Self-imaging Phenomenon Research Articles

Unidirectional self-imaging in multiple shifted photonic crystal interfaces.

In this study, we investigate the unidirectional self-imaging phenomenon in the shifted photonic crystal (PC) heterostructure. A spin-locked topological edge state, which originates from the mismatch of the Wannier center positions, can propagate along the shifted PC interface without backscattering. When the neighboring shifted PC interfaces are close enough, the coupling between the edge states happens, and coupled edge states (CES) can be found. Based on the finite element method (FEM) simulation, the spin-locked multimode interference (MMI) and self-imaging phenomenon of CES, including paired and symmetrical interference, are achieved in multiple shifted PC interfaces. To illustrate the application of the frequency splitters, the T-shaped and double cross-shaped structures with backscattering immunity and spin-locked characteristics are proposed. Our work provides an alternative way toward the design of a topological splitter by utilizing the photonic frequency and spin degrees of freedom at the same time.

Talbot phenomenon in binary optical gratings under Gaussian illumination

Binary optical gratings are used in applications such as optical metrology. Due to the fact, that self-imaging phenomenon depends on the grating fill factor, in present work the effect of fill factor on Talbot image formation has been analyzed when the grating is illuminated with a Gaussian beam. A model based on Fresnel regime is used to determine the intensity distribution in the near field. Self-images are obtained under different initial beam conditions and it is found several regimes of the effect of Gaussian beam intensity distribution on the self-images are found: (I) decreasing intensity of grating slit at the beam border when Gaussian waist radius is 10 times greater than grating period, (II) transforming binary-like self-image to the cosine-like one in case when Gaussian waist radius ranges from 2 to 5 grating periods, and (III) disappearing regular grating structure when Gaussian waist radius is less than grating period. Additionally it is analyzed transform from Fresnel to Fraunhofer regime in case of Gaussian beam and effect of wavefront curvature radius value on the distance where different regimes appear.

Spin-wave self-imaging: Experimental and numerical demonstration of caustic and Talbot-like diffraction patterns

Extending the scope of the self-imaging phenomenon, traditionally associated with linear optics, to the domain of magnonics, this study presents the experimental demonstration and numerical analysis of spin-wave (SW) self-imaging in an in-plane magnetized yttrium iron garnet film. We explore this phenomenon using a setup in which a plane SW passes through a diffraction grating, and the resulting interference pattern is detected using Brillouin light scattering. We have varied the frequencies of the source dynamic magnetic field to discern the influence of the anisotropic dispersion relation and the caustic effect on the analyzed phenomenon. We found that at low frequencies and diffraction fields, the caustics determine the interference pattern. However, at large distances from the grating, when the waves of high diffraction order and number of slits contribute to the interference pattern, the self-imaging phenomenon and Talbot-like patterns are formed. This methodological approach not only sheds light on the behavior of SW interference under different conditions but also enhances our understanding of the SW self-imaging process in both isotropic and anisotropic media.

Adaptive methods of generating complex light arrays.

Structured light arrays of various shapes have been a cornerstone in optical science, driven by the complexities of precise and adaptable generation. This study introduces an approach using a spatial light modulator (SLM) as a generator for these arrays. By projecting a holographic mask onto the SLM, it functions simultaneously as an optical convolution device, focusing mechanism, and structured light beam mask. Our approach offers unmatched versatility, allowing for the experimental fabrication of traditional beam arrays like azimuthal Laguerre-Gaussian (LG), Bessel-Gaussian (BG), and Hermite-Gauss (HG) in the far-field. Notably, it has enabled a method of generating Ince-Gauss (IG) and LG radial mode beam arrays using a convolution solution. Our system provides exceptional control over array periodicity and intensity distribution, bypassing the Talbot self-imaging phenomenon seen in traditional setups. We provide an in-depth theoretical discussion, supported by empirical evidence, of our far-field results. This method has vast potential for applications in optical communication, data processing, and multi-particle manipulation. It paves the way for rapid generation of structured light with high spatial frequencies and complex shapes, promising transformative advances in these domains.

