Nondiffracting Fields Research Articles

High-visibility calculating ghost imaging with self-reconstruction capability and extendible depth-of-field

We customized light speckle fields with both super-bunching and non-diffracting properties, accordingly named as the super-bunching, non-diffracting (SP-ND) speckle fields, by introducing pupil function of a ring aperture with azimuthally correlated phases in the vertically opposite angles. Calculating ghost imaging based on the SP-ND speckle fields was demonstrated to be of higher visibility, higher spatial resolution and larger depth of field than that based on the conventional speckle fields such as pseudo-thermal fields. Interestingly, the SP-ND speckles are also of self-healing capability in respect of not only the speckle intensity distribution but also the high-order coherence properties. Therefore, even when the SP-ND speckle fields are seriously disturbed, for example, blocked partially by an opaque obstacle, ghost images are able to be reconstructed once the object is placed in the self-healed speckle fields.

Tailoring nondiffracting fields with a non-Markovian phase imprint.

We experimentally generate nondiffracting speckles that carry non-Markovian properties by encoding the wavefront of a monochromatic laser beam with ring-shaped non-Markovian phases. The resulting non-Markovian nondiffracting fields present a ring-shaped pattern and central dark notches, which are analyzed with an expression of the orbital angular momentum spectra of the wavefront possessing ring-shaped non-Markovian phases. Furthermore, we demonstrate that the intensity profiles of these non-Markovian nondiffracting fields exhibit stability over multiple Rayleigh ranges, and their statistical properties could be controlled with the non-Markovianity of the input phase masks. This work presents an approach for simultaneously tailoring the diffracting property and non-Markovianity of optical fields and provides a deeper understanding of non-Markovian processes.

Self-healing of the statistical properties of exact non-Rayleigh nondiffracting speckle fields

Self-healing of the statistical properties of exact non-Rayleigh nondiffracting speckle fields

Circular Airy-like beams through leaky-wave antennas

A planar nonuniform radially periodic leaky-wave antenna is proposed for the generation of circular, azimuthally symmetric Airy beams. The design is compact and low cost, and it is excited by an integrated coaxial cable. An annular metal strip grating is considered as background structure, designed to support a fast, backward, radially propagating space harmonic, which is capable of generating nondiffracting fields. The period and slots width are then properly modulated to synthesize the relevant Airy-like aperture-field distribution. An approximate formula is proposed to describe the aperture field, which is then used to retrieve the pattern of the annular strips. The near field produced by the structure is evaluated through the radiation integral, and validated by means of numerical full-wave simulations.

Exact solutions for non-Rayleigh nondiffracting speckles

We report on a speckle field that is non-Rayleigh, nondiffracting, and an exact solution to the scalar Helmholtz equation. We have shown that these fields can be directly optimized to a continuous range of contrast values corresponding to the sub-Rayleigh or super-Rayleigh statistics maintaining its nondiffracting characteristics. Besides, this work extends the range of non-Rayleigh statistics of nondiffracting fields, which may find many applications in the areas of solid-state physics, cold atoms, and optical imaging.

Structured beams invariant to coherent diffusion.

Bessel beams are renowned members of a wide family of non-diffracting (propagation-invariant) fields. We report on experiments showing that non-diffracting fields are also immune to diffusion. We map the phase and magnitude of structured laser fields onto the spatial coherence between two internal states of warm atoms undergoing diffusion. We measure the field after a controllable, effective, diffusion time by continuously generating light from the spatial coherence. The coherent diffusion of Bessel-Gaussian fields and more intricate, non-diffracting fields is quantitatively analyzed and directly compared to that of diffracting fields. To elucidate the origin of diffusion invariance, we show results for non-diffracting fields whose phase pattern we flatten.

Non-diffracting optical fields with a Fourier spectrum azimuthally modulated by a periodic phase function

We analyze non-diffracting fields (NDFs) with Fourier spectra that are phase-only azimuthally modulated. In this context, we identify a weak interference regime of the different Bessel beams that compose each NDF, which allows the use of a simple method to control several features of this field. The approach is illustrated considering periodic sinusoidal and binary azimuth phases. For generation of the NDFs, we employ an experimental setup that operates using a sequential double phase modulation in a spatial light modulator.

Multi-beams engineered to increase patterns of vortex lattices by employing zero lines of the coherent non-diffracting field.

