Talbot carpet at the transverse plane produced in the diffraction of plane wave from amplitude radial gratings

Voltage-controlled two-dimensional Fresnel diffraction pattern in quantum dot molecules

This study explores the influence of inter-dot tunneling effects within a quantum dot molecule on the Fresnel diffraction phenomenon. Our findings indicate that the Fresnel diffraction of the output probe Gaussian field can be manipulated by adjusting the inter-dot tunneling parameter's strength and the characteristics of the coupling field. The inter-dot tunneling effect establishes a closed-loop system, setting conditions for the interference of the applied fields. We specifically examine a Laguerre-Gaussian (LG) coupling field, investigating how its properties-such as strength, value, and sign of the orbital angular momentum (OAM)-impact the Fresnel diffraction of the output probe field. Increasing the inter-dot tunneling parameter and the coupling LG field's strength allows for control over the spatial distribution of the Fresnel diffraction pattern. Notably, the inter-dot tunneling parameter can disturb the symmetry of the diffraction patterns. Additionally, considering a negative OAM for the coupling LG field transforms the diffraction pattern into its inverse shape. This suggests that, in the presence of the inter-dot tunneling effect, the Fresnel diffraction pattern is contingent on the direction of rotation of the helical phase front of the coupling LG field. Our results offer insights into quantum control of Fresnel diffraction patterns and the identification of OAM in LG beams, presenting potential applications in quantum technologies.

Three-dimensional optical multiple trapping using pure amplitude octagonal almost periodic structures

We demonstrate a novel method for three-dimensional optical multiple trapping using pure amplitude octagonal almost periodic structures (PAOAPSs). We use a Gaussian beam to diffract through these structures and create a three-dimensional array of trapping spots with the aid of an objective lens. Our device is simple, cost-effective, and easy to fabricate, and it has several advantages over conventional methods for trapping multiple particles. By adjusting the rotation of the PAOAPS and the polarization of the beam, we can simultaneously rotate the trapped particles in both axial and orbital directions. We show that our device achieves an ∼19-fold increase in trapping efficiency compared to a recently introduced method based on an amplitude radial grating. Furthermore, our device transfers about 1/70 of the transmitted beam power to each optical trap, which is much more efficient than a spatial light modulator (SLM).

Elliptical-ring-shaped Talbot effect in uniaxial crystals

In this paper, we propose a type of anisotropic elliptical-ring-shaped Talbot effect occurring in uniaxial crystals. The effect is realized by propagating a phase-only periodic elliptical-ring structure in the uniaxial crystal, orthogonal to the optical axis. Both phenomena of self-imaging at the Talbot distance and N-rings to one-ring convergence at the fractional Talbot distance were discussed. Numerical simulations were performed to demonstrate the correctness of theoretical derivation and the existence of the elliptical-ring-shaped Talbot effect. With the specific phase distribution, the N series of periodic elliptical rings of the incident plane will converge to one series of elliptical rings equally spaced at the fractional Talbot distance, where N is an even integer.

Gaussian beam diffraction from radial structures: detailed study on the diffraction from sinusoidal amplitude radial gratings

In this work, we report a comprehensive theoretical investigation on the diffraction of a Gaussian beam from structured radial apertures. In particular, the study of near- and far-field diffraction of a Gaussian beam from an amplitude radial grating having a sinusoidal profile provides new theoretical insights and possible applications. We observe a high self-healing feature at far-field for the Gaussian beam in the diffraction from amplitude radial structures. It is also shown that by increasing the spokes number of the grating, the strength of the self-healing decreases, and reforming of the diffracted pattern into a Gaussian beam occurs at longer propagation distances. The energy flow towards the central lobe of the diffraction pattern and its dependence on the propagation distance are also investigated. In the near-field regime, the diffraction pattern is very similar to the intensity distribution in the central area of the radial carpet beams generated in the diffraction of a plane wave from the same grating. It is shown that by optimally choosing the waist radius of the Gaussian beam, in the near-field regime, it is possible to have a petal-like diffraction pattern, which has been experimentally used in multiple-particle trapping. Compared to radial carpet beams, since in this case there is no energy in the geometric shadow of the radial spokes of the grating, the main part of the power of the incident Gaussian beam is transferred to the main intensity spots of the petal-like pattern, which significantly increases the multi-particle trapping efficiency. We also show that regardless of the grating spokes number, at the far field, the diffraction pattern becomes a Gaussian beam, and its power share reaches 2/3 of the total power passed through the grating.

