[go: up one dir, main page]

 
 
Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (10)

Search Parameters:
Keywords = S-waveplate

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
15 pages, 5061 KiB  
Article
Spatially Variable Ripple and Groove Formation on Gallium Arsenide Using Linear, Radial, and Azimuthal Polarizations of Laser Beam
by Kalvis Kalnins, Vyacheslav V. Kim, Andra Naresh Kumar Reddy, Anatolijs Sarakovskis and Rashid A. Ganeev
Photonics 2024, 11(8), 710; https://doi.org/10.3390/photonics11080710 - 30 Jul 2024
Viewed by 556
Abstract
We demonstrated the linear, radial, and annular ripple formation on the surface of GaAs. The formation of linear ripples was optimized by the number of shots and the fluence of 30 ps, 532 nm pulses. The radial and annular nanoripples were produced under [...] Read more.
We demonstrated the linear, radial, and annular ripple formation on the surface of GaAs. The formation of linear ripples was optimized by the number of shots and the fluence of 30 ps, 532 nm pulses. The radial and annular nanoripples were produced under the ablation using doughnut-like beams possessing azimuthal and radial polarizations, respectively. We compare the ripples and grooves formed by a linearly polarized Gaussian beam relative to an annular vector beam. The joint overlap of sub-wavelength grooves with ripples formed by azimuthally and radially polarized beams was reported. The conditions under which the shape of radial and ring-like nano- or micro-relief on the GaAs surface can be modified by modulating the polarization of laser pulse were determined. The resultant surface processing of GaAs using a laser beam with different polarization modes is useful for exploring valuable insights and benefits in different applications. Full article
(This article belongs to the Section Lasers, Light Sources and Sensors)
Show Figures

Figure 1

Figure 1
<p>(<b>a</b>) Experimental scheme for LIPSS formation on the surface of GaAs using 532 nm, 30 ps pulses. The bottom insets show the spatial shapes of (<b>b</b>) a linearly polarized Gaussian beam, (<b>c</b>) a radially polarized annular beam, and (<b>d</b>) an azimuthally polarized annular beam and (<b>e</b>–<b>g</b>) their corresponding line-outs of spatial distribution. White arrows are the directions of polarization.</p>
Full article ">Figure 2
<p>SEM images of ablated GaAs using (<b>a</b>) 5 shots, (<b>b</b>) 15 shots, and (<b>c</b>) 25 shots of 532 nm, 30 ps pulses at the fluence 0.18 J cm<sup>−2</sup> on the target surface. The bottom panels of (<b>a</b>–<b>c</b>) correspond to the enlarged parts of the corresponding areas marked in red. White lines correspond to 10 μm. Blue arrows show the direction of polarization of the Gaussian beam.</p>
Full article ">Figure 3
<p>(<b>a</b>) Appearance of orthogonally directed lines (HSFL) with a smaller spatial period at a larger number of shots (30) on the same place of GaAs. (<b>b</b>) Enlarged part of <a href="#photonics-11-00710-f003" class="html-fig">Figure 3</a>a. The blue arrow shows the direction of polarization of the laser beam. The white line corresponds to 1 μm. The average spatial periods of orthogonal (LSFL and HSFL) ripples were 480 and 270 nm, respectively.</p>
Full article ">Figure 4
<p>(<b>a</b>) Spatial shape of the ablated area on the surface of GaAs by the doughnut-like beam with a radial distribution of polarization (white arrows). (<b>b</b>) The enlarged square of <a href="#photonics-11-00710-f004" class="html-fig">Figure 4</a>a shows the part of the ablated ring dominated by the presence of the grooves growing parallel to the polarization. (<b>c</b>) An enlarged part of <a href="#photonics-11-00710-f004" class="html-fig">Figure 4</a>b shows the inner region of the ring. One can see the rings of ripples, followed by the grooves. These ripples remain almost unchanged on the right side of <a href="#photonics-11-00710-f004" class="html-fig">Figure 4</a>c while appearing under the grooves. (<b>d</b>) The enlarged part of <a href="#photonics-11-00710-f004" class="html-fig">Figure 4</a>b shows the outer region of the ring. One can see the LSFL at the smallest fluence of the laser beam, followed by the appearance of the grooves above the rings on the left side of <a href="#photonics-11-00710-f004" class="html-fig">Figure 4</a>d. The white bars correspond to 40 μm (<a href="#photonics-11-00710-f004" class="html-fig">Figure 4</a>a) and 10 μm (<a href="#photonics-11-00710-f004" class="html-fig">Figure 4</a>b–d).</p>
Full article ">Figure 5
<p>(<b>a</b>) The shape of the ablated area using the radially polarized beam at F = 0.18 J cm<sup>−2</sup> and N = 5. (<b>b</b>) Enlarged part of <a href="#photonics-11-00710-f005" class="html-fig">Figure 5</a>a showing the ring-like LSFL throughout the ablation area. The white bars correspond to 60 μm (<a href="#photonics-11-00710-f005" class="html-fig">Figure 5</a>a) and 10 μm (<a href="#photonics-11-00710-f005" class="html-fig">Figure 5</a>b). While arrows show the direction of polarization of the laser beam.</p>
Full article ">Figure 6
<p>(<b>a</b>) SEM image of the whole area of ablation using 20 shots of the azimuthally polarized beam. Almost the whole ablated area was filled in with grooves. (<b>b</b>,<b>c</b>) Enlarged parts of the ablated area and outer border of the ablated area, respectively. The ripples were observed only in the area of the outer border of the ablation. (<b>d</b>) SEM image of the whole area of ablation using 5 shots of the azimuthally polarized beam at the same fluence of heating radiation (F = 0.22 J cm<sup>−2</sup>) as in the case shown in <a href="#photonics-11-00710-f006" class="html-fig">Figure 6</a>a. (<b>e</b>,<b>f</b>) Enlarged parts of the ablated area and inner border of the ablated area, respectively. LSFL, in that case, dominated along the whole ablated area. The white bars correspond to 80 μm (<a href="#photonics-11-00710-f006" class="html-fig">Figure 6</a>a,d) and 10 μm (<a href="#photonics-11-00710-f006" class="html-fig">Figure 6</a>c,f). While arrows show the direction of polarization of the laser beam.</p>
Full article ">Figure 7
<p>(<b>a</b>,<b>d</b>) The intensity profiles of the linearly polarized Gaussian beam and radially polarized beam, respectively. (<b>b</b>,<b>e</b>) The corresponding images of ablated areas. (<b>c</b>,<b>f</b>) The enlarged parts of the red squares are marked in <a href="#photonics-11-00710-f007" class="html-fig">Figure 7</a>b and <a href="#photonics-11-00710-f007" class="html-fig">Figure 7</a>e, respectively. Blue arrows show the direction of polarization of the laser beam.</p>
Full article ">Figure 8
<p>Left panels of <a href="#photonics-11-00710-f008" class="html-fig">Figure 8</a>a,b: the images of the ablation areas after laser–matter interaction in the case of the rotation of the S-waveplate by (<b>a</b>) 22.5° and (<b>b</b>) 45° from the position corresponding to the pure radial polarization of the annular beam. The enlarged images of the ablation areas in these two cases are shown in the right panels. Red curved lines show the leaned directions of polarizations at different points of the ablation. The grooves follow these leaned directions of polarization.</p>
Full article ">
17 pages, 5234 KiB  
Article
Full-Automatic High-Efficiency Mueller Matrix Microscopy Imaging for Tissue Microarray Inspection
by Hanyue Wei, Yifu Zhou, Feiya Ma, Rui Yang, Jian Liang and Liyong Ren
Sensors 2024, 24(14), 4703; https://doi.org/10.3390/s24144703 - 20 Jul 2024
Viewed by 761
Abstract
This paper proposes a full-automatic high-efficiency Mueller matrix microscopic imaging (MMMI) system based on the tissue microarray (TMA) for cancer inspection for the first time. By performing a polar decomposition on the sample’s Mueller matrix (MM) obtained by a transmissive MMMI system we [...] Read more.
This paper proposes a full-automatic high-efficiency Mueller matrix microscopic imaging (MMMI) system based on the tissue microarray (TMA) for cancer inspection for the first time. By performing a polar decomposition on the sample’s Mueller matrix (MM) obtained by a transmissive MMMI system we established, the linear phase retardance equivalent waveplate fast-axis azimuth and the linear phase retardance are obtained for distinguishing the cancerous tissues from the normal ones based on the differences in their polarization characteristics, where three analyses methods including statistical analysis, the gray-level co-occurrence matrix analysis (GLCM) and the Tamura image processing method (TIPM) are used. Previous MMMI medical diagnostics typically utilized discrete slices for inspection under a high-magnification objective (20×–50×) with a small field of view, while we use the TMA under a low-magnification objective (5×) with a large field of view. Experimental results indicate that MMMI based on TMA can effectively analyze the pathological variations in biological tissues, inspect cancerous cervical tissues, and thus contribute to the diagnosis of postoperative cancer biopsies. Such an inspection method, using a large number of samples within a TMA, is beneficial for obtaining consistent findings and good reproducibility. Full article
(This article belongs to the Special Issue Advances in Optical Sensing, Instrumentation and Systems: 2nd Edition)
Show Figures

