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Journal articles on the topic 'Numerical aperture'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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1

Moheb, H., J. Shaker, and L. Shafai. "Numerical and experimental investigation of cavity-backed arbitrary slot antennas." Canadian Journal of Physics 74, no. 3-4 (March 1, 1996): 122–31. http://dx.doi.org/10.1139/p96-019.

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The equivalence principle and the generalized network formulation are used to model the tangential electric field on arbitrary apertures, backed by a rectangular wave guide or cavity, in terms of equivalent magnetic currents. The coupling is through the aperture whose characteristics are expressed by the aperture admittance matrices of the cavity and half-space regions. The aperture coupling is then expressed as the sum of the two independent aperture admittances, with source terms related to the incident field. The result is an integral equation for the unknown aperture current. This integral equation is then reduced to a matrix equation using the method of moments. The formulation is then used to, investigate the electrical characteristics, i.e., aperture field distribution, aperture admittance, and radiation patterns of low-gain antennas such as H, cross, end-loaded, and centre-loaded slots backed by a cavity. Experimental results are also provided to verify the numerical results.

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2

Qin, Zipeng, Gang Li, Yan Tian, Yuwei Ma, and Pengfei Shen. "Numerical Simulation of Thermal Conductivity of Foam Glass Based on the Steady-State Method." Materials 12, no. 1 (December 24, 2018): 54. http://dx.doi.org/10.3390/ma12010054.

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The effects of fly ash, sodium carbonate content, foaming temperature and foaming time on foam glass aperture sizes and their distribution were analyzed by the orthogonal experimental design. Results from the steady-state method showed a normal distribution of the number of apertures with change in average aperture, which ranges from 0.1 to 2.0 mm for more than 93% of apertures. For a given porosity, the thermal conductivity decreases with the increase of the aperture size. The apertures in the sample have obvious effects in blocking the heat flow transmission: heat flow is quickly diverted to both sides when encountered with the aperture. When the thickness of the sample is constant, the thermal resistance of the foam glass sample increases with increasing porosity, leading to better thermal insulation. Furthermore, our results suggest that the more evenly distributed and orderly arranged the apertures are in the foam glass material, the larger the thermal resistance of the material and hence, the better the thermal insulation.

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3

Tandler, H., L. Schreiber, U. Simon, and H. E. Keller. "Resolution in Light Microscopy." Microscopy and Microanalysis 3, S2 (August 1997): 1175–76. http://dx.doi.org/10.1017/s1431927600012769.

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The resolution in conventional light microscopy was defined by Abbe as: Wavelength (λ) and Numerical Aperture (NA) have a direct influence while the factor (c) is dependent upon the geometry of the illumination and observation beam paths. Some typical examples are:High illumination apertures in darkfield or oblique illumination or specific ratios between illumination and observation aperture can substantially improve resolution. Various shapes of the illumination aperture, annular, point, centered or off axis at different azimuths directly influence numerical aperture and coherence and with this resolution, contrast and depth.In mirror objectives low apertures become vignetted, the resolution is enhanced at the expense of contrast. In studies of Hopkins and Barham the factor “c” can range from 0.5 to 0.8. For the practically attainable condition, where illumination and observation aperture are identical, “c” becomes 0.61 and we have partial coherence.Exceeding the observation aperture on the illumination side reduces “c” further but diffraction significantly reduces contrast.

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4

Liu, Richeng, Yujing Jiang, Hongwen Jing, and Liyuan Yu. "Nonlinear Flow Characteristics of a System of Two Intersecting Fractures with Different Apertures." Processes 6, no. 7 (July 20, 2018): 94. http://dx.doi.org/10.3390/pr6070094.