Orbital angular momentum in the near-field of a fork grating

Light beams with Orbital Angular Momentum (OAM) are explored in applications from microscopy to quantum communication, while the Talbot effect revives in applications from atomic systems to x-ray phase contrast interferometry. We evidence the topological charge of an OAM carrying THz beam in the near-field of a binary amplitude fork-grating by means of the Talbot effect, which we show to persist over several fundamental Talbot lengths. We measure and analyze the evolution of the diffracted beam behind the fork grating in Fourier domain to recover the typical donut-shaped power distribution, and we compare experimental data to simulations. We isolate the inherent phase vortex using the Fourier phase retrieval method. To complement the analysis, we assess the OAM diffraction orders of a fork grating in the far-field using a cylindrical lens.

Theory and generation of heterogeneous 2D arrays of optical vortices by using 2D fork-shaped gratings: topological charge and power sharing management

In this work, by providing comprehensive theoretical foundations, we revisit and improve a simple and efficient method that has been used for generation of 2D orthogonal arrays of optical vortices with components having different topological charges (TCs). This method has been implemented by the diffraction of a plane wave from 2D gratings where the gratings' profiles are determined by iterative computational process. Here, based on the theoretical predictions, specifications of the diffraction gratings can be easily adjusted in a way to generate experimentally a heterogeneous vortex array with the desired power shares among different elements of the array. We use the diffraction of a Gaussian beam from a class of pure phase 2D orthogonal periodic structures having sinusoidal or binary profiles possessing a phase singularity, calling pure phase 2D fork-shaped gratings (FSGs). The transmittance of each of the introduced gratings is obtained by multiplying the transmittance of two pure phase 1D FSGs along x and y directions, having topological defect numbers l_x and l_y and phase variation amplitudes γ_x and γ_y, respectively. By solving the Fresnel integral, we show that the diffraction of a Gaussian beam from a pure phase 2D FSG leads to generation of a 2D array of vortex beams having different TCs and power shares. The power distribution among the generated optical vortices over the different diffraction orders can be adjusted by γ_x and γ_y, and it strongly depends on the profile of the grating. Meanwhile the TCs of the generated vortices depend on l_x and l_y and the corresponding diffraction orders, namely l_m,n = -(ml_x + nl_y) presents the TC of (m, n)th diffraction order. We recorded the intensity patterns of the experimentally generated vortex arrays which are fully consistent with the theoretically predicted results. Furthermore, the TCs of the experimentally generated vortices are measured individually by the diffraction of each of them through a pure amplitude quadratic curved-line (parabolic-line) grating. The absolute values and signs of the measured TCs are consistent with the theoretical prediction. The generated configuration of vortices with adjustable TC and power sharing features might find many applications such as non-homogeneous mixing of a solution consisting trapped particles.

Diffraction of Gaussian and Laguerre-Gauss beams from a circular aperture using the moment expansion method

A method based on the distribution theory is introduced to compute the Fresnel diffraction integral. It is applied to the diffraction of Gaussian and Laguerre-Gauss beams by a circular aperture. Expressions of the diffracting field are recast into a perturbation series describing the near- and far-field regions.

Optical vortex beam controlling based on fork grating stored in a dye-doped liquid crystal cell

