Light Diffraction Patterns Research Articles

University students’ recognition of typical wave optics patterns

The recognition and distinction of typical interference and diffraction patterns are among the expected learning outcomes of studying wave optics. Previous studies have reported high school students’ difficulties with this task. In this study, we investigated university students’ ability to distinguish typical wave optics patterns obtained by the double slit, single slit, and diffraction grating. We also used eye tracking to obtain an insight into the distribution of students’ visual attention during the task. The results showed that university students had similar difficulties in recognizing wave optics patterns as high school students. They mostly struggled with identification of the double-slit interference patterns and diffraction grating patterns of monochromatic light while they were more successful in recognition of the diffraction pattern of white light on an optical grating and single-slit diffraction patterns. The eye-tracking data also revealed that students spent more time attending colourful than grey patterns in questions regarding diffraction of white light on an optical grating, thus suggesting that they were aware that the diffraction grating separates white light into colours. In questions regarding monochromatic light patterns, students overall mostly attended the single-slit diffraction pattern probably because of its distinct central maximum. Furthermore, the longer fixation duration for patterns compared to the text implies that students found it easier to extract information from the text than from the patterns. No prior research has compared the number of transitions during problem solving with the accuracy of the answers. In this study, we observed that students who incorrectly solved a task demonstrated a significantly higher number of gaze transitions between the question and the options, as well as among different options. The results of this study indicate that the recognition of typical wave optics patterns is also difficult for university students, thus suggesting that more attention should be paid to systematic observation and identification of key features of basic wave optics phenomena in lecture demonstrations and student laboratories.

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.

Retrieving positions of closely packed subwavelength nanoparticles from their diffraction patterns

Distinguishing two objects or point sources located closer than the Rayleigh distance is impossible in conventional microscopy. Understandably, the task becomes increasingly harder with a growing number of particles placed in close proximity. It has been recently demonstrated that subwavelength nanoparticles in closely packed clusters can be counted by AI-enabled analysis of the diffraction patterns of coherent light scattered by the cluster. Here, we show that deep learning analysis can return the actual positions of nanoparticles in the cluster. The Pearson correlation coefficient between the ground truth and reconstructed positions of nanoparticles exceeds 0.7 for clusters of ten nanoparticles and 0.8 for clusters of two nanoparticles of 0.16λ in diameter, even if they are separated by distances below the Rayleigh resolution limit of 0.68λ, corresponding to a lens with numerical aperture NA = 0.9.

Study on the co-phasing simulation and experimental of segmented mirror based on broadband light

At present, the co-phasing detection algorithms for segmented mirrors struggle to balance the measurement range and accuracy. This paper proposes a coarse co-phasing measurement method using the incoherent properties of a broadband (400–800 nm) light source combined with the incoherence of two semicircular diffraction patterns of visible light as a template to detect the piston error, and a narrowband algorithm for fine co-phasing measurement. The diversity factors between template patterns and actual diffraction patterns can be calculated by the cross-correlation algorithm. This proposed method addresses long measurement time caused by low target flow rate and is characterized by wide measurement range, high precision and high energy utilization. The method is theoretically researched and simulated and an experimental system which was constructed to verify the effectiveness of this method achieves 15 nm detection accuracy, and the measurement range using the proposed method can match the measurement range of the actuator.

Optomechanically induced grating in a graphene based nanocavity

The optomechanically induced grating (OMIG) in a nanocavity using a bilayer graphene system as the intracavity medium has been proposed. We investigate the effects of different parameters on the Fraunhofer diffraction pattern of the incident probe light. Here, one mirror of the nanocavity is considered coherently driven by the standing wave coupling and probe fields, whereas the second mirror has mechanical oscillation due to the radiation pressure. We consider interaction of bilayer graphene with the optomechanical cavity and show that OMIG can be obtained corresponding to output probe field frequency. Moreover, we find that under specific parametric conditions, most of the probe energy can transfer to the higher orders of the diffraction and only a small portion remains in the zero order.