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The nonlinear flow regimes of a crossed fracture model consisting of two fractures have been investigated, in which the influences of hydraulic gradient, surface roughness, intersecting angle, and scale effect have been taken into account. However, in these attempts, the aperture of the two crossed fractures is the same and effects of aperture ratio have not been considered. This study aims to extend their works, characterizing nonlinear flow through a system of two intersecting fractures with different apertures. First, three experiment models with two fractures having different apertures were established and flow tests were carried out. Then, numerical simulations by solving the Navier-Stokes equations were performed and the results compared with the experiment results. Finally, the effects of fracture aperture on the critical pressure difference and the ratio of hydraulic aperture to mechanical aperture were systematically analyzed. The results show that the numerical simulation results agree well with those of the fluid flow tests, which indicates that the visualization techniques and the numerical simulation code are reliable. With the increment of flow rate, the pressure difference increases first linearly and then nonlinearly, which can be best fitted using Forchheimer’s law. The two coefficients in Forchheimer’s law decrease with the increasing number of outlets. When increasing fracture aperture from 3 mm to 5 mm, the critical pressure difference increases significantly. However, when continuously increasing fracture aperture from 5 mm to 7 mm, the critical pressure difference changes are negligibly small. The ratio of hydraulic aperture to mechanical aperture decreases more significantly for a fracture that has a larger aperture. Increasing fracture aperture from 5 mm to 7 mm, that has a negligibly small effect on the critical pressure difference will however significantly influence the ratio of hydraulic aperture to mechanical aperture.

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5

Normatov, Alexander, Boris Spektor, and Joseph Shamir. "Analysis of Phase Distribution of Focused Light in High Numerical Aperture Systems." Key Engineering Materials 437 (May 2010): 616–20. http://dx.doi.org/10.4028/www.scientific.net/kem.437.616.

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High numerical aperture focusing is becoming increasingly important for nanotechnology related applications. Rigorous, vector evaluation of the focused field, in such cases, is usually performed using the Richards-Wolf method which is based on the Debye approach. The resulting field is known to have a piecewise quasi planar phase. A corresponding result, produced by a Fresnel-Kirchhoff integral for aplanatic optical systems of medium and low numerical apertures, leads to the well known physical fact that a quadratic phase exists when the entrance pupil is not located at the front focal plane. Yet, the amplitudes produced in both ways are in a good agreement. In this work we investigated the difference, presented above, in a 2D system with the help of the Stratton-Chu diffraction integral. The amplitude obtained by the Stratton-Chu integral was quite similar to the classic results while the phase exhibited a quadratic behavior, with the quadratic coefficient depending on the numerical aperture of the optical system. For lower numerical apertures it approached the result obtained by the Fresnel-Kirchhoff integral while for higher numerical apertures it was approaching the Richards-Wolf result. A mathematical expression for the quadratic coefficient was derived and verified for various values of numerical aperture.

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6

Benı́tez, Pablo, and Juan C. Miñano. "Ultrahigh-numerical-aperture imaging concentrator." Journal of the Optical Society of America A 14, no. 8 (August 1, 1997): 1988. http://dx.doi.org/10.1364/josaa.14.001988.

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7

Singh, R. N., A. E. Rosenbluth, G. L. T. Chiu, and J. S. Wilczynski. "High-numerical-aperture optical designs." IBM Journal of Research and Development 41, no. 1.2 (January 1997): 39–48. http://dx.doi.org/10.1147/rd.411.0039.

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8

Liu, Yong-Qiang, Jinhai Sun, Yongxing Che, Kainan Qi, Liangsheng Li, and Hongcheng Yin. "High numerical aperture microwave metalens." Optics Letters 45, no. 22 (November 12, 2020): 6262. http://dx.doi.org/10.1364/ol.412040.

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9

Gallatin, Gregg M. "High-numerical-aperture scalar imaging." Applied Optics 40, no. 28 (October 1, 2001): 4958. http://dx.doi.org/10.1364/ao.40.004958.

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10

Wadsworth, W. J., R. M. Percival, G. Bouwmans, J. C. Knight, T. A. Birks, T. D. Hedley, and P. St. J. Russell. "Very High Numerical Aperture Fibers." IEEE Photonics Technology Letters 16, no. 3 (March 2004): 843–45. http://dx.doi.org/10.1109/lpt.2004.823689.

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11

Kotlyar, V. V., A. G. Nalimov, S. S. Stafeev, Changyu Hu, L. O’Faolain, M. V. Kotlyar, D. Gibson, and S. Song. "Thin high numerical aperture metalens." Optics Express 25, no. 7 (March 30, 2017): 8158. http://dx.doi.org/10.1364/oe.25.008158.

