show Figures

Figure 1

Figure 1
<p>IRX3 Shack–Hartmann aberrometer used in this study (Imagine Eyes, France).</p>
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<p>Different fixation targets used while measuring eyes aberrations: (<b>a</b>) bigger E-letter; (<b>b</b>) smaller E-letter; (<b>c</b>) bigger Maltese cross; (<b>d</b>) smaller Maltese cross.</p>
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<p>Effect of target size on (<b>a</b>) mean of total RMS; (<b>b</b>) mean of HOA; (<b>c</b>) mean of comatic aberrations; (<b>d</b>) and median of spherical-like aberrations.</p>
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<p>Effect of target shape on (<b>a</b>) mean of total RMS; (<b>b</b>) mean of HOA; (<b>c</b>) mean of comatic aberrations; (<b>d</b>) and median of spherical-like aberrations.</p>
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14 pages, 309 KiB  
Article
Theoretical Investigation of the Influence of Correlated Electric Fields on Wavefront Shaping
by Niklas Fritzsche, Felix Ott, David Hevisov, Dominik Reitzle and Alwin Kienle
Photonics 2024, 11(9), 797; https://doi.org/10.3390/photonics11090797 - 27 Aug 2024
Viewed by 3096
Abstract
Wavefront shaping is a well-known method of restoring a focus deep within scattering media by manipulating the incident light. However, the achievable focus enhancement depends on and is limited by the optical and geometrical properties of the medium. These properties contribute to the [...] Read more.
Wavefront shaping is a well-known method of restoring a focus deep within scattering media by manipulating the incident light. However, the achievable focus enhancement depends on and is limited by the optical and geometrical properties of the medium. These properties contribute to the number of linearly independent transmission channels for light propagating through the turbid medium. Correlations occur when the number of incident waves coupled into the scattering medium exceeds this finite number of transmission channels. This paper investigates the wavefront shaping of such correlated electric fields. The influence of the observed correlations persists even though the average electric field distribution at positions in the focal plane follows a circular complex Gaussian. We show that correlations of the transmitted electric fields reduce the achievable intensity enhancement, even deep in the turbid medium. The investigations are carried out using a Monte Carlo algorithm. It is based on the speckle statistics of independent waves and introduces correlations of neighbouring electric fields via a Cholesky decomposition of the covariance matrix. Additional investigations include scenarios where the electric fields are not completely randomized, such as for ballistic or insufficiently scattered light. Significant contributions from such little-scattered light are observed to reduce the intensity enhancement further. Data from simulations solving Maxwell’s equations are compared with the results obtained from the Monte Carlo simulations for validation throughout this paper. Full article
(This article belongs to the Special Issue Photonics: 10th Anniversary)
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Figure 1

Figure 1
<p>Intensity enhancement <math display="inline"><semantics> <mi>η</mi> </semantics></math> over the number of channels <span class="html-italic">N</span> resulting from simulations solving Maxwell’s equations. The black dashed line shows the theoretically expected value according to Equation (<a href="#FD1-photonics-11-00797" class="html-disp-formula">1</a>) following [<a href="#B1-photonics-11-00797" class="html-bibr">1</a>]. <math display="inline"><semantics> <msub> <mi>I</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> <mi>i</mi> <mi>s</mi> <mi>h</mi> <mi>i</mi> <mi>f</mi> <mi>t</mi> </mrow> </msub> </semantics></math> data taken from [<a href="#B24-photonics-11-00797" class="html-bibr">24</a>].</p>
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<p>Average autocorrelation of the uncorrelated (red, <math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>) and correlated (blue, <math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <mn>0.118</mn> </mrow> </semantics></math>) electric fields over the k-vector spacing at <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>221</mn> </mrow> </semantics></math>.</p>
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<p>Normalized, average distribution of the amplitude (<b>left</b>) and the phase (<b>right</b>) of the electric fields. Depicted in red is the uncorrelated (<math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>) case, and in light blue is the correlated case (<math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <mn>0.928</mn> </mrow> </semantics></math>). The black solid lines show the theoretical density functions (<b>left</b>: Equation (<a href="#FD4-photonics-11-00797" class="html-disp-formula">4</a>), <b>right</b>: Equation (<a href="#FD5-photonics-11-00797" class="html-disp-formula">5</a>)).</p>
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<p>Comparison of the intensity enhancement <math display="inline"><semantics> <mi>η</mi> </semantics></math> over the number of channels <span class="html-italic">N</span> obtained by solving Maxwell’s equations (orange) and the Monte Carlo (MC) simulation. The correlation coefficient in the uncorrelated case (red) is given with <math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>. For the correlated fields (light blue) <math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <mn>0.928</mn> </mrow> </semantics></math>. The black dashed line shows the theoretically expected value according to Equation (<a href="#FD1-photonics-11-00797" class="html-disp-formula">1</a>) following [<a href="#B1-photonics-11-00797" class="html-bibr">1</a>]. Indicated by the vertically dashed grey line at <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, the point is marked, where the intensity enhancements of the correlated and uncorrelated electric fields approximately start to deviate.</p>
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<p>Normalized average distribution of the amplitude (<b>left</b>) and the phase (<b>right</b>) of the correlated electric fields at a depth of approx. <math display="inline"><semantics> <mrow> <mn>0</mn> <mi>λ</mi> </mrow> </semantics></math> (green) and approx. <math display="inline"><semantics> <mrow> <mn>20</mn> <mi>λ</mi> </mrow> </semantics></math> (blue). The black solid lines show the theoretical density functions of the amplitude and the phase for circular complex Gaussian-distributed electric fields.</p>
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<p>MC simulation of the intensity enhancement <math display="inline"><semantics> <mi>η</mi> </semantics></math> over the number of channels <span class="html-italic">N</span> for not completely circular complex Gaussian distributed electric fields. Depicted are the intensity enhancement for depths of approx. <math display="inline"><semantics> <mrow> <mn>20</mn> <mi>λ</mi> </mrow> </semantics></math> (blue), approx. <math display="inline"><semantics> <mrow> <mn>40</mn> <mi>λ</mi> </mrow> </semantics></math> (orange), and approx. <math display="inline"><semantics> <mrow> <mn>80</mn> <mi>λ</mi> </mrow> </semantics></math> (red). All electric fields were calculated with their respective adapted correlation factor. The black dashed line shows the theoretically expected value according to Equation (<a href="#FD1-photonics-11-00797" class="html-disp-formula">1</a>) following [<a href="#B1-photonics-11-00797" class="html-bibr">1</a>].</p>
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10 pages, 1081 KiB  
Article
Three-Dimensional Exploding Light Wave Packets
by Marcos G. Barriopedro, Manuel Holguín, Pablo de Lara-Montoya, Nilo Mata-Cervera and Miguel A. Porras
Photonics 2024, 11(7), 652; https://doi.org/10.3390/photonics11070652 - 11 Jul 2024
Viewed by 833
Abstract
We describe a family of paraxial and quasi-monochromatic optical wave packets with finite energy and smoothly shaped amplitude in space and time that develops a singularity in the intensity when spatio-temporally focused by imparting a converging spherical wavefront and a negative temporal chirp. [...] Read more.
