Fraunhofer Diffraction Research Articles

Joint phase control in metasurfaces for optical convolution operations

Combining the propagation and geometric phases in a metasurface facilitates the independent control of multiple parameters of the light field. However, the geometric phase often displays a random distribution, making it difficult to observe directly. We introduce a frequency-dependent phase response: at frequency f1, there is a superposition of the geometric and propagation phases, whereas at frequency f2, the propagation phase remains constant, and only the geometric phase is applied. The superposition can be interpreted as a convolution process in far-field Fraunhofer diffraction, enabling convolution metasurface devices to generate complex orbital angular momentum beams array and patterned array. Notably, the geometric phase aligns with the characteristic distribution of orbital angular momentum beams, allowing direct observation of the loaded geometric phase. These findings open what we believe to be new avenues for manipulating and calculating complex vector optical fields, optical information coding, controlling light-matter interactions, and enhancing optical communication.

Dynamic response characteristics of optical beam deflection in liquid crystal optical phased array

The beam deflector based on liquid crystal optical phased array (LCOPA) is a crucial component of space laser communication systems. Understanding and mastering the beam deflection characteristics under the dynamic response of LCOPA is essential for achieving real-time acquisition and tracking in space laser communication. This paper thoroughly explores the beam deflection characteristics during the dynamic response process by analyzing the dynamic response and far-field diffraction models of LCOPA. It presents the far-field diffraction patterns under the dynamic response of LCOPA and validates the analysis through experiments. This study not only enhances the understanding of the dynamic performance of LCOPA but also provides a theoretical basis for its control in space laser communication systems.

High-efficiency hard X-ray blazed diffraction via refraction by nanometer-scale prism arrays

X-ray transmission gratings are widely utilized as wavelength dispersion elements in inertial confinement fusion and X-ray astronomy fields due to their high tolerance for alignment errors, light weight and compact size. However, the high transmittance of the grating bars in the hard X-ray range can lead to reduced efficiency of all other diffraction orders except for straight through zeroth order. We propose a novel blazed refraction grating design for the hard X-ray range that combines the advantages of transmission gratings and compound refraction lenses for the first time, demonstrating its superior performance in high broadband efficiency through compound refraction and diffraction from nanometer-scale periodic arrays of silicon prisms using beam propagation method and Fraunhofer diffraction simulation. This research develops blaze methods in gratings design and provides a new solution for compact and sensitive spectrum measurement in hard X-ray range.

Investigation of thermally induced nonlinear optical response of polyurethane-graphene composite by SSPM method

We conducted a study on composites made of polyurethane and graphene (PU-G). We synthesized these composites and then examined their far-field diffraction patterns at various concentrations of dimethylformamide (DMF) using the spatial self-phase modulation (SSPM) method. By analyzing the intensity-dependent far-field ring patterns, we were able to estimate the samples' thermally induced nonlinear refractive index and thermo-optical coefficient. We found that these variables, as well as other observable phenomena such as the “diffraction ring collapse effect” and “variation in nonlinear refractive index,” depended on the sample's concentration rate. Our results indicate that the laser-induced thermal effect is a significant factor in the SSPM phenomena observed in our experiments. Furthermore, our findings suggest that the PU/G combination in DMF has promising nonlinear optical properties that could be beneficial in a variety of nonlinear optics applications.

Experimental demonstration of a silicon nanophotonic antenna for far-field broadened optical phased arrays

Optical antennas play a pivotal role in interfacing integrated photonic circuits with free-space systems. Designing antennas for optical phased arrays ideally requires achieving compact antenna apertures, wide radiation angles, and high radiation efficiency all at once, which presents a significant challenge. Here, we experimentally demonstrate a novel ultra-compact silicon grating antenna, utilizing subwavelength grating nanostructures arranged in a transversally interleaved topology to control the antenna radiation pattern. Through near-field phase engineering, we increase the antenna’s far-field beam width beyond the Fraunhofer limit for a given aperture size. The antenna incorporates a single-etch grating and a Bragg reflector implemented on a 300-nm-thick silicon-on-insulator (SOI) platform. Experimental characterizations demonstrate a beam width of 44°×52° with −3.22 dB diffraction efficiency, for an aperture size of 3.4 μm×1.78 μm. Furthermore, to the best of our knowledge, a novel topology of a 2D antenna array is demonstrated for the first time, leveraging evanescently coupled architecture to yield a very compact antenna array. We validated the functionality of our antenna design through its integration into this new 2D array topology. Specifically, we demonstrate a small proof-of-concept two-dimensional optical phased array with 2×4 elements and a wide beam steering range of 19.3º × 39.7º. A path towards scalability and larger-scale integration is also demonstrated on the antenna array of 8×20 elements with a transverse beam steering of 31.4º.