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12

Zhao, Jicong, Mingmin Ge, Shitao Lv, Haiyan Sun, and Chenguang Song. "Numerical Investigation of an AlN-Based Resonant Detector with a Plasmon Aperture Absorber for Dual-Band IR Sensing." Electronics 9, no. 8 (August 6, 2020): 1264. http://dx.doi.org/10.3390/electronics9081264.

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An aluminum nitride (AlN) piezoelectric resonant infrared (IR) detector based on a Lame-wave resonator (LWR) and plasmon apertures was designed for dual-band sensing, and was investigated by using the finite element method (FEM) and finite difference time domain (FDTD) simulations. A plasmon structure with the apertures was designed on the surface of the detector in order to maintain electrical performance and to obtain ultrahigh dual-band IR absorption. The electrical performance of the LWR with the plasmon apertures was comparable to that of the LWR with floating electrodes, which was found to be superior to that of the LWRs with plasmon particles or open electrodes. Both of the rectangle aperture and cross-shaped aperture absorbers can achieve ultrahigh dual-band absorptions of up to 97%, and the cross-shaped aperture absorber is insensitive to the polarization angle. Moreover, a detailed optimization analysis for the thermal properties of the detector was conducted to obtain favorable responsivity and response speed. The calculated results demonstrate that the proposed resonant detector has great potential applications in IR detection.

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13

Grebenyuk, A. A., and V. P. Ryabukho. "Numerically focused optical coherence microscopy with structured illumination aperture." Computer Optics 42, no. 2 (July 24, 2018): 248–53. http://dx.doi.org/10.18287/2412-6179-2018-42-2-248-253.

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Abstract In optical coherence microscopy (OCM) with a given numerical aperture (NA) of the objectives the transverse resolution can be increased by increasing the numerical aperture of illumination (NAi). However, this may also lead to attenuation of the signal with defocus preventing the effective numerically focused 3D imaging of the required sample volume. This paper presents an approach to structuring the illumination aperture, which allows combining the advantages of increased transverse resolution (peculiar to high NAi) with small attenuation of the signal with defocus (peculiar to low NAi) for high-resolution numerically focused 3D imaging in OCM.

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14

Sarwar, Jawad, Arun Srinivasa, and Konstantinos Kakosimos. "Numerical investigations of the aperture size effect for maintaining a constant temperature in a novel sulfur-ammonia water splitting cycle application." Thermal Science 21, no. 2 (2017): 953–62. http://dx.doi.org/10.2298/tsci141220075s.

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Solar-driven thermochemical water splitting cycle is a promising, energy efficient and environmentally friendly approach to produce hydrogen. In this paper, numerical work has been undertaken using a cylindrical solar receiver to investigate fixed and variable aperture sizes to maintain constant steady-state temperature over a day for thermochemical part of a novel hybrid photo-thermochemical sulfur-ammonia cycle. A previously developed and validated optical model in commercial software, TracePro? is used to simulate the light sources of 10, 15, and 28 kW. The sunlight intensity variations for the designated reference day for this study is selected as July 1, 2011, at 39.74 N, 105.18 W and at an elevation of 1829 m. A developed and validated finite volume based coupled Monte Carlo, Heat Transfer model is used to calculate the steady-state temperatures in the receiver by utilizing the output of the optical model. The simulations are performed at different aperture diameters from 2 to 14 cm to quantify the effect of fixed aperture size on the steady-state temperatures of the receiver. Furthermore, simulations to maintain steady-state temperatures of 673, 823, and 1123 K for different sub-cycles of the selected cycle via variable aperture has been performed and compared with selected fixed apertures. It is found that the variable apertures can maintain desired constant temperatures over the day for each thermochemical sub-cycle. The comparison of overall power consumption and savings for fixed and variable apertures has also been investigated and reported.

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15

Li, Ying, Jianshu Luo, Guyan Ni, and Jiyuan Shi. "Electromagnetic Topology Analysis to Coupling Wires Enclosed in Cavities with Apertures." Mathematical Problems in Engineering 2010 (2010): 1–11. http://dx.doi.org/10.1155/2010/209591.