Milky translucent haze of a large-scale topological defect array in nematic liquid crystal

ABSTRACTA large two-dimensional (2D) topological defect array in nematic liquid crystal (NLC) shows a translucent watery hazy texture. The haze is a composition of three optical phenomena: scattering of light, lens imaging and diffraction. The scattering of light causes the milky haze. Vertically aligned NLC cells with pixel electrodes were fabricated to produce the crowded irregular defects. The key parameters are the electrode shape (pad or annulus), the array structure (square or hexagonal) and the pixel size (from 15μm×15μm to 200μm×200μm). Location and topological charge of the defects are identified under a polarised optical microscope. 2D Fourier transform of the defect distribution gives the spatial frequency spectrum, which is the diffraction pattern of light through the defects. Large pad electrodes produce ordered defects and significant diffraction. Crowded irregular defects render the milky translucent haze and a continuous spatial spectrum. The traditional haze measurement is not able to distinguish the scattered and diffracted light. The spatial spectrum can accurately describe the appearance perceived by the viewers. Small annulus electrodes in a hexagonal array produce the messiest defects, the haziest texture and the most comfortable visual experience among the others.

Fabrication of ultraviolet/thermal-sensitive PMMA/PDMS wrinkle structures and the demonstration as smart optical diffusers

Although smart optical diffusers have received increasing attention for the next generation of flexible optoelectronics, the exploration and fabrication of low-cost ultraviolet/thermal-sensitive optical diffusers are still challenging. In this study, we used a cost-effective method to fabricate flexible PMMA/PDMS wrinkle structures, demonstrating their applicability as tunable ultraviolet/thermal-sensitive optical diffusers. As the temperature gradually increased, the wrinkle wavelength changed slightly while the amplitude decreased. The wrinkle wavelength remained unchanged after UV light exposure, while the wrinkle amplitude decreased with the illumination time. When the fabricated structures were used as optical diffusers, the number of light diffraction pattern rings decreased with the wavelength of the wrinkle structures. Optical diffusers with different wrinkle patterns and the same aspect ratio exhibited different diffusing properties. The number of apertures and the coverage area of the diffused spot gradually decreased when the optical diffuser structure was exposed to heating. Remarkably, the optical diffusers could recover to their original state quickly after cooling. The number of apertures and the coverage area of the diffused spot gradually decreased with UV irradiation time. The prepared PMMA/PDMS wrinkle structures exhibit great potential for intelligent displays, wise medical systems, and other smart devices.

Control of emission diffraction angles and laser threshold in mixed-order sampled distributed feedback laser with organic gain media

The control of laser emission angles in laser devices is essential for many optoelectronic and photonic applications such as optical sensing and displays. In this context, we studied the light diffraction pattern of laser beams in a one-dimensional sampled distributed feedback resonator having organic gain media. The gratings consist of the repetition of supercells having a mixed-order sampled grating in which 1st-order gratings surround a 2nd-order grating. The experimental results showed that the diffraction angles of the laser beams are quite diverse depending on the supercell structures. We demonstrate that the interval of the diffraction angle (θ) of the laser beams is inversely proportional to the length of the supercell experimentally and theoretically. By tuning the length of supercells as well as the length of 1st-order and 2nd-order regions, the interval θ was tuned from 0.1° to 43° with the different arc emission patterns. With the reduction of θ, i.e., the longer 1st-order region, a significant decrease in the laser threshold was obtained, resulting in the lowest lasing threshold of 2.5 ± 0.1 μJ/cm2 with ∼3.5 ns of a long pulse width excitation source.

Azimuthal controlling of electromagnetically induced phase grating in five-level quantum systems

In this paper, we suggest a theoretical model for creating a two-dimensional (2D) electromagnetically induced phase grating in a five-level quantum system interacting with a weak probe light, two coupling standing light in the x and y directions and a Laguerre–Gaussian (LG) field. By derivation of the Maxwell’s wave equation, we obtain the dynamic response of the probe light in the quantum system. Then, we perform the analytical solution of the probe susceptibility for obtaining the linear and nonlinear properties of the medium. By numerical calculations, we discuss the amplitude and phase modulations and Fraunhofer diffraction patterns of the probe light in different parametric conditions. We show that by adjusting the orbital angular momentum (OAM) of the LG light a 2D grating is observed. Moreover, we find that the probe energy can be transferred from zero order to high order of direction when we change the OAM number of LG light. Our proposed model may have potential applications in fundamental research and quantum information processing based on OAM light in quantum systems.