We describe a family of paraxial and quasi-monochromatic optical wave packets with finite energy and smoothly shaped amplitude in space and time that develops a singularity in the intensity when spatio-temporally focused by imparting a converging spherical wavefront and a negative temporal chirp. This singular behavior upon ideal focusing is manifested in actual focusing with finite apertures and in media with high-order dispersion with “exploding” behavior featuring an indefinitely increasing concentration of the energy when opening the aperture radius, thus exercising continuous control on the focal intensity and spatial and temporal resolution. These wave packets offer a new way of focusing that outperforms what can be achieved with standard Gaussian wave packets in terms of focal intensity and resolution, providing new possibilities in applications where energy concentration and its control are crucial. Full article
(This article belongs to the Special Issue Structured Light Beams: Science and Applications)
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Figure 1

Figure 1
<p>EWP at <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1.4</mn> </mrow> </semantics></math> rad/fs (<math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1.346</mn> <mspace width="0.166667em"/> <mspace width="0.166667em"/> <mi mathvariant="sans-serif">μ</mi> </mrow> </semantics></math>m) ideally focused in fused silica (<math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>6754</mn> </mrow> </semantics></math> mm<sup>−1</sup>, <math display="inline"><semantics> <mrow> <msubsup> <mi>k</mi> <mn>0</mn> <mo>′</mo> </msubsup> <mo>=</mo> <mn>4876</mn> </mrow> </semantics></math> fs mm<sup>−1</sup>, <math display="inline"><semantics> <mrow> <msubsup> <mi>k</mi> <mn>0</mn> <mrow> <mo>″</mo> </mrow> </msubsup> <mo>=</mo> <mo>−</mo> <mn>6.508</mn> </mrow> </semantics></math> fs<sup>2</sup> mm<sup>−1</sup>). (<b>a</b>) Spatio-temporal radial intensity profile of the EWP (blue) with <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.25</mn> </mrow> </semantics></math> mm and <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math>, and of the Gaussian wave packet (orange) with <math display="inline"><semantics> <mrow> <mi>w</mi> <mo>=</mo> <mn>0.428</mn> </mrow> </semantics></math> mm of the same peak intensity and energy <math display="inline"><semantics> <mrow> <mi>E</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mi mathvariant="sans-serif">μ</mi> </semantics></math>J. (<b>b</b>) Their focused intensity profiles with <span class="html-italic">f</span> = 50 mm. (<b>c</b>) The same EWP (top) and Gaussian wave packet (bottom) in space and real-time with a width of duration <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>t</mi> <mo>=</mo> <msqrt> <mrow> <msub> <mi>k</mi> <mn>0</mn> </msub> <mrow> <mo>|</mo> <msubsup> <mi>k</mi> <mn>0</mn> <mrow> <mo>″</mo> </mrow> </msubsup> <mo>|</mo> </mrow> </mrow> </msqrt> <mi>β</mi> <mo>=</mo> <mn>104.8</mn> </mrow> </semantics></math> fs. (<b>d</b>) Their focused intensity profiles. The different colors represent the different values of the intensity specified in the vertical axes in (<b>c</b>,<b>d</b>).</p>
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<p>On-axis intensity of the same EWP (blue) and Gaussian wave packet (orange) as in <a href="#photonics-11-00652-f001" class="html-fig">Figure 1</a> as functions of propagation distance <span class="html-italic">z</span>.</p>
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<p>EWP at <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1.2</mn> </mrow> </semantics></math> rad/fs (<math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1.57</mn> <mspace width="0.166667em"/> <mspace width="0.166667em"/> <mi mathvariant="sans-serif">μ</mi> </mrow> </semantics></math>m) focused in fused silica modeled by a Sellmeier relation with three resonances. Comparison between the temporal shape at the focus of the EWP with <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.25</mn> </mrow> </semantics></math> (blue) and a Gaussian wave packet (orange) of the same initial peak intensity and the same energy with (<math display="inline"><semantics> <mrow> <mi>w</mi> <mo>=</mo> <mn>0.428</mn> </mrow> </semantics></math> mm) when the raddi of the aperture are <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> mm (<b>a</b>), <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> mm (<b>b</b>), and <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> mm (<b>c</b>). Comparison between the respective temporal frequency spectral densities is shown in (<b>d</b>–<b>f</b>). The double vertical scales help to compare the spectral widths.</p>
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<p>EWPs at <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1.2</mn> </mrow> </semantics></math> rad/fs (<math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>1.57</mn> <mspace width="0.166667em"/> <mspace width="0.166667em"/> <mi mathvariant="sans-serif">μ</mi> </mrow> </semantics></math>m) focused in fused silica modeled by a Sellmeier relation with three resonances. Comparison between the radial profiles at the focal plane at instant of time of maximum intensity of the EWP with <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.25</mn> </mrow> </semantics></math> (blue) and of the Gaussian wave packet (orange) of the same initial peak intensity and energy when the aperture radii are <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> mm (<b>a</b>), <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> mm (<b>b</b>), and <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> mm (<b>c</b>).</p>
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<p>Properties of EWPs at <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1.2</mn> </mrow> </semantics></math> rad/fs (<math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>1.57</mn> <mspace width="0.166667em"/> <mspace width="0.166667em"/> <mi mathvariant="sans-serif">μ</mi> </mrow> </semantics></math>m) and <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.25</mn> </mrow> </semantics></math> mm focused in fused silica modeled by a Sellmeier relation with three resonances. (<b>a</b>) Peak intensity for the indicated values of the decay parameter <math display="inline"><semantics> <mi mathvariant="sans-serif">μ</mi> </semantics></math> as a function of the radius of the aperture <span class="html-italic">R</span>, compared to the same property for Gaussian wave packets of the same peak intensity and energy. (<b>b</b>) Radial FWHM of the same EWPs and Gaussian wave packets as functions of <span class="html-italic">R</span>. (<b>c</b>) Temporal FWHM of the EWPs and Gaussian wave packets as functions of <span class="html-italic">R</span>.</p>
Full article ">
13 pages, 4732 KiB  
Article
Wavefront Changes during a Sustained Reading Task in Presbyopic Eyes
by Ebrahim Safarian Baloujeh and José M. González-Méijome
Sensors 2024, 24(12), 3866; https://doi.org/10.3390/s24123866 - 14 Jun 2024
Cited by 1 | Viewed by 638
Abstract
The objective of this study was to assess the effect of sustained reading on the temporal changes in the wavefront error in the presbyopic eye. The wavefront aberration of the eyes was measured using an IRX3 Shack–Hartmann aberrometer before and after (immediately, 5 [...] Read more.
The objective of this study was to assess the effect of sustained reading on the temporal changes in the wavefront error in the presbyopic eye. The wavefront aberration of the eyes was measured using an IRX3 Shack–Hartmann aberrometer before and after (immediately, 5 min, and 10 min after) a reading task. Temporal changes in C20, C40, and C31 coefficient values of the eyes were plotted, showing a predominant number of V-shaped patterns (for C40 and C31) and inverse V-shaped patterns (for C20) among the study group, and the percentages (between 27 and 73%) were reported. The median of the total RMS of aberrations and the RMS of HOA (higher-order aberrations), which included comatic (3rd order) and spherical-like aberrations (4th and 6th order), increased immediately after finishing the near-vision reading task and then decreased. The median of RMS of comatic aberrations had a similar pattern of variations, while the median of RMS of spherical-like aberrations displayed an opposite pattern. Simulating the aberration changes due to lens decentration caused by relaxed zonules during 4 D accommodation in an eye model demonstrated that the expected range of changes for the vertical coma and spherical aberrations are in the order of 0.001 and 0.01 μm, respectively, which could justify why the observed changes were not statistically significant. The observed dynamic changes in HOA might be linked to the biomechanical characteristics and alterations in the displacement of the crystalline lens following prolonged near-vision tasks in presbyopic people. Although some predominant patterns under some conditions were shown, they exhibit considerable inter-subject and inter-ocular variability. This might be due to slight misalignments while fixating on the internal extended object in the aberrometer. Full article
(This article belongs to the Special Issue Recent Advances in Optical Imaging and 3D Display Technologies)
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Figure 1

Figure 1
<p>A presbyope undergoing sustained near-vision task.</p>
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<p>Different patterns of behavior of the coefficients: (<b>a</b>) the V-shaped pattern; (<b>b</b>) the inverse V-shaped pattern.</p>
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<p><math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="normal">C</mi> <mn>2</mn> <mn>0</mn> </msubsup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="normal">C</mi> <mn>4</mn> <mn>0</mn> </msubsup> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="normal">C</mi> <mn>3</mn> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> </mrow> </semantics></math> coefficient values of the right eyes of subjects, before, right after, after 5 min, and after 10 min of near-vision task, respectively, for high- and low-lighting conditions, with respect to distance to the stimulus. Each pattern is for one subject.</p>
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<p><math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="normal">C</mi> <mn>2</mn> <mn>0</mn> </msubsup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="normal">C</mi> <mn>4</mn> <mn>0</mn> </msubsup> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="normal">C</mi> <mn>3</mn> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> </mrow> </semantics></math> coefficient values of the left eyes of subjects, before, right after, after 5 min, and after 10 min of near-vision task, respectively, for high- and low-lighting conditions, with respect to distance to the stimulus. Each pattern is for one subject.</p>
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<p>Changes in the Zernike coefficients (ΔZ values as represented in <a href="#sensors-24-03866-f002" class="html-fig">Figure 2</a>) with distance to stimulus: (<b>a</b>) ΔZ<sub>2</sub> in defocus in high lighting condition in the left eyes; (<b>b</b>) ΔZ<sub>1</sub> in vertical coma in high lighting condition in the right eyes; (<b>c</b>) ΔZ<sub>2</sub> in vertical coma in high lighting condition in the left eyes; (<b>d</b>) ΔZ<sub>1</sub> in spherical aberration in low lighting condition in the left eyes.</p>
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<p>Medians of the root mean squares of aberrations for right and left eyes in high- and low-lighting conditions, before, right after, after 5 min, and after 10 min of near-vision task: (<b>a</b>) median of total RMS for right eyes; (<b>b</b>) median of total RMS for left eyes; (<b>c</b>) median of RMS of HOA for right eyes; (<b>d</b>) median of RMS of HOA for right eyes.</p>
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<p>Medians of the root mean squares of higher order aberrations for right and left eyes in high- and low-lighting conditions, before, right after, after 5 min, and after 10 min of near-vision task: (<b>a</b>) median of RMS of comatic aberrations for right eyes; (<b>b</b>) median of RMS of comatic aberrations for left eyes; (<b>c</b>) median of RMS of spherical-like aberrations for right eyes; (<b>d</b>) median of RMS of spherical-like aberrations for right eyes.</p>
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<p>Changes in the aberrations as a function of lens decentration using Navarro’s accommodated eye model [<a href="#B39-sensors-24-03866" class="html-bibr">39</a>]: (<b>a</b>) changes in the vertical coma; (<b>b</b>) changes in spherical aberrations.</p>
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<p>Visual quality of a pre-presbyope eye (subject JG, 47-year-old) before and after the reading task.</p>
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12 pages, 1296 KiB  
Article
Clinical Outcomes after Bilateral Implantation of a Wavefront-Shaping Extended Depth of Focus (EDOF) IOL with Mini-Monovision
by Yeo Kyoung Won, Sung Ho Choi, Tae-Young Chung and Dong Hui Lim
J. Clin. Med. 2024, 13(11), 3225; https://doi.org/10.3390/jcm13113225 - 30 May 2024
Viewed by 1227
Abstract
Background: To compare the visual outcomes and optical quality of patients who underwent bilateral implantation of EDOF (AcrySof® IQ Vivity IOL, DFT015) for mini-monovision, trifocal (AcrySof® IQ PanOptix, TNFT00), or monofocal (AcrySof® IQ IOL, SN60WF) IOL. Methods: The [...] Read more.