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We use both electromagnetic topology (EMT) and the Baum-Liu-Tesche (BLT) equation to analyze a cavity model with an aperture. More precisely, we combine the aperture coupling theory and EMT to study the issues of the electromagnetic field penetration through apertures into a cavity and the coupling to a two-wire transmission line in it. We employ the equivalence principle to establish the equivalent source on the aperture. Then, we obtain the semi analytic solutions of the load response of the two-wire line in the cavity based on the Baum-Liu-Tesche (BLT) equation. In addition, based on the Agrawal model, we give the coupling current distribution at two loads for a two-wire line in the cavity. Finally, we present some numerical results to demonstrate the semi-analytic approach of this paper. In fact, these numerical results on the electric field shielding (EFS) of a rectangular cavity with an aperture agree well with the experimental results in the literature. Furthermore, for a two-wire line in the cavity with an aperture the induced current peaks at loads are observed in the frequency range, some of which are associated with the resonance of the aperture, and others correspond to the resonant frequencies of the cavity.

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16

Wang, Yuan, Chenglong Wu, and Yuntian Zhou. "Effect Study of Aperture Distribution on the Capillary Pressure-Saturation Relation for the Single Fracture." Geofluids 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/9656393.

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A systematic numerical method was presented to investigate the effect of aperture distribution on the relation of capillary pressure versus fluid saturation (P-S relation) for a single fracture. The fracture was conceptualized as a two-dimensional lattice-grid model and its aperture field was described by a probability distribution. Based on the invasion percolation theory, a program was developed to simulate the quasi-static displacement. The simulation was verified validly by comparisons of the experimental results. The effects of the statistical parameters were further quantified. The results show that the largest local aperture on the fracture boundary determines the AEV. The larger mean decreases the variation coefficient, which causes the more uniform aperture field, smoother air invasion front, and steeper capillary pressure-saturation curve (CPSC). The larger standard deviation increases not only the range but also the contrast degree of the apertures, thus providing a nondeterministic rule in the P-S relation. The larger correlation length causes a more homogeneous aperture field and a dual connectivity of the fracture. The increase of the difference and contrast degree between the small and large apertures results in dual-aperture fields. The dual-aperture field and dual connectivity of the fracture both contribute to the bimodal characteristic of the CPSC.

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17

HUANG, NA, RICHENG LIU, and YUJING JIANG. "EVALUATING THE EFFECT OF APERTURE VARIATION ON THE HYDRAULIC PROPERTIES OF THE THREE-DIMENSIONAL FRACTAL-LIKE TREE NETWORK MODEL." Fractals 28, no. 06 (September 2020): 2050112. http://dx.doi.org/10.1142/s0218348x20501121.

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Hydraulic properties of rock fractures are important issues for many geoengineering practices. Previous studies have revealed that natural rock fractures have variable apertures that could significantly influence the permeability of single rock fractures, yet the effect of aperture variation on the hydraulic properties of fractured rock masses has received little attention. The present study implemented a series of flow calculations on two kinds of 3D fractal-like tree network models constituted by fractures with heterogeneous aperture distributions and parallel plates with uniform apertures to gain insight into the effect of aperture variation on the hydraulic properties of fractured rock masses. The fluid flows through the two kinds of models are simulated using a developed numerical code, whose validity is verified by comparisons with the analytical solutions and previous experimental results. The effects of heterogeneous aperture distributions on the permeability of the models are illustrated by changing the geometrical parameters including the aperture ratio and mean aperture of the initial fracture branch. The results show that a significant channeling flow is observed in the 3D fractal-like tree network models constituted by fractures with heterogeneous aperture distributions. These preferential flow paths are mainly located in the large aperture channels, bypassing the contacts and/or low aperture barriers. The equivalent permeability of the 3D fractal-like tree network models increases with increasing fracture aperture ratio and/or increasing mean aperture of the initial fracture branch. The permeability ratio of the model of fractures with heterogeneous aperture distributions to the model with uniform mean apertures is always smaller than 1.0, and the ratio increases following a logarithmic relationship as the mean aperture of the initial fracture branch increases. A regression function is proposed to estimate the equivalent permeability of the model of fractures with heterogeneous aperture distributions. The deviations between the predicted permeability and the simulated/experimental results are less than half of the order of magnitude, which verifies that the proposed equation is capable of predicting the equivalent permeability of 3D fractal-like tree networks as a first-order estimation.

