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38 pages, 1755 KiB

Open AccessArticle

The Fresnel Approximation and Diffraction of Focused Waves

by Colin J. R. Sheppard

Photonics 2024, 11(4), 346; https://doi.org/10.3390/photonics11040346 - 9 Apr 2024

Cited by 5 | Viewed by 4250

In this paper, diffraction of scalar waves by a screen with a circular aperture is explored, considering the incidence of either a collimated beam or a focused wave, a historical review of the development of the theory is presented, and the introduction of [...] Read more.

In this paper, diffraction of scalar waves by a screen with a circular aperture is explored, considering the incidence of either a collimated beam or a focused wave, a historical review of the development of the theory is presented, and the introduction of the Fresnel approximation is described. For diffraction by a focused wave, the general case is considered for both high numerical aperture and for finite values of the Fresnel number. One aim is to develop a theory based on the use of dimensionless optical coordinates that can help to determined the general behaviour and trends of different system parameters. An important phenomenon, the focal shift effect, is discussed as well. Explicit expressions are provided for focal shift and the peak intensity for different numerical apertures and Fresnel numbers. This is one application where the Rayleigh–Sommerfeld diffraction integrals provide inaccurate results. Full article

(This article belongs to the Special Issue Laser Beam Propagation and Control)

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17 pages, 2434 KiB

Open AccessArticle

A Systematic Summary and Comparison of Scalar Diffraction Theories for Structured Light Beams

by Fuping Wu, Yi Luo and Zhiwei Cui

Photonics 2023, 10(9), 1041; https://doi.org/10.3390/photonics10091041 - 13 Sep 2023

Cited by 4 | Viewed by 2256

Abstract

Structured light beams have recently attracted enormous research interest for their unique properties and potential applications in optical communications, imaging, sensing, etc. Since most of these applications involve the propagation of structured light beams, which is accompanied by the phenomenon of diffraction, it [...] Read more.

Structured light beams have recently attracted enormous research interest for their unique properties and potential applications in optical communications, imaging, sensing, etc. Since most of these applications involve the propagation of structured light beams, which is accompanied by the phenomenon of diffraction, it is very necessary to employ diffraction theories to analyze the obstacle effects on structured light beams during propagation. The aim of this work is to provide a systematic summary and comparison of the scalar diffraction theories for structured light beams. We first present the scalar fields of typical structured light beams in the source plane, including the fundamental Gaussian beams, higher-order Hermite–Gaussian beams, Laguerre–Gaussian vortex beams, non-diffracting Bessel beams, and self-accelerating Airy beams. Then, we summarize and compare the main scalar diffraction theories of structured light beams, including the Fresnel diffraction integral, Collins formula, angular spectrum representation, and Rayleigh–Sommerfeld diffraction integral. Finally, based on these theories, we derive in detail the analytical propagation expressions of typical structured light beams under different conditions. In addition, the propagation of typical structured light beams is simulated. We hope this work can be helpful for the efficient study of the propagation of structured light beams. Full article

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12 pages, 3177 KiB

Open AccessCommunication

Focusing of Radially Polarized Electromagnetic Waves by a Parabolic Mirror

by Zerihun Tadele Godana, János Hebling and László Pálfalvi

Photonics 2023, 10(7), 848; https://doi.org/10.3390/photonics10070848 - 21 Jul 2023

Cited by 3 | Viewed by 2151

Abstract

It is well-known that a strong longitudinal electric field and a small spot size are observed when radially polarized beams are tightly focused using a high numerical aperture parabolic mirror. The longitudinal electric field component can accelerate electrons along the propagation axis at [...] Read more.

It is well-known that a strong longitudinal electric field and a small spot size are observed when radially polarized beams are tightly focused using a high numerical aperture parabolic mirror. The longitudinal electric field component can accelerate electrons along the propagation axis at high intensities in the focal region, which opens an application in particle acceleration. In this paper, we present a rigorous derivation of the electric field obtained when a radially polarized, monochromatic, flat-top beam is focused by a parabolic mirror. The formulae were deduced from the Stratton–Chu integral known from vector diffraction theory. We examined the influence of the focusing parameters on the distribution of both the longitudinal and radial electric field components. In the small numerical aperture and short wavelength regimes, excellent agreement was found with the results obtained from the Rayleigh–Sommerfeld formula. The calculation method can be adapted for various beam types and for electromagnetic pulses as well. Full article