Superwavelength self-healing of spoof surface sonic Airy-Talbot waves

Self-imaging phenomena for nonperiodic waves along a parabolic trajectory encompass both the Talbot effect and the accelerating Airy beams. Beyond the ability to guide waves along a bent trajectory, the self-imaging component offers invaluable advantages to lensless imaging comprising periodic repetition of planar field distributions. In order to circumvent thermoviscous and diffraction effects, we structure subwavelength resonators in an acoustically impenetrable surface supporting spoof surface acoustic waves (SSAWs) to provide highly confined Airy-Talbot effect, extending Talbot distances along the propagation path and compressing subwavelength lobes in the perpendicular direction. From a linear array of loudspeakers, we judiciously control the amplitude and phase of the SSAWs above the structured surface and quantitatively evaluate the self-healing performance of the Airy-Talbot effect by demonstrating how the distinctive scattering patterns remain largely unaffected against superwavelength obstacles. Furthermore, we introduce a new mechanism utilizing subwavelength Airy beam as a coding/decoding degree of freedom for acoustic communication with high information density comprising robust transport of encoded signals.

Talbot wavefront sensor measurement possibilities under gaussian illumination

Present paper deals with the measurement errors in Talbot wavefront sensor under Gaussian illumination conditions. The measurement possibilities of wavefront sensor based on the self-imaging phenomenon is investigated theoretically and based on the simulation results. A theoretical model based on Fresnel regime is used in order to determine the intensity distribution in the near field. The effect of Gaussian field is described in the terms of spatial spectrum of the grating image. On the basis of four different gratings was shown that Gaussian field affects on the spatial spectrum of the grating self-image if Gaussian waist is less than two grating periods and self-images of used gratings are almost the same. Four kinds of gratings are tested for their performance in the wavefront sensor. Simulation results show that binary gratings with square and circle unit cells show less value of measurement error in comparison with gratings that have cosine and Gaussian profiles.

Discrete Talbot effect in modulated lattices with PT symmetric perturbations

We demonstrate both theoretically and numerically that the periodic self-imaging phenomenon of light patterns with certain input periods can be effectively realized in a three-layered optical lattice with parity–time symmetric modulations, which can introduce a modulation phase to the lattice structure. By varying the ratio of coupling coefficients, the Talbot distance can be engineered, which can be further tuned by adjusting the modulation phase. The Talbot effect occurs only if the modulation phase belongs to a specific set: {±π/3,±π/2,±2π/3,±π}.

Unidirectional mode interference in magneto-optical photonic heterostructure

We investigate a unidirectional mode interference effect based on one-way coupled topological edge states (CTESs), which originate from the coupling of topological edge states (TESs) in magneto-optical photonic crystal (MOPC) heterostructure. By using the finite element method, the self-imaging phenomenon in the MOPC heterostructure is predicted. As an example of applications, a one-way tunable frequency and power splitter based on unidirectional mode interference is designed, which is reflectionless. Besides, the splitting ratio can be tuned by adjusting the external magnetic field. Moreover, the splitter is robust against common disorders, including the radius- and position-fluctuations of pillars and nonuniform magnetizations, which keep the bandgap open. Our findings provide a new, to the extent of our knowledge, way of designing integrated photonic circuit applications such as reflectionless filters, couplers, multiplexers, switches, or even nonreciprocal devices, and so on.

Aberration measurements by a Talbot wavefront sensor in the presence of intensity variations

This paper deals with theoretical investigations of the measurement accuracy of optical aberrations by a Talbot wavefront sensor in the presence of random amplitude variations. The theoretical prediction of the intensity distribution for gratings of any type based on their spatial spectrum is obtained, and it is shown that the grating is fully restored in the Talbot plane even for a high fraction of random amplitude. The possibilities of the self-imaging phenomenon are investigated based on the simulation results. The simulation results show that pit displacement error increases when the correlation length decreases or when the grating spatial spectrum increases. For second- and third-order aberrations, the intensity variations decrease the measured value and increment value of aberrations of the same order.

Detailed investigation of spectral properties of SMS fiber segment and its sensing performance under varying multimode fiber lengths

Here, a comprehensive analysis of the impact of the multimode fiber (MMF) lengths on different sensitivities of single mode-multi mode-single mode (SMS) fiber segment sensor probe under different external perturbations such as temperature, strain and refractive index has been propounded and studied thoroughly. In addition, different phenomenal characteristics of the SMS segment namely fast Fourier transform, fringe visibility, the free spectral range of the observed transmission spectrum and most importantly the self-imaging phenomena have been investigated meticulously. These aforementioned characteristics are also verified theoretically. The experimental results show that the sensitivities increase with an increase of the MMF length and are restricted to 12 cm length due to the superimposing and less resolution of the probing dips beyond this. Experimental results illustrate that our proposed sensing probe is capable to achieve superior sensitivities better than 93 pm/°C, −2.56 pm/ με and −38.55 nm/RIU for temperature, strain and refractive index, respectively for the 12 cm length of the MMF. The higher sensitivities and resolutions assure potential employment and promising solution of the proposed sensor in various sensing applications.