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18

Kotlyar, V. V., A. G. Nalimov, S. S. Stafeev, L. O'Faolain, and M. V. Kotlyar. "THIN METALENS WITH HIGH NUMERICAL APERTURE." Computer Optics 41, no. 1 (January 1, 2017): 5–12. http://dx.doi.org/10.18287/2412-6179-2017-41-1-5-12.

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19

Flagello, Donis G., and Tom D. Milster. "High-numerical-aperture effects in photoresist." Applied Optics 36, no. 34 (December 1, 1997): 8944. http://dx.doi.org/10.1364/ao.36.008944.

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20

Ying Kiang and T. Klieber. "Macrobending effects on fiber numerical aperture." Journal of Lightwave Technology 5, no. 5 (1987): 709–11. http://dx.doi.org/10.1109/jlt.1987.1075561.

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21

Nölscher, Christoph, Leonhard Mader, Sabine Guttenberger, and Wolfgang Arden. "Search for the optimum numerical aperture." Microelectronic Engineering 11, no. 1-4 (April 1990): 161–66. http://dx.doi.org/10.1016/0167-9317(90)90092-8.

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22

Flagello, D. G., A. E. Rosenbluth, C. Progler, and J. Armitage. "Understanding high numerical aperture optical lithography." Microelectronic Engineering 17, no. 1-4 (March 1992): 105–8. http://dx.doi.org/10.1016/0167-9317(92)90021-i.

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23

Ouyang, Zhiyong, Yasuhiro Okamoto, Yuta Ogino, Tomokazu Sakagawa, and Akira Okada. "Influence of Numerical Aperture on Molten Area Formation in Fusion Micro-Welding of Glass by Picosecond Pulsed Laser." Applied Sciences 9, no. 7 (April 3, 2019): 1412. http://dx.doi.org/10.3390/app9071412.

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Focusing condition such as numerical aperture (N.A.) has a great influence on the creation of molten area and the stable welding process in fusion micro-welding of glass. In this study, a picosecond pulsed laser of 1064 nm in wavelength and 12.5 ps in pulse duration was tightly focused inside a borosilicate glass using objective lenses of numerical apertures 0.45, 0.65, and 0.85 with spherical aberration correction. Influence of numerical aperture on molten area formation was experimentally investigated through analysis of focusing situation in glass, and movement of absorption point, and then molten area characteristics were discussed. It is concluded that N.A. of 0.65 with superior focusing characteristics can form a large and continuous molten area without cracks, which enables achievement of stable joining of glass material by picosecond pulsed laser.

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24

Xia, Gui Shu, and Chao Zhou. "Research of Shielding Effectiveness of Metallic Experiment Box Based on ModalMethod of Moments." Applied Mechanics and Materials 380-384 (August 2013): 4376–82. http://dx.doi.org/10.4028/www.scientific.net/amm.380-384.4376.

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In this paper, electric field shielding effectiveness (SE) of metallic experiment boxwith aperturesilluminated by vertical polarization plane wave has been studied by using modal method of moment technique. Electric field SE has been calculated at three different points on the same plane inside enclosure. The numerical results of the proposed technique are in very good agreement with data available in the literature and experimental results. It is shown that apertures position, aperture number and calculation points have noticeable effect on the electric field SE,four apertures is a better select to improve the shielding ability of an enclosure than one aperture while they have the same area.

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25

Khonina, Svetlana N., and Andrey V. Ustinov. "Thin Light Tube Formation by Tightly Focused Azimuthally Polarized Light Beams." ISRN Optics 2013 (August 19, 2013): 1–6. http://dx.doi.org/10.1155/2013/185495.

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Theoretical and numerical analysis of the transmission function of the focusing system with high numerical aperture was conducted. The purpose of the study was to form a thin light tube in a focal area using the azimuthally polarized radiation. It was analytically shown that, due to destructive interference of two beams formed by two narrow rings, it is possible to overcome not only the full aperture diffraction limit but also the circular aperture limit. In this case, however, the intensity at the center of the focal plane is significantly reduced, which practically leads to the tube rupture. It was numerically shown that long thin one-piece tubes may be formed through the aperture apodization with diffractive axicon phase function or with complex transmission function of Laguerre-Gaussian or Airy-Gaussian beams.