Background: To compare the visual outcomes and optical quality of patients who underwent bilateral implantation of EDOF (AcrySof® IQ Vivity IOL, DFT015) for mini-monovision, trifocal (AcrySof® IQ PanOptix, TNFT00), or monofocal (AcrySof® IQ IOL, SN60WF) IOL. Methods: The monocular-corrected and uncorrected distance visual acuities (CDVA and UDVA, respectively) were evaluated postoperatively at 1 and 3 months. The binocular visual acuity by distance, the binocular defocus curve, contrast sensitivity, and patient satisfaction were examined 3 months postoperatively. All patients were asked to complete questionnaires regarding their satisfaction, visual symptoms, and spectacle dependency. Results: This study included 178 eyes from 89 patients. The postoperative binocular UDVA did not differ significantly among the three groups. In the defocus curve, the Vivity group showed better visual acuity over a range of far and intermediate (60 cm) than the other two IOLs groups. In near-vision, the PanOptix group showed the best near-vision, and the Vivity group showed significantly better vision than the IQ group. The Vivity group showed contrast sensitivity and optical quality comparable to the IQ group. Conclusions: The bilateral implantation of AcrySof® IQ Vivity IOL with the mini-monovision approach provided excellent distance and intermediate visual acuity with good near-vision, resulting in high satisfaction. Full article
(This article belongs to the Special Issue Corneal and Cataract Surgery: Clinical Updates)
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<p>Binocular defocus curves for the three groups. All outcomes were compared among the three groups. Bonferroni correction for multiple comparisons: significant <span class="html-italic">p</span>-values (<span class="html-italic">p</span> &lt; 0.017) in bold with symbols. *: Vivity versus IQ, §: PanOptix versus IQ, ¶: Vivity versus PanOptix.</p>
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<p>Contrast sensitivity for the three groups. (<b>a</b>). Photopic. (<b>b</b>). Mesopic with glare off. (<b>c</b>). Mesopic with glare on. All outcomes were compared among the three groups. Bonferroni correction for multiple comparisons: significant <span class="html-italic">p</span>-values (<span class="html-italic">p</span> &lt; 0.017) in bold with symbols. §: PanOptix versus IQ, ¶: Vivity versus PanOptix. Opaque area represents the normal value range.</p>
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<p>Postoperative questionnaire at 3 months. (<b>a</b>) Quality of vision (visual artifacts) questionnaire. (<b>b</b>) Overall satisfaction (near, intermediate, and far) questionnaire. (<b>c</b>) Spectacle dependence (near, intermediate, and far) in the three groups. All outcomes were compared among the three groups. Bonferroni correction for multiple comparisons: significant <span class="html-italic">p</span>-values (<span class="html-italic">p</span> &lt; 0.017) in bold with symbols. *: Vivity versus IQ, §: PanOptix versus IQ, ¶: Vivity versus PanOptix. The patients were shown images and asked to rate the frequency, severity, and bothersome visual symptoms as none, minimal, moderate, or severe (0, 1, 2, or 3 points, respectively). The mean score was then calculated. The overall satisfaction was evaluated using 5 levels (very satisfied, satisfied, neither satisfied nor dissatisfied, unsatisfied, and very unsatisfied). Spectacle dependence for each distance was investigated using the following scale: 0 = never to 10 = always.</p>
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10 pages, 1752 KiB  
Article
Multifunctional Meta-Devices for Full-Polarization Rotation and Focusing in the Near-Infrared
by Hengyi Wan, Kai Ou, Hui Yang and Zeyong Wei
Micromachines 2024, 15(6), 710; https://doi.org/10.3390/mi15060710 - 28 May 2024
Viewed by 3190
Abstract
The creation of multi-channel focused beams with arbitrary polarization states and their corresponding optical torques finds effective applications in the field of optical manipulation at the micro-nanoscale. The existing metasurface-based technologies for polarization rotation have made some progress, but they have been limited [...] Read more.
The creation of multi-channel focused beams with arbitrary polarization states and their corresponding optical torques finds effective applications in the field of optical manipulation at the micro-nanoscale. The existing metasurface-based technologies for polarization rotation have made some progress, but they have been limited to single functions and have not yet achieved the generation of full polarization. In this work, we propose a multi-channel and spatial-multiplexing interference strategy for the generation of multi-channel focusing beams with arbitrary polarization rotation based on all-dielectric birefringent metasurfaces via simultaneously regulating the propagation phase and the geometric phase and independently controlling the wavefronts at different circular polarizations. For the proof of concept, we demonstrate highly efficient multi-channel polarization rotation meta-devices. The meta-devices demonstrate ultra-high polarization extinction ratios and high focusing efficiencies at each polarization channel. Our work provides a compact and versatile wavefront-shaping methodology for full-polarization control, paving a new path for planar multifunctional meta-optical devices in optical manipulation at micro–nano dimensions. Full article
(This article belongs to the Special Issue Integrated Photonics and Optoelectronics, 2nd Edition)
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<p>Schematic illustration of high-efficiency multi-channel rotated polarization focusing meta-device. The all-dielectric polarization-rotated metasurface operates in transmission mode. Near-infrared beams with XLP incident on the meta-device which creates multi-channel rotated polarization intensity distribution.</p>
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<p>An efficient and high-extinction ratio multi-channel polarization rotation design method based on all-dielectric metasurfaces. (<b>a</b>,<b>b</b>) Phase maps of elliptical nanopillar as a function of the major-axis <span class="html-italic">Rx</span> and minor-axis <span class="html-italic">Ry</span> for <span class="html-italic">x</span>- and <span class="html-italic">y</span>-polarizations, respectively. Triangular markers denote the specific meta-atoms selected during the design process. The inset in (<b>a</b>) annotates the structural parameters of the meta-atom and the inset in (<b>b</b>) illustrates the cell lattice of meta-atoms. (<b>c</b>) The polarization conversion efficiency (PCE) and transmittance of the meta-atoms marked by the white triangle at a design wavelength of 1.55 μm in (<b>a</b>). The polarization conversion efficiency (PCE) is calculated as the ratio of transmitted optical power <math display="inline"><semantics> <mrow> <mo stretchy="false">(</mo> <msub> <mrow> <mi>E</mi> </mrow> <mrow> <mi>C</mi> <mi>P</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </semantics></math> with opposite helicity to the total power (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>E</mi> </mrow> <mrow> <mi>t</mi> <mi>o</mi> <mi>t</mi> <mi>a</mi> <mi>l</mi> </mrow> </msub> </mrow> </semantics></math>):<math display="inline"><semantics> <mrow> <mi mathvariant="normal">P</mi> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">E</mi> <mo>=</mo> <mrow> <mrow> <msub> <mrow> <mi>E</mi> </mrow> <mrow> <mi>C</mi> <mi>P</mi> </mrow> </msub> </mrow> <mo>/</mo> <mrow> <msub> <mrow> <mi>E</mi> </mrow> <mrow> <mi>t</mi> <mi>o</mi> <mi>t</mi> <mi>a</mi> <mi>l</mi> </mrow> </msub> </mrow> </mrow> </mrow> </semantics></math>. (<b>d</b>) The realized and required phase profiles for multi-channel superposition. (<b>e</b>) Phase shifts for <span class="html-italic">x</span>- and <span class="html-italic">y</span>-polarized incidences for the selected and optimal meta-atoms used in the design.</p>
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<p>Simulation characterization of linearly polarization rotation metalens. (<b>a</b>) Focal plane intensity distribution with multi-channel focused polarization rotation. Focal spots numbered 1–4 correspond to uniform polarization rotations of 0–180°, respectively. (<b>b</b>) Calculated efficiency and polarization extinction ratio for each focal spot. (<b>c</b>) The intensity distribution of each focus is analyzed using orthogonal linear deviation states. (<b>d</b>) The normalized intensity distribution at the dotted line position in (<b>c</b>) after analyzing the intensity distribution of each focusing.</p>
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<p>High-efficiency rotated focusing with full-polarization controlled metalens. (<b>a</b>) Focal plane intensity distribution with multi-channel focused polarization rotation. Focal spots numbered 1–6 correspond to XLP, YLP, LCP, RCP, EP1, and EP2, respectively. (<b>b</b>) Multi-channel focusing efficiency and extinction ratio for different polarization states. (<b>c</b>) The intensity distribution of each focus is analyzed using orthogonal SOP. (<b>d</b>) The normalized intensity curve corresponding to the focus for each different polarization state is shown as the red dotted line in (<b>c</b>).</p>
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13 pages, 5328 KiB  
Communication
Observation of Oblique Laser-Supported Detonation Wave Propagating in Atmospheric Air
by Kohei Matsui, Kimiya Komurasaki, Keisuke Kanda and Hiroyuki Koizumi
Aerospace 2024, 11(4), 327; https://doi.org/10.3390/aerospace11040327 - 22 Apr 2024
Cited by 1 | Viewed by 1249
Abstract
Elucidation of the propagation velocity of a laser-supported detonation (LSD) wave and its propagation mechanism is necessary for various engineering applications. This study was conducted to observe an oblique laser-supported detonation wave off the laser axis. The relation between the local laser intensity [...] Read more.