Electronic analogue of Fourier optics with massless Dirac fermions scattered by quantum dot lattice

Abstract The field of electron optics exploits the analogy between the movement of electrons or charged quasiparticles, primarily in two-dimensional materials subjected to electric and magnetic (EM) fields and the propagation of electromagnetic waves in a dielectric medium with varied refractive index. We significantly extend this analogy by introducing an electronic analogue of Fourier optics dubbed as Fourier electron optics (FEO) with massless Dirac fermions (MDF), namely the charge carriers of single-layer graphene under ambient conditions, by considering their scattering from a two-dimensional quantum dot lattice (TDQDL) treated within Lippmann–Schwinger formalism. By considering the scattering of MDF from TDQDL with a defect region, as well as the moiré pattern of twisted TDQDLs, we establish an electronic analogue of Babinet’s principle in optics. Exploiting the similarity of the resulting differential scattering cross-section with the Fraunhofer diffraction pattern, we construct a dictionary for such FEO. Subsequently, we evaluate the resistivity of such scattered MDF using the Boltzmann approach as a function of the angle made between the direction of propagation of these charge-carriers and the symmetry axis of the dot-lattice, and Fourier analyze them to show that the spatial frequency associated with the angle-resolved resistivity gets filtered according to the structural changes in the dot lattice, indicating wider applicability of FEO of MDF.

A Free-Space Diffraction BSDF

Free-space diffractions are an optical phenomenon where light appears to "bend" around the geometric edges and corners of scene objects. In this paper we present an efficient method to simulate such effects. We derive an edge-based formulation of Fraunhofer diffraction, which is well suited to the common (triangular) geometric meshes used in computer graphics. Our method dynamically constructs a free-space diffraction BSDF by considering the geometry around the intersection point of a ray of light with an object, and we present an importance sampling strategy for these BSDFs. Our method is unique in requiring only ray tracing to produce free-space diffractions, works with general meshes, requires no geometry preprocessing, and is designed to work with path tracers with a linear rendering equation. We show that we are able to reproduce accurate diffraction lobes, and, in contrast to any existing method, are able to handle complex, real-world geometry. This work serves to connect free-space diffractions to the efficient path tracing tools from computer graphics.

Expanding wave packets and the quantum to classical transition

The standard description of the transition from quantum to classical mechanics presented in most text books is the proof that the quantum expectation values of position and momentum obey equations of Newtonian form. This is the Ehrenfest theorem. It is combined with the requirement that wave packets remain localised to describe a single particle moving according to classical mechanics. Hence, the natural spreading of wave packets is viewed as a quantum effect. In contradiction to this view, here it is argued that the spreading, where different momentum components separate, is the signature of the quantum to classical transition. The asymptotic spatial wave function becomes proportional to the initial momentum space wave function, which mirrors exactly the well-known far-field diffraction pattern in optics. Trajectories, defined as the locus of the normals to the expanding wave front, are used to illustrate the transition from quantum to classical motion. Again this is the analogue of the wave to beam transition in optics. It is suggested that this analysis of the quantum to classical transition should be incorporated routinely into introductory quantum mechanics courses.

Introducing wave-particle duality with low-cost quantitative experiments on light diffraction

We present a quantitative optical low-cost experiment aimed at introducing students to wave-particle duality from a phenomenological point of view. The experiment, focused on light diffraction, clearly shows the intermediate crossover regime which characterize the transition from geometric optics (in which light behaves like a stream of particles) to the Fraunhofer diffraction regime (where the wave aspects are most evident). It can also be considered for introducing students to the uncertainty relations through diffraction of light waves. The experiments do not require expensive materials or specific laboratory instruments and employ the sensors and camera of common mobile devices. The experiments were tested with master students in mathematics and physics, who aim at becoming high school teachers.

P‐102: Measurement of Inkjet Droplet Volume based on Fraunhofer Diffraction

This paper presents the feasibility of Fraunhofer diffraction analysis as a measure of the size of fast‐moving inkjet droplets. This measurement method showed that an inkjet droplet measurement tool was possible with a good balance of real‐time measurement and accuracy.

Localized phase contrast imaging at the Wendelstein 7-X stellarator

In its basic form, phase contrast imaging (PCI) provides line-integrated measurements of electron density fluctuations in plasmas. As turbulent fluctuations in magnetically confined plasmas have wave vectors almost perpendicular to the background magnetic field, the signals scattered by fluctuations from different parts of the PCI line-of-sight (LoS) are spatially separated in focal planes of the plasma. This allows localized PCI measurements by placing a mask in such a plane, to only permit signals from specific parts of the LoS to reach the PCI detectors. The present paper describes modeling and design of localization masks for the PCI system at the Wendelstein 7-X (W7-X) stellarator as well as the first results obtained using the masks in the recent long-pulse W7-X experimental campaign. During this project, we have extended the theory describing the mask response within the Fraunhofer diffraction model. As a novel development, we show from first principles that the mask response is determined by the fraction of power of the scattered beam spots that passes the mask. These insights have been used to select the W7-X mask design, consisting of a circular cutout, allowing the unscattered beam spot to pass the mask, with wedges covering a fixed angular range outside the central cutout. In the recent W7-X experimental campaign, the masks have verified the location of the main turbulence features observed by the PCI system and provided new information about the location of short-wavelength magnetohydrodynamic modes.