Figure 1

Figure 1
<p>Schematic diagram of MMMI system. P1 and P2, polarizers; R1 and R2, quarter waveplates.</p>
Full article ">Figure 2
<p>Original images of TMA. (<b>a</b>) is the original image of the TMA captured by a general camera; (<b>b</b>,<b>c</b>) are the original microscopic images of cancerous cervical tissue; (<b>d</b>,<b>e</b>) are the original microscopic image of normal cervical tissue.</p>
Full article ">Figure 3
<p>Mueller matrices images of four spots on TMA. (<b>a</b>,<b>b</b>) are cancerous tissues; (<b>c</b>,<b>d</b>) are normal tissues.</p>
Full article ">Figure 4
<p>Mueller-matrix-derived polarization parameter images <span class="html-italic">θ</span> and <span class="html-italic">δ</span> of cancerous cervical tissues and normal cervical tissues. (<b>a</b>,<b>b</b>,<b>e</b>,<b>f</b>) are cancerous tissues; (<b>c</b>,<b>d</b>,<b>g</b>,<b>h</b>) are normal tissues.</p>
Full article ">Figure 5
<p>Histograms of grayscale images for <span class="html-italic">θ</span> and <span class="html-italic">δ</span> parameters. (<b>a</b>) is histograms of grayscale images for <span class="html-italic">θ</span> parameters; (<b>b</b>) is histograms of grayscale images for <span class="html-italic">δ</span> parameters.</p>
Full article ">Figure 6
<p>Statistics method parameter boxplots of <span class="html-italic">θ</span>, <span class="html-italic">δ</span> images. (<b>a</b>,<b>b</b>) are statistics method parameters boxplots of <span class="html-italic">θ</span> images; (<b>c</b>,<b>d</b>) are statistics method parameters boxplots of <span class="html-italic">δ</span> images.</p>
Full article ">Figure 7
<p>Boxplots of the GLCM parameters for all samples in the TMA. (<b>a</b>–<b>d</b>) are GLCM parameters boxplots of <span class="html-italic">θ</span> images; (<b>e</b>–<b>h</b>) are GLCM parameters boxplots of <span class="html-italic">δ</span> images.</p>
Full article ">Figure 8
<p>Boxplots of the TIPM parameters for all samples in the TMA. (<b>a</b>–<b>c</b>) are TIPM parameters boxplots of <span class="html-italic">θ</span> images; (<b>d</b>–<b>f</b>) are TIPM parameters boxplots of <span class="html-italic">δ</span> images.</p>
Full article ">
13 pages, 1516 KiB  
Article
Environmental Surveillance through Machine Learning-Empowered Utilization of Optical Networks
by Hasan Awad, Fehmida Usmani, Emanuele Virgillito, Rudi Bratovich, Roberto Proietti, Stefano Straullu, Francesco Aquilino, Rosanna Pastorelli and Vittorio Curri
Sensors 2024, 24(10), 3041; https://doi.org/10.3390/s24103041 - 10 May 2024
Viewed by 1026
Abstract
We present the use of interconnected optical mesh networks for early earthquake detection and localization, exploiting the existing terrestrial fiber infrastructure. Employing a waveplate model, we integrate real ground displacement data from seven earthquakes with magnitudes ranging from four to six to simulate [...] Read more.
We present the use of interconnected optical mesh networks for early earthquake detection and localization, exploiting the existing terrestrial fiber infrastructure. Employing a waveplate model, we integrate real ground displacement data from seven earthquakes with magnitudes ranging from four to six to simulate the strains within fiber cables and collect a large set of light polarization evolution data. These simulations help to enhance a machine learning model that is trained and validated to detect primary wave arrivals that precede earthquakes’ destructive surface waves. The validation results show that the model achieves over 95% accuracy. The machine learning model is then tested against an M4.3 earthquake, exploiting three interconnected mesh networks as a smart sensing grid. Each network is equipped with a sensing fiber placed to correspond with three distinct seismic stations. The objective is to confirm earthquake detection across the interconnected networks, localize the epicenter coordinates via a triangulation method and calculate the fiber-to-epicenter distance. This setup allows early warning generation for municipalities close to the epicenter location, progressing to those further away. The model testing shows a 98% accuracy in detecting primary waves and a one second detection time, affording nearby areas 21 s to take countermeasures, which extends to 57 s in more distant areas. Full article
(This article belongs to the Special Issue Feature Papers in Optical Sensors 2024)
Show Figures