In this paper, we investigate the generation and controlling of the optical vortex beam using a dye-doped liquid crystal (DDLC) cell. The spatial distribution of the quasi-sinusoidal orientation of the liquid crystal molecules creates a quasi-sinusoidal phase grating (PG) in the DDLC cell. Depending on the incident light pattern, Trans to Cis photoisomerization of the dye molecules affects the orientation of the liquid crystal molecules. To do so, an amplitude fork grating (FG) is used as a mask, and its pattern is stored in the cell by a pattern printing method as the PG. One of the particular features of the stored grating in the cell is its capability in the diffraction efficiency controlled by the applied electric field. The results show, based on the central defect in the FG pattern, the diffracted probe beam in different orders is optical vortices. As a new technique, this type of stored pattern acts like an amplitude grating but according to the results, its structure is in fact a PG. This technique leads to the vortex beam switching capability by applying an electric field to the cell. The results show that by applying 22 V, all the diffraction orders vanish. Meanwhile, the vortex beams reappear by removing the applied voltage. The diffraction efficiency of the vortex beams as well as its generation dependency on the polarization of the incident beam studied. The maximum efficiency of the first diffraction order for linear polarized incident beam was obtained at 0 V, about 8%. Based on the presented theory, a simulation has been done which shows the Cis form of the dye molecules has been able to change the angle of LC molecules on average about 12.7°. The study of diffracted beam profiles proves that they are electrically controllable vortex beams.

1D spatially chirped periodic structures: managing their spatial spectrum and investigating their near-field diffraction

This work introduces a class of 1D spatial-frequency-modulated structures with transmittance T(x), in which the period changes along the x axis so that the corresponding spatial frequency f(x) sinusoidally alternates between two values. It is shown that T(x) generally is an almost-periodic function and has an impulsive spatial spectrum. However, we find the condition under which T(x) is a periodic function and its spatial spectrum form a lattice of impulses. When the periodicity condition is fulfilled, we call these structures as 1D spatially chirped periodic structures. These structures are characterized by two natural numbers, named as n _c and n _{a v} , and a real parameter named as frequency modulation strength (FMS). As an important special case, we define a 1D spatially chirped amplitude sinusoidal grating (SCASG) based on the transmission function of a conventional amplitude sinusoidal grating, in which the phase of conventional amplitude sinusoidal grating is replaced by desired chirped phase. Then the spatial spectrum of a 1D SCASG is investigated in detail, and it is shown that the spatial spectrum can be managed by changing the value of FMS. In other words, the grating's spectrum can be manipulated by adjusting the value of FMS. This feature might find applications in optical sharing of the incident power among different diffraction orders. Moreover, near-field diffraction from 1D SCASGs is studied by using the so-called angular (spatial) spectrum method, and Talbot distances for these gratings are determined and verified experimentally. It is shown that the intensity profiles at quartet- and octant-Talbot distances strongly depend on the values of the parameters n _c and n _{a v} . In comparison with the conventional gratings, we see some new and interesting aspects in the diffraction from 1D SCASGs. For instance, unlike the conventional gratings, in some propagation distances, the diffraction patterns possess sharp and smooth intensity bars at which the intensity is several times of the incident light beam's intensity. It is shown that the maximum intensity of these bright bars over the diffraction patterns depends on the characteristic parameters of the grating, including n _c , n _{a v} , and FMS of the grating. These intensity bars might find applications for trapping and aggregation of particles along straight lines.

Generation of combined half-integer Bessel-like beams using synthetic phase holograms

We discuss the generation of combined half-integer Bessel-like (CHB) beams using synthetic phase holograms (SPHs). We assess the efficiency and accuracy of the SPHs, in the task of generating CHB beams. The proposal is illustrated by the implementation of CHB beams, which are experimentally generated in a setup based on a phase spatial light modulator. Also, we analyze, numerically and experimentally, the propagation of the generated CHB beams. As the main result, the SPHs are able to generate several CHB beams with relatively high accuracy. Additionally, it is obtained that the efficiency values of the SPHs are close to the theoretical predictions.

Retrieving the Talbot length of arbitrary 2D gratings

The Talbot effect has been revived in many fields of modern optics. As a key number of self-imaging, the fundamental Talbot length plays a crucial role in many applications. However, the inspection of the Talbot carpet for determining the Talbot length is applicable only if the 2D field distribution behind the grating is represented by a 1D cross section. In this Letter, we show an effective way to overcome this limitation to explore the self-imaging of gratings with complex 2D periodicities. For that purpose, the near-field diffraction is analyzed using the Pearson correlation coefficient of the intensity distribution in Fourier space. We report results on linear, ring, and spiral gratings.