(This article belongs to the Special Issue Photonics: Theory, Technologies and Applications)

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15 pages, 10544 KiB

Open AccessArticle

A Full-Color Holographic System Based on Taylor Rayleigh–Sommerfeld Diffraction Point Cloud Grid Algorithm

by Qinhui Yang, Yu Zhao, Wei Liu, Jingwen Bu and Jiahui Ji

Appl. Sci. 2023, 13(7), 4466; https://doi.org/10.3390/app13074466 - 31 Mar 2023

Cited by 7 | Viewed by 1815

Abstract

Real objects-based full-color holographic display systems usually collect data with a depth camera and then modulate the input light source to reconstruct the color three-dimensional scene of the real object. However, at present, the main problems of the real-time high quality full-color 3D [...] Read more.

Real objects-based full-color holographic display systems usually collect data with a depth camera and then modulate the input light source to reconstruct the color three-dimensional scene of the real object. However, at present, the main problems of the real-time high quality full-color 3D display are slow speed, low reconstruction quality, and high consumption of hardware resources caused by excessive computing. Based on the hybrid Taylor Rayleigh–Sommerfeld diffraction algorithm and previous studies on full-color holographic systems, our paper proposes Taylor Rayleigh–Sommerfeld diffraction point cloud grid algorithm (TR-PCG), which is to perform Taylor expansion on the radial value of Rayleigh–Sommerfeld diffraction in the hologram generation stage and modify the data type to effectively accelerate the calculation speed and ensure the reconstruction quality. Compared with the wave-front recording plane, traditional point cloud gridding (PCG), C-PCG, and Rayleigh–Sommerfeld PCG without Taylor expansion, the computational complexity is significantly reduced. We demonstrate the feasibility of the proposed method through experiments. Full article

(This article belongs to the Special Issue Digital Holography: Novel Techniques and Its Applications)

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12 pages, 2470 KiB

Open AccessArticle

Customized Design of Aperiodic Liquid Crystal Grating for Generation of Multiple Optical Patterns

by Chen Liu, Zhenghao Guo, Jun Wu, Dong Yuan, Guofu Zhou, Biao Tang and Huapeng Ye

Crystals 2023, 13(2), 300; https://doi.org/10.3390/cryst13020300 - 11 Feb 2023

Cited by 2 | Viewed by 2429

Abstract

Liquid crystal (LC) grating has drawn extensive attention due to its merits, including tunability, easy preparation process, cost effectiveness, and high diffraction efficiency. However, limited efforts have been made to explore LC grating for the generation of customized diffraction patterns, despite the fact [...] Read more.

Liquid crystal (LC) grating has drawn extensive attention due to its merits, including tunability, easy preparation process, cost effectiveness, and high diffraction efficiency. However, limited efforts have been made to explore LC grating for the generation of customized diffraction patterns, despite the fact that the patterning size of LC molecular director orientation has been tremendously reduced even to subwavelength scale via high-precision photoalignment techniques. Here, we propose a versatile method based on the binary particle swarm optimization algorithm to efficiently design aperiodic LC gratings for customized optical patterns generation, including needle beam, multi-foci, and hollow beam. The optical performance of the LC gratings was simulated using both the vectorial Rayleigh–Sommerfeld method (with discrete zero or π phase, in this article) and the actual director orientations. These results matched each other well, which proves the effectiveness of the optimization method based on discrete phase. This study paves the way for designing LC gratings with engineered functionalities, which may find applications in optical tweezers, laser delivery systems, and laser scanning imaging. Full article

(This article belongs to the Special Issue Liquid Crystals and Their Advanced Applications)

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13 pages, 4642 KiB

Open AccessArticle

Theoretical Zero-Thickness Broadband Holograms Based on Acoustic Sieve Metasurfaces

by Ye Tian, Shuyu Zuo, Qian Lv, Guanjun Yin and Jianzhong Guo

Appl. Sci. 2022, 12(13), 6453; https://doi.org/10.3390/app12136453 - 25 Jun 2022

Cited by 1 | Viewed by 1943

Abstract

Acoustic holography is an essential tool for controlling sound waves, generating highly complex and customizable sound fields, and enabling the visualization of sound fields. Based on acoustic sieve metasurfaces (ASMs), this paper proposes a theoretical design approach for zero-thickness broadband holograms. The ASM [...] Read more.