Elucidation of the propagation velocity of a laser-supported detonation (LSD) wave and its propagation mechanism is necessary for various engineering applications. This study was conducted to observe an oblique laser-supported detonation wave off the laser axis. The relation between the local laser intensity and detonation-wave propagation velocity was investigated. For this purpose, the time-space distribution of the laser intensity was measured precisely. The change of the LSD wavefront shape was visualized using an ultrahigh-speed camera. The relation between the local laser intensity and the propagation velocity of the oblique LSD wave measured off the laser axis was found to be identical to the relation between the local laser intensity and the detonation propagation velocity at the laser axis. Full article
(This article belongs to the Special Issue Laser Propulsion Science and Technology)
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<p>Earlier studies of relations between laser intensity and propagation velocity [<a href="#B7-aerospace-11-00327" class="html-bibr">7</a>,<a href="#B10-aerospace-11-00327" class="html-bibr">10</a>,<a href="#B16-aerospace-11-00327" class="html-bibr">16</a>,<a href="#B17-aerospace-11-00327" class="html-bibr">17</a>,<a href="#B18-aerospace-11-00327" class="html-bibr">18</a>,<a href="#B19-aerospace-11-00327" class="html-bibr">19</a>]. All experiments were conducted in air. Because of different focusing optics, the velocity is not determined uniquely by laser intensity.</p>
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<p>Typical image of a bow-shaped ionization front. The oblique propagation velocity is calculated from <span class="html-italic">V</span> and the angle of the ionization wave front.</p>
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<p>Historical profile of laser power and cumulative energy of the CO<sub>2</sub> laser, with the burn pattern of the laser before focusing.</p>
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<p>Schematics showing the experiment setup. (<b>a</b>) Focusing optics of <span class="html-italic">D</span> = 4.1 mm, which consist of two mirrors with focal lengths of 500 mm in <span class="html-italic">r</span><sub>1</sub> and 400 mm in <span class="html-italic">r</span><sub>2</sub> direction. (<b>b</b>) Focusing optics of <span class="html-italic">D</span> = 2.9 mm and <span class="html-italic">D</span> = 1.2 mm, with respective focal lengths of 317.5 mm and 127 mm.</p>
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<p>Measured and fitted laser intensity profiles at the beam waist with <span class="html-italic">D</span> = 4.1 mm in the <span class="html-italic">r</span><sub>1</sub> and <span class="html-italic">r</span><sub>2</sub> directions, with Gaussian and top-hat profiles. <span class="html-italic">W</span><sub>G0</sub> and <span class="html-italic">W</span><sub>T0</sub> are beam radii at the beam waist.</p>
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<p>Relation between beam radius in <span class="html-italic">r</span><sub>2</sub> direction and distance from beam waist of each focusing optics. Typical LSD propagation limits for beam diameters are displayed as broken lines. The detonation wave propagates from left to right in this figure.</p>
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<p>Dependence of propagation of an ionization front with various beam diameters on laser intensity at the laser axis. All experiments were conducted in air at a pressure of 1 atm. Trends against laser intensity differ between <span class="html-italic">D</span> ≥ 2.9 mm and <span class="html-italic">D</span> = 1.2 mm. Fitted lines with power function are shown as line 1 and line 2.</p>
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<p>(<b>a</b>) Photograph of an ionization front propagating from t = 0.675 μs to 1.835 μs with <span class="html-italic">D</span> = 2.9 mm in the <span class="html-italic">r</span><sub>1</sub> direction. Laser is irradiated from upper side of photographs. (<b>b</b>) Historical change of wavefront shape analyzed from <a href="#aerospace-11-00327-f004" class="html-fig">Figure 4</a>a and estimated laser intensity profile with <span class="html-italic">D</span> = 2.9 mm in the <span class="html-italic">r</span><sub>1</sub> direction. The elapsed time from starting points of laser irradiation is shown.</p>
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<p>Relation between local propagation velocity in a direction normal to the wavefront and local laser intensity of each beam diameter. Closed and opened plots, respectively, show LSD and LSC conditions: (<b>a</b>) <span class="html-italic">r</span><sub>1</sub> direction (Gaussian profile), (<b>b</b>) <span class="html-italic">r</span><sub>2</sub> direction (top-hat profile).</p>
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<p>Relation between local propagation velocity in a direction normal to the wavefront and local laser intensity of each beam diameter. Closed and opened plots, respectively, show LSD and LSC conditions: (<b>a</b>) <span class="html-italic">r</span><sub>1</sub> direction (Gaussian profile), (<b>b</b>) <span class="html-italic">r</span><sub>2</sub> direction (top-hat profile).</p>
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<p>Schlieren image of LSD of <span class="html-italic">r</span><sub>1</sub> direction with <span class="html-italic">D</span> = 4.1 mm. The shock front is separated from the ionization front at large <span class="html-italic">r</span>/<span class="html-italic">W</span><sub>G0</sub>.</p>
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<p>Relation between local propagation velocity in the direction normal to the wavefront and local laser intensity of each beam diameter in the <span class="html-italic">r</span><sub>1</sub> direction. In a region below 500 GW/m<sup>2</sup> of <span class="html-italic">D</span> ≥ 2.9 mm, the velocity is larger than that of the laser axis. It shows a tendency as Line 3.</p>
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<p>Relation between propagation velocity and laser intensity at the laser axis. Line 3 is obtained from analysis of the local propagation velocity. It shows the same tendency as the velocity in the direction of the laser axis.</p>
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13 pages, 3274 KiB  
Article
An Optically Augmented Visual Aid for Individuals with Age-Related Macular Degeneration
by Nahed H. Solouma, Noura Negm, Hafsah Ahmad and Yusuf Gamal
Photonics 2024, 11(3), 245; https://doi.org/10.3390/photonics11030245 - 8 Mar 2024
Viewed by 1166
Abstract
Normal vision is a precious gift to mankind. Any vision defect or degradation is actually an intimidating problem for individuals and societies. Therefore, researchers are continually working to find effective solutions for vision disorders. In some retinal diseases such as Age-related Macular Degeneration [...] Read more.