A Data Transmission Method with Spectral Switches via Electroabsorption

In the past, the waveguide electroabsorption effect has generally been used as an intensity modulator for quasi-monochromatic light, such as lasers. Here, we study how this effect affects polychromatic light spectra. We find that for light with a Gaussian distribution spectrum, the spectral peak shift (red shift or blue shift) can be controlled by the magnitude of the applied voltage, as long as the center wavelength and the spectral band are properly selected. This result can be used as a data transmission scheme at the integrated chip level or in free space. It may offer a good option for some other light sources, such as low-cost LED or ELED (edge emitting LED), with wider spectral bandwidths.

Tunneling-induced Talbot effect

We investigate the reforming of a plane wave into a periodic waveform in its propagation through a structural asymmetry four-level quantum dot molecule (QDM) system that is induced by an inter-dot tunneling process and present the resulting tunneling-induced Talbot effect. The tunneling process between two neighborhood dots is provided with the aid of a gate voltage. Using a periodic coupling field the response of the medium to the propagating plane probe beam becomes periodic. The needed periodic coupling field is generated with the interference of two coherent plane waves having a small angle and propagating almost parallel to the probe beam direction. In the presence of the tunneling effect of an electron between two adjacent QDs, for the probe beam propagating through the QDM system, the medium becomes transparent where the coupling fields interfere constructively. As a result, the spatial periodicity of the coupling field modulates the passing plane probe beam. We determine the minimum length of the QDM system to generate a periodic intensity profile with a visibility value equal to 1 for the probe field at the exit plane of the medium. It is also shown that by increasing the propagation length of the probe beam through the QDM medium, the profile of the maximum intensity areas becomes sharper. This feature is quantified by considering a sharpness factor for the intensity profile of the probe beam at the transverse plane. Finally, we investigate free space propagation of the induced periodic field and present the Talbot images of the tunneling-induced periodic patterns at different propagation distances for different values of the QDM medium lengths. The presented dynamically designing method of the periodic coherent intensity patterns might find applications in science and technology. For instance, in optical lithography, the need to use micro/nanofabricated physical transmission diffraction gratings, in which preparation of them is expensive and time-consuming, can be eliminated.

Vector vortex state preservation in Fresnel cylindrical diffraction

The vector vortex light beam, which exhibits a space-variant polarization state and is coupled with orbital angular momentum of light, has been drawing much attention due to its fundamental interest and potential applications in a wide range. Here we reveal both theoretically and experimentally that a diffractive structure having cylindrical symmetry is shown to be transparent for the vector vortex state of light with arbitrary topology. We demonstrate such an intriguing phenomenon in the Fresnel diffraction condition, where the vector Helmholtz wave equation can be utilized in the paraxial regime. Our demonstration has implications in control and manipulation of vector vortex light beams in diffractive optics, and hence, it may find potential applications.

Gear-like rotatable optical trapping with radial carpet beams

Optical tweezers have become a powerful tool in the fields of biology, soft condensed matter physics, and nanotechnology. Here, we report the use of recently introduced radial carpet beams (RCBs) in the optical tweezers setup to trap multiple particles. An RCB is produced by diffraction of a plane or Gaussian beam from an amplitude radial grating. Because of the radial symmetry of the grating, all the diffraction orders are propagated along the optical axis and are used for trapping. Based on the number of grating spokes, the produced RCB has a definite number of high-intensity spots on the transverse plane located over a circular ring. These high-intensity spots of the beam provide multi-traps when it passes through an objective lens and have enough gradient force to trap polystyrene and silica particles. Moreover, the diffracted light from the grating has this property to transfer the angular momentum. We show that the multi-trapped birefringent particles could rotate in their own traps when polarization of the trapping RCB to be circular. In addition, the orbital rotation of the particles is simply executable by manually rotating the grating in its plane around the optical axis.

Talbot effect of azimuthally periodic Bessel-based structures

In this work, the theory of self-imaging in the polar coordinates for azimuthally periodic Bessel-based structures (APBBSs) is presented. For the first time, to the best of our knowledge, we define single- and multi-frequency APBBSs and show that these structures have self-images under plane-wave illumination. We also define sinusoidal and binary-like single-frequency APBBSs and theoretically and experimentally investigate the near-field diffraction of these structures. The diffraction from these structures provides 2D arrays of optical traps that can be used in multi-trapping.

