Fraunhofer Diffraction Research Articles

Detection of topological charge for composite perfect vortex beams in atmospheric turbulence

Aiming at the problem of detecting the orbital angular momentum (OAM) states of the composite perfect vortex beams (CPVBs) under atmospheric turbulence (AT) channels, we propose and investigate a joint scheme of combing an optical detection method and the Gerchberg-Saxton (GS) algorithm. We firstly used the GS algorithm to pre-compensate the distorted CPVBs, and then the optical intensity distribution, together with the far-field diffraction patterns of the CPVBs after they passing through an elliptical aperture which shields part of the azimuth angle (EA-shielded), can tell us the topological charges (TCs) carried by each sub beam. The results show that the tailing direction of the bright stripes in the CPVBs intensity distribution denotes the sign of the higerh-order TC, counterclockwise is positive, clockwise is negative. The difference between the TCs of the two beams is indicated by the number of stripes, that is, the number of stripes is equal to the absolute values of differences between the two beams. After passing through the EA-shielded, the far-field diffraction intensity patterns is related to the magnitude and sign of the lower-order TC. If the bright stripes are distributed above, the TC is positive, otherwise, the TC is negative, and the number of dark stripes is equal to the lower-order TC-1. The results provide a new method for detecting the TC information of the CPVBs after phase distortion.

Optical micro mechanical accelerometer with double grating: design and simulation.

A double-grating-based optical micro mechanical accelerometer with differential detection structure is reported in order to enhance the optical scale factor. A theoretical model is established based on the multi-slits Fraunhofer diffraction model. According to the calculation and analysis, the normalized optical scale factor is improved from 5.491E6 with the single-side detection structure to 10.98E6 with the differential detection structure. Mechanical sensitivity with 4.04nm/g and natural frequency with 7756.8Hz of the optical accelerometer are shown by finite element simulation. The results of simulations show a novel scheme for an optical micro mechanical accelerometer with high resolution, to the best of our knowledge. Furthermore, micro-opto-electro-mechanical system fabrication flow is given in this work, which provides a reference for other kinds of optical sensors.

Electromagnetically induced grating in a nonlinear optomechanical cavity

Abstract We investigate theoretically the Fraunhofer diffraction pattern of the output field in a nonlinear optomechanical cavity with a degenerate optical parametric amplifier (OPA) and a higher order excited atomic ensemble. Studies show that the higher-order-excitation atom, which is similar to the degenerate OPA that acts as a nonlinear medium, induces an electromagnetically induced grating in the output spectrum of the probe field. The coherence of the mechanical oscillator leads to transfer of the probe energy in different diffraction orders of the probe field spectrum such that the phenomenon of optomechanically induced grating is generated from the output probe field. In particular, the presence of nonlinearities with the degenerate OPA and the higher order excited atoms can significantly affect the efficiency of the diffraction pattern providing an additional flexibility for controlling optical properties.

Dual-wavelength amplified spontaneous emission from interface-engineered polymer films using atomically thin red coral

Naturally available two-dimensional (2D) materials having van der Waal's heterostructure are an impetus for generating amplified spontaneous emission (ASE) from dye-based polymer films. Under continuous wave (CW) laser pumping, the problem of scatterer mobility due to induced thermal gradient can be mitigated by such films. In this work, liquid-phase exfoliation (LPE) method has been used to synthesize 2D red coral (2D-RC) from its bulk form. In order to obtain CW-pumped ASE from a rhodamine B (RhB) dye mixed polyvinyl alcohol (PVA) film, 2D-RC has been used as a passive scatterer. Dual-wavelength ASE at ∼591 nm and ∼626 nm has been obtained by designing a step on the film and by introducing film-glass interfaces. Enhanced ASE has been obtained by designing a film-based Fabry-Pérot (FP) cavity in addition to the interfaces. Far-field diffraction patterns obtained due to induced optical non-linearity and thermal lensing in the system have been used to demonstrate scatterer ability by comparing with other commonly used passive scatterers. Thus, dual-wavelength ASE from dye-mixed polymer films has been demonstrated by means of interface engineering and induced step using the newly synthesized van der Waal's heterostructure, namely 2D-RC, as a passive scatterer which may pave the way towards further exciting NLO effects based applications.