A diffraction experiment at the near field: the homemade Talbot effect

Diffraction refers to a kind of optical phenomena which occurs when light approaches an element (object or aperture) whose features are in the range of the illuminating wavelength (small apertures, sharp edges). It can be explained by means of the undulatory nature of light or also geometrically by using simple ray optics. Diffraction phenomena are impressive and not intuitive, so it makes them very interesting to bring examples to the classroom. The most popular diffraction experiments show effects in Fraunhofer regime, that is to be said, far from the diffractive object. Common examples are the single or double slit experiments. In this manuscript, we propose and show a less common diffractive effect that occurs in the Fresnel regime, near to the diffractive object. It is the Talbot effect or self-imaging phenomenon, which appears by illuminating a diffraction grating with a collimated monochromatic beam. It consists of the apparition of replicas (self-images) of the grating intensity pattern at periodic distances, multiples of the so-called Talbot distance. We show how this effect may be shown into the classroom with cheap and easy to find elements. In addition, we take advantage of its dependence on the coherence degree of the source to introduce the concept of optical coherence and show its effect on the contrast of the Talbot self-images. These experiments could be appropriate for undergraduate students or introductory physics courses.

Reconstruction of Talbot self-image using Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is used to merge a sequence of low-resolution Talbot images into a high-resolution image with a large field of view such that both integer and fractional Talbot lengths are clearly resolved. It is also revealed that the diffraction orders present in the dark field Fourier plane images reconstructed based on the Talbot effect i.e. the microscope’s back focal plane images are the ones responsible for rendering FPM amenable for the self-imaging phenomena. These diffraction spots have an arced-shaped diffraction patterns which are consistent with the Talbot image when illuminated with a parabolic wavefront. i.e. Gaussian sums only for the dark field images, and are crucial for FPM to successfully achieve a full complex image recovery. Herein, the Talbot image is treated as a phase-recovery problem, and further analyses are presented by comparing the performance of FPM when the periodic grating Talbot effect is imaged with other standard phase-recovery methods, namely the Fienup and Gercberg-Saxton algorithms.

Simple setup to measure the phase map of transparent objects based on incoherent self-imaging

We demonstrate how a simple optical setup based on the incoherent self-imaging phenomenon can be used to capture two-dimensional phase maps of transparent (phase) objects. We prove that the derivative of the object’s phase map can be extracted from the self-image. Simulations of self-images from a semi-spherical transparent object confirm the theoretical results. As proof-of-principle examples, experimental phase profiles obtained for water droplets on glass, and also a hydrophobic substrate are presented and compared. The phase maps are extracted from a single self-image, using the Fourier analysis, that makes this technique favorable for real-time measurements on dynamic samples.

Scaling quasi-self-imaging effect based on the one-dimensional Pearcey beam

We present a new type of self-imaging phenomenon named the scaling quasi-self-imaging effect, which is produced by adding shifted copies of the fundamental Pearcey beam. The recurrent solutions of two kinds of incident beams comprising one-dimensional ideal infinite Pearcey and apodized Gaussian Pearcey beams are found. The diffraction process is equivalent to that obtained where a disorder wave is transmitted through a “virtual” periodic grating at focusing plane; both the integer and fractional self-images of the intensity distribution on focusing plane can be induced at constant revival distance accompanied by a scaling, autofocusing, and inverse envelope propagation. The self-imaging image begins to invert after the focus plane, where the rate of scaling reaches a maximum value and a series of Gaussian-like bright spots is generated. Our theoretical predictions are numerically confirmed.

Aberration measuring in the random phase field by the Talbot wavefront sensor.