An azimuthally-modified linear phase grating: Generation of varied radial carpet beams over different diffraction orders with controlled intensity sharing among the generated beams

Diffraction gratings are important optical components and are used in many areas of optics such as in spectroscopy. A diffraction grating is a periodic structure that splits and diffracts the impinging light beam into several beams travelling in different directions. The diffracted beams from a grating are commonly called diffraction orders. The directions of the diffraction orders depend on the grating period and the wavelength of the impinging light beam so that a grating can be used as a dispersive element. In the diffraction of a plane wave from a conventional grating, the intensities of diffracted beams decrease with increasing order of diffraction. Here, we introduce a new type of grating where in the diffraction of a plane wave, the intensity of a given higher order diffracted beam can be higher than the intensity of the lower orders. We construct these gratings by adding an azimuthal periodic dependency to the argument of the transmission function of a linear phase grating that has a sinusoidal profile and we call them azimuthally-modified linear phase gratings (AMLPGs). In this work, in addition to introducing AMLPGs, we present the generation of varied radial carpet beams over different diffraction orders of an AMLPG with controlled intensity sharing among the generated beams. A radial carpet beam is generated in the diffraction of a plane wave from a radial phase grating. We show that for a given value of the phase amplitude over the host linear phase grating, one of the diffraction orders is predominant and by increasing the value of the phase amplitude, the intensity sharing changes in favor of the higher orders. The theory of the work and experimental results are presented. In comparison with the diffraction of a plane wave from radial phase gratings, the use of AMLPGs provides high contrast diffraction patterns and presents varied radial carpet beams over the different diffraction orders of the host linear phase grating. The resulting patterns over different diffraction orders are specified and their differences are determined. The diffraction grating introduced with controlled intensity sharing among different diffraction orders might find wide applications in many areas of optics such as optical switches. We show that AMLPG-based radial carpet beams can be engineered in which they acquire sheet-like spokes. This feature nominates them for potential applications in light sheet microscopy. In addition, a detailed analysis of the multiplication of the diffraction pattern of an AMLPG by the 2D structure of a spatial light modulator is presented. The presented theory is confirmed by respective experiments.

Colorful radial Talbot carpet at the transverse plane

In this work we theoretically and experimentally investigate the diffraction of spatially coherent and collimated white light beam from radial amplitude gratings. Theoretical part of the work is resolved with the Fresnel-Kirchhoff integral. In the experimental part, a collimated wave-front of a white light beam emitting from a halogen lamp is transmitted through a radial amplitude grating. We digitally record the diffraction pattern in various distances from the grating using a CCD camera. The resulted diffraction pattern that we call it "Colorful radial Talbot carpet at the transverse plane" has a shape-invariant form under propagation. The other significant aspects of this pattern are the existence of a quite patternless dark area located around the optical axis and an intense rainbow-like ring in the vicinity of the patternless area. The rainbow color changes radially from the violet in the vicinity of the patternless area to red by increasing the radius in which the purity of the colors in the inner side is dominant. We call this phenomena "diffraction-based rainbow". In addition, the transverse plane Talbot carpet pattern consists colorful self-images of the grating's spokes at the larger radii. The theoretical calculations and experimental results verify each other completely. The introduced diffraction-based rainbow can be utilized in spectrometry.

Theory of diffraction of vortex beams from structured apertures and generation of elegant elliptical vortex Hermite-Gaussian beams

In this work, a comprehensive analytic study of the diffraction of vortex beams from structured apertures is presented. We formulate the near- and far-field diffraction of a vortex beam from an aperture having an arbitrary functionality in the Cartesian coordinates by two general and different approaches. We show that each of the resulting diffraction patterns can be determined by a number of successive derivatives of the 2D Fourier transform of the corresponding hypothetical aperture function or equally can be obtained by a summation of 2D Fourier transforms of the corresponding modified aperture function. We implement both introduced analytic approaches in predicting the diffraction of a vortex beam from an elliptic Gaussian aperture, an elliptic Gaussian phase mask, and a hyperbolic Gaussian phase mask in the near- and far-field regimes. It is shown that the predicted diffraction patterns by both these approaches are exactly the same. It is shown that the diffraction of a vortex beam from an elliptic Gaussian aperture at the far-field regime forms a light beam that belongs to a family of light beams we call elegant elliptical vortex Hermite-Gaussian beams. In addition, the diffractions of a vortex beam from a Fresnel zone plate in general form for the on- and off-axis situations are formulated, and sinusoidal and binary zone plates are investigated in detail. Our general analytic formula can be used for a large variety of apertures including off-center situations and asymmetrical cases.