Diffraction of light by a slit in anisotropic media with closed and open wave vector surface

Fraunhofer diffraction of an electromagnetic wave by a slit on an opaque screen located between vacuum and an anisotropic medium with closed and open wave vectors surface is considered. A formula for diffraction in a material medium is obtained, including the case of diffraction into a uniaxial anisotropic medium in the absence of absorption, and the formation of diffraction minima and maxima is studied.

Two-dimensional sound pressure distribution: Visualization and calibration-free quantification via optical wave microphone CT scanning

In recent years, the optical wave microphone has emerged as an innovative technique, employing Fraunhofer diffraction of a laser beam, and shows promising applications in various acoustic domains where high electric and/or magnetic fields preclude the use of traditional microphones. This study utilized an optical wave microphone computed tomography (CT) scan and calibration-free quantification to ascertain sound pressure levels at multiple distances from the ultrasonic oscillator. The cornerstone of this study, which is different from the author’s previous studies, is the quantification of sound pressure distribution via a theoretical model that encompasses all physical parameters pertinent to the optical wave microphone’s experimental arrangement. This method has proven effective in visualizing and quantifying the two-dimensional sound pressure distribution emitted by an ultrasonic oscillator (40 kHz) without the necessity for calibration. The results demonstrate that the sound pressure distribution determined using the calibration-free optical wave microphone CT scan is in good agreement with the measurements obtained through a condenser microphone.

THE DETECTOR METHODS OF COLOR CHANGING TO NON-INVASIVE AND ECONOMICAL NANOFILLER COMPOSITE RESIN BASED ON OPTICAL IMAGING

It has been developed the detector method of color changing to non-invasive and economical nanofiller composite resin based on optical imaging. The method is chosen due to the easiness of information in images form to be understood. The color changing is represented by the changing of brightness intensity laser which transmitted by samples. The light source uses green pointer laser with 532 nm of wavelength of and webcam sensor which can be obtained in the local market. Fraunhofer diffraction principle is used to utilize set up and test material treatment. By utilizing IC LM 317, it is made a series of regulators so that the laser pointer can be the input voltage from voltage source (AC). The light source of laser pointer is exposed to the test materials for detecting the intensity of transmission. Samples are made as thin as possible in order to transmit light and are given treatment in form of immersion in tea and coffee solution. Immersion is done for 1 week for 4 hours per day. The transmission intensity of samples captured by webcam and processed using the Delphi program. The data collections in form of transmission intensity are in pixel scale. The results indicate that the longer time immersion used affect the transmission intensity of samples decrease. These results can be seen from graph of the relation between transmission intensity with longer time of immersion. This detector can be used to help characterization of color's stability determination on the material which is portable gear.

Scaled Model for Studying the Propagation of Radio Waves Diffracted from Tunnels

One of the major challenges in designing a wireless indoor–outdoor communication network operating in tunnels and long corridors is to identify the optimal location of the outside station for attaining a proper coverage. It is required to formulate a combined model, describing the propagation along the tunnel and the resulting diffracted outdoor pattern from its exit. An integrated model enables estimations of the radiation patterns at the rectangular tunnel exit, as well as in the free space outside of the tunnel. The tunnel propagation model is based on a ray-tracing image model, while the free-space diffraction model is based on applying the far-field Fraunhofer diffraction equation. The model predictions of sensing the radiation intensity at the tunnel end and at a plane located at a distance ahead were compared with experimental data obtained using a down-scaled tunnel model and shorter radiation wavelength correspondingly. This down-scaling enabled detailed measurements of the radiation patterns at the tunnel exit and at the far field. The experimental measurements for the scaled tunnel case fit the theoretical model predictions. The presented model accurately described the multi-path effects emerging from inside the tunnel and the resulting outdoor diffracted pattern at a distance from the tunnel exit.

Asymmetric two-dimensional diffraction grating via a vortex field in an inverted-Y-type atomic system

We propose a theoretical scheme to realize a two-dimensional (2D) diffraction grating in a four-level inverted-Y-type atomic system coupled by a standing-wave (SW) field and a Laguerre–Gaussian (LG) vortex field. Owing to asymmetric spatial modulation of the LG vortex field, the incident probe field can be lopsidedly diffracted into four domains and an asymmetric 2D electromagnetically induced grating is created. By adjusting the detunings of the probe field and the LG vortex field, the intensities of the LG vortex field and the coherent SW field, as well as the interaction length, the diffraction properties and efficiency, can be effectively manipulated. In addition, the effect of the azimuthal parameter on the Fraunhofer diffraction of the probe field is also discussed. This asymmetric 2D diffraction grating scheme may provide a versatile platform for designing quantum devices that require asymmetric light transmission.