Ultrahigh Sensitivity Solar‐Blind UV Detection via Multistage‐Concentric‐Annulus Architecture Metasurface

AbstractHigh‐sensitivity photodetection capability has become an indispensable requirement for detecting feeble solar‐blind ultraviolet (UV) light. Micro‐nano metallic metasurface structures are employed to enhance the detector photoelectric performances. However, existing approaches are confronted with bottlenecks of structure simplification and efficacy mediocrity. Here, a distinctive diamond solar‐blind UV photodetector with a synthetic multistage‐concentric‐annulus (MCA) architecture metasurface is reported, which is prepared through a facile and peculiar Fraunhofer diffraction technique. The detector achieves an excellent photo‐to‐dark‐current ratio of 2.4×108 and maintains an extremely low dark current on the order of pA magnitude. The intrinsic response peak and resonance absorption phenomenon in solar‐blind UV are evident from the optical properties. Moreover, the surface potential distribution intuitively reveals that plasmon resonance enhances the UV scattering and absorption cross sections, thus facilitating the photogeneration of carriers. Meanwhile, it expressly demonstrates that multi‐level dipole interaction in the MCA structure accelerates the separation and extraction of electron–hole pairs through enhancing the localized electric field intensity. In addition, a wide range of variable temperature measurements further prove the device possesses capacity for working in extreme environments. This photodetection technology by virtue of a delicate and viable diffraction metasurface is anticipated to provide a leap forward for future applications in wide‐band‐gap semiconductor UV detectors.

Incoherent pumping field and Er3+ ion concentration effects on diffraction pattern of transmitted light in Er3+ doped YAG crystal

The effect of Er[Formula: see text] ion concentration and incoherent pumping field on the Fraunhofer diffraction pattern of the transmitted light beam in Er[Formula: see text]: YAG crystal is discussed. It is shown that under different concentration of Er[Formula: see text] ion in crystal, the energy of the probe light can transfer to the higher orders of the grating. Also, it is shown that the switching from electromagnetically induced grating to electromagnetically induced phase gratin or vice versa can be obtained by different concentration of Er[Formula: see text] ion and incoherent pumping rate in crystal. Moreover, we have found that by replacing the probe light by optical vortex light, the asymmetric diffraction pattern can be obtained by tuning the optical vorticity of optical vortex light. In this case, the asymmetric diffraction pattern can also be controlled at different ion concentration.

Wavefront measurements using the Ronchi test for high-NA lithography projection lenses.

The Ronchi test is widely used for wavefront measurements in advanced lithography tools, and a physical optics explanation of the Ronchi test based on scalar diffraction theory can be found in numerous publications. However, for high-numerical aperture (high-NA) lithography projection lenses, the vector nature of light should be considered when performing wavefront measurements, especially the effect of polarization aberrations on the wavefront test results. In this paper, a vector model for describing shearing interferometry for high-NA lithography projection lenses is established. In addition to considering the vector nature of light, the vector model also calculates the Ronchigram on the screen of a detector at any distance from a diffraction grating, as opposed to the distance restriction for the Fraunhofer diffraction approximation used by the existing methods. Using the developed mathematical model of the Ronchi test, the Ronchigrams of high-NA lithography projection lenses under non-polarized illumination are simulated, and the effect of the distance between the diffraction grating and the detection screen on the wavefront measurement accuracy are discussed.

A simple experiment to study the array theorem using Fraunhofer diffraction of a two-dimensional grating

A transmission electron microscopy (TEM) grid comprises an array of identical square apertures. In this study, the Fraunhofer diffraction pattern of a TEM grid was obtained by a 532 nm wavelength diode laser. It was compared with the Fraunhofer diffraction pattern computed by using the array theorem and employed to estimate the mesh size of the TEM grid.

On the streamwise vorticity generation and distribution in an angular particle wake

We investigate the streamwise vorticity generation mechanism and distribution pattern in an unbounded steady inertial flow past a fixed Platonic polyhedron. Three angular positions are selected: an edge facing the flow (E), a face facing the flow (F) and a vertex facing the flow (V). We provide compelling evidence that the generation of the streamwise vorticity is primarily caused by the tilting of the transverse vorticity that originates from the particle front surface. Each inclined face on the front surface generates a pair of opposite-signed streamwise vortices. They are advected to the particle wake and form a chiral vorticity pattern which preserves the symmetry of the particle front surface. Two particles at dual angular positions exhibit highly similar vorticity patterns. Our study reveals a striking similarity between the vorticity patterns and the far-field optics diffraction pattern of a light beam past a polygonal aperture. We discover the deterministic vorticity generation mechanism to predict the streamwise vorticity patterns based on the distribution of edges and inclined faces on the particle front surface. Conversely, the vorticity patterns themselves can serve as a diagnostic tool to infer the geometry of the opaque particle front surface. Additionally, the vorticity patterns can be used to predict the stable angular position of a freely settling angular particle, which tends to be such that the number of streamwise vorticity pairs in the wake is maximized.