Normal vision is a precious gift to mankind. Any vision defect or degradation is actually an intimidating problem for individuals and societies. Therefore, researchers are continually working to find effective solutions for vision disorders. In some retinal diseases such as Age-related Macular Degeneration (AMD), visual aids are required to improve vision ability and/or stop the progress of the disease. Recently, augmented vision techniques have been used to provide aid to people suffering from retinal impairment. However, in such techniques, the images of real scenes are electronically deformed to compensate for vision impairment. Therefore, the natural scene is displayed as an electronic image on glasses. Intuitively, it is annoying to the patient to see electronic rather than natural scenes. Moreover, these visual aids are bulky and produce electric fields that might be harmful with continuous use. In this work, a novel optical solution to provide a visual aid to patients with central vision loss has been proposed. The proposed optical solution deforms the wavefront of the scene to entirely fall on the healthy parts of the retina. This, in turn, conveys all scene information to the brain to be perceived by the patient. As it provides optical processing, the proposed solution overcomes all drawbacks of the electronic solutions. To prove the validity of the proposed solution, three lenses were designed, fabricated, and tested to visualize simple shapes, reading, and obtaining aid during walking and driving. Obtaining the expected results from these tests, they were tried by three volunteers to clinically prove the validity and feasibility of the proposed optical aid. The feedback from the three patients was promising since all of them could recognize some of the details they used to miss with at least one of the lenses. Full article
(This article belongs to the Special Issue Optical Technologies for Biomedical Science)
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<p>Simple eye anatomy. Upper: propagation of light rays number 1,2,3 and 4 show the wavefront until forming the image on the retina. Lower: a section of the retina showing different layers, the rods, and the cones [<a href="#B5-photonics-11-00245" class="html-bibr">5</a>].</p>
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<p>Geometrical structure of the eye and light focusing on the retina [<a href="#B34-photonics-11-00245" class="html-bibr">34</a>].</p>
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<p>The proposed bi-cone lens. (<b>a</b>) Top, side, and front views of the lens and (<b>b</b>) schematic diagram of the bi-cone lens and its central spatial transformation effect illustrated by the red-colored rays.</p>
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<p>Geometrical ray tracing through the proposed bi-conical lens.</p>
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<p>Relation between the deviation distance and the cone base angle. (<b>a</b>) Deviation distance or radius of blind region <math display="inline"><semantics> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </semantics></math> against cone base angle <math display="inline"><semantics> <mrow> <mi>α</mi> </mrow> </semantics></math> for two different bi-cone lenses and (<b>b</b>) deviation distance <math display="inline"><semantics> <mrow> <mi>b</mi> <mi>r</mi> </mrow> </semantics></math> against cone base angle <math display="inline"><semantics> <mrow> <mi>α</mi> </mrow> </semantics></math> for three different lens materials.</p>
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<p>Ray tracing for ray matrix evaluation.</p>
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<p>Demonstration of the use experiment I bi-cone lens. (<b>a</b>,<b>d</b>,<b>g</b>,<b>j</b>): original shapes, (<b>b</b>,<b>e</b>,<b>h</b>,<b>k</b>): simulation of how these shapes can be seen by a patient with central vision loss, and (<b>c</b>,<b>f</b>,<b>i</b>,<b>l</b>): images captured when using the bi-cone lens with the central regions of each shape appearing as rings of lighter colors around the black circle.</p>
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<p>Effect of using the proposed bi-cone lens in reading. (<b>a</b>,<b>d</b>) The original scenes, (<b>b</b>,<b>c</b>,<b>e</b>,<b>f</b>) the obtained results.</p>
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<p>Testing the feasibility of using the proposed lens during walking: (<b>a</b>) a minaret original scene from about 700 m distance, (<b>b</b>) simulating how the scene can be observed by a central vision loss patient, and (<b>c</b>) the scene captured when placing the bi-cone lens before the camera with the hidden details of (<b>b</b>) appearing as a spatially-deformed region.</p>
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<p>Testing the feasibility of using the proposed lens during driving: (<b>a</b>) a street original scene with a white bus and a gray sedan car. (<b>b</b>) Simulation of how the scene can be observed by a central vision loss patient while the car is blocked. (<b>c</b>) The scene captured when placing the bi-cone lens before the camera, with the hidden car in (<b>b</b>) appearing as a spatially-deformed region in (<b>c</b>).</p>
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13 pages, 8071 KiB  
Article
Exploring Wavefront Detection in Imaging Systems with Rectangular Apertures Using Phase Diversity
by Yibo Li, Jiang Guo and Rengcong Liu
Sensors 2024, 24(4), 1191; https://doi.org/10.3390/s24041191 - 11 Feb 2024
Viewed by 1029
Abstract
The attainment of a substantial aperture in the rotating synthetic aperture imaging system involves the rotation of a slender rectangular primary mirror. This constitutes a pivotal avenue of exploration in space telescope research. Due to the considerable aspect ratio of the primary mirror, [...] Read more.
The attainment of a substantial aperture in the rotating synthetic aperture imaging system involves the rotation of a slender rectangular primary mirror. This constitutes a pivotal avenue of exploration in space telescope research. Due to the considerable aspect ratio of the primary mirror, environmental disturbances can significantly impact its surface shape. Active optical technology can rectify surface shape irregularities through the detection of wavefront information. The Phase Diversity (PD) method utilizes images captured by the imaging system to compute wavefront information. In this study, the PD method is applied to rotating synthetic and other rectangular aperture imaging systems, employing Legendre polynomials to model the wavefront. The study delved into the ramifications stemming from the aperture aspect ratio and aberration size. Full article
(This article belongs to the Section Optical Sensors)
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<p>Flow chart of the PD method.</p>
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<p>1st–10th terms of the two-dimensional Legendre polynomial. The colors in the graph indicate the values of the polynomial function at each point. Red means positive and blue means negative, and the brighter the color, the larger the absolute value.</p>
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<p>Simulation images and their PSFs with different aspect ratio. PSF values increase with red intensity.</p>
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<p>Rectangular region with a circular obscuration.</p>
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<p>The impact of obscuration size on the calculation accuracy of PD method.</p>
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<p>The impact of SNR and aberration size on the calculation accuracy of PD method when <span class="html-italic">P</span> = 1, 2, 4 and 8.</p>
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<p>Imaging device. A Celestron CGEM 1100HD telescope became a rectangular imaging system with a rectangular diaphragm. A Canon R50 camera was connected to the displacement platform as the detector.</p>
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<p>Schematic diagram of self-collimating examination.</p>
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<p>Comparison of wavefront map gained by the two methods.</p>
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23 pages, 8730 KiB  
Article
The Lattice Boltzmann Method Using Parallel Computation: A Great Potential Solution for Various Complicated Acoustic Problems
by Pranowo, Djoko Budiyanto Setyohadi and Agung Tri Wijayanta
Math. Comput. Appl. 2024, 29(1), 12; https://doi.org/10.3390/mca29010012 - 4 Feb 2024
Cited by 1 | Viewed by 1750
Abstract
This paper proposes the D2Q5 Lattice Boltzmann method (LBM) method, in two dimensions with five discrete lattice velocities, for simulating linear sound wave propagation in closed rooms. A second-order linear acoustic equation obtained from the LBM method was used as the model equation. [...] Read more.