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26

Xiaodong Chen, Xiaodong Chen, Yong Lei Yong Lei, Yi Wang Yi Wang, and Daoyin Yu Daoyin Yu. "Resolution enhancement with improved range Doppler algorithm in high numerical aperture OCT." Chinese Optics Letters 9, no. 12 (2011): 121001–4. http://dx.doi.org/10.3788/col201109.121001.

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27

Gardner, Dennis F., Bosheng Zhang, Matthew D. Seaberg, Leigh S. Martin, Daniel E. Adams, Farhad Salmassi, Eric Gullikson, Henry Kapteyn, and Margaret Murnane. "High numerical aperture reflection mode coherent diffraction microscopy using off-axis apertured illumination." Optics Express 20, no. 17 (August 3, 2012): 19050. http://dx.doi.org/10.1364/oe.20.019050.

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28

Chen Baosuan, 陈宝算, and 蒲继雄 Pu Jixiong. "Focusing Properties of High-Numerical Aperture Focusing." Laser & Optoelectronics Progress 47, no. 10 (2010): 100501. http://dx.doi.org/10.3788/lop47.100501.

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29

Liang, Haowen, Qiaoling Lin, Xiangsheng Xie, Qian Sun, Yin Wang, Lidan Zhou, Lin Liu, et al. "Ultrahigh Numerical Aperture Metalens at Visible Wavelengths." Nano Letters 18, no. 7 (June 25, 2018): 4460–66. http://dx.doi.org/10.1021/acs.nanolett.8b01570.

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30

Khmou, Youssef, Said Safi, and Miloud Frikel. "A Numerical Analysis of Double-Aperture Interferences." International Journal of Advanced Science and Technology 114 (May 31, 2018): 151–60. http://dx.doi.org/10.14257/ijast.2018.114.14.

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31

Choi, Youngwoon, Changhyeong Yoon, Moonseok Kim, Juhee Yang, and Wonshik Choi. "Disorder-mediated enhancement of fiber numerical aperture." Optics Letters 38, no. 13 (June 24, 2013): 2253. http://dx.doi.org/10.1364/ol.38.002253.

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32

Chen Fa-Xin, Zheng Jian, and Yang Jian-Lun. "Numerical simulation of neutron thick aperture imaging." Acta Physica Sinica 55, no. 11 (2006): 5947. http://dx.doi.org/10.7498/aps.55.5947.

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33

Hogan, R. E., R. B. Diver, and Wm B. Stine. "Comparison of a Cavity Solar Receiver Numerical Model and Experimental Data." Journal of Solar Energy Engineering 112, no. 3 (August 1, 1990): 183–90. http://dx.doi.org/10.1115/1.2930478.

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Results from a numerical model of axisymmetric solar cavity receivers are compared with experimental data for tests of a novel test bed receiver in the Sandia National Laboratories solar furnace. The computed energy transfer rates and temperatures are compared with the experimental data for different receiver geometries, aperture sizes, and operating conditions. In general, the agreement between the numerical model and the experimental data is better for the small-to-midsized apertures than for the large apertures. The analysis indicates that for the larger apertures, the convective heat losses are over predicted. It also suggests that these losses could be better characterized. Sensitivity analyses show that both the total solar energy input rate and the convective heat-loss coefficient significantly affect the receiver thermal performance and that the distribution of the input solar flux significantly affects the temperature distribution in the receiver.

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34

Isakov, V. N., and V. S. Lankina. "Modeling of the electromagnetic field of radiating aperture." Russian Technological Journal 9, no. 4 (August 26, 2021): 56–67. http://dx.doi.org/10.32362/2500-316x-2021-9-4-56-67.