The accuracy of measuring optical aberrations in the random phase field by the Talbot wavefront sensor is theoretically investigated. The possibilities of a grating self-imaging phenomenon in the random phase field are investigated based on the simulation results. Random fields of two different types are considered: amplitude and phase Gaussian fields. Simulation results show that the cosine grating is more stable for phase noise in comparison with gratings that have Gaussian and square binary profiles on each cell unit. It is found that phase noise gives increments of high-order aberrations for wavefront reconstruction.

A simple approach to the suppression of the Gibbs phenomenon in diffractive numerical calculations

The Gibbs phenomenon is a well-known effect that is produced at discontinuities of a function represented by the Fourier expansion when it is truncated to perform numerical calculations. This phenomenon appears because it is not possible to fit a discontinuous function as the summation of continuous functions, such as it is done with the Fourier expansion. Only considering infinite terms of the summation, the Fourier expansion fits the real signal. From a general point of view, it will affect to the final results since the representation of the signal does not include higher frequencies. It is true that the higher is the truncation, the better are the results, but an error is always committed. The Gibbs phenomenon has been studied in electric signal and diffractive optics, where the Fourier expansion is commonly used. In this work, we drop complex mathematics to show the effect of the Gibbs phenomenon on the near field propagation of diffraction gratings (self-imaging phenomenon) and also possible implementations of some corrections which allow diminishing the analytical or numerical errors in comparison with less accurate approaches. Anyway, the conclusions of this work would be applicable to other numerically solved diffractive problems which include sharp edges apertures. Simulations are compared with experiments giving interesting results.

Exposed-core fiber multimode interference sensor

In this manuscript, we report on, to the best of our knowledge, the first experimental realization of a multimode interference device based on self-image phenomenon accomplished by using a microstructured-cladding exposed-core fiber set in a singlemode-multimode-singlemode (SMS) configuration. Its application as a refractive index sensor is also demonstrated. The specialty multimode fiber studied herein exhibits a holey microstructure that surrounds and defines the fiber core. The latter, in turn, interfaces the external fiber environment thanks to lateral access along the entire fiber length. To explore the device's sensing capabilities, numerical simulations have been carried out, and the system sensitivity and spectral characteristics were evaluated. The experimental results demonstrate a refractive index sensitivity of 890 nm/RIU in the refractive index range from 1.41 to 1.43 with a detection limit of 2.7 × 10−3 RIU. This novel SMS configuration has the potential to extend the capabilities of current multimode interference-based sensors by providing an additional path to the realization of refractive index monitoring in liquid samples.

Coherent-mode representation of self-imaging optical fields

The coherent-mode representation is a fundamental tool that helps us understand the processes of producing and propagating optical fields. In this work, such representation for self-imaging phenomena under partially coherent illumination is presented within the frame of partial coherence theory in the space-frequency domain. Additionally, it is shown that the well-known Talbot and Lau effects are particular cases included in this new formalism. When complete coherence of the field is considered, the general expression for coherent self-imaging of optical fields is obtained (Talbot effect for both linear and circular gratings are presented); on the other hand, when an incoherent superposition of an infinite number of modes are considered, the expression to describe the Lau effect is obtained.

Accelerating self-imaging effect based on cosh-Airy beams

We have investigated theoretically and numerically the accelerating self-imaging phenomenon for a superposition of cosh-Airy beams. The results show that when the real or imaginary part of the parameter of the cosh modulation function works, the accelerating self-imaging effect of the finite energy Airy beam and the quasi accelerating self-imaging effect of Airy beam with different initial launch angle can be obtained, respectively. Moreover, the cosh parameter cannot only change the accelerating self-imaging range but also control the trajectory of accelerating self-imaging. In addition, the accelerating self-imaging effect generated by selecting a large transverse displacement is further discussed. The numerical results are in good agreement with the theoretical results.

Spin-wave Talbot effect in a thin ferromagnetic film

The Talbot effect has been known in linear optics since the 19th century and has found various technological applications. In this paper, with the help of micromagnetic simulations, we demonstrate the self-imaging phenomenon for spin waves in a thin, out-of-plane and in-plane magnetized ferromagnetic film whose propagation is described by the Landau-Lifshitz nonlinear equation. We show that the main features of the obtained Talbot carpets for spin waves can be described, to a large extent, by the approximate analytical formulas yielded by the general analysis of the wave phenomena. Our results indicate a route to a feasible experimental realization of the Talbot effect at low and high frequencies and offer interesting effects and possible applications in magnonics.