Random lasing at localization induced in correlated colloidal system

Random lasers have the potential for cheap and coherent light sources which, in the particular case of colloidal suspensions, are completely flexible and can take on any desired shape. Here, we studied random lasing in correlated colloidal systems composed by TiO2@Silica nanoparticles suspended in ethanol solutions of Rhodamine 6G. TiO2 particles with two different silica layers (thicknesses of 40 nm and 70 nm) were prepared. The Random laser performance improves when the silica shell is thicker (70 nm), which was attributed to a stronger localization of light (higher density of localized states) induced by stronger correlation in the scatterers' (TiO2@Silica) position as a consequence of a stronger and longer-range Coulomb interaction between the scatterers. Light diffraction patterns in both TiO2@Silica suspensions showed a stronger correlation in the scatterers’ position, being stronger when the silica shell is thicker.

Deeply sub-wavelength non-contact optical metrology of sub-wavelength objects

Microscopes and various forms of interferometers have been used for decades in optical metrology of objects that are typically larger than the wavelength of light λ. Metrology of sub-wavelength objects, however, was deemed impossible due to the diffraction limit. We report the measurement of the physical size of sub-wavelength objects with deeply sub-wavelength accuracy by analyzing the diffraction pattern of coherent light scattered by the objects with deep learning enabled analysis. With a 633 nm laser, we show that the width of sub-wavelength slits in an opaque screen can be measured with an accuracy of ∼λ/130 for a single-shot measurement or ∼λ/260 (i.e., 2.4 nm) when combining measurements of diffraction patterns at different distances from the object, thus challenging the accuracy of scanning electron microscopy and ion beam lithography. In numerical experiments, we show that the technique could reach an accuracy beyond λ/1000. It is suitable for high-rate non-contact measurements of nanometric sizes of randomly positioned objects in smart manufacturing applications with integrated metrology and processing tools.

Emission from silicon as a real-time figure of merit for laser-induced periodic surface structure formation

In this work femtosecond laser treatment of crystalline silicon was performed with the aim of producing laser-induced periodic surface structures (LIPSSs), and emission from the processing area was measured. Broad photoluminescence (PL) of the oxidized silicon, second-harmonic generation (SHG) of the laser radiation on the structured surface and sharp emission lines (ELs) of the ablated silicon atoms were detected. The ratio of intensities of SHG to PL (or SHG to EL) is suggested as a real-time figure of merit for LIPSS formation. Diffraction patterns of white light on the produced LIPSS confirm this suggestion.

Student recognition of interference and diffraction patterns: An eye-tracking study

Previous studies have demonstrated that students have difficulties in applying the wave model of light to explain single-slit diffraction and double-slit interference patterns. In this study, we investigated if students could recognize typical interference and diffraction patterns at all. Eye movements of high-school students were measured while they were identifying patterns produced by monochromatic light on a double slit, single slit, and diffraction grating, and by white light on a diffraction grating. Most students had difficulties with recognizing double-slit interference pattern and diffraction grating pattern of monochromatic light. Identification of the single-slit diffraction pattern was easier probably due to its distinguishable central maximum. The easiest task for students was recognizing the diffraction pattern of white light on an optical grating. Eye-tracking data suggested that even students who incorrectly answered this question were aware that the diffraction grating separates white light into colors. Additionally, eye tracking revealed that students who identified patterns correctly attended more the correct pattern than other options, thus corroborating previous findings. Overall, the results indicate that the recognition of interference and diffraction patterns is quite demanding for students, suggesting that more attention should be paid to observing and understanding basic wave optics phenomena.