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The article is devoted to the issues of numerical calculation of the characteristics of the electromagnetic field of radiating apertures. Тhe radiating aperture is a universal electrodynamic model used in the analysis of a special class of antennas, in particular, mirror and horn antennas, in the study of diffraction phenomena, in the planning of radio wave propagation paths, and when solving problems of wireless transmission of electric energy at a distance. The structure of the electromagnetic field of a radiating aperture in the intermediate and far zones is of the greatest interest according to the needs of practice. However, the theoretical solutions of these problems are usually difficult to obtain, except for some special cases related to the far zone. This leads to the development of appropriate computational models. This paper is aimed at generalization and systematization of experience in developing software for the simulation of electromagnetic field characteristics of radiating apertures in the intermediate and far zones. This paper considers an approach to developing a computational model of a radiating aperture that may be used to calculate the characteristics of electromagnetic field in the intermediate and far zones. Examples of results obtained for circular and ring apertures describing the structure of their electromagnetic field are given. Examples of flight diagrams of a circular aperture are given. The effect of “searchlight” localization of the electromagnetic field in the intermediate zone of a circular emitting aperture is demonstrated. The effect of mutual compensation of neighbouring Fresnel zones using the circular emitting aperture model is demonstrated. A program was developed for calculating the characteristics of the electromagnetic field of radiating holes in the intermediate and far zones. The results can also be used as illustration material for teaching the academic disciplines “Electrodynamics and radio wave propagation” and “Microwave devices and antennas”.

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35

Zhou, Xin, Jianlong Sheng, Ruili Lu, Zuyang Ye, and Wang Luo. "Numerical Simulation of the Nonlinear Flow Properties in Self-Affine Aperture-Based Fractures." Advances in Civil Engineering 2021 (June 5, 2021): 1–11. http://dx.doi.org/10.1155/2021/6687878.

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In order to study the effect of fracture geometry on the nonlinear flow properties in aperture-based fractures, a fractal model based on the self-affinity is proposed to characterize the three-dimensional geometry of rough-walled fractures. By solving the N–S (Navier–Stokes) equation directly, the relationships between the Forchheimer-flow characteristics, fractal dimension, and standard deviation of the aperture have been obtained. The Forchheimer equation is validated to describe the nonlinear relationship between flow rate and pressure gradient. For lower flow rate, the influence of the fractal dimension almost can be ignored, but the linear coefficient increases and the hydraulic aperture decreases with increasing standard deviation of the aperture, respectively. For larger flow rate, the nonlinear coefficient increases with the growth of the standard deviation of the aperture and fractal dimension. Thus, an empirical relationship between the nonlinear coefficient, fractal dimension, and standard deviation of aperture is proposed. In addition, the critical Reynolds number decreases with the increase of the standard deviation of the aperture and the fractal dimension, and the numerical results are generally consistent with the experimental data.

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36

Shanshan Mao, Shanshan Mao, Yanqiu Li Yanqiu Li, Jiahua Jiang Jiahua Jiang, Shihuan Shen Shihuan Shen, Ke Liu Ke Liu, and Meng Zheng Meng Zheng. "Design of a hyper-numerical-aperture deep ultraviolet lithography objective with freeform surfaces." Chinese Optics Letters 16, no. 3 (2018): 030801. http://dx.doi.org/10.3788/col201816.030801.

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37

Gao, Yin Han, Jun Jie Gu, Kai Yu Yang, Ji Zhi Li, and Hang Zhang. "Study on the Aperture Leakage EMI Problems and its Simulation." Applied Mechanics and Materials 239-240 (December 2012): 274–77. http://dx.doi.org/10.4028/www.scientific.net/amm.239-240.274.

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In the design and production process of car’s electronic equipment, the SE of the shield is reduced greatly for the existence of aperture.There is a modeling analysis to the aperture leakage EMI problems and derived a numerical calculation formula of the SE influenced by aperture leakage based on the slot antenna theory, also put forward the way to increase the SE of the shield by using Matlab software to simulate the SE of the shield with three regular apertures in different interference frequency. The simulation results have universal utility and which can provide data support for the design and layout of car’s internal circuits and devices.

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38

Zhou, Chao, and Ling Tong. "Study on the Shielding Effectiveness of a Metallic Rectangular Enclosure with Four Square Apertures having Different Position Arrays." Applied Mechanics and Materials 321-324 (June 2013): 2737–44. http://dx.doi.org/10.4028/www.scientific.net/amm.321-324.2737.

