Diffraction-free Beams Research Articles

Omni-resonant space-time wave packets.

We describe theoretically and verify experimentally a novel, to the best of our knowledge, class of diffraction-free pulsed optical beams that are "omni-resonant": they have the remarkable property of transmission through planar Fabry-Perot resonators without spectral filtering, even if their bandwidth far exceeds the cavity linewidth. Ultrashort wave packets endowed with a specific spatiotemporal structure couple to a single resonant mode independent of its linewidth. We confirm that such "space-time" omni-resonant wave packets retain their bandwidth (1.6 nm), spatiotemporal profile (1.3-ps pulse width, 4-µm beam width), and diffraction-free behavior upon transmission through cavities with resonant linewidths of 0.3 nm and 0.15 nm.

Effective formation of diffraction-free laser beams based on the diaphragm of the annular spatial spectrum

In this article, we simulate the formation of diffraction-free beams, which combine some of the properties required for technologies such as planar microscopy, information coding and optical manipulation. Analytical functions in combination with a diaphragmed annular spatial spectrum are proposed as an optical beam. The analysis is carried out at distribution in the free environment and lens systems.

Calculation of diffractive optical elements for the formation of thin light sheet

In the work, the calculation and study of diffractive optical elements (DOE) for the formation of a diffraction-free beam in the form of a thin light sheet, which can be used in planar microscopy, were performed. The calculation of phase DOEs is made on the basis of an iterative algorithm, taking into account the quantization of the phase function.

Efficient nonlinear beam shaping in three-dimensional lithium niobate nonlinear photonic crystals

Nonlinear beam shaping refers to spatial reconfiguration of a light beam at a new frequency, which can be achieved by using nonlinear photonic crystals (NPCs). Direct nonlinear beam shaping has been achieved to convert second-harmonic waves into focusing spots, vortex beams, and diffraction-free beams. However, previous nonlinear beam shaping configurations in one-dimensional and two-dimensional (2D) NPCs generally suffer from low efficiency because of unfulfilled phase-matching condition. Here, we present efficient generations of second-harmonic vortex and Hermite-Gaussian beams in the recently-developed three-dimensional (3D) lithium niobate NPCs fabricated by using a femtosecond-laser-engineering technique. Since 3D χ(2) modulations can be designed to simultaneously fulfill the requirements of nonlinear wave-front shaping and quasi-phase-matching, the conversion efficiency is enhanced up to two orders of magnitude in a tens-of-microns-long 3D NPC in comparison to the 2D case. Efficient nonlinear beam shaping paves a way for its applications in optical communication, super-resolution imaging, high-dimensional entangled source, etc.

Fractional two-parameter parabolic diffraction-free beams

We consider two-parameter real-valued parabolic diffraction-free beams. An analytical expression for the complex amplitude of the beam is obtained using the superposition of the Bessel functions. Symmetry properties of beams are analyzed and numerically demonstrated for different cases. The variety of the formed pictures increases significantly in comparison with earlier regarded parabolic beams. Particularly interesting properties exhibit beams with half-integer indices, they have symmetry properties different from the symmetry of beams with integer indices. For an arbitrary fractional index, the beams have a more complex distribution and do not have any symmetry. This fact facilitates the solution of the inverse problem when it is necessary to form similar structures, since just small changes in two parameters of the analytical expression are needed. This is much simpler than the implementation of iterative procedures, which, as a rule, provide essentially non-smooth solutions that are complex in optical implementation. Experimental generation of the fractional two-parameter parabolic beams is implemented for the first time by a spatial light modulator using phase coding of the calculated complex amplitudes. The different types of experimentally generated parabolic beams are in a good agreement with the modeling results.

Discrete propagation of trapped modes in acoustic waveguide arrays

Arrays of evanescently coupled waveguides in which wave behavior becomes discretized exhibit unique wave dynamics, and they offer the possibility to investigate analogous fundamental quantum phenomena at accessible time and length scales. In this Rapid Communication, we investigate the discretelike propagation of trapped modes in airborne acoustic waveguide arrays. Using numerical simulations and experiments, we analyze the emergence of acoustic discrete diffraction and spatial Bloch oscillations in the array. Furthermore, exploiting the Bloch oscillations phenomenon, we demonstrate the possibility to generate diffraction-free acoustic beams and to focus the acoustic energy within a single lattice site at distances orders of magnitude larger than the operating wavelength.

Experimental realization of dark and antidark diffraction-free beams.

We report the first, to the best of our knowledge, experimental realization of high-quality dark and antidark diffraction-free beams, first theoretically proposed by Ponomarenko etal. [Opt. Lett.32, 2508 (2007)OPLEDP0146-959210.1364/OL.32.002508]. Our method employs a single spatial light modulator (SLM) and is based on superposing mutually uncorrelated but spatially coherent in the time domain Bessel modes with modal weights proportional to the SLM display times of the corresponding modes. We also experimentally verify diffraction-free properties of the generated beams upon their free space propagation.

Implementation of nondiffracting Bessel beam sources in FDTD for scattering by complex particles.