An Analytical Study of the Diffraction of Light by a Circular Aperture Using Spherical Harmonics for n≤1

Based on the importance of spherical harmonics and their applicability in many physical problems, this research aimed to study the diffraction pattern of light by a circular aperture starting from the first Rayleigh–Sommerfeld diffraction equation and to expand the polar radius of a point on the surface of the circular aperture based on spherical harmonics. We depended on this theoretical framework in our paper. We calculated the optical intensity compounds C00,C10,C11,C1−1 for n=0,1,m=−1,0,1. We studied the intensity distributions in three special cases (along the optical axis, at the geometrical focal plane, and along the boundary of the geometrical shadow). We presented numerical comparative examples to illustrate the variation of the intensity versus a ratio (Z/A is the ratio of the distance between the circular aperture and the observation plane to a radius of the circular aperture), and we used Maple program to represent these results. We noticed that the expansion we made using spherical harmonic analysis led to an increase in the number of fringes bright enough to be visible to the naked eye. We then concluded with a brief discussion of the results.

Chromaticity analysis of diffraction pattern of white light under the grating

From the D65 daylight source, the ten monochromatic lights were evenly selected to be mixed into white light. After grating diffraction, color mixing was performed by using the chromaticity method with the relative intensity as the proportionality factor. The mixed color and its chromaticity parameters at specific diffraction angle positions were obtained to calculate L*, a*, b* and dominant wavelength. The relationship between the parameters of the grating and the chromaticity parameters of the mixed color was studied separately. The results showed that the color of the white light diffraction pattern at the diffraction angle θ = 2° is most significantly affected by d, followed by N. There is well linear correlation between b and L*, a*, b* values; but the effect of b on the color is not obvious. Then the relationship between the light intensity of ten kinds of monochromatic lights and the grating constant according to the grating diffraction intensity equation were drew, and the “rainbow” phenomenon was found. Current method for calculating the average wavelength of mixed colors directly from the “rainbow” graph is verified to be equivalent to the chromaticity method.

Quantitative phase imaging based on Fresnel diffraction from a phase plate

The structural complexity and instability of many interference phase microscopy methods are the major obstacles toward high-precision phase measurement. In this vein, improving more efficient configurations as well as proposing methods are the subjects of growing interest. Here, we introduce Fresnel diffraction from a phase step to the realm of quantitative phase imaging. By employing Fresnel diffraction of a divergent (or convergent) beam of light from a plane-parallel phase plate, we provide a viable, simple, and compact platform for three-dimensional imaging of micrometer-sized specimens. The recorded diffraction pattern of the outgoing light from an imaging system in the vicinity of the plate edge can be served as a hologram, which would be analyzed via the Fourier transform method to measure the sample phase information. The period of diffraction fringes is adjustable simply by rotating the plate without the reduction of both the field of view and fringe contrast. The high stability of the presented method is affirmatively confirmed through comparison of the result with that of the conventional Mach–Zehnder based digital holographic method. Quantitative phase measurements on silica microspheres, onion skins, and red blood cells ensure the validity of the method and its ability for monitoring nanometer-scale fluctuations of living cells, particularly in real-time.

The Spatial Resolution of Bat Biosonar Quantified with a Visual-Resolution Paradigm

Bats are navigation super-performers, flying at high speed through nocturnal forests. Numerous field observations and formal experiments have impressively shown how well bats tackle navigation in 3D with biosonar, i.e., the auditory analysis of self-generated ultrasonic emissions [1-7]. However, unlike in the visual system, where space is explicitly coded at very high resolution in the retinal fovea, the inner ear encodes frequency and time, not space. Spatial attributes of echoes are represented in the space-dependent filtering of the bats' pinnae [8, 9] and binaural computations, like interaural time and level differences [10, 11], as first proposed by Lord Rayleigh [12]. Remarkably, Rayleigh also provided a clear definition of spatial resolution: based on the shape of optical diffraction patterns arising from two closely spaced light sources, Rayleigh defined resolution as the capability to detect a trough in their joint light diffraction patterns [13, 14]. Here, we recruit Rayleigh's classical resolution paradigm to quantify how well bats can resolve multiple simultaneously presented reflectors in space. We show that biosonar spatial resolution in azimuth is no better than about 80° compared to a human visual resolution down to 0.02° [14]. We suggest that bats compensate this effective lack of spatial resolution by sequentially probing their environment in flight. Our data show that low-resolution environment perception is a viable alternative to high-resolution vision to support intelligent behavior in complex environments.