Figure 1

Figure 1
<p>Schematic representation of fiber sections, each with uniform internal birefringence.</p>
Full article ">Figure 2
<p>Four SOP evolutions for the same seismic event with different sets of plate angles.</p>
Full article ">Figure 3
<p>ML model architecture.</p>
Full article ">Figure 4
<p>ML model training and validation accuracy.</p>
Full article ">Figure 5
<p>M4.3 earthquake time: 23 May 2012 21:41:18 (UTC). Region: Modena and corresponding interconnected sensing grid in the Modena region.</p>
Full article ">Figure 6
<p>Strain evolution over the T0821 fiber (<b>left</b>), MNTV fiber (<b>middle</b>), and ZCCA fiber (<b>right</b>).</p>
Full article ">Figure 7
<p>SOPAS evolution over the T0821 fiber (<b>left</b>), MNTV fiber (<b>middle</b>), and ZCCA fiber (<b>right</b>).</p>
Full article ">Figure 8
<p>Confusion matrices over the T0821 fiber (<b>left</b>), MNTV fiber (<b>middle</b>), and ZCCA fiber (<b>right</b>).</p>
Full article ">Figure 9
<p>ML detection time of P waves using SOPAS data across three seismic stations/sensing fibers: T0821 (<b>left</b>), MNTV (<b>middle</b>) and ZCCA (<b>right</b>).</p>
Full article ">
7 pages, 1487 KiB  
Communication
Automated Long-Term Stability of a High-Energy Laser
by Jack Morse, William Carter, Pedro Oliveira and Marco Galimberti
Optics 2023, 4(4), 595-601; https://doi.org/10.3390/opt4040044 - 29 Nov 2023
Viewed by 1079
Abstract
We present a method for regulating the laser energy output with a software-controlled waveplate–polariser configuration. By implementing this technology, we have effectively eliminated energy output fluctuations over time, allowing for the laser to reach its nominal energy up to 2 h earlier. Our [...] Read more.
We present a method for regulating the laser energy output with a software-controlled waveplate–polariser configuration. By implementing this technology, we have effectively eliminated energy output fluctuations over time, allowing for the laser to reach its nominal energy up to 2 h earlier. Our testing demonstrates a stability of 2.8% (RMS), verifying the system’s reliability. We provide an overview of the software and its basic operation, along with practical evidence of the system’s efficacy in maintaining a stable laser energy output. Full article
Show Figures

Figure 1

Figure 1
<p>A schematic of the laser cavity. WP is the controllable waveplate, P1 and P2 are polarisers, PC is a Pockels’ cell, RGA is the regenerative amplifier, SHG is the second harmonic KDP crystal. The camera takes a Near-Field image on the penultimate mirror.</p>
Full article ">Figure 2
<p>Practical measurement of uEye camera’s calorimetry response using a Gentec MAESTRO energy detector. The extrapolated region is assumed as linear.</p>
Full article ">Figure 3
<p>The blue curve represents the original calibration function; the dashed blue curve represents the translated calibration function; <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mn>1</mn> </msub> <mo>=</mo> </mrow> </semantics></math> current angle; <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mn>2</mn> </msub> <mo>=</mo> </mrow> </semantics></math> calculated angle.</p>
Full article ">Figure 4
<p>A cubic calibration function (red) fit to measured energies from the camera as a function of angle.</p>
Full article ">Figure 5
<p>A capture of the UI of the Stability2 Hz software, developed in C#.</p>
Full article ">Figure 6
<p>The plot shows how the laser has a warm up period of around 2 h (orange trace). The blue curve sits at the same level as the set energy (red dashed line) for the duration of the day. Both plots have been converted to Joules using (<a href="#FD1-optics-04-00044" class="html-disp-formula">1</a>).</p>
Full article ">
12 pages, 9747 KiB  
Article
Four-Polarisation Camera for Anisotropy Mapping at Three Orientations: Micro-Grain of Olivine
by Shuji Kamegaki, Daniel Smith, Meguya Ryu, Soon Hock Ng, Hsin-Hui Huang, Pegah Maasoumi, Jitraporn Vongsvivut, Daniel Moraru, Tomas Katkus, Saulius Juodkazis and Junko Morikawa
Coatings 2023, 13(9), 1640; https://doi.org/10.3390/coatings13091640 - 18 Sep 2023
Cited by 2 | Viewed by 1869
Abstract
A four-polarisation camera was used to map the absorbance of olivine micro-grains before and after high-temperature annealing (HTA). It is shown that HTA of olivine xenoliths at above 1200 °C in O2 flow makes them magnetised. Different modes of operation of [...] Read more.
A four-polarisation camera was used to map the absorbance of olivine micro-grains before and after high-temperature annealing (HTA). It is shown that HTA of olivine xenoliths at above 1200 °C in O2 flow makes them magnetised. Different modes of operation of the polariscope with polarisation control before and after the sample in transmission and reflection modes were used. The reflection type was assembled for non-transparent samples of olivine after HTA. The sample for optical observation in transmission was placed on an achromatic, plastic, quarter-wavelength waveplate as a sample holder. Inspection of the sample’s birefringence (retardance), as well as absorbance, was undertaken. The best fit for the transmitted intensity or transmittance T (hence, absorbance A=log10T) is obtainable using a simple best fit with only three orientations (from the four orientations measured by the camera). When the intensity of transmitted light at one of the orientations is very low due to a cross-polarised condition (polariser–analyser arrangement), the three-point fit can be used. The three-point fit in transmission and reflection modes was validated for T(θ)=Amp×cos(2θ2θshift)+offset, where the amplitude Amp, offset offset, and orientation azimuth θshift were extracted for each pixel via the best fit. Full article
(This article belongs to the Special Issue New Advances in Novel Optical Materials and Devices)
Show Figures