Acoustic holography is an essential tool for controlling sound waves, generating highly complex and customizable sound fields, and enabling the visualization of sound fields. Based on acoustic sieve metasurfaces (ASMs), this paper proposes a theoretical design approach for zero-thickness broadband holograms. The ASM is a zero-thickness rigid screen with a large number of small holes that allow sound waves to pass through and produce the desired real image in the target plane. The hole arrangement rules are determined using a genetic algorithm and the Rayleigh–Sommerfeld theory. Because the wave from a hole has no extra phase or amplitude modulation, the intractable modulation dispersion can be physically avoided, allowing the proposed ASM-based hologram to potentially function in any frequency band as long as the condition of paraxial approximation is satisfied. Using a numerical simulation based on the combination of the finite element method (FEM) and the boundary element method (BEM), this research achieves broadband holographic imaging with a good effect. The proposed theoretical zero-thickness broadband hologram may provide new possibilities for acoustic holography applications. Full article

(This article belongs to the Special Issue Recent Advance in Acoustic Metamaterials)

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20 pages, 3967 KiB

Open AccessArticle

Evaluation and Improvements to Interfacial Curvature Predictions in interFoam

by Arpit Agarwal, Mohan Ananth and Mario F. Trujillo

Fluids 2022, 7(4), 128; https://doi.org/10.3390/fluids7040128 - 1 Apr 2022

Cited by 3 | Viewed by 3657

Abstract

Improvements to the interfacial curvature of interFoam based on (i) the smoothing of the liquid fraction field and (ii) the creation of a signed distance function (

ϕ

-based) are implemented. While previous work in this area has focused on evaluating spurious currents [...] Read more.

Improvements to the interfacial curvature of interFoam based on (i) the smoothing of the liquid fraction field and (ii) the creation of a signed distance function (

ϕ

-based) are implemented. While previous work in this area has focused on evaluating spurious currents and similar configurations, the tests implemented in this work are more applicable to sprays and hydrodynamic breakup problems. For the

ϕ

-based method, a dual approach is developed based on a geometric reconstruction of the interface at interfacial cells and the solution of the Hamilton-Jacobi equation away from these cells. The more promising results are from this method, where the lack of convergence of Laplace pressure predictions existing in the standard version of interFoam is fixed, resulting in second-order convergence. Similar but less drastic improvements are observed for other exercises consisting of the oscillation of a droplet, a 2-phase Orr–Sommerfeld problem, the Rayleigh–Plateau instability, and the retraction of a liquid column. It is only when the dynamics are either entirely governed by surface tension or are heavily influenced by it that we see the need to substitute the standard interFoam curvature approach with a more accurate scheme. For more realistic problems, which naturally include more complicated dynamics, the difference between the standard approach and the

ϕ

-based approach is minimal. Full article

(This article belongs to the Special Issue Advances in Numerical Methods for Computational Fluid Dynamics With Open-Source Software)

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9 pages, 2499 KiB

Open AccessArticle

Long-GRIN-Lens Microendoscopy Enabled by Wavefront Shaping for a Biomedical Microdevice: An Analytical Investigation

by Guigen Liu, Jeon Woong Kang and Oliver Jonas

Materials 2021, 14(12), 3392; https://doi.org/10.3390/ma14123392 - 18 Jun 2021

Cited by 4 | Viewed by 2617

Abstract

We analytically investigate the feasibility of long graded-index (GRIN)-lens-based microendoscopes through wavefront shaping. Following the very well-defined ray trajectories in a GRIN lens, mode-dependent phase delay is first determined. Then, the phase compensation needed for obtaining diffraction limited resolution is derived. Finally, the [...] Read more.

We analytically investigate the feasibility of long graded-index (GRIN)-lens-based microendoscopes through wavefront shaping. Following the very well-defined ray trajectories in a GRIN lens, mode-dependent phase delay is first determined. Then, the phase compensation needed for obtaining diffraction limited resolution is derived. Finally, the diffraction pattern of the lens output is computed using the Rayleigh–Sommerfeld diffraction theory. We show that diffraction-limited resolution is obtained for a 0.5 mm diameter lens with a length over 1 m. It is also demonstrated that different imaging working distances (WDs) can be realized by modifying the phase compensation. When a short design WD is used, a large imaging numerical aperture (NA) higher than 0.4 is achievable even when a low NA lens (NA = 0.1) is used. The long- and thin-GRIN-lens-based microendoscope investigated here, which is attractive for biomedical applications, is being prioritized for use in a clinical stage microdevice that measures three-dimensional drug responses inside the body. The advance described in this work may enable superior imaging capabilities in clinical applications in which long and flexible imaging probes are favored. Full article

(This article belongs to the Special Issue Advances in Optical Sensors for Biomedical Applications)

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16 pages, 6087 KiB

Open AccessArticle

Modeling Focused-Ultrasound Response for Non-Invasive Treatment Using Machine Learning

by Tariq Mohammad Arif, Zhiming Ji, Md Adilur Rahim and Bharath Babu Nunna

Bioengineering 2021, 8(6), 74; https://doi.org/10.3390/bioengineering8060074 - 1 Jun 2021

Cited by 4 | Viewed by 4702

Abstract

The interactions between body tissues and a focused ultrasound beam can be evaluated using various numerical models. Among these, the Rayleigh–Sommerfeld and angular spectrum methods are considered to be the most effective in terms of accuracy. However, they are computationally expensive, which is [...] Read more.

The interactions between body tissues and a focused ultrasound beam can be evaluated using various numerical models. Among these, the Rayleigh–Sommerfeld and angular spectrum methods are considered to be the most effective in terms of accuracy. However, they are computationally expensive, which is one of the underlying issues of most computational models. Typically, evaluations using these models require a significant amount of time (hours to days) if realistic scenarios such as tissue inhomogeneity or non-linearity are considered. This study aims to address this issue by developing a rapid estimation model for ultrasound therapy using a machine learning algorithm. Several machine learning models were trained on a very-large dataset (19,227 simulations), and the performance of these models were evaluated with metrics such as Root Mean Squared Error (RMSE), R-squared (R²), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC). The resulted random forest provides superior accuracy with an R² value of 0.997, an RMSE of 0.0123, an AIC of −82.56, and a BIC of −81.65 on an external test dataset. The results indicate the efficacy of the random forest-based model for the focused ultrasound response, and practical adoption of this approach will improve the therapeutic planning process by minimizing simulation time. Full article

(This article belongs to the Special Issue Smart Nano Biomedical Devices in Advanced Healthcare)

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17 pages, 6766 KiB

Open AccessArticle

Leaky Lamb Wave Radiation from a Waveguide Plate with Finite Width

by Sang-Jin Park, Hoe-Woong Kim and Young-Sang Joo

Appl. Sci. 2020, 10(22), 8104; https://doi.org/10.3390/app10228104 - 16 Nov 2020

Cited by 4 | Viewed by 3849

Abstract

In this paper, leaky Lamb wave radiation from a waveguide plate with finite width is investigated to gain a basic understanding of the radiation characteristics of the plate-type waveguide sensor. Although the leaky Lamb wave behavior has already been theoretically revealed, most studies [...] Read more.

In this paper, leaky Lamb wave radiation from a waveguide plate with finite width is investigated to gain a basic understanding of the radiation characteristics of the plate-type waveguide sensor. Although the leaky Lamb wave behavior has already been theoretically revealed, most studies have only dealt with two dimensional radiations of a single leaky Lamb wave mode in an infinitely wide plate, and the effect of the width modes (that are additionally formed by the lateral sides of the plate) on leaky Lamb wave radiation has not been fully addressed. This work aimed to explain the propagation behavior and characteristics of the Lamb waves induced by the existence of the width modes and to reveal their effects on leaky Lamb wave radiation for the performance improvement of the waveguide sensor. To investigate the effect of the width modes in a waveguide plate with finite width, propagation characteristics of the Lamb waves were analyzed by the semi-analytical finite element (SAFE) method. Then, the Lamb wave radiation was computationally modeled on the basis of the analyzed propagation characteristics and was also experimentally measured for comparison. From the modeled and measured results of the leaky radiation beam, it was found that the width modes could affect leaky Lamb wave radiation with the mode superposition and radiation characteristics were significantly changed depending on the wave phase of the superposed modes on the radiation surface. Full article

(This article belongs to the Special Issue Novel Approaches for Nondestructive Testing and Evaluation)

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21 pages, 41666 KiB

Open AccessArticle

The Spec-Radiation Method as a Fast Alternative to the Re-Radiation Method for the Detection of Flaws in Wooden Particleboards

by Andreas Sebastian Schmelt and Jens Twiefel

Appl. Sci. 2020, 10(19), 6663; https://doi.org/10.3390/app10196663 - 23 Sep 2020

Cited by 2 | Viewed by 2584

Abstract

For real-time evaluation of non-destructive air-coupled ultrasonic testing of wood-based materials, efficient and reliable calculation methods from ultrasonic holography are essential. Presented here is the spec-radiation method as a fast alternative to the re-radiation method. The spec-radiation method offers a more accurate and [...] Read more.

For real-time evaluation of non-destructive air-coupled ultrasonic testing of wood-based materials, efficient and reliable calculation methods from ultrasonic holography are essential. Presented here is the spec-radiation method as a fast alternative to the re-radiation method. The spec-radiation method offers a more accurate and up to 88% faster evaluation than the re-radiation method for the determination of flaws in particleboards. Flaws of sub-wavelength sizes can be identified and their shape and location can be determined with this method. The spec-radiation method produces a better reproduction of the sound field than the re-radiation method, especially in the area of the measuring plane. Full article

(This article belongs to the Special Issue Nondestructive Testing (NDT): Volume II)

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7 pages, 2269 KiB

Open AccessArticle

Grating Lobe-Free Beam Steering through Optical Phase Array Using Phase-Compensated Two Index-Mismatched Silicon Wires-Based Emitters

by Rong-An Zhang, Ting-Sheng Lin, Wai-Ting Liu, Shih-Hsiang Hsu and Che-Chang Chang

Appl. Sci. 2020, 10(4), 1225; https://doi.org/10.3390/app10041225 - 11 Feb 2020

Cited by 1 | Viewed by 3554

Abstract

The beam formation can be treated as the diffraction pattern. A 1-D light detection and ranging beam steering could be derived through a phase shifter array using Rayleigh–Sommerfeld Diffraction, which is then utilized to demonstrate grating lobe-free beam steering from the optical phase [...] Read more.

The beam formation can be treated as the diffraction pattern. A 1-D light detection and ranging beam steering could be derived through a phase shifter array using Rayleigh–Sommerfeld Diffraction, which is then utilized to demonstrate grating lobe-free beam steering from the optical phase array emitter with half-wavelength pitches. The half-wavelength pitch cannot demonstrate beam formation without any evanescent coupling blocking between emitters. Here, two index-mismatched silicon wires in the emitter array are proposed by the optical phase compensation through waveguide width adjustment, to avoid the complex and addressable thermal control on the phase shifters. Moreover, the same output optical waveguide mode needs to be further considered to demonstrate the grating lobe-free beam steering. In order to get the adiabatic connection between two different pitches between the phase shifter and emitter, an optical path equalization will also be applied. Full article

(This article belongs to the Section Optics and Lasers)

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19 pages, 51111 KiB

Open AccessArticle

Investigation and Enhancement of the Detectability of Flaws with a Coarse Measuring Grid and Air Coupled Ultrasound for NDT of Panel Materials Using the Re-Radiation Method

by Andreas Sebastian Schmelt, Torben Marhenke, Jörg Hasener and Jens Twiefel

Appl. Sci. 2020, 10(3), 1155; https://doi.org/10.3390/app10031155 - 8 Feb 2020

Cited by 7 | Viewed by 2973

Abstract

Non-destructive ultrasonic testing is utilized widely by industries for quality assurance. For sensitive materials or surfaces, non-contact, non-destructive testing methods are in demand. The air-coupled ultrasound (ACU) is one possible solution. This can be used to investigate large, panel-like objects for delaminations and [...] Read more.

Non-destructive ultrasonic testing is utilized widely by industries for quality assurance. For sensitive materials or surfaces, non-contact, non-destructive testing methods are in demand. The air-coupled ultrasound (ACU) is one possible solution. This can be used to investigate large, panel-like objects for delaminations and other flaws. For a high detectability, fine measurement grids are required (typically <

λ

is used), which results in extremely long data acquisition times that are only practicable for laboratory applications. This paper aimed at reducing the required measurement grid points for obtaining high detectability evaluations. The novel method presented in this paper allows a measurement grid that is much coarser than the resulting grid. The method combines a software refinement of the measured data with the Rayleigh–Sommerfeld diffraction integral for the calculation of the pressure distribution on the object’s surface. This result allows the precise prediction of delaminations and flaws in the tested object. The presented method shows a decrease in the total investigation time by up to 98%. Full article

(This article belongs to the Special Issue IWPMA (International Workshop on Piezoelectric Materials and Applications in Actuators) 2019)

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11 pages, 3961 KiB

Open AccessArticle

A Novel Racing Array Transducer for Noninvasive Ultrasonic Retinal Stimulation: A Simulation Study

by Yanyan Yu, Zhiqiang Zhang, Feiyan Cai, Min Su, Qiuju Jiang, Qifa Zhou, Mark S. Humayun, Weibao Qiu and Hairong Zheng

Sensors 2019, 19(8), 1825; https://doi.org/10.3390/s19081825 - 17 Apr 2019

Cited by 12 | Viewed by 5025

Abstract

Neurostimulation has proved to be an effective method for the restoration of visual perception lost due to retinal diseases. However, the clinically available retinal neurostimulation method is based on invasive electrodes, making it a high-cost and high-risk procedure. Recently, ultrasound has been demonstrated [...] Read more.

Neurostimulation has proved to be an effective method for the restoration of visual perception lost due to retinal diseases. However, the clinically available retinal neurostimulation method is based on invasive electrodes, making it a high-cost and high-risk procedure. Recently, ultrasound has been demonstrated to be an effective way to achieve noninvasive neurostimulation. In this work, a novel racing array transducer with a contact lens shape is proposed for ultrasonic retinal stimulation. The transducer is flexible and placed outside the eyeball, similar to the application of a contact lens. Ultrasound emitted from the transducer can reach the retina without passing through the lens, thus greatly minimizing the acoustic absorption in the lens. The discretized Rayleigh–Sommerfeld method was employed for the acoustic field simulation, and patterned stimulation was achieved. A 5 MHz racing array transducer with different element numbers was simulated to optimize the array configuration. The results show that a 512-element racing array is the most appropriate configuration considering the necessary tradeoff between the element number and the stimulation resolution. The stimulation resolution at a focus of 24 mm is about 0.6 mm. The obtained results indicate that the proposed racing array design of the ultrasound transducer can improve the feasibility of an ultrasound retinal prosthesis. Full article

(This article belongs to the Special Issue Ultrasound Transducers)

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17 pages, 7827 KiB

Open AccessArticle

Nonparaxial Propagation Properties of Specially Correlated Radially Polarized Beams in Free Space

by Lina Guo, Li Chen, Rong Lin, Minghui Zhang, Yiming Dong, Yahong Chen and Yangjian Cai

Appl. Sci. 2019, 9(5), 997; https://doi.org/10.3390/app9050997 - 10 Mar 2019

Cited by 5 | Viewed by 3303

Abstract

A specially correlated radially polarized (SCRP) beam with unusual physical properties on propagation in the paraxial regime was introduced and generated recently. In this paper, we extend the paraxial propagation of an SCRP beam to the nonparaxial regime. The closed-form 3 × 3 [...] Read more.

A specially correlated radially polarized (SCRP) beam with unusual physical properties on propagation in the paraxial regime was introduced and generated recently. In this paper, we extend the paraxial propagation of an SCRP beam to the nonparaxial regime. The closed-form 3 × 3 cross-spectral density matrix of a nonparaxial SCRP beam propagating in free space is derived with the aid of the generalized Rayleigh–Sommerfeld diffraction integral. The statistical properties, such as average intensity, degree of polarization, and spectral degree of coherence, are studied comparatively for the nonparaxial SCRP beam and the partially coherent radially polarized (PCRP) beam with a conventional Gaussian–Schell-model correlation function. It is found that the nonparaxial properties of an SCRP beam are strikingly different from those of a PCRP beam. These nonparaxial properties are closely related to the correlation functions and the beam waist width. Our results may find potential applications in beam shaping and optical trapping in nonparaxial systems. Full article

(This article belongs to the Special Issue Recent Advances in Statistical Optics and Plasmonics)

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