Electromagnetically induced grating in azimuthal dependent three-level quantum dot system

The Fraunhofer diffraction pattern in a three-level quantum dot nanostructure is examined. A probe light, a two-dimensional standing wave field, and a weak signal light are the three optical laser fields that the graphene quantum dot interacts with them. The Fraunhofer diffraction pattern of the probe transmitted light has been addressed under two different coupling situations, including when the weak signal light into an optical vortex beam and a plane wave. The Fraunhofer diffraction pattern becomes symmetric for plane wave coupling light, and the diffracted light can be adjusted by the relative phase between applied lights. However, using the orbital angular momentum of light, it is possible to obtain an asymmetric diffraction pattern for optical light. It has been discovered that in both instances, phase modulation of the probe light’s transmission function allows the probe energy to move from zero order to higher orders.

Asymmetric Fraunhofer diffraction in a quantum dot molecule via tunneling-induced transparency

We manipulate the coupling effect between interdot tunneling and the external control field to study the optical diffractive property in a quantum dot molecule (QDM) system. Based on the density matrix approach, an analytical relation is obtained for the optical susceptibility, which shows tunneling-induced transparency (TIT) in the absorption spectra. We propose an innovative optoelectronic device called tunneling-induced grating, which operates based on the diffraction of the forward-transmitted probe laser light. The diffraction integrals for the far-field regime (i.e., Fraunhofer diffraction) are numerically solved, and the effect of interdot tunneling coupling strength on the diffraction patterns is studied. It is shown that the transmission is increased under tunneling-induced quantum coherence. The weak probe light can be diffracted into higher-order directions upon applying a standing-wave control field. The optimal parametric condition for maximum first- and second-order diffractions is obtained. The results find the potential applications in quantum information processing devices, such as all-optical grating and switches at low light levels.

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.

Orbital angular momentum induced asymmetric diffraction grating in quantum dot molecule

In this paper, we study the Fraunhofer diffraction pattern in a four-level quantum dot nanostructure. The quantum dot interacts with two weak probe and signal laser fields and two strong coupling lights where one of them is a two-dimensional standing wave field. We study the Fraunhofer diffraction pattern of the transmitted probe light when the coherent driving light becomes plan wave or Laguerre Gaussian (LG) vortex light. We found that by controlling the relative phase of the applied lights and orbital angular momentum (OAM) of LG light, the Fraunhofer diffraction pattern can be controlled and the probe energy transfer from zero order to the higher orders, respectively. Moreover, we realized that by controlling the OAM number of the vortex light the asymmetric diffraction pattern is possible.

Matrix technology of linear–angular measurements

Subject of study. An important technological aspect of fabricating microelectronic elements is the design of high-precision methods for measuring linear and angular displacements. This study proposed a new technique for linear–angular measurements based on using a multi-element mark and obtaining measurement information about the angular and linear shift based on a set of measurements for all elements of the mark image. Method. The image of an optical mark, i.e., an ordered set of simple elements created using high-precision photolithography technology, was recorded using a photodetector matrix of a digital camera used as a metric space for measuring the coordinates of the mark image elements with their subsequent processing. Main results. The main aspects of the proposed measurement technique and the estimation of measurement errors are presented in this study. The results of simulating the measurement process of both linear and angular displacements were considered. The processing of the mark image and a set of computational procedures enabled the determination of both linear and angular displacements of the mark image with high accuracy (linear and angular displacements at the level of a few nanometers and hundredths of an arc second or less, respectively). The main directions for developing the proposed technique of matrix measurements were formulated. Among them, using digital liquid crystal displays to form a measuring mark and developing sensors using a shadow patterns (Fraunhofer diffraction) image of the mark are of particular interest. Practical significance. The proposed techniques for measuring linear and angular displacements can be successfully used to develop high-precision compact length and angle meters, linear–angle sensors, and technological modules for microelectronics in photomask fabrication.