This paper proposes the D2Q5 Lattice Boltzmann method (LBM) method, in two dimensions with five discrete lattice velocities, for simulating linear sound wave propagation in closed rooms. A second-order linear acoustic equation obtained from the LBM method was used as the model equation. Boundary conditions at the domain boundary use the bounce-back scheme. The LBM numerical calculation algorithm in this paper is relatively simpler and easy to implement. Parallelization with the GPU CUDA was implemented to speed up the execution time. The calculation results show that the use of parallel GPU CUDA programming can accelerate the proposed simulation 27.47 times faster than serial CPU programming. The simulation results are validated with analytical solutions for acoustic pulse reflected by the flat and oblique walls, the comparisons show very good concordance, and the D2Q5 LBM has second-order accuracy. In addition, the simulation results in the form of wavefront propagation images in complicated shaped rooms are also compared with experimental photographs, and the comparison also shows excellent concordance. The numerical results of the D2Q5 LBM are promising and also demonstrate the great capability of the D2Q5 LBM for investigating room acoustics in various complexities. Full article
(This article belongs to the Section Engineering)
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<p>The two-dimensional lattice D2Q5 model.</p>
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<p>Illustration of the streaming step.</p>
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<p>Illustration of kernel execution and thread organization.</p>
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<p>The convergence rate of the D2Q5 LBM.</p>
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<p>Closed rectangle domain and the location of source and receiver.</p>
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<p>Snapshots of reflected waves by the flat bottom wall: (<b>a</b>) at <span class="html-italic">t</span> = 3 ms; (<b>b</b>) at <span class="html-italic">t</span> = 9 ms; (<b>c</b>) at <span class="html-italic">t</span> = 15 ms; (<b>d</b>) at <span class="html-italic">t</span> = 21 ms.</p>
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<p>Signal recorded at the receiver of the first example (<b>a</b>) comparing numerical pressure and analytical solutions of pressure at the receiver; (<b>b</b>) discrepancies of numerical and analytical solutions.</p>
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<p>Closed five-sided polygonal domain and the location of source and receiver.</p>
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<p>Snapshots of reflected waves by oblique wall: (<b>a</b>) at <span class="html-italic">t</span> = 1.25 ms; (<b>b</b>) at <span class="html-italic">t</span> = 5.00 ms; (<b>c</b>) at <span class="html-italic">t</span> = 8.75 ms; (<b>d</b>) at <span class="html-italic">t</span> = 12.50 ms.</p>
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<p>Snapshots of reflected waves by oblique wall: (<b>a</b>) at <span class="html-italic">t</span> = 1.25 ms; (<b>b</b>) at <span class="html-italic">t</span> = 5.00 ms; (<b>c</b>) at <span class="html-italic">t</span> = 8.75 ms; (<b>d</b>) at <span class="html-italic">t</span> = 12.50 ms.</p>
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<p>Signal recorded at the receiver of the second example (<b>a</b>) comparison between numerical pressure and analytical solutions of pressure at the receiver; (<b>b</b>) discrepancies of numerical and analytical solutions.</p>
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<p>Complex room geometry: (<b>a</b>) Type 1; (<b>b</b>) Type 2 [<a href="#B38-mca-29-00012" class="html-bibr">38</a>].</p>
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<p>Snapshots of the acoustic pulse propagation in complex room Type 1: (<b>a</b>) at <span class="html-italic">t</span> = 2 ms; (<b>b</b>) at <span class="html-italic">t</span> = 7 ms; (<b>c</b>) at <span class="html-italic">t</span> = 19.333 ms; (<b>d</b>) at <span class="html-italic">t</span> = 31.667 ms.</p>
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<p>Two successive sound photographs in architectural models for room Type 1 [<a href="#B38-mca-29-00012" class="html-bibr">38</a>].</p>
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<p>Snapshots of the acoustic pulse propagation in complex room Type 1: (<b>a</b>) at <span class="html-italic">t</span> = 2.4 ms; (<b>b</b>) at <span class="html-italic">t</span> = 6.4 ms; (<b>c</b>) at <span class="html-italic">t</span> = 18.8 ms; (<b>d</b>) at <span class="html-italic">t</span> = 36 ms.</p>
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<p>Two successive sound photographs in architectural models for room Type 2 [<a href="#B38-mca-29-00012" class="html-bibr">38</a>].</p>
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<p>Pressure fluctuation recorded at the room receiver: (<b>a</b>) Type 1; (<b>b</b>) Type 2.</p>
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<p>Staggered grids.</p>
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<p>Staircase boundary.</p>
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<p>Comparisons of signal recorded at the receiver (<b>a</b>) comparison between numerical (LBM and FDTD) pressure and analytical solutions of pressure at the receiver; (<b>b</b>) discrepancies of numerical (LBM and FDTD) and analytical solutions.</p>
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<p>Comparisons of signal recorded at the receiver (<b>a</b>) comparison between numerical (LBM and FDTD) pressure and analytical solutions of pressure at the receiver; (<b>b</b>) discrepancies of numerical (LBM and FDTD) and analytical solutions.</p>
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20 pages, 4240 KiB  
Review
Generation of Orbital Angular Momentum Light by Patterning Azopolymer Thin Films
by Temitope M. Olaleye, Maria Raposo and Paulo A. Ribeiro
Photonics 2023, 10(12), 1319; https://doi.org/10.3390/photonics10121319 - 29 Nov 2023
Viewed by 1714
Abstract
Orbital angular momentum (OAM) encoding is a promising technique to boost data transmission capacity in optical communications. Most recently, azobenzene films have gained attention as a versatile tool for creating and altering OAM-carrying beams. Unique features of azobenzene films make it possible to [...] Read more.
Orbital angular momentum (OAM) encoding is a promising technique to boost data transmission capacity in optical communications. Most recently, azobenzene films have gained attention as a versatile tool for creating and altering OAM-carrying beams. Unique features of azobenzene films make it possible to control molecular alignment through light-induced isomerization about the azo bond. This feature enables the fabrication of diffractive optical devices such as spiral phase plates and holograms by accurately imprinting a phase profile on the incident light. By forming azobenzene sheets into diffractive optical elements, such as spiral phase plates, one can selectively create OAM-carrying beams. Due to the helical wavefront and phase variation shown by these beams, multiple distinct channels can be encoded within a single optical beam. This can significantly increase the data transmission capacity of optical communication systems with this OAM multiplexing technique. Additionally, holographic optical components made from azobenzene films can be used to build and reconstruct intricate wavefronts. It is possible to create OAM-based holograms by imprinting holographic designs on azobenzene films, which makes it simpler to control and shape optical beams for specific communication requirements. In addition, azobenzene-based materials can then be suitable for integration into optical communication devices because of their reconfigurability, compactness, and infrastructure compatibility, which are the main future perspectives for achieving OAM-based technologies for the next generation, among other factors. In this paper, we see the possible use of azobenzene films in the generation and modification of OAM beams for optical communications through light-induced isomerization. In addition, the potential role of azobenzene films in the development of novel OAM-based devices that paves the way for the realization of high-capacity, OAM-enabled optical communication networks are discussed. Full article
(This article belongs to the Special Issue Advanced Photonic Sensing and Measurement II)
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Figure 1
<p>Wavefront, phase profile, and intensity profiles of OAM beams. (<b>a</b>) <span class="html-italic">ℓ</span> = 0 represents a donut-shaped Gaussian beam with no twist/OAM in the wavefront; (<b>b</b>) <span class="html-italic">ℓ</span> = 1, which defines one twist per wavelength; (<b>c</b>) <span class="html-italic">ℓ</span> = 2, which defines two twists per wavelength; (<b>d</b>) <span class="html-italic">ℓ</span> = 3, which defines three twists per wavelength. Reprinted from Ref. [<a href="#B26-photonics-10-01319" class="html-bibr">26</a>].</p>
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<p>Intensity and phase profiles of LG modes. In the top row a combination of <span class="html-italic">p</span> = 0 and <span class="html-italic">ℓ</span> = 0 represents a Gaussian mode. The other modes represents LG. In each row, azimuthal mode number <span class="html-italic">ℓ</span> increases from left to right (−4 to +5), while the radial mode number <span class="html-italic">p</span> increases from top to bottom (0 to 2). Reprinted from [<a href="#B32-photonics-10-01319" class="html-bibr">32</a>].</p>
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<p>Emerging application of OAM beams. Reprinted from [<a href="#B38-photonics-10-01319" class="html-bibr">38</a>].</p>
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<p>Schema of the <span class="html-italic">trans</span> and <span class="html-italic">cis</span> isomeric forms of azobenzene molecules or chemical groups.</p>
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<p>(<b>a</b>) Schematic of the orientation of an azobenzene molecule relative to the electric field of light and its dipole moment <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>μ</mi> </mrow> <mo>→</mo> </mover> </mrow> </semantics></math>; (<b>b</b>) schematization of the orientation of chromophores by the incidence of linearly polarized light: <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>E</mi> </mrow> <mo>→</mo> </mover> </mrow> </semantics></math> represents the electric field vector, and <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>k</mi> </mrow> <mo>→</mo> </mover> </mrow> </semantics></math> represents the wave vector. The region where the light falls tends to have chromophores oriented in the direction perpendicular to that of the light electric field.</p>