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In this paper, electric field shielding effectiveness (SE) of rectangular enclosure with four apertures illuminated by vertical polarization plane wave has been studied by using modal method of moment technique. Electric field SE of enclosure with four square apertures has been calculated at three different points on the same plane inside enclosure. The numerical results of the proposed technique are in very good agreement with data available in the literature and experimental results. It is shown that apertures’ position and aperture’ number have noticeable effect on the electric field SE.

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39

Xiao Yun, 肖昀, 张运海 Zhang Yunhai, 杨皓旻 Yang Haomin, and 檀慧明 Tan Huiming. "Focusing of High Numerical Aperture Azimuthally Polarized Beams." Laser & Optoelectronics Progress 52, no. 3 (2015): 031801. http://dx.doi.org/10.3788/lop52.031801.

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XU Ming-fei, 徐明飞, 庞武斌 PANG Wu-bin, 徐象如 XU Xiang-ru, 王新华 WANG Xin-hua, and 黄玮 HUANG Wei. "Optical design of high-numerical aperture lithographic lenses." Optics and Precision Engineering 24, no. 4 (2016): 740–46. http://dx.doi.org/10.3788/ope.20162404.0740.

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41

Zhou Yuan, 周远, and 李艳秋 Li Yanqiu. "Bulk Effects in Hyper-Numerical Aperture Optical Lithography." Acta Optica Sinica 28, no. 6 (2008): 1091–95. http://dx.doi.org/10.3788/aos20082806.1091.

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42

Paniagua-Domínguez, Ramón, Ye Feng Yu, Egor Khaidarov, Sumin Choi, Victor Leong, Reuben M. Bakker, Xinan Liang, et al. "A Metalens with a Near-Unity Numerical Aperture." Nano Letters 18, no. 3 (February 27, 2018): 2124–32. http://dx.doi.org/10.1021/acs.nanolett.8b00368.

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43

Estroff, Andrew. "Mask-induced polarization effects at high numerical aperture." Journal of Micro/Nanolithography, MEMS, and MOEMS 4, no. 3 (July 1, 2005): 031107. http://dx.doi.org/10.1117/1.2037507.

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44

Itonaga, Makoto, Fumihiko Ito, Ryo Saito, Toshiya Saito, Takuji Ohira, and Yoshinari Yokochi. "Single Objective Lens with Numerical Aperture of 0.95." Japanese Journal of Applied Physics 44, no. 5B (May 24, 2005): 3420–22. http://dx.doi.org/10.1143/jjap.44.3420.

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45

Patino-Jurado, Brayan, Juan F. Botero-Cadavid, and Jorge Garcia-Sucerquia. "Step-Index Optical Fibers With 0.88 Numerical Aperture." Journal of Lightwave Technology 37, no. 15 (August 1, 2019): 3734–39. http://dx.doi.org/10.1109/jlt.2019.2919669.

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46

Asahara, Yoshiyuki, Hiroyuki Sakai, Sigeaki Ohmi, Shin Nakayama, Yoshitaka Yoneda, and Tetsuro Izumitani. "Gradient-index slab lens with high numerical aperture." Applied Optics 25, no. 19 (October 1, 1986): 3384. http://dx.doi.org/10.1364/ao.25.003384.

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47

Nussbaum, Ph. "Low numerical aperture refractive microlenses in fused silica." Optical Engineering 40, no. 7 (July 1, 2001): 1412. http://dx.doi.org/10.1117/1.1385335.

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Ippolito, S. B., B. B. Goldberg, and M. S. Ünlü. "Theoretical analysis of numerical aperture increasing lens microscopy." Journal of Applied Physics 97, no. 5 (March 2005): 053105. http://dx.doi.org/10.1063/1.1858060.

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49

Sheppard, C. J. R., and K. G. Larkin. "Effect of numerical aperture on interference fringe spacing." Applied Optics 34, no. 22 (August 1, 1995): 4731. http://dx.doi.org/10.1364/ao.34.004731.

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50

Murray, Kevin T., Andrew J. Morgan, Mauro Prasciolu, Istvan Mohacsi, Henry N. Chapman, and Saša Bajt. "Characterization of High Numerical Aperture Multilayer Laue Lenses." Microscopy and Microanalysis 24, S2 (August 2018): 282–83. http://dx.doi.org/10.1017/s1431927618013740.

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