Anisotropy effects on the kinetics of colloidal crystallization and melting: comparison of spheres and ellipsoids.

We use alternating current (AC) electric field assisted self-assembly to produce two-dimensional, millimeter scale arrays of ellipsoidal colloids and study the kinetics of their phase reconfiguration by means of confocal microscopy, light scattering, and computer simulation. We find that the kinetics of orientational and positional ordering can be manipulated by changing the shape of the colloids: ellipsoids with aspect ratio 2.0 melt into disordered structures 5.7 times faster compared to spheres. On the other hand, ellipsoids self-assemble into ordered crystals at a similar rate to spheres. Confocal microscopy is used to directly visualize defects in the self-assembled structures. Small-angle light scattering (SALS) quantifies the light diffraction response, which is sensitive to the kinetics of positional and orientational ordering in the self-assembled anisotropic structures. We find three different light diffraction patterns: a phase with high orientational order (with chain-like structure in real space), a phase with high positional and orientational order (characteristic of a close-packed structure), and a phase that is disordered in position but with intermediate orientational order. The large influence of aspect ratio on the kinetics of the positionally and orientationally ordered phase is explored through simulation; it is found that the number of particle degrees of freedom controls the difference between the melting rates of the ellipsoids and spheres. This research contributes to the understanding of reconfiguration kinetics and optical properties of colloidal crystals produced from anisotropic colloids.

Solid-state Morphology Evolution of Sodium Neutralized Poly(ethylene-ran-methacrylic acid) Ionomer Under Dry and Wet Thermal Annealing

The DSC low temperature endothermic peak shown by sodium neutralized poly(ethylene-random-methacrylic acid) (E/MAA-Na+) ionomers in the range of 50-70 oC is attributed to the endothermic reordering of polyethylene chain segments belonging to two populations of quasi-crystals set from melt, initially showing no birefringence. Dry or wet thermal annealing improve their polyethylene chain segments packing expelling out the non-crystallizable methacrylic mers by absorbing and storing heat, converting them into better-organized crystals. Upon heating further they melt, using the stored energy. Hydrothermal annealing separates the relaxation of the PE chain segments inside the ionic clusters and their reordering: i) water plasticizes the ionic clusters, downshifting the relaxation temperature, detected either by static (DSC) or dynamic (DMTA) thermal analysis and, ii) shifts upwards the endothermic peak due to the reordering of PE chain segments, detected optically by cross-polarized light and X-Ray diffraction patterns.

Experimental study of 1-μm-pitch light modulation of a liquid crystal separated by dielectric shield walls formed by nanoimprint technology for electronic holographic displays

One-dimensional 1-μm-pitch light modulation was achieved experimentally using a liquid crystal (LC) device for wide viewing-zone angle holographic displays. When the pixel pitch of the LC device is 1 μm, individual pixel driving is extremely difficult due to electric field leakage and penetration of the elastic force of the LC from adjacent pixels. To overcome these problems, a dielectric shield wall structure is suggested, with dielectric walls between pixels. An LC cell with a dielectric shield wall structure was fabricated using nanoimprint technology; the individuality of the light modulation and diffraction pattern produced by the LC cell was evaluated. Our results showed that the dielectric shield wall structure achieved individual 1-μm-pitch light modulation and a diffraction angle of 19 deg at a wavelength of 633 nm. The remaining layer of the dielectric resin, which is surplus dielectric resin under the dielectric walls produced by the nanoimprint procedure, should be reduced as it tends to increase the driving voltage and electric field leakage from adjacent pixels.