Figure 1

Figure 1
<p>(<b>a</b>) Transmission setup with four-polarisation camera for measurements of absorbance and transmittance for characterisation of micro-grains of olivine. (<b>b</b>) Optical images of transmitted light at four polarisations. Measurements were carried out with linearly polarised illumination and four-polarisation detection (the achromatic <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math> plate was aligned with the linear polariser and used as a sample holder). This setup can be used for retardance and absorbance measurements. The circular polariser was realised using a pair of <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>/</mo> <mn>4</mn> </mrow> </semantics></math> plates at a <math display="inline"><semantics> <mrow> <mo>±</mo> <mi>π</mi> <mo>/</mo> <mn>4</mn> </mrow> </semantics></math> angle for orientation of the <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math> plate (plastic pair, Edmund optics).</p>
Full article ">Figure 2
<p>Absorbance measurements for an olivine micro-particle. (<b>a</b>) Absorbance measurement with linearly polarised illumination and four-polarisation detection. A pair of <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>/</mo> <mn>4</mn> </mrow> </semantics></math> plates were used to make an achromatic plastic circular polariser (Edmund optics) at <math display="inline"><semantics> <msup> <mn>0</mn> <mo>°</mo> </msup> </semantics></math> orientation; this corresponds to the linearly polarised illumination (the x-polarisation of the microscope condenser). (<b>b</b>) Optical image of olivine micro-grain using combined intensity with the four-polarisation camera. Illumination was set as circular using a single <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>/</mo> <mn>4</mn> </mrow> </semantics></math> plastic plate (Edmund optics) at <math display="inline"><semantics> <msup> <mn>45</mn> <mo>°</mo> </msup> </semantics></math> orientation and a 550 nm bandpass filter (∼20 nm). (<b>c</b>) Absorbance <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>≡</mo> <mo>−</mo> <msub> <mo form="prefix">log</mo> <mn>10</mn> </msub> <mi>T</mi> </mrow> </semantics></math> spectra for two distinct experimental results selected from (<b>d</b>) to illustrate the fit. The amplitude <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>m</mi> <mi>p</mi> </mrow> </semantics></math> and offset <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>f</mi> <mi>f</mi> <mi>s</mi> <mi>e</mi> <mi>t</mi> </mrow> </semantics></math> values were retrieved from the best fit. Four markers at the four-polarisation camera orientations are shown. (<b>d</b>) The fit results for each pixel for the values of <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>m</mi> <mi>p</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>f</mi> <mi>f</mi> <mi>s</mi> <mi>e</mi> <mi>t</mi> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mn>2</mn> <msub> <mi>θ</mi> <mrow> <mi>s</mi> <mi>h</mi> <mi>i</mi> <mi>f</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math> over a selected region of interest (ROI). The orientation <math display="inline"><semantics> <mrow> <mn>2</mn> <msub> <mi>θ</mi> <mrow> <mi>s</mi> <mi>h</mi> <mi>i</mi> <mi>f</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math> corresponds to the largest absorbance.</p>
Full article ">Figure 3
<p>(<b>a</b>) Setup for sample’s illumination with circular-polarisation (isotropic) illumination and four-polarisation camera imaging. (<b>b</b>) Four-point fit of absorbance <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>=</mo> <mo>−</mo> <mo form="prefix">lg</mo> <mrow> <mo>(</mo> <mi>T</mi> <mrow> <mo>(</mo> <mi>θ</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>≡</mo> <mo>−</mo> <mo form="prefix">lg</mo> <mrow> <mo>[</mo> <msub> <mi>I</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <mi>θ</mi> <mo>)</mo> </mrow> <mo>/</mo> <msub> <mi>I</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>θ</mi> <mo>)</mo> </mrow> <mo>]</mo> </mrow> <mo>=</mo> <mi>A</mi> <mi>m</mi> <mi>p</mi> <mo>×</mo> <mo form="prefix">cos</mo> <mrow> <mo>(</mo> <mn>2</mn> <mi>θ</mi> <mo>−</mo> <mn>2</mn> <msub> <mi>θ</mi> <mrow> <mi>s</mi> <mi>h</mi> <mi>i</mi> <mi>f</mi> <mi>t</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>O</mi> <mi>f</mi> <mi>f</mi> <mi>s</mi> <mi>e</mi> <mi>t</mi> </mrow> </semantics></math>. (<b>c</b>) The standard deviation <math display="inline"><semantics> <mi>σ</mi> </semantics></math> of the intensity fit <math display="inline"><semantics> <mrow> <mi>I</mi> <mo>(</mo> <mi>θ</mi> <mo>)</mo> </mrow> </semantics></math>: <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <msqrt> <mrow> <mo>[</mo> <msub> <mo>∑</mo> <mi>i</mi> </msub> <msup> <mrow> <mo>(</mo> <msup> <mi>I</mi> <mrow> <mi>e</mi> <mi>x</mi> <mi>p</mi> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>−</mo> <msup> <mi>I</mi> <mrow> <mi>f</mi> <mi>i</mi> <mi>t</mi> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>]</mo> <mo>/</mo> <mn>4</mn> </mrow> </msqrt> </mrow> </semantics></math>, with <span class="html-italic">i</span> being the index for four-polarisation angles. (<b>d</b>) Maps for the best-fit parameters amplitude <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>m</mi> <mi>p</mi> </mrow> </semantics></math>, phase azimuth <math display="inline"><semantics> <msub> <mi>θ</mi> <mrow> <mi>s</mi> <mi>h</mi> <mi>i</mi> <mi>f</mi> <mi>t</mi> </mrow> </msub> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>f</mi> <mi>f</mi> <mi>s</mi> <mi>e</mi> <mi>t</mi> </mrow> </semantics></math> are shown in corresponding panels for the circularly polarised illumination. The offset had no bounds defined for the fit and the angle <math display="inline"><semantics> <mrow> <mn>2</mn> <msub> <mi>θ</mi> <mrow> <mi>s</mi> <mi>h</mi> <mi>i</mi> <mi>f</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math> was bound to the <math display="inline"><semantics> <mrow> <mn>0</mn> <mo>−</mo> <mn>2</mn> <mi>π</mi> </mrow> </semantics></math> range during the fitting procedure.</p>
Full article ">Figure 4
<p>(<b>a</b>) Transmittance of the <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math> plate at different orientation angles: dots—experiment, lines—Mueller matrix calculations (see <a href="#sec2dot2-coatings-13-01640" class="html-sec">Section 2.2</a>); the selected area of <math display="inline"><semantics> <mrow> <mn>1224</mn> <mo>×</mo> <mn>1024</mn> </mrow> </semantics></math> pixels was averaged for plotting. Three-point fit to <math display="inline"><semantics> <mrow> <mi>T</mi> <mrow> <mo>(</mo> <mi>θ</mi> <mo>)</mo> </mrow> <mo>≡</mo> <msub> <mi>I</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <mi>θ</mi> <mo>)</mo> </mrow> <mo>/</mo> <msub> <mi>I</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>θ</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>A</mi> <mi>m</mi> <mi>p</mi> <mo>×</mo> <mo form="prefix">cos</mo> <mrow> <mo>(</mo> <mn>2</mn> <mi>θ</mi> <mo>−</mo> <mn>2</mn> <msub> <mi>θ</mi> <mrow> <mi>s</mi> <mi>h</mi> <mi>i</mi> <mi>f</mi> <mi>t</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>O</mi> <mi>f</mi> <mi>f</mi> <mi>s</mi> <mi>e</mi> <mi>t</mi> </mrow> </semantics></math>. Maps for the best-fit parameters amplitude <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>m</mi> <mi>p</mi> </mrow> </semantics></math>, phase azimuth <math display="inline"><semantics> <msub> <mi>θ</mi> <mrow> <mi>s</mi> <mi>h</mi> <mi>i</mi> <mi>f</mi> <mi>t</mi> </mrow> </msub> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>f</mi> <mi>f</mi> <mi>s</mi> <mi>e</mi> <mi>t</mi> </mrow> </semantics></math> are shown in corresponding panels for the linearly polarised illumination with different orientations of the <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math> plate: <math display="inline"><semantics> <mrow> <mo>+</mo> <mi>π</mi> <mo>/</mo> <mn>4</mn> </mrow> </semantics></math> (<b>a</b>) and 0 (<b>b</b>). Amplitude and offset were set to be positive and the angle <math display="inline"><semantics> <mrow> <mn>2</mn> <msub> <mi>θ</mi> <mrow> <mi>s</mi> <mi>h</mi> <mi>i</mi> <mi>f</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math> was bound to the <math display="inline"><semantics> <mrow> <mn>0</mn> <mo>−</mo> <mn>2</mn> <mi>π</mi> </mrow> </semantics></math> range during the fitting procedure. An achromatic polymer <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math> waveplate was used as a sample holder. A cross with the <math display="inline"><semantics> <msub> <mi>θ</mi> <mrow> <mi>s</mi> <mi>h</mi> <mi>i</mi> <mi>f</mi> <mi>t</mi> </mrow> </msub> </semantics></math> marker between phase maps in (<b>b</b>,<b>c</b>) illustrates the ⊥ orientation of the background colour maps, as expected for the <math display="inline"><semantics> <mrow> <mi>π</mi> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math> phase difference for the <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>/</mo> <mn>4</mn> </mrow> </semantics></math> plate at 0 vs. <math display="inline"><semantics> <mrow> <mi>π</mi> <mo>/</mo> <mn>4</mn> </mrow> </semantics></math> orientations.</p>
Full article ">Figure 5
<p>Three-point (<math display="inline"><semantics> <mrow> <mn>0</mn> <mo>,</mo> <mo>±</mo> <mi>π</mi> <mo>/</mo> <mn>4</mn> </mrow> </semantics></math>) fit of absorbance for the illumination of olivine grains by linear polarised light using <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>/</mo> <mn>4</mn> </mrow> </semantics></math> plate at <math display="inline"><semantics> <msup> <mn>0</mn> <mo>°</mo> </msup> </semantics></math> (same sample as in <a href="#coatings-13-01640-f003" class="html-fig">Figure 3</a>). The standard deviation <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>&lt;</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math> showed a good fit for the three points (angles). An interference bandpass filter with <math display="inline"><semantics> <mrow> <mn>550</mn> <mo>±</mo> <mn>10</mn> </mrow> </semantics></math> nm was used for illumination.</p>
Full article ">Figure 6
<p>High-temperature annealing (HTA) of olivine xenolith. (<b>a</b>) Sample annealed at 1500 <math display="inline"><semantics> <mo>°</mo> </semantics></math>C for 2 h held on a magnet rod (<b>left</b>) and after its fragmentation (<b>right</b>). Micro/millimetre-sized grains of high-temperature-annealed olivine were gathered by magnets placed below the slide glass for microscopy observation. (<b>b</b>) A reflection-type microscope assembly was used for this study (set up with Nikon Optiphot-pol). Two plastic achromatic <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>/</mo> <mn>4</mn> </mrow> </semantics></math> waveplates were used to provide the capability to detect circular dichroism or optical activity. The slow axes of the plates were crossed and the linear polariser was rotated <math display="inline"><semantics> <mrow> <mo>±</mo> <mi>π</mi> <mo>/</mo> <mn>4</mn> </mrow> </semantics></math> to set up the right or left circular polarisations (RCP/LCP), respectively. The convention of the sign was <math display="inline"><semantics> <mrow> <mo>−</mo> <mi>π</mi> <mo>/</mo> <mn>4</mn> </mrow> </semantics></math> for the anti-clockwise rotation of the linear polariser at the IN-port (see inset in (<b>b</b>)).</p>
Full article ">Figure 7
<p>High-temperature annealing (HTA) of olivine xenolith. Optical images at increasing magnification (left to right) of a sample annealed at 1500 <math display="inline"><semantics> <mo>°</mo> </semantics></math>C for 2 h in O<sub>2</sub> flow. The left inset shows typical olivine macro-grains before annealing. The right inset shows a photo of samples after HTA at 1500 <math display="inline"><semantics> <mo>°</mo> </semantics></math>C for 2 h in O<sub>2</sub> and N<sub>2</sub> flow.</p>
Full article ">Figure 8
<p>High-temperature-annealed olivine (magnetic). Reflectance spectra were fit with the three points that were most intense in the four-polarisation camera; reflection from the macro-particle (∼1 mm in size; top row) with linearly polarised illumination (<math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math> at <math display="inline"><semantics> <msup> <mn>0</mn> <mo>°</mo> </msup> </semantics></math>). Smaller grains of high-temperature-annealed olivine: linear and circular polarised illumination (<math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>/</mo> <mn>4</mn> </mrow> </semantics></math> at 0 (lin.) and <math display="inline"><semantics> <mrow> <mo>±</mo> <msup> <mn>45</mn> <mo>°</mo> </msup> </mrow> </semantics></math> (circ.)); the left inset shows schematics of the reflection experiment. HTA took place at 1500 <math display="inline"><semantics> <mo>°</mo> </semantics></math>C for 2 h in O<sub>2</sub>. The grain was fixed to a washer magnet and brought into reflection mode (top row). The three-point-fit method was used for the reflectance <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mi>A</mi> <mi>m</mi> <mi>p</mi> <mo>×</mo> <mo form="prefix">cos</mo> <mo>(</mo> <mn>2</mn> <mi>θ</mi> <mo>−</mo> <mn>2</mn> <msub> <mi>θ</mi> <mrow> <mi>s</mi> <mi>h</mi> <mi>i</mi> <mi>f</mi> <mi>t</mi> </mrow> </msub> <mo>)</mo> <mo>+</mo> <mi>O</mi> <mi>f</mi> <mi>f</mi> <mi>s</mi> <mi>e</mi> <mi>t</mi> </mrow> </semantics></math>; the background was measured from a Au mirror with the sample moved out of the beam. Standard deviation maps (not shown) indicated <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>&lt;</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math> for all measurements.</p>
Full article ">
18 pages, 7029 KiB  
Article
Creep Monitoring of Submersible Observation Windows Using Mueller Matrix Imaging
by Haibo Tu, Xingying Bu, Ran Liao, Hailong Zhang, Guoliang Ma, Hening Li, Jiachen Wan and Hui Ma
Materials 2023, 16(13), 4733; https://doi.org/10.3390/ma16134733 - 30 Jun 2023
Viewed by 1108
Abstract
Safety of the observation window is one of the core concerns for manned submersibles. When subjected to underwater static pressure, extrusion and creep deformation always occur in the observation window, which can pose a threat to both safety and optical performance. To assess [...] Read more.
Safety of the observation window is one of the core concerns for manned submersibles. When subjected to underwater static pressure, extrusion and creep deformation always occur in the observation window, which can pose a threat to both safety and optical performance. To assess the deformation, real-time and non-contact monitoring methods are necessary. In this study, a conceptual setup based on the waveplate rotation and dual-DoFP (division of focal-plane polarimeter) polarization camera is built for the observation window’s creep monitoring by measuring the Mueller matrix images of the samples under different pressures and durations. Then, a series of characteristic parameters, such as t1, R, r, R′, are extracted from the Muller matrix images by Mueller matrix transformation (MMT), Mueller matrix polar decomposition (MMPD), correlation analysis and phase unwrapping method. The results demonstrate that these parameters can effectively describe the observation window’s creep at different pressure levels which are simulated by finite element analysis. Additionally, more characterization parameters, such as ψ, A and D, are given from the Mueller matrix images and discussed to illustrate the method’s potential for further applications and investigations. Ultimately, future devices based on this method could serve as a valuable tool for real-time and non-contact creep monitoring of the submersible observation windows. Full article
(This article belongs to the Section Optical and Photonic Materials)
Show Figures

Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>(<b>a</b>) Dimensional drawing and (<b>b</b>) physical drawing of the sample. (unit: mm).</p>
Full article ">Figure 2
<p>Experimental setup.</p>
Full article ">Figure 3
<p>Parameters <span class="html-italic">t</span><sub>1</sub> (<b>a</b>) unpressurized and (<b>b</b>) at different pressures and times.</p>
Full article ">Figure 4
<p><span class="html-italic">R</span> (<b>a</b>) unpressurized and (<b>b</b>) at different pressures and times.</p>
Full article ">Figure 5
<p>(<b>a</b>) <span class="html-italic">R</span> image and (<b>b</b>) <span class="html-italic">R</span>′ image at 150 MPa. (<b>c</b>) Maximum phase difference for <span class="html-italic">R</span>′ images versus creep time and (<b>d</b>) standard deviation for <span class="html-italic">R</span>′ images versus creep time at pressures of 60 MPa, 90 MPa, 120 MPa and 150 MPa.</p>
Full article ">Figure 6
<p>(<b>a</b>) Radius versus creep time and (<b>b</b>) correlation coefficient versus creep time at 60 MPa, 90 MPa, 120 MPa and 150 MPa.</p>
Full article ">Figure 7
<p>(<b>a</b>) Geometry of observation window (unit: mm), (<b>b</b>) 3D layout of the observation window and window seat, (<b>c</b>) 2D layout of observation window and window seat (unit: mm), (<b>d</b>) mesh generation and (<b>e</b>) static structure of the model. (unit: μm).</p>
Full article ">Figure 8
<p>Finite element analysis results of observation window under 120 MPa pressure: (<b>a</b>) Von-Mises stress nephogram with <span class="html-italic">t</span> = 360 min, (<b>b</b>) strain nephogram with <span class="html-italic">t</span> = 0 s, (<b>c</b>) strain nephogram with <span class="html-italic">t</span> = 360 min, (<b>d</b>) equivalent creep strain nephogram with <span class="html-italic">t</span> = 1 min, (<b>e</b>) equivalent creep strain nephogram with <span class="html-italic">t</span> = 360 min.</p>
Full article ">Figure 9
<p>Total deformation distribution versus creep time for the latter face with different pressures: (<b>a</b>) 60 MPa, (<b>b</b>) 90 MPa, (<b>c</b>) 120 MPa, (<b>d</b>) 150 MPa.</p>
Full article ">Figure 10
<p>Equivalent creep strain for different pressures versus creep time.</p>
Full article ">Figure 11
<p>(<b>a</b>) <span class="html-italic">ψ</span> images and (<b>b</b>) their mean values versus creep time. (<b>c</b>) <span class="html-italic">A</span> images and (<b>d</b>) their mean values versus creep time. (<b>e</b>) <span class="html-italic">D</span> images and (<b>f</b>) their standard deviation versus creep time.</p>
Full article ">
8 pages, 1780 KiB  
Article
Design of Waveguide Polarization Convertor Based on Asymmetric 1D Photonic Crystals
by Fu-Li Hsiao, Chia-Ying Ni, Ying-Pin Tsai, Ting-Wei Chiang, Yen-Tung Yang, Cheng-Jui Fan, Hsuan-Ming Chang, Chien-Chung Chen, Hsin-Feng Lee, Bor-Shyh Lin, Kai-Chun Chan and Chii-Chang Chen
Nanomaterials 2022, 12(14), 2454; https://doi.org/10.3390/nano12142454 - 18 Jul 2022
Cited by 4 | Viewed by 2286
Abstract
Photonic crystals possess metastructures with a unique dispersion relation. An integrated optical circuit plays a crucial role in quantum computing, for which miniaturized optical components can be designed according to the characteristics of photonic crystals. Because the stable light transmission mode for a [...] Read more.
Photonic crystals possess metastructures with a unique dispersion relation. An integrated optical circuit plays a crucial role in quantum computing, for which miniaturized optical components can be designed according to the characteristics of photonic crystals. Because the stable light transmission mode for a square waveguide is transverse electric or transverse magnetic polarization, we designed a half-waveplate element with a photonic crystal that can rotate the polarization direction of the light incident on a waveguide by 90°. Using the dispersion relation of photonic crystals, the polarization rotation length and the optical axis’s angle of deviation from the electric field in the eigenmode can be effectively calculated. Polarization rotators designed on the basis of photonic crystal structures can effectively reduce the insertion loss of components and exhibit favorable polarization rotation performance. Full article
(This article belongs to the Special Issue Nanophotonics and Integrated Optics Devices)
Show Figures