The number of zero lines of the real and imaginary parts of the optical vortex (OV), both are the same as the topological charge (TC), and all of these lines intersect at one point where the phase singularity is. Furthermore, zero crossings distribute regularly on the transverse plane of the OV lattice. Zero lines of the real and imaginary parts of the non-diffracting fields without OV that generated by multi-waves interference are periodic but coincident. We stack two groups of these kind of zero lines which can be regarded as a set of zero lines of the real part and a set of zero lines of the imaginary part respectively, to satisfy the cross state of zero lines of an OV lattice. Then two groups of multi-waves corresponding to the two fields can be obtained. The expected OV lattice that generated by the two groups of engineered waves interference together is validated through both numerical simulations and experiments.

Multilevel axicon for perfect optical vortex generation

We present the fabrication of a beam shaper with 32 levels for the generation of nondiffractive optical fields representing quasi-Bessel beams of order zero. This optical element is designed for visible light (λ=633 nm) and fabricated using standard photolithography and a fine calibrated reactive ion etching process. A large number of levels approximates a continuous conical surface so that the optical quality of the element is very good. It is investigated the possibility of generating perfect optical vortices with this class of optical elements.

Conversion of any finite bandwidth optical field into a shape invariant beam

We discuss a method to transform any optical field, with finite frequency bandwidth, into a shape invariant beam with transverse scaling, dependent on the propagation distance. The method consists in modulating the field with a quadratic phase of appropriate curvature radius. As a particular application, we employ the method to extend the existence region of a finite non-diffracting field to an unbounded domain.

Shaping the on-axis intensity profile of generalized Bessel beams by iterative optimization methods

The Bessel beam belongs to a typical class of non-diffractive optical fields that are characterized by their invariant transverse profiles with the beam propagation. The extended and uniformed intensity profile in the axial direction is of great interest in many applications. However, ideal Bessel beams only rigorously exist in theory; the Bessel beams generated in the experiment are always quasi-Bessel beams with finite focal extensions and varying intensity profiles along the propagation axis. The ability to shape the on-axis intensity profile to meet specific needs is essential for many applications. Here, we demonstrate an iterative optimization based approach to engineer the on-axis intensity of Bessel beams through design and fine-tune processes. Starting with a standard axicon phase mask, the design process uses the computed on-axis beam profile as a feedback in the iterative optimization process, which searches for the optimal radial phase distribution that can generate a so-called generalized Bessel beam with the desired on-axis intensity profile. The fine-tune process repeats the optimization processing by using the adjusted target on-axis profile according to the measured one. Our proposed method has been demonstrated in engineering several quasi-Bessel beams with customized on-axis profiles. The high accuracy and high energy throughput merit its use in many applications. This method is also suitable to engineer higher-order Bessel beams by adding appropriate vortex phases into the designed phase mask.

Talbot effect in optical lattices with topological charge.

We studied the interference resulting from the superposition of optical lattices, which are non-diffracting fields propagating in free space, and showed a Talbot self-imaging effect. These lattices are formed by spatially Fourier transforming a "quasi"-orbital angular momentum (OAM) state. We experimentally observed that although the Talbot images change, the Talbot length is insensitive to the topological charge of the "quasi"-OAM state. Our findings can be useful for laser-written photonic lattices.

Towards the Ronchi test for gravitational lenses: the gravitoronchigram

The aim of this work is to present a Ronchi test for a gravitational lens. To this end, we use the geometrical optics point of view of the Ronchi test and the definition of the exact lens equation without reference to a background space-time to introduce the analog of the ideal ronchigram, which we named the gravitoronchigram. We first present the ideal ronchigram for an axicon lens and then using the space-time perspective of the lensing phenomenon we obtain analytical equations of the ideal gravitoronchigram for the Schwarzschild lens in the thin lens approximation and in an exact way. Finally, because the caustic associated with the deflected light by the axicon and the Schwarzschild lenses is a line along the optical axis we conjecture the generation of a gravitoBessel beam by illuminating the Schwarzschild lens with a point light source analogous to that generated by an axicon lens. That is, a particular example of the so-called non-diffracting light fields.

Non-diffracting speckles of a perfect vortex beam

We generate perfect optical vortex (POV) beams, whose intensity distribution is independent of the order, and scatter them through a rough surface. We show that the size of produced speckles is independent of the order of the POV and their Fourier transform gives the random non-diffracting fields. The invariant size of speckles over the free space propagation verifies their non-diffracting or non-diverging nature. The size of speckles can be easily controlled by changing the axicon parameter, used to generate the Bessel–Gauss beams whose Fourier transform provides the POV. These results may be useful in applications of POV for authentication in cryptography.