In this paper, the nondiffracting Bessel beam sources are implemented in finite-difference time-domain (FDTD) method. The high-order scattered-field algorithm of the FDTD (SF-FDTD (2, 4)) method is employed to investigate the scattering of particles illuminated by Bessel beams. In the SF-FDTD (2, 4) method, the scattered fields of the whole region are calculated directly by time stepping and the incident fields are obtained by the vector expressions of the diffraction-free Bessel beam. Some numerical results are included to illustrate the validity and capability of the proposed method. This study is expected to provide a new efficient method to investigate the interactions between nondiffracting beams and complex particles.

Coherence of a Bessel beam and a conic wave in turbulent atmosphere

Coherent properties of diffraction-free Bessel-like optical beams propagating in the turbulent atmosphere are theoretically studied. An analytical solution of the equation for the second-order transverse function of mutual coherence of the optical radiation field, which was obtained from paraxial approximation of the scalar wave equation, is analyzed. The behavior of the degree of coherence, coherence radius, and integral scale of the degree of coherence of the Bessel–Gaussian beam and conic wave obtained through conic focusing of a Gaussian beam by an axicon is analyzed for different beam parameters and characteristics of the turbulent atmosphere. Significant qualitative and quantitative differences are discovered between the studied coherence characteristics of the Bessel–Gaussian beam and the conic wave. In general, under identical propagation conditions in the turbulent atmosphere, the coherence of the conic wave is higher than that of the Bessel–Gaussian beam. The comparison of two spatial scales of the degree of coherence of optical beams reveals that the integral scale for diffraction-free beams is a more representative characteristic than the coherence radius. The integral scale of the degree of coherence of diffraction-free beams is more unequivocally connected with the conditions of propagation of optical radiation in the turbulent atmosphere.

Intensity distribution of diffractive axicon with the optical angular spectrum theory

Diffractive axicon is lightweight and easy to be manufactured, it is also efficiently used to produce diffraction-free Bessel beam. But, deducing its expression of the field distribution of light is difficult in theory and the theoretical equation expression has approximation by using the Huygen-Fresnel diffraction integral. Here, the rigorous optical angular spectrum theory that follows the Helmholtz equation is used. The propagation theory of angular-spectrum with fewer approximation, will result in more accurate results. A mathematical model to analyze the field distribution of light of the diffractive axicon is set up. The diffraction intensity distribution of the diffractive axicon with the monochromatic Gaussian beam illumination and multicolor illumination is numerically calculated and discussed. The results of numerical calculation with a monochromatic laser source show that not all the intensity distribution in the focal depth of field has the characteristics of the diffraction-free Bessel beam, and the on-axis diffraction intensity shows direct correlation of the lateral intensity distribution of the incident waves and the period of the diffractive axicon. The extended depth of field of the diffractive axicon with multicolor illumination is increasing as the wavelength reducing. It is expected that our study can provide very useful information for analyzing the diffractive axicon which exists in the optical trapping systems and laser-processing applications and imaging systems.

Harnessing Laguerre-Gaussian Beams to Construct Quasi-Nondiffracting Optical Ring Lattices

We construct a family of optical ring lattices that manifest the quasi-nondiffracting property via superposition of high-radial-order Laguerre-Gaussian beams. A theoretical derivation of the optical ring lattice along with the validity condition is presented, and its evolution behaviors are investigated in comparison with the diffraction-free Bessel beams. Moreover, multiple ultralong bright channels or optical tubes with various transverse profiles can be formed with the ring optical lattices. As a proof of concept, flexible generation of the lattice beams was demonstrated by complex wavefront engineering using a binary digital micromirror device. We anticipate that the quasi-nondiffracting ring lattices and the ultralong optical channels might motivate novel applications in optical trapping and high-resolution microscopy.

Generation and applications of non-diffraction beam

In recent years, with the development of laser technology, various non-diffraction beams each with a central spot unchanged after a long distance propagation, have been generated, they being the Bessel beam, higher Bessel beam, Mathieu beam, higher Mathieu beam, cosine beam, parabolic beam, and Airy beam. Diffraction-free beams are widely used in laser drilling, laser precision alignment, optical precision control, optical micromanipulation, optical communication, plasma guidance, light bullet, synthesis of autofocusing beam, nonlinear optics, etc. In this paper, the expressions, generation methods and corresponding experimental results of the various non-diffraction beams are presented. There are many ways to generate the Bessel beam, they being circular slit, computed hologram, spherical aberration lens, resonant cavity, axicon, and metasurface. The main methods of generating the non-diffraction beams are summarized, and each method is analyzed in depth from the cost of the system, and then some suggestions for improving and perfecting are made. For the generation of non-diffraction beams, the passive methods are used most to convert other beams into corresponding non-diffraction beams by optical components. Due to the low damage threshold and high cost of optical components, the power, energy and beam quality of a non-diffracting beam will be limited. How to generate a high-power, high-beam quality non-diffracting beam will be a hot research spot. Diffractionless beams have attracted a great deal of interest due to their unique non-diffraction, transverse-accelerating (or self-bending) and self-healing property. Transverse-accelerating property refers to that non-diffraction beams propagate along a parabola trajectory. The diffractionless beams' propagation trajectory control method implemented by changing system parameters is simple and easily successful, but cannot reverse acceleration direction, and its controlling range is limited. The self-healing property means that the non-diffraction beam tends to reform during propagation in spite