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<p>Atomic force microscopy (AFM) image of a relief grid of a PDAC/CR self-assembled film. Reprinted from Ref. [<a href="#B69-photonics-10-01319" class="html-bibr">69</a>].</p>
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<p>Implementation of polarization-sensitive patterning of azopolymer thin films. (<b>a</b>) Intensity distributions (top row) and the longitudinal components (middle row) of focused linearly polarized (LP) Gaussian laser beams with different polarization directions, as well as images of the microstructures formed in azopolymers thin films under the illumination of these beams (bottom row). (<b>b</b>) Splitting of a single LP Gaussian laser beam into a set of LP laser beams with a one-dimensional diffractive grating. (<b>c</b>) Principle of spatial polarization filtering and generation of a set of LP laser beams with different polarization directions using a 4-f optical system with a polarizing filter. Reprinted from [<a href="#B108-photonics-10-01319" class="html-bibr">108</a>].</p>
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<p>Spiral relief patterns obtained for different illumination doses from a Gaussian laser beam injected into a microscope. AFM images of the topographical structures were obtained with the varying illumination intensity and fixed time of exposure (and polarization direction) for topological charge <span class="html-italic">ℓ</span> = 10. The white arrow indicates the polarization direction. Different panels correspond to different values of the laser power injected in the microscope: (<b>a</b>) 15 mW; (<b>b</b>) 18 mW; (<b>c</b>) 21 mW; (<b>d</b>) 29 mW; (<b>e</b>) 41 mW; (<b>f</b>) 54 mW. Similar results were obtained for varying the time of exposure at a fixed intensity. Reprinted from [<a href="#B121-photonics-10-01319" class="html-bibr">121</a>].</p>
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<p>SLM-based experimental setup for generating 3D chiral microstructures in isotropic polymer by interfering beams of helical phase wavefronts and plane waves. In this experimental setup Fs Laser is a femtosecond laser, L1 and L2 are telescope lenses, HW1 and HW2 are half-wave plates, P is a polarizer, M is a mirror, SLM is a liquid-crystal spatial light modulator, I is an iris, L3 and L4 are lenses, DM is a dichroic mirror, S is the sample, and OBJ is a ×100 microscope objective. The square images below in the figure are SEM images of chiral microstructures achieved.Reprinted from [<a href="#B127-photonics-10-01319" class="html-bibr">127</a>].</p>
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<p>Generation of multi-spiral structures. (<b>a</b>) Spiral-shaped Intensity distribution/pattern generated by the interference of optical vortex beams with topological charges (ℓ = +1, +2, +3, and +5) and a gaussian beam with a spherical wavefront; (<b>b</b>) spiral-shaped intensity pattern formed in a spatial light modulator by interfering a focused optical vortex (OAM beam), produced by a phase mask on the modulator with a non-modulated portion of a Gaussian beam. Reprinted from [<a href="#B134-photonics-10-01319" class="html-bibr">134</a>].</p>
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<p>Production of OAM laser beams using multi-spiral microstructures created in azopolymer thin films using direct multi-spiral laser patterning. (<b>a</b>) The experimental setup to examine the light field created as a result of the diffraction of a linearly polarized Gaussian beam on the manufactured microstructures; (<b>b</b>) intensity distributions and interference fringes produced at a 30-micrometer separation from the azopolymer thin film surface. Reprinted from [<a href="#B134-photonics-10-01319" class="html-bibr">134</a>].</p>
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15 pages, 16631 KiB  
Article
Full-Space Wavefront Shaping of Broadband Vortex Beam with Switchable Terahertz Metasurface Based on Vanadium Dioxide
by Xueying Li, Ying Zhang, Jiuxing Jiang, Yongtao Yao and Xunjun He
Nanomaterials 2023, 13(23), 3023; https://doi.org/10.3390/nano13233023 - 26 Nov 2023
Cited by 4 | Viewed by 1509
Abstract
Currently, vortex beams are extensively utilized in the information transmission and storage of communication systems due to their additional degree of freedom. However, traditional terahertz metasurfaces only focus on the generation of narrowband vortex beams in reflection or transmission mode, which is unbeneficial [...] Read more.
Currently, vortex beams are extensively utilized in the information transmission and storage of communication systems due to their additional degree of freedom. However, traditional terahertz metasurfaces only focus on the generation of narrowband vortex beams in reflection or transmission mode, which is unbeneficial for practical applications. Here, we propose and design terahertz metasurface unit cells composed of anisotropic Z-shaped metal structures, two dielectric layers, and a VO2 film layer. By utilizing the Pancharatnam–Berry phase theory, independent control of a full 2π phase over a wide frequency range can be achieved by rotating the unit cell. Moreover, the full-space mode (transmission and reflection) can also be implemented by utilizing the phase transition of VO2 film. Based on the convolution operation, three different terahertz metasurfaces are created to generate vortex beams with different wavefronts in full-space, such as deflected vortex beams, focused vortex beams, and non-diffraction vortex beams. Additionally, the divergences of these vortex beams are also analyzed. Therefore, our designed metasurfaces are capable of efficiently shaping the wavefronts of broadband vortex beams in full-space, making them promising applications for long-distance transmission, high integration, and large capacity in 6G terahertz communications. Full article
(This article belongs to the Special Issue Nanomaterials for Terahertz Technology Applications)
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<p>Schematic diagram of terahertz metasurfaces working in full-space: (<b>a</b>) functional illumination of metasurfaces; (<b>b</b>) structure and parameters of metasurface unit cell.</p>
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<p>The change in conductivity of VO<sub>2</sub> at different temperatures.</p>
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<p>Terahertz responses of the designed unit cell under the RCP incident waves: (<b>a</b>) PCR and transmission amplitudes of the cross-polarized and co-polarized output waves; (<b>b</b>) PCR and reflection amplitudes of the cross-polarized and co-polarized output waves.</p>
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<p>Surface current distributions of the unit cell for different states of VO<sub>2</sub> under RCP incident wave: (<b>a</b>) top view and (<b>b</b>) sectional view at the insulating state; (<b>c</b>) top view and (<b>d</b>) sectional view at the metallic state.</p>
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<p>Amplitude and phase of the cross-polarized output wave under different rotation angle <span class="html-italic">θ</span>: (<b>a</b>) transmission intensity; (<b>b</b>) transmission phase; (<b>c</b>) reflection intensity; and (<b>d</b>) reflection phase.</p>
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<p>Amplitudes and phases of the cross-polarized wave for eight unit cells at different working modes: (<b>left</b>) transmission intensity and phase at 3.6 THz for insulating state; (<b>right</b>) reflection intensity and phase at 3.2 THz for the metallic state.</p>
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<p>Convolutional phase process of the deflected vortex beam at insulating state under RCP wave illumination: (<b>a</b>) phase distribution of the deflected beam along the negative <span class="html-italic">x</span>-axis; (<b>b</b>) phase distribution of the vortex beam with <span class="html-italic">l</span> = 1; and (<b>c</b>) phase distribution of the vortex beam with <span class="html-italic">l</span> = 1 deflected along the negative <span class="html-italic">x</span>-axis.</p>
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<p>3D far-field radiation patterns of the deflected vortex beam at different working states: (<b>a</b>) insulating state (transmission mode); (<b>b</b>) metallic state (reflection mode).</p>
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<p>Convolutional phase process of the focused vortex beam at insulating state under RCP wave illumination: (<b>a</b>) phase distribution of the focused beam with <span class="html-italic">F</span> = 300 μm; (<b>b</b>) phase distribution of the vortex beam with <span class="html-italic">l</span> = 1; and (<b>c</b>) phase distribution of the focused vortex beam with <span class="html-italic">F</span> = 300 μm and with <span class="html-italic">l</span> = 1.</p>
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<p>Energy and phase distributions of the focused vortex beam at different working states: (<b>a</b>) insulating state (transmission mode); (<b>b</b>) metallic state (reflection mode).</p>
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<p>Superposition phase distribution of the non-diffraction vortex beam at insulating state under RCP wave illumination: (<b>a</b>) phase distribution of the zero-order Bessel beam with <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mi>B</mi> </mrow> </msub> </mrow> </semantics></math> = 22°; (<b>b</b>) phase distribution of the vortex beam with <span class="html-italic">l</span> = 1; and (<b>c</b>) phase distribution of the non-diffraction vortex beam with <span class="html-italic">l</span> = 1 and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mi>B</mi> </mrow> </msub> </mrow> </semantics></math> = 22°.</p>
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<p>Energy and phase distributions of the non-diffractive vortex beam under different working states: (<b>a</b>) insulating state (transmission mode); (<b>b</b>) metallic state (reflection mode).</p>
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<p>Normalized reflection energy intensity of the vortex beam, focused vortex beam, and non-diffracting vortex beam in different <span class="html-italic">xoy</span> planes: (<b>a</b>) z = 500 μm; (<b>b</b>) z = 800 μm.</p>
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19 pages, 9226 KiB  
Article
Pile Arrangement for Minimizing Plastic Deformation in Pile-Supported Immersed Tunnel under Seismic Loads
by Hu Fan, Yan Zhuang, Jinxin Li and Zhi Chen
Appl. Sci. 2023, 13(22), 12331; https://doi.org/10.3390/app132212331 - 15 Nov 2023
Viewed by 882
Abstract
The plastic region of piles under seismic loads is a crucial concern in seafloor improvement design. This paper establishes a physical model of the sand compaction pile-immersed tunnel–water pressure system. This research studies pile arrangements that minimize the sand compaction pile plastic region [...] Read more.