Further considerations about light and gravity in terms of classical mechanics

Explanations are proposed for several light behaviors using classical mechanics. The Planck‐Einstein relation is the starting point. A careful inspection reveals that this relationship has two dynamic interacting entities. One is a free (moving) photon, fp , represented by its angular frequency, ω. The other is a proposed, resting, independent, electromagnetic field denoted by the reduced Planck constant ħ, which is the product of energy and period. Consistent with these entities are several proposals supported by well-established equations. They include the presence of a hidden factor that allows for the photon’s internal dynamics, a more precise description of the electromagnetic interactions of gravity with light, the mechanism behind Fraunhofer diffraction, the role of gravity in the fine structure constant, the role of gravity in the refraction of light and its implications for relativity, and the mechanism of Fermat’s principle.

An efficient optical diffuser fabricated from fungal mycelium

Scattering of light from randomly textured materials is ubiquitous and of great interest in biology and for diverse applications—including filtering, light trapping in solar cells, and speckle photography. One attractive means to build these materials is by harnessing the complexity present in structures of biological origin. Here, we report on the development of a random phase diffuser based on intertwined filamentous cells (hyphae) of the fungus Trichoderma atroviride. A fungal colony (mycelium) is grown on the surface of a gel medium, and then removed, fixated, and dehydrated, resulting in a free-standing, two-dimensional random mesh (1 cm × 1 cm × 5 μm) composed of rigid hyphae separated by air gaps. A laser beam incident on the bioplate results in speckle patterns of nearly equal intensity in transmission and reflection. By modeling the bioplate as composed of optical phase elements and computing Fraunhofer diffraction, we recover the overall shape of the observed diffuse light spot. As the hyphal density composing the sample is increased, all optical power is in the speckle pattern, and approximate Lambertian transmissivity is reached. Altogether, our observations suggest that a planar fungal colony can scatter light efficiently by imparting a random phase. These results underscore the potential of a biological structure to develop optical elements and to use light scattering to evaluate morphology in complex structures—such as filamentous mycelia.

Position measurement and the Huygens-Fresnel principle: A quantum model of Fraunhofer diffraction for polarized pure states

Starting only from the postulates of quantum mechanics, the author presents a model of Fraunhofer diffraction by an aperture by treating the diaphragm as a position-measurement device, and explains how this model leads to experimentally testable consequences for large diffraction angles and polarization of the diffracted light.

Investigation of the Beam Quality of a Compact Non-Chain Pulsed DF Laser with a Confocal Positive Branch Unstable Resonator

The results of detailed studies on the beam quality of a non-chain pulsed electric discharged DF laser based on a compact inner cavity confocal positive branch unstable resonator were presented herein. The theoretical and experimental divergence angles for magnification M = 1.65, 1.85, 2.05, and 2.25 were calculated according to Fraunhofer diffraction and measured by the method of calibrated apertures. The smallest divergence of θ = 0.66 mrad was obtained with M = 2.25 in our experiment, which is 1.95 times the theoretical value. The corresponding far-field energy density at 10 km distance from the laser exit was 82.8 mJ/m2. The beam quality and energy density were increased by 11 and 91 times, respectively, compared with a similar stable resonator in our lab.

Fraunhofer Diffraction by Slit Into a Homogeneous Anisotropic Medium with an Open Surface of Wave Vectors

Fraunhofer Diffraction by Slit Into a Homogeneous Anisotropic Medium with an Open Surface of Wave Vectors

Thermally Triggered Multilevel Diffractive Optical Elements Tailored by Shape-Memory Polymers for Temperature History Sensors.

The morphological transitions induced by external stimuli in shape-memory polymers (SMPs) can be exploited with the real-time response of far-field diffraction patterns in diffractive optical elements (DOEs). In this paper, we combine the temperature characteristics of SMPs and the display characteristics of DOEs to obtain an optical temperature sensing film where the temperature information is taken as a change of far-field diffraction images. This process was achieved by imprinting the micropatterns of the DOEs on the epoxy-based SMP film, which can be programmed to hold a temporary optical image and revert to its original image upon exposure to a specific temperature. Furthermore, the specific temperature at which the image transformation occurs can be customized by varying the chain flexibility of the SMP. Based on a range of transition points, by imprinting the desired combination of SMP-DOEs on a film, a sensor that can record and inform the temperature history is demonstrated. As for the feasible application of this technique, it can be used for the compact and reliable optical temperature indicators, which can be applied in temperature-sensitive industries such as food and pharmaceuticals.