Information transmission using radial carpet beams

A radial carpet (RC) beam is a new class of beams that is a subfamily of combined half-integer Bessel-like beams, which are a set of solutions for wave equations and introduced recently. In this paper, we propose an indoor optical communication link using RC beams encoding/decoding. By employing spatial light modulators, loaded with radial gratings and fork-shaped gratings as encoders and decoders, respectively, we generate and detect different modes of RC beams as encoding states. In the experiment, we transmit a 2-bit gray-scale image of 50×50 pixels by four different states of RC modes. The system bit error rate (BER) is measured, and a zero BER is achieved after transmitting 2500 modes. We then transmit an 8-bit RGB image of 70×77 pixels by 16 different modes of hexadecimal states to analyze the performance of the communication link in the presence of RC modes with higher RC orders. By defining an optimum threshold value, the maximum improvement of 100% in the fidelity for transmitting 32,340 hexadecimal states in an indoor ideal medium is achieved. The obtained results show acceptable performance for the proposed communication system based on RC beams, especially in the case of lower RC orders.

Spectra restoration and image reconstruction of a J0 amplitude transmittance object with circular symmetry

It is known that image reconstruction (Talbot images) and spectra restoration (Talbot spectra) phenomena can be found for light diffraction of linear periodic structures. In this work the possibility of finding similar effects for a circular symmetric object, especially for one with amplitude transmittance J₀(ρ) (zero-order Bessel function of the first kind) is discussed theoretically. The transfer function approach and the spatial-spectral correspondence relationship are used to investigate these effects, and conditions for image reconstruction and spectra restoration in the near field are obtained. The discussion of a more general form of amplitude transmittance is also included, and a comparison between the two types (linear periodic and circular symmetric structures) is made.

Diffraction from two-dimensional orthogonal nonseparable periodic structures: Talbot distance dependence on the number theoretic properties of the structures

In this work, the diffraction-based discrimination of two-dimensional (2D) orthogonal separable and nonseparable periodic structures and prediction of the reduced Talbot distances for 2D orthogonal nonseparable periodic structures are presented. 2D orthogonal periodic structures are defined and classified into separable (multiplicative or additive) and nonseparable categories with the aid of a spatial spectrum lattice. For both the separable and nonseparable cases, the spatial spectra or far-field impulses are 2D orthogonal lattices. We prove that for a 2D orthogonal separable structure, in addition to the DC impulse, there are other impulses on the coordinate axes. As a result, if all the spectrum impulses of a structure on the coordinate axes, except for the DC impulse, vanish, we conclude that the structure is nonseparable. In the second part of this work, using a unified formulation, the near-field diffraction of the 2D orthogonal separable and nonseparable periodic structures is investigated. In general, the Talbot distance equals the least common multiple of the individual Talbot distances in the orthogonal directions, say, z _t =z _lcm . For the 2D orthogonal nonseparable periodic structures having Fourier coefficients only with odd indices, we have found surprising results. It is shown that for this kind of structure, the Talbot distance strongly depends on the number theoretic properties of the structure. Depending on the ratio of the structure's periods in the orthogonal directions, p_xp_y, the Talbot distance reduces to z _lcm 2, z _lcm 4, or z _lcm 8. In addition, for the 2D orthogonal nonseparable sinusoidal grating, we show that, regardless of the value of p_xp_y, self-images are formed at distances smaller than the conventional Talbot distances attributed to p_x and p_y that we name the reduced Talbot (RT) distances. Halfway between two adjacent RT distances, the formation of negative self-images with a complementary amplitude of the self-images is predicted. Halfway between two adjacent self-image and negative-elf-image, subimages are formed. As another interesting result, we show that the intensity patterns of the subimages are 2D multiplicatively separable with halved periods in both directions. Finally, we show that 2D almost periodic structures with impulses on zone-plate-like concentric circles have self-images under plane wave illumination.