The plastic region of piles under seismic loads is a crucial concern in seafloor improvement design. This paper establishes a physical model of the sand compaction pile-immersed tunnel–water pressure system. This research studies pile arrangements that minimize the sand compaction pile plastic region under seismic loads. The experiments were validated through numerical simulations. The results show that “X-shaped” and rectangular pile groups increase the Energy Residual Index (ERI) due to differences in pile spacing and the instability of the quadrilateral prism damping units formed by piles and soil. In this scenario, piles are limited to heavy and mild plastic regions, with boundary depths at L = 2.25 D and L = 2.08 D (L represents the pile length, and D is the pile diameter). Furthermore, increased water pressure amplifies the structural resonance injury, increasing ERI. In conjunction with the soil, hexagonal pile groups create triangular prism damping units that counteract seismic wavefronts. The total kinetic energy and strain energy of the piled foundation are lower than those of the “X-shaped” and rectangular pile groups. The boundaries between the heavy plastic region, the moderate plastic region, and the mild plastic region are located at depths of L = 4 D and L = 8 D, respectively. This study also reveals that a top-heavy mass distribution in the structure leads to maximum deformation in the heavy plastic region. Pile–soil damping units primarily operate within the moderate plastic region. Full article
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<p>Experimental equipment: (<b>a</b>) model scale; (<b>b</b>) schematic diagram of the equipment.</p>
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<p>Arrangement angle of the SCP.</p>
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<p>Basic physical properties: (<b>a</b>) gradation curve; (<b>b</b>) shear strength.</p>
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<p>Time history acceleration.</p>
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<p>Bending moment distribution of the piles.</p>
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<p>Friction-displacement curves of the pile–soil interface.</p>
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<p>Plastic hysteresis curves for different <span class="html-italic">θ</span> values of the piled foundation: (<b>a</b>) <span class="html-italic">H</span> = 23 m; (<b>b</b>) <span class="html-italic">H</span> = 32.12 m; (<b>c</b>) <span class="html-italic">H</span> = 44.78 m; (<b>d</b>) Area different of hysteresis curves.</p>
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<p>Plastic hysteresis curves for different <span class="html-italic">θ</span> values of the piled foundation: (<b>a</b>) <span class="html-italic">H</span> = 23 m; (<b>b</b>) <span class="html-italic">H</span> = 32.12 m; (<b>c</b>) <span class="html-italic">H</span> = 44.78 m; (<b>d</b>) Area different of hysteresis curves.</p>
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<p>Damping coefficients ratio of the piled foundation.</p>
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<p>Schematic of the numerical model. 1—backfill; 2—immersed tunnel; 3—SCP; 4—gravel cushion; 5—incident wave.</p>
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<p>Result validation: (<b>a</b>) settlement of the foundation; (<b>b</b>) transverse load of the foundation.</p>
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<p>Kinetic energy change: (<b>a</b>) Kinetic energy of the SCP; (<b>b</b>) Kinetic energy of foundation.</p>
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<p>Strain energy at different depths of the piles: (<b>a</b>) <span class="html-italic">θ</span><sub>1</sub> = 45°, <span class="html-italic">H</span> = 44.78 m; (<b>b</b>) <span class="html-italic">θ</span><sub>2</sub> = 60°, <span class="html-italic">H</span> = 44.78 m; (<b>c</b>) <span class="html-italic">θ</span><sub>3</sub> = 90°, <span class="html-italic">H</span> = 44.78 m.</p>
Full article ">Figure 12 Cont.
<p>Strain energy at different depths of the piles: (<b>a</b>) <span class="html-italic">θ</span><sub>1</sub> = 45°, <span class="html-italic">H</span> = 44.78 m; (<b>b</b>) <span class="html-italic">θ</span><sub>2</sub> = 60°, <span class="html-italic">H</span> = 44.78 m; (<b>c</b>) <span class="html-italic">θ</span><sub>3</sub> = 90°, <span class="html-italic">H</span> = 44.78 m.</p>
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<p>Plastic regions of the pile.</p>
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13 pages, 24803 KiB  
Article
Reconfigurable Amplitude-Phase-Coding Metasurface with Flexible Beamforming Capability
by Lu Gao, Yuxin Zhou, Hailiang Zhu, Pei Zheng, Jiaqi Liu, Zhonghang He, Ziwei Xu and Yichun Cui
Electronics 2023, 12(22), 4565; https://doi.org/10.3390/electronics12224565 - 8 Nov 2023
Cited by 2 | Viewed by 1442
Abstract
Recently, reconfigurable coding metasurfaces have attracted extensive attention due to their dynamic and flexible manipulation of electromagnetic (EM) waves, making them an effective solution to connect physical reality and information science. Nevertheless, most previously reported reconfigurable metasurfaces suffer from limited applications, as they [...] Read more.
Recently, reconfigurable coding metasurfaces have attracted extensive attention due to their dynamic and flexible manipulation of electromagnetic (EM) waves, making them an effective solution to connect physical reality and information science. Nevertheless, most previously reported reconfigurable metasurfaces suffer from limited applications, as they solely possess either phase or amplitude modulation. In this article, we propose a reconfigurable coding metasurface that can regulate both phase and amplitude response independently. In the field of the metasurface, the phase response can tailor the wavefronts, and the amplitude response can adjust the redistribution of the energy of the EM waves. Specifically, by integrating a PIN diode into the meta-atom and controlling its bias voltage, the reflection phase can be switched between two opposite phases with a phase difference of about 180°, and the reflection amplitude can be manipulated from 0.02 to 0.98 continuously at 11 GHz. The unit element consists of simple multi-layer structures, reducing its production cost and processing difficulty. By loading 1-bit phase code and multi-bit amplitude code to each unit element severally, this metasurface can modulate the distribution of reflected EM waves in two-dimensional (2-D) space while simultaneously suppressing the sidelobes for any quantity of scattered beams over a wide operating band ranging from 10.5 to 11.5 GHz. This metasurface exhibits promising potential for manipulating the distribution of EM wave energy and shaping of EM beams, which can be expected to facilitate wireless communication technology. Full article
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<p>Functional of RAPM. (<b>a</b>) Dynamic multibeam-forming ability of RAPM; (<b>b</b>) sidelobe-suppression ability of RAPM.</p>
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<p>Structural schematics of RAPM and its unit elements. (<b>a</b>) Schematic of RAPM; (<b>b</b>) structural schematic of a unit element; (<b>c</b>) the equivalent circuit of the PIN diode load in the unit element.</p>
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<p>The amplitude and phase responses of the proposed unit element. (<b>a</b>–<b>d</b>) Simulated amplitude and phase responses of the unit element with different RDs from 10 to 12 GHz; (<b>e</b>) simulated amplitude and phase responses of the unit element with different RDs at 11 GHz.</p>
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<p>(<b>a</b>–<b>c</b>) Phase and amplitude-coding sequences of metasurfaces named A1, A2, and A3; (<b>d</b>–<b>f</b>) simulated far-field radiation pattern of A1, A2, and A3 in MATLAB R2021a software at 11 GHz (The beams energy intensity is normalized).</p>
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<p>(<b>a</b>–<b>c</b>) Simulated 3-D far-field radiation pattern of A1, A2, and A3 in CST 2022 at 11 GHz; (<b>d</b>–<b>f</b>) simulated 2-D far-field radiation patterns of RAPM in CST 2022 at 11 GHz, in which PC is the abbreviation of the phase-coding sequence and AC is the abbreviation of the amplitude-coding sequence.</p>
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<p>(<b>a</b>–<b>c</b>) Simulated 3-D far-field radiation pattern of A1, A2, and A3 at 10.5 GHz; (<b>d</b>–<b>f</b>) simulated 2-D far-field radiation patterns of RAPM at 10.5 GHz.</p>
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<p>(<b>a</b>–<b>c</b>) Simulated 3-D far-field radiation pattern of A1, A2, and A3 at 11.5 GHz; (<b>d</b>–<b>f</b>) simulated 2-D far-field radiation patterns of RAPM at 11.5 GHz.</p>
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<p>(<b>a</b>,<b>d</b>) Different phase-coding sequences of metasurfaces; (<b>b</b>,<b>e</b>) simulated 3-D far-field radiation pattern with different phase-coding sequences; (<b>c</b>,<b>f</b>) simulated 2-D far-field radiation patterns with different phase-coding sequences.</p>
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<p>RAPM assists in network signal supplementary coverage.</p>
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