Figure 1

Figure 1
<p>Schematics of the (<b>a</b>) full structure and (<b>b</b>) unit cell of the photonic crystal waveplate.</p>
Full article ">Figure 2
<p>(<b>a</b>) Band structure diagram (the insets display the electric field distributions of the first and second modes), (<b>b</b>) distribution and intensity maps of the y-component electric field, and (<b>c</b>) distribution and intensity maps of the z-component electric field of the structure with <span class="html-italic">DC</span> = 0.5, <span class="html-italic">DP</span> = 0.5, and <span class="html-italic">DW</span> = 0.5.</p>
Full article ">Figure 3
<p>(<b>a</b>) Contour map of the optical axis deviation angle when DC = 0.5, (<b>b</b>) polarization rotation length, and (<b>c</b>) <span class="html-italic">IL</span> when <span class="html-italic">θ</span> = 45°.</p>
Full article ">Figure 4
<p>Product of the polarization rotation length and <span class="html-italic">IL</span> when <span class="html-italic">θ</span> = 45° (the inset depicts the electric field distribution at the minimum value of this product).</p>
Full article ">
15 pages, 6566 KiB  
Article
Arbitrary Phase Modulation of General Transmittance Function of First-Order Optical Comb Filter with Ordered Sets of Quarter- and Half-Wave Plates
by Jaehoon Jung and Yong Wook Lee
Appl. Sci. 2020, 10(16), 5434; https://doi.org/10.3390/app10165434 - 6 Aug 2020
Cited by 2 | Viewed by 2031
Abstract
Here we theoretically and experimentally demonstrated the arbitrary phase modulation of a general transmittance function (GTF) of the first-order optical comb filter based on a polarization-diversity loop structure, which employed two ordered waveplate sets (OWS’s) of a quarter-wave plate (QWP) and a half-wave [...] Read more.
Here we theoretically and experimentally demonstrated the arbitrary phase modulation of a general transmittance function (GTF) of the first-order optical comb filter based on a polarization-diversity loop structure, which employed two ordered waveplate sets (OWS’s) of a quarter-wave plate (QWP) and a half-wave plate (HWP). The proposed comb filter is composed of a polarization beam splitter (PBS), two equal-length polarization-maintaining fiber (PMF) segments, and two OWS’s of a QWP and an HWP with each set located before each PMF segment. The second PMF segment is butt-coupled to one port of the PBS so that its principal axis should be 22.5° away from the horizontal axis of the PBS. First, we explained a scheme to find four waveplate orientation angles (WOA’s) allowing the phase of a GTF to be arbitrarily modulated, using the way each component of the filter, such as a waveplate or PMF segment, affects its input or output polarization. Then, with the WOA finding method, we derived WOA sets of the four waveplates, which could give arbitrary phase retardations ϕ’s from 0° to 360° to a GTF chosen here arbitrarily. Finally, we showed phase-modulated GTF’s calculated at eight selected WOA sets allowing ϕ’s to be 0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°, and then the predicted results were verified by experimentally measured results. It is concluded from the theoretical and experimental demonstrations that the GTF of our filter based on the OWS of a QWP and an HWP can be arbitrarily phase-modulated by properly controlling the WOA’s of the four waveplates. Full article
(This article belongs to the Section Nanotechnology and Applied Nanosciences)
Show Figures

Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>(<b>a</b>) Schematic diagram of the PDLS-based first-order fiber comb filter and (<b>b</b>) propagation path of light travelling through the filter.</p>
Full article ">Figure 2
<p>(<b>a</b>) Poincare sphere representation of the spectral evolution of SOP<sub>in</sub> of PMF 2 at Set I<sub>n</sub> (<span class="html-italic">ϕ</span> = 0°), which is denoted by <span class="html-italic">SE<sub>in</sub></span> (indicated by pink circles) and (<b>b</b>) Poincare sphere representation of the spectral evolution of SOP<sub>out</sub> of PMF 2, which is denoted by <span class="html-italic">SE<sub>out</sub></span> (indicated by pink circles), and two <span class="html-italic">O</span>(<span class="html-italic">λ</span><sub>0</sub>) positions at two chosen WOA sets (Sets I<sub>n</sub> and II<sub>n</sub>). All the SOP traces are obtained in the CW path of <a href="#applsci-10-05434-f001" class="html-fig">Figure 1</a>b over a wavelength range from <span class="html-italic">λ</span><sub>0</sub> to <span class="html-italic">λ</span><sub>0</sub> + ∆<span class="html-italic">λ</span>.</p>
Full article ">Figure 3
<p>Wavelength-dependent variation of SOP’s in <span class="html-italic">t<sub>GTF</sub></span><sub>1</sub> obtained at Set I<sub>GTF1</sub>: (<b>a</b>) SOP<sub>out</sub> and (<b>b</b>) SOP<sub>in</sub> traces of PMF 2 at Set I<sub>GTF1</sub>. Spectral evolution of SOP’s in the phase-modulated version of <span class="html-italic">t<sub>GTF</sub></span><sub>1</sub>, obtained at Set II<sub>GTF1</sub>: (<b>c</b>) SOP<sub>in</sub> trace of PMF 2, (<b>d</b>) SOP<sub>out</sub> trace of QWP 2, (<b>e</b>) SOP<sub>out</sub> trace of PMF 1, (<b>f</b>) SOP<sub>out</sub> of HWP 1, and (<b>g</b>) SOP<sub>out</sub> trace of PMF 2. (<b>h</b>) Two calculated transmission spectra obtained at Sets I<sub>GTF1</sub> and II<sub>GTF1</sub>, indicated as blue and red solid lines, respectively.</p>
Full article ">Figure 4
<p>(<b>a</b>) Four WOA’s <span class="html-italic">θ<sub>Q</sub></span><sub>1</sub> (blue circles), <span class="html-italic">θ<sub>H</sub></span><sub>1</sub> (green squares), <span class="html-italic">θ<sub>Q</sub></span><sub>2</sub> (red diamonds), and <span class="html-italic">θ<sub>H</sub></span><sub>2</sub> (violet triangles) as a function of extra phase difference <span class="html-italic">ϕ</span> (from 0° to 360° with a step of 1°) for phase modulation of another GTF (<span class="html-italic">t<sub>GTF</sub></span><sub>2</sub>) at <span class="html-italic">θ<sub>P</sub></span><sub>1</sub> = 0° and <span class="html-italic">θ<sub>P</sub></span><sub>2</sub> = 22.5°. (<b>b</b>) Loci of (<span class="html-italic">θ<sub>H</sub></span><sub>2</sub>, <span class="html-italic">θ<sub>H</sub></span><sub>1</sub>) and (<span class="html-italic">θ<sub>H</sub></span><sub>2</sub>, <span class="html-italic">θ<sub>Q</sub></span><sub>1</sub>), displayed by blueish squares and reddish circles, respectively. (<b>c</b>) Loci of (<span class="html-italic">θ<sub>Q</sub></span><sub>1</sub>, <span class="html-italic">θ<sub>H</sub></span><sub>1</sub>) and (<span class="html-italic">θ<sub>Q</sub></span><sub>1</sub>, <span class="html-italic">θ <sub>Q</sub></span><sub>2</sub>), indicated as blueish squares (<span class="html-italic">ϕ</span>: 0°–180°) and reddish circles (<span class="html-italic">ϕ</span>: 0°–360°), respectively. (<b>d</b>) Loci of (<span class="html-italic">θ<sub>Q</sub></span><sub>2</sub>, <span class="html-italic">θ<sub>H</sub></span><sub>1</sub>) and (<span class="html-italic">θ<sub>Q</sub></span><sub>2</sub>, <span class="html-italic">θ<sub>H</sub></span><sub>2</sub>), displayed by blueish squares and reddish circles, respectively.</p>
Full article ">Figure 5
<p>Calculated phase-modulated transmission spectra of GTF (<span class="html-italic">t<sub>GTF</sub></span><sub>2</sub>), obtained at eight WOA sets (Sets I<sub>GTF2</sub>–VIII<sub>GTF2</sub>) where <span class="html-italic">ϕ</span> of <span class="html-italic">t<sub>GTF</sub></span><sub>2</sub> is chosen as 0° to 315° with an increment of 45°.</p>
Full article ">Figure 6
<p>Actual experimental setup for measurement of phase-modulated transmission spectra of GTF (<span class="html-italic">t<sub>GTF</sub></span><sub>2</sub>).</p>
Full article ">Figure 7
<p>Experimental phase-modulated transmission spectra of GTF (<span class="html-italic">t<sub>GTF</sub></span><sub>2</sub>), measured at eight WOA sets (Sets I<sub>GTF2</sub>–VIII<sub>GTF2</sub>).</p>
Full article ">
11 pages, 5948 KiB  
Article
An Orthogonal Type Two-Axis Lloyd’s Mirror for Holographic Fabrication of Two-Dimensional Planar Scale Gratings with Large Area
by Xinghui Li, Haiou Lu, Qian Zhou, Guanhao Wu, Kai Ni and Xiaohao Wang
Appl. Sci. 2018, 8(11), 2283; https://doi.org/10.3390/app8112283 - 19 Nov 2018
Cited by 26 | Viewed by 4232
Abstract
In this paper, an orthogonal type two-axis Lloyd’s mirror interference lithography technique was employed to fabricate two-dimensional planar scale gratings for surface encoder application. The two-axis Lloyd’s mirror interferometer is composed of a substrate and two reflective mirrors (X- and Y-mirrors), which are [...] Read more.
In this paper, an orthogonal type two-axis Lloyd’s mirror interference lithography technique was employed to fabricate two-dimensional planar scale gratings for surface encoder application. The two-axis Lloyd’s mirror interferometer is composed of a substrate and two reflective mirrors (X- and Y-mirrors), which are placed edge by edge perpendicularly. An expanded and collimated beam was divided into three beams by this interferometer, a direct beam and two reflected beams, projected onto the substrate, X- and Y-mirrors, respectively. The unexpected beam sections having twice reflected off the mirrors were blocked by a filter. The remaining two reflected beams interfered with the direct beam on the substrate, generating perpendicularly cross patterns thus forming two-dimensional scale gratings. However, the two reflected beams undesirably interfere with each other and generate a grating pattern along 45-degree direction against the two orthogonal direction, which influence the pattern uniformity. Though an undesired grating pattern can be eliminated by polarization modulation with introduction of waveplates, spatial configuration of waveplates inevitably downsized the eventual grating, which is a key parameter for grating interferometry application. For solving this problem, theoretical and experimental study was carefully carried out to evaluate the fabrication quality with and without polarization modulation. Two-dimensional scale gratings with a 1 μm period in X- and Y-directions were achieved by using the constructed experiment system with a 442 nm He-Cd laser source. Atomic force microscopy (AFM) images and the result of diffraction performances demonstrated that the orthogonal type two-axis Lloyd’s mirror interferometer can stand a small order undesired interference, that is, a degree of orthogonality between two reflected beams, denoted by γ, no larger than a nominal value of 0.1. Full article
(This article belongs to the Special Issue Precision Dimensional Measurements)
Show Figures