Subwavelength Bessel beams in wire media

Recent progress is emerging on nondiffracting subwavelength fields propagating in complex plasmonic nanostructures. In this paper, we present a thorough discussion on diffraction-free localized solutions of Maxwell’s equations in a periodic structure composed of nanowires. This self-focusing mechanism differs from others previously reported, which lie on regimes with ultraflat spatial dispersion. By means of the Maxwell–Garnett model, we provide a general analytical expression of the electromagnetic fields that can propagate along the direction of the cylinder’s axis, keeping its transverse waveform unaltered. Numerical simulations based on the finite element method support our analytical approach. In particular, moderate filling fractions of the metallic composite lead to nonresonant-plasmonic spots of light propagating with a size that remains far below the limit of diffraction.

Monolithic generators of pseudo-nondiffracting optical vortex beams at the microscale

We report on the fabrication and characterization of micro-optical elements with typical size of 100 μm, which enable the production of pseudo-nondiffracting optical vortex beams of arbitrary order. This is made possible from the monolithic integration of spiral phase plates and axicons into helical axicons by direct laser writing using femtosecond laser nanopolymerization. The optical performances of the fabricated three-dimensional singular microstructures are experimentally measured and compared with their expected theoretical behavior, both in intensity and phase. The proposed approach thus represents an attempt to merge the field of singular integrated optics with that of nondiffracting light fields.

Generation of arbitrary complex quasi-non-diffracting optical patterns

Due to their unique ability to maintain an intensity distribution upon propagation, non-diffracting light fields are used extensively in various areas of science, including optical tweezers, nonlinear optics and quantum optics, in applications where complex transverse field distributions are required. However, the number and type of rigorously non-diffracting beams is severely limited because their symmetry is dictated by one of the coordinate system where the Helmholtz equation governing beam propagation is separable. Here, we demonstrate a powerful technique that allows the generation of a rich variety of quasi-non-diffracting optical beams featuring nearly arbitrary intensity distributions in the transverse plane. These can be readily engineered via modifications of the angular spectrum of the beam in order to meet the requirements of particular applications. Such beams are not rigorously non-diffracting but they maintain their shape over large distances, which may be tuned by varying the width of the angular spectrum. We report the generation of unique spiral patterns and patterns involving arbitrary combinations of truncated harmonic, Bessel, Mathieu, or parabolic beams occupying different spatial domains. Optical trapping experiments illustrate the opto-mechanical properties of such beams.

On the generation of optical fields satisfying the upper bound diffraction efficiency using phase holograms

This paper presents a mathematical framework for the generation of optical field with upper bound diffraction efficiency. The first part of the contribution provides the necessary and sufficient condition for the optical field to be encoded with upper bound diffraction efficiency. Our approach shows that an arbitrary field is encoded using its kinoform and the upper bound amplitude gain. In this way, the energy of the kinoform is composed by the energies of the encoded field and the coding noise. Removing the coding noise, the optical field is generated with upper bound diffraction efficiency. In the second part, we analytically show that the Fourier spectra of the field and coding noise for the class the periodic and quasiperiodic nondiffractive optical fields composed by superposition of plane waves are not overlapping.

Embedding defect sites into hexagonal nondiffracting wave fields

We present a highly purposive technique to optically induce periodic photonic lattices enriched with a negative defect site by using a properly designed nondiffracting (ND) beam. As the interference of two or more ND beams with adequate mutual spatial frequency relations in turn reproduces an ND beam, we adeptly superpose a hexagonal and a Bessel beam to create the ND defect beam of demand. The presented wavelength-independent technique is of utmost universality in terms of structural scalability and does not make any specific requirements to the photosensitive medium. In addition, the technique is easily transferable to all pattern-forming holographic methods in general and its application is highly appropriate, e.g., in the fields of particle as well as atom trapping.

Fully Vectorial Accelerating Diffraction-Free Helmholtz Beams

We show that new families of diffraction-free nonparaxial accelerating optical beams can be generated by considering the symmetries of the underlying vectorial Helmholtz equation. Both two-dimensional transverse electric and magnetic accelerating wave fronts are possible, capable of moving along elliptic trajectories. Experimental results corroborate these predictions when these waves are launched from either the major or minor axis of the ellipse. In addition, three-dimensional spherical nondiffracting field configurations are presented along with their evolution dynamics. Finally, fully vectorial self-similar accelerating optical wave solutions are obtained via oblate-prolate spheroidal wave functions. In all occasions, these effects are illustrated via pertinent examples.