Microwave assisted Fraunhofer diffraction pattern in a four-level light–matter coupling scheme

The experimental realization of two-dimensional (2D) electromagnetically induced grating is explored by monitoring the Fraunhofer diffraction pattern in a microwave-driven four-level Y-type atomic medium under the action of two orthogonal standing-wave (SW) fields. Due to the position-dependent atom–field interaction, the information about the high diffraction order of the probe light can be obtained via the Fraunhofer diffraction pattern of the probe light. It is found that the diffraction behavior is significantly improved due to the joint quantum interference induced by the SW and microwave-driven cycling fields. Most importantly, the amplitude and phase diagram of the transmission function of the probe light can be modulated at a particular position and the probe energy may transfer to the high orders of the diffraction by properly adjusting the system parameters. The proposed scheme may provide a promising way to achieve highly sensitive diffraction patterns with applications in quantum information processing.

Towards constructing a DOE-based practical optical neural system for ship recognition in remote sensing images

The optical neural network system based on the 4f system (4f-ONN) is a feasible solution for on-orbit real-time target detection and recognition on remote sensing images, as it can directly modulate and encode the two-dimensional image information. However, traditional 4f systems based on spatial light modulators (SLMs) often encounter misalignment errors during assembly due to the reflective optical path used in SLMs. Additionally, implementing electronic SLM in space-based applications introduces problems such as particle number reversal, significantly reducing the reliability of the system. To address these issues, this paper proposes the adoption of diffractive optical elements (DOEs) to construct the 4f-ONN system. The DOE-based design offers a more compact structure, enhanced reliability, and reduced energy consumption, making it highly suitable for on-orbit image processing applications. Due to the expensive and time-consuming nature of the DOE manufacturing process, a design approach for a 4f system based on DOE was pursued through software simulation in this paper. The simulation phase involved the utilization of electronic neural networks to acquire the physical parameters of the DOE mask, while incorporating the array theorem and Fraunhofer diffraction theorem to accurately calculate the physical dimensions of the DOE. The effectiveness of the adopted DOE-based 4f system was initially validated through experiments on a simple pattern dataset. Subsequently, simulation experiments were conducted on three public datasets, namely Mnist, Fashion-mnist, and QuickDraw16, to confirm the efficacy of the DOE-based 4f system in classification tasks. Lastly, target recognition experiments were performed on the GF-2 dataset, and a corresponding hardware system was developed to demonstrate the potential of the DOE-based 4f system in on-orbit image processing.

Gabor-type holography solved analytically for complex-valued phase disks

Solving the holography equation has long been a numerical task. While effective, the numeric approach has its own set of limitations. Relying solely on numerical approaches often obscures the intricate interplay and influence of the individual terms within the equation. This not only hampers a deeper understanding of the underlying physics but also makes it challenging to predict or control specific outcomes. In this study, we address these challenges by leveraging our recently published updated Fraunhofer diffraction expression. This approach allows us to derive an analytic solution for complex-valued phase disks in in-line holography. This solution facilitates the direct computation of each term’s influence within the holographic equation, paving the way for a more profound comprehension and application of the holographic process. When compared to experimental results and the numeric Fresnel diffraction solution, our analytic approach shows impressive accuracy, considering the inherent approximations. Notably, it remains precise for Fresnel numbers that extend well beyond the traditionally accepted boundaries of the Fraunhofer regime.

Satellite laser ranging to Galileo satellites: symmetry conditions and improved normal point formation strategies

High-precision satellite laser ranging measurements to Galileo retroreflector panels are analyzed to determine the angle of incidence of the laser beam based on specific orientations of the panel with respect to the observing station. During the measurements, the panel aligns with respect to the observing station in such a way that multiple retroreflectors appear at the same range, forming regions of increased data density—separated by a few millimeters. First, measurements to a spare IOV-type retroreflector mounted on an astronomical mount at a remote location 32 km away from the Graz laser ranging station are performed. In addition, more than 100 symmetry passes to Galileo satellites in orbit have been measured. Two novel techniques are described to form laser ranging normal points with improved precision compared to traditional methods. An individual normal point can be formed for each set of retroreflectors at a constant range. The central normal point was shown to be up to 4 mm more accurate when compared with a precise orbit solution. Similar offsets are determined by applying a pattern correlation technique comparing simulated with measured data, and the first method is verified. Irregular reflection patterns of Galileo FOC panels indicate accumulated far-field diffraction patterns resulting from non-uniform retroreflector distributions.