Figure 1

Figure 1
<p>The optical configuration of the orthogonal type two-axis Lloyd’s mirror interferometer-based laser interference lithography (LIL) system.</p>
Full article ">Figure 2
<p>The global coordinate system of exposure system. (<b>a</b>) Two-axis Lloyd’s mirror unit and definition of incident angle <span class="html-italic">θ</span> and azimuth angle <span class="html-italic">ϕ</span>. (<b>b</b>) Photograph of half-wavelength plates (HWPs) setup.</p>
Full article ">Figure 3
<p>Optical configurations of orthogonal two-axis Lloyd’s mirror interferometer. (<b>a</b>) The sections of collimated beam (from the direction of the incident beam). (<b>b</b>) Improved physical filter.</p>
Full article ">Figure 4
<p>Interference fringe patterns generated by two of beam 1, 2, and 3. (<b>a</b>) beams 1 and 2; (<b>b</b>) beams 1 and 3; and (<b>c</b>) beams 2 and 3.</p>
Full article ">Figure 5
<p>Photographs of the fabricated 2D gratings under the initial polarization status of (<b>a</b>) (s, s, s) under conditions of exposure time 30 s, development time 8 s and (<b>b</b>) (s, −33.5°, 33.5°) under exposure time 30 s, development time 8 s.</p>
Full article ">Figure 6
<p>Atomic force microscopy (AFM) images and grating shape details of the fabricated 2D gratings under the initial polarization status of (<b>a</b>) (s, s, s) and (<b>b</b>) modulated polarization status (s, −33.5°, 33.5°).</p>
Full article ">Figure 7
<p>Diffraction efficiency testing setup (<b>a</b>) and measurement points on the grating surface (<b>b</b>).</p>
Full article ">Figure 8
<p>AFM images of fabricated grating without polarization under different incident angle <span class="html-italic">θ</span> shown in <a href="#applsci-08-02283-f002" class="html-fig">Figure 2</a>: (<b>a</b>) 60° and (<b>b</b>) 85°.</p>
Full article ">
9094 KiB  
Article
Interferometric Sensor of Wavelength Detuning Using a Liquid Crystalline Polymer Waveplate
by Paweł Wierzba
Sensors 2016, 16(5), 633; https://doi.org/10.3390/s16050633 - 9 May 2016
Cited by 3 | Viewed by 4542
Abstract
Operation of a polarization interferometer for measurement of the wavelength changes of a tunable semiconductor laser was investigated. A λ/8 waveplate made from liquid crystalline polymer is placed in one of interferometers’ arms in order to generate two output signals in quadrature. [...] Read more.
Operation of a polarization interferometer for measurement of the wavelength changes of a tunable semiconductor laser was investigated. A λ/8 waveplate made from liquid crystalline polymer is placed in one of interferometers’ arms in order to generate two output signals in quadrature. Wavelength was measured with resolution of 2 pm in the wavelength range 628–635 nm. Drift of the interferometer, measured in the period of 500 s, was 8 nm, which corresponded to the change in the wavelength of 1.3 pm. If needed, wavelength-dependent Heydemann correction can be used to expand the range of operation of such interferometer. Full article
(This article belongs to the Special Issue Infrared and THz Sensing and Imaging)
Show Figures

Figure 1

Figure 1
<p>Polarization interferometer for measurement of change in the wavelength of a tunable semiconductor laser. D1, D2—photodiodes, M1, M2—mirrors, <span class="html-italic">U</span><sub>x</sub>, <span class="html-italic">U</span><sub>y</sub>—output voltages.</p>
Full article ">Figure 2
<p>Manufacturing process flow of the LCP waveplate.</p>
Full article ">Figure 3
<p>Detection electronics (one channel of two). D—photodiode. Further explanations in the text.</p>
Full article ">Figure 4
<p>Polarization interferometer during the alignment procedure. M1, M2—mirrors; BS—beamsplitter; WP—Wollaston prism; D1, D2—photodiodes.</p>
Full article ">Figure 5
<p>Drift of the optical power emitted by the tunable laser.</p>
Full article ">Figure 6
<p>Drift of the interferometer. Upper trace—drift before applying the Heydemann correction, lower trace—drift after applying the Heydemann correction.</p>
Full article ">Figure 7
<p>Output signals <span class="html-italic">U</span><sub>x</sub> and <span class="html-italic">U</span><sub>y</sub> from the interferometer after removal of the constant components and application of the Heydemann correction.</p>
Full article ">
Back to TopTop