Fresnel-Kirchhoff Diffraction Research Articles

Dipolar Huygens-Kerker radiation for surface waves.

Exotic dipolar radiation with zero light emission in one direction but maximal light emission in the opposite direction was envisioned by Huygens in 1690, and it could emerge in vacuum if the ratio between the source's electric and magnetic dipole moments fulfills the Kerker condition as revealed by Kerker in 1983. Due to its intricate connection with both the Huygens principle and Kerker condition, this radiation phenomenon is suggested to be termed as dipolar Huygens-Kerker radiation, and at this moment, the ratio is termed as the Huygens-Kerker ratio. However, the dipolar Huygens-Kerker radiation remains underexplored in non-vacuum matters, inside which the source locates, especially for surface waves. Here we find that the dipolar Huygens-Kerker radiation of surface waves in principle could occur in non-vacuum matters and is essentially featured with the same normalized radiation pattern, which is closely related to the inclination factor that appears in the Fresnel-Kirchhoff diffraction theory. Moreover, the corresponding Huygens-Kerker ratio is intrinsically determined by the phase velocity of excited surface waves. To be specific, the Huygens-Kerker ratio is proportional to the phase velocity for transverse-magnetic surface waves but becomes inversely proportional to the phase velocity for transverse-electric surface waves.

The Generation of Equal-Intensity and Multi-Focus Optical Vortices by a Composite Spiral Zone Plate

We propose a new vortex lens for producing multiple focused coaxial vortices with approximately equal intensities along the optical axis, termed equal-intensity multi-focus composite spiral zone plates (EMCSZPs). In this typical methodology, two concentric conventional spiral zone plates (SZPs) of different focal lengths were composited together and the alternate transparent and opaque zones were arranged with specific m-bonacci sequence. Based on the Fresnel–Kirchhoff diffraction theory, the focusing properties of the EMCSZPs were calculated in detail and the corresponding demonstration experiment was been carried out to verify our proposal. The investigations indicate that the EMCSZPs indeed exhibit superior performance, which accords well with our physical design. In addition, the topological charges (TCs) of the multi-focus vortices can be flexibly selected and controlled by optimizing the parameters of the zone plates. These findings which were demonstrated by the performed experiment may open new avenues towards improving the performance of biomedical imaging, quantum computation and optical manipulation.

Beam steering using delays generated from an optical OAM mode shifting recirculating loop

This paper investigates the performance of generated delays from an orbital angular momentum mode shifting recirculating delay loop (OAM-SL) in simulation using Kirchhoff-Fresnel diffraction (KFD) and the delays applicability for RF signal beam steering applications. OAM-SL is a novel structure that has been recently reported to produce multiple delayed signal replicas on independent OAM carriers using a single compact system. The objective of this research is to explore the impact of several limiting factors on the quality of OAM-SL delays for beam steering applications, such as where there is (i) displacement of the OAM mode shifter, (ii) displacement of the center of the OAM mode demultiplexer at the loop output, and (iii) the limited resolution. The methodology includes: (i) simulating the beam propagation using KFD, (ii) producing the output as a coherent summation of the recirculating beams, and (iii) characterizing the SCR by dividing the power of the recirculating beam (ρ) on its OAM mode by the power accumulated from the other recirculating beams. Our findings show that delays generated from a system with lin=−30, lshift=+1, and a resolution of 1024 pixels can steer a 100 MHz signal at a steering angle of 11.5° in a four antenna system with 0.1° error if loop alignment is perfect. Also, for steering the 100 MHz signal in an eight antenna system, we analyze the system assuming the system loss can be compensated, and a similar result of 0.1° error is obtained. Additionally, we report the beam steering performance at 23.6° and 36.8°.

Effect of gamma ray on self-induced diffraction patterns of organic compound Poly (methyl-methacrylate films

Poly (methyl-methacrylate) (PMMA) doped organic compound (2-(2,3-dimethylphenyl-amino)-N-Phenyl benzamide) (2-NPb (films are produced on glass substrates with 5 μm thickness. The influence that gamma (γ) radiation has on the structure of the surface morphology of polymer films, the structure dependence of the optoelectronic properties and the optical properties of a prepared 2-NPb:PMMA film was studied under different doses (21, 42 and 64 KGy) of γ- rays emitted by a 137Cs source with an exposure rate of 0.56 Gy/min. The surface morphology of the 2-NPb:PMMA film for un-irradiated and irradiated sample was studied using a microscope with a digital camera along with texture, waviness and roughenss analysis of the entire surface of the films. The optical properties, together with an in-depth analysis of the dispersion energies and parameters, optoelectrical characteristics, and certain nonlinear optical parameters were comprehensively examined and addressed. In addition, the study of optical properties also included some nonlinear optical parameters. Results show that by doping organic compound (2-NPb) in PMMA, the absorption spectra of samples are decreased and superficial morphology of the film has been affected by γ-rays. As the polymer film was irradiated with a continuous-solid state laser (Solid-State-Laser −532–100 T) beam of 532 nm, self-diffraction ring patterns were seen, and it was shown that the diffraction ring patterns rely heavily on ring numbers and radiation dosage. The nonlinear refractive index,n2, for polymer film for un-irradiated and irradiated are estimated to be 0.23×10-6, 0.92×10-6, 1.64×10-6, 3.14×10-6cm2/W, respectively due to diffraction ring patterns. The diffraction ring patterns that were acquired via experimentation are then numerically estimated by making use of the Fresnel-Kirchhoff diffraction integral. The results of these calculations have satisfactory qualitative and quantitative accords.

Effect of sample position on formation of spatial-self phase modulation ring patterns in poly(azaneylylidene-acylene)

Poly(azaneylylidene-acylene) "DAZA" polymer has been synthesized and characterized using different spectroscopic techniques. Self-diffraction ring patterns at far field were observed, when the DAZA polymer was irradiated with a CW laser beam. The influence of sample position, geometrical pumping and laser power has been investigated on the formation of the far field self-diffraction ring patterns of the Gaussian laser beam passing through the DAZA polymer as nonlinear medium. Then, the Fresnel-Kirchhoff diffraction formula was applied to perform simulation of the self-diffraction ring patterns with different laser power at two sample positions before and after the focal point (z = 0) with respect to the geometrical pumping. Our results have shown the effect of type of geometrically pumping on the sample cell (horizontally /vertically) with respect to the distortion of the SSPM patterns. It has been found that, good consistent agreements between experimental and theoretical patterns.

Fraunhofer diffraction pattern of a Gaussian beam passing through a photorefractive crystal Bi12GeO20

In this theoretical–experimental study, we use the Fresnel–Kirchhoff diffraction theory to simulate the formation of the far-field diffraction pattern of a divergent Gaussian beam propagated through a photorefractive crystal Bi12GeO20 (BGO). We show that for the BGO, in addition to the wavefront curvature and change in the refractive index of the medium due to light intensity, there is a third contribution affecting the medium-induced nonlinear phase shift; the latter is related to the additional change in the refractive index produced by the photorefractive nature effect. We consider that this work contributes to the characterization of photorefractive materials using diffraction patterns.

Terahertz metasurface for near-field beam conversion.

A uniform illumination over a screen is crucial for terahertz imaging. As such, conversion from a Gaussian beam to a flattop beam becomes necessary. Most of the current beam conversion techniques rely on bulky multi-lens systems for collimated input and operate in the far-field. We present a single metasurface lens to efficiently convert a quasi-Gaussian beam from the near-field region of a WR-3.4 horn antenna to a flattop beam. The design process is divided into three sections to minimize simulation time, and the conventional Gerchberg-Saxton (GS) algorithm is supplemented with the Kirchhoff-Fresnel diffraction equation. Experimental validation confirms that a flattop beam with an efficiency of 80% has been achieved at 275 GHz. Such high-efficiency conversion is desirable for practical terahertz systems and the design approach can be generally used for beam shaping in the near-field.

Ray-Tracing Model for Generalized Geodesic-Lens Multiple-Beam Antennas

geodesic-lenses are a compelling alternative to traditional planar dielectric lens antennas, as they are low loss and can be manufactured with a simple mechanical design. However, a general approach for the design and analysis of more advanced geodesic-lens antennas has been elusive, limiting the available tools to rotationally symmetric surfaces. In this article, we present a fast and efficient implementation built on geometrical optics and scalar diffraction theory. A numerical calculation of the shortest ray path (geodesic) using an open-source library helps quantify the phase of the electric field in the lens aperture, while the amplitude is evaluated by applying ray-tube power conservation theory. The Kirchhoff-Fresnel diffraction formula is then employed to compute the far field of the lens antenna. This approach is validated by comparing the radiation patterns of a transversely compressed geodesic Luneburg lens (elliptical base instead of circular) with the ones computed using commercial full-wave simulators, demonstrating a substantial reduction in computational resources. The proposed method is then used in combination with an optimization procedure to study possible compact alternatives of the geodesic Luneburg lens with size reduction in both the transverse and vertical directions.

Spatiotemporal characteristics of dynamic speckle from a 3D target in atmospheric turbulence

Spatiotemporal correlation function is the basic characteristic of dynamic laser speckle and the basis of various applications. The correlation function of the speckle intensity from a 3D target in turbulent atmosphere is derived based on the model of random phase screen and Fresnel Kirchhoff Diffraction Formula, and a fast algorithm based on FFT is developed. The particularity of dynamic speckle in turbulence is numerically analyzed and discussed. The results show that the speckle intensity fluctuates at two independent scales both in space and time domain, which are affected by target size and atmospheric turbulence respectively. In particular, the time scale caused by turbulence is also affected by the target translating velocity and the wind direction. The theory and algorithm developed in this paper can play important roles in applications of laser speckle such as remote detection in atmospheric environment.

Wave effect of gravitational waves intersected with a microlens field: A new algorithm and supplementary study

The increase in gravitational wave (GW) events has allowed receiving strong lensing image pairs of GWs. However, the wave effect (diffraction and interference) due to the microlens field contaminates the parameter estimation of the image pair, which may lead to a misjudgment of strong lensing signals. To quantify the influence of the microlens field, researchers need a large sample of statistical research. Nevertheless, due to the oscillation characteristic, the Fresnel-Kirchhoff diffraction integral's computational time hinders this aspect's study. Although many algorithms are available, most cannot be well applied to the case where the microlens field is embedded in galaxy/galaxy clusters. This work proposes a faster and more accurate algorithm for studying the wave optics effect of microlenses embedded in different types of strong lensing images. Additionally, we provide a quantitative estimation criterion for the lens plane boundary for the Fresnel-Kirchhoff diffraction integral. This algorithm can significantly facilitate the study of wave optics, particularly in the case of microlens fields embedded in galaxy/galaxy clusters.

Long-Range Blockage Prediction Based on Diffraction Fringe Characteristics for mmWave Communications

Blockage prediction is significant to support mobility for millimeter wave (mmWave) communications, while the prediction range is limited to centimeters in current work. This letter proposes a long-range blockage prediction scheme leveraging the frequency-dependent diffraction fringe characteristics. Firstly, Fresnel-Kirchhoff diffraction is introduced into a communication blockage scenario to analyze the received power of a mobile terminal. An interesting diffraction phenomenon is found that the received power fluctuates with an increasing amplitude before the blockage occurs, and the fluctuation range is frequency-dependent. Inspired by the diffraction fringe characteristics, a blockage feature (BF) based scheme is proposed to predict an upcoming blockage. Then, long-range mmWave blockage prediction is achieved by leveraging sub-6 GHz BF. Finally, a ray-tracing based simulation is utilized to validate our scheme and blockage prediction range can be extended to several meters.

Shadow radiation and Fresnel diffraction of acoustic waves.

Fresnel diffraction is a fundamental wave phenomenon. This article explains its physical nature using the examples of the diffraction of acoustic waves at soft and hard half-planes and at large apertures on a black screen. It is shown that the shadow radiation by opaque screens plays a central role in these diffraction phenomena. Fresnel-Kirchhoff diffraction at large apertures is presented as an asymptotic form of the shadow radiation. Fresnel and Grimaldi-type diffraction at the soft and hard half-planes is revealed as interference of the shadow radiation and the incident wave.

Doppler Analysis of Forward Scattering Radar With Opportunistic Signals From LEO Satellites

Recently microwave communication signals from low Earth orbit (LEO) satellites have been proposed to be used to detect flying objects in a ground-based forward scattering passive radar setup. In this work the Doppler shift and the Doppler spread due to the flying object in such a system are derived directly from the Fresnel-Kirchhoff diffraction formula using a rotational Cartesian coordinate system to accommodate the continuously moving signal source from the LEO satellites. Coordinate transformations for flying objects including those in the atmosphere with rectilinear motion relative to the ground and those in space with circular orbits are investigated. Both analytical and simulation results demonstrate that the Doppler shift and Doppler spread are related to the velocity and volumetric profile of the flying object, thereby in future they may be used to help identify its size and velocity.

Wave optics and weak gravitational lensing of lights from spherically symmetric static scalar vector tensor Brans Dicke wormholes

This paper has three parts. In first step we use modified scalar tensor vector Brans Dicke gravity \cite{GH0} to obtain metric solution of a spherically symmetric static black hole via perturbation method which asymptotically behaves as modified Schwarzschild de Sitter black hole in weak field limits. Corrections on the line element with respect to the point mass Schwarzschild de Sitter black hole are two parts: power law function for black hole mass instead of point mass and additional logarithmic metric potential which they are produced from effects of interacting timelike dynamical vector fields. Second part of the paper is dedicated to review Fresnel-Kirchhoff diffraction theory for massless scalar field instead of the vector electromagnetic waves. In third part of the work we consider the obtained black hole metric to be lens and we study weak gravitational lensing of moving light originated from point star. Production of stationary images is investigated via both interference of waves and geometric optics approaches. At last we compare results of these approaches and give some outlooks.

A Retroreflection Reduction Technique Based on the Wavefront Coded Imaging System

A novel anti-cat-eye effect imaging technique based on wavefront coding is proposed as a solution to the problem of previous anti-cat-eye effect imaging techniques where imaging quality was sacrificed to reduce the retroreflection from the photoelectric imaging equipment. With the application of the Fresnel–Kirchhoff diffraction theory, and the definition of generalized pupil function combining both phase modulation and defocus factors, the cat-eye echo formation of the wavefront coded imaging system is theoretically modeled. Based on the physical model, the diffracted spot profile distribution and the light intensity distribution on the observation plane are further simulated with the changes in the defocus parameter and the phase modulation coefficient. A verification test on the cat-eye laser echo power of the wavefront coded imaging system and that of the conventional imaging system at a 20 m distance are conducted, respectively. Simulations and experiment results show that compared with conventional imaging systems, the wavefront coding imaging system can reduce the retroreflection echo by two orders of magnitude while maintaining better imaging quality through defocusing.

Generation of Flexible hyperbolic Airy-like beams using a truncated acousto-optical effect

In this paper, we demonstrate the shaping of an incident Gaussian beam into a tunable hyperbolic Airy-like beam, using an acoustooptics cell. The latter contains a transparent liquid (water), where an ultrasound wave propagating and creating a sinusoidal refractive index variation (giving rise to a sinusoidal phase transmittance). By adding an aperture, this sinusoidal phase transmittance becomes equivalent to a cubic phase (sin(x)≈x−x3/3! for x<0.2λa, λa is the ultrasound wavelength), which allows the generation of a tunable Airy-like beam. Using the Fresnel-Kirchhoff diffraction integral, we derive analytical expressions for the diffracted Gaussian beam by the acoustooptics cell in two cases; (a) with and (b) without the aperture. For the first case, the algebra is straightforward and the field has a closed analytical expression, however for the second case, the diffraction integral has no analytical expression, thus, we expand the aperture into a weighted sum of Gaussian functions, to overcome such problem. Based on the obtained mathematical expressions, we study the effect of each parameter of the acoustooptics interaction, on the propagation behavior of the generated Airy-like beam. We believe that the results of this paper could be useful for many interesting applications, involving Airy beams, such as particle manipulation, optical tweezing, and optical communication.

Modeling, characterization, and fabrication of bell-tip microneedle array by diffraction and self-aligned lens effects

Microneedle arrays have been proposed in a wide range of biomedical applications, such as transdermal drug delivery and sensing. However, a scalable manufacturing process of precise microneedle fabrication of the microneedle has been challenged. This paper demonstrates UV-lithography-based one-step fabrication of fine-tuned bell-tip microneedles using a combination of light diffraction and the self-aligned lens effect. Microscale photopatterns can derive the predictive diffraction patterns where the higher light intensity at the center of the photopattern solidifies the liquid photoresist and forms a microlens shape in a self-aligned manner. The light through the microlens focuses down to a sharp point to form a conical shape for the body of the microneedle. Then light propagation through the vertex of the cone causes light emission, creating a fine bell-tip. The described light propagation behavior was characterized and explained in terms of the light intensity distribution from the diffraction based on the extended Fresnel–Kirchhoff diffraction model. The optics finite element analysis software was used to verify the light propagation and the intensity distribution. The step-by-step fabrication process was demonstrated using biocompatible photosensitive resins and validated the light attenuation and the cross-linking energy. The 20 × 20 bell-tip microneedles' array was able to be fabricated from the predicted model. Finally, a microneedle array with various shapes and heights on the same substrate was fabricated by single light exposure, demonstrating numerous achievable shapes using the proposed microneedle fabrication method.

Nonlinear optical properties investigation of a newly synthesised Azo-(β)- diketone dye

Azo-β-diketone compound is prepared via coupling reaction of dizonium salt of sulfanilamide with acetylacetone. The compound is characterized by FTIR, Mass and 1H NMR spectrocopies. The optimization of synthesized azo-β-diketone is carried out using B3LYP method 6-31G (d,p) basis sets. Nonlinear optical properties of synthesized azo-β-diketone is investigated via some quantum chemical descriptors calculation using DFT/B3LYP method with 6‐31G(d,p) basis set. The UV–vis spectrum of the synthesized azo-β-diketone is also calculated using TD-DFT with same optimization method and level. The nonlinear index of refraction of the azo-β-diketone at 473 nm is calculated using the spatial self-phase modulation and Z-scan techniques where as high as 3.259 × 10−7 cm2/W is obtained due to the first technique and 2.4 × 10−8 cm2/W due to the second technique. The compound optical limiting property is tested at the same wavelength with limiting threshold of 12 mW is obtained. The diffraction ring patterns are theoretically simulated based on the Fresnel-Kirchhoff diffraction integral with results agree well with experimental findings.

Study on an artificial phenomenon observed in terahertz biological imaging.

Terahertz (THz) wave-based imaging of biological samples is an emerging but promising field. In the present work, we report an artificial phenomenon observed in imaging melanoma slices, which can lead to mistakenly interpretation of the experimental results. It was observed that a structure similar to but smaller than the sample contour appeared inside the melanoma slice image. The underlying mechanism of this phenomenon was then investigated both experimentally and theoretically. By imaging a regular standard sample (vinyl coverslip) with a THz time domain spectroscopy (THz-TDS) system and reconstructing its images at 0.8 and 1.2 THz, we can clearly observe the afore-mentioned artifacts. The experimental results are highly consistent with the simulations based on the Fresnel-Kirchhoff diffraction theory in which possible optical aberrations were incorporated. It can be concluded that this artifact was caused by the frequency-dependent diffraction of the sample edge. The work demonstrated here is essential for correct interpretation of the images obtained by the THz-TDS technique.

Light propagation in anisotropic and metamaterial media by a Finslerian vector eikonal method

A systematic study of light propagation in anisotropic and metamaterial media is presented by using a Finslerian vector eikonal method, that is, by considering the approximation of very short wavelengths of light in Maxwell’s equations and using particular metric tensors of the general Finsler metric tensor induced by an anisotropic medium. Green’s vector functions, and therefore general solutions, are obtained as a product of a complex scalar function with a local polarization unitary vector. The phase (wave surface or eikonal function) of such a complex scalar function is calculated using a Fermat integral derived from the Maxwell equations. This integral can be considered as the integral form of the eikonal equation and provides a Finslerian metric tensor which allows, together with energy conservation in anisotropic media, the derivation of a general expression depending on the eikonal function for obtaining the scalar amplitude of such a complex function. Likewise, the local polarization unitary vector u ( r ) is calculated by solving an approximated homogeneous linear equations system also depending on the eikonal function. Exact solutions are obtained for uniaxial materials and hyperbolic metamaterials, and approximate solutions are proposed for biaxial materials. Finally, an approximated vector Fresnel–Kirchhoff diffraction formula is presented by using vector Green’s functions in order to study optical propagation. For the sake of completeness, interference patterns produced by anisotropic materials are presented using the results obtained. This systematic study of anisotropic and metamaterial media by a Finslerian vector eikonal method is intended in particular for university physics teachers and as an advanced topic for undergraduate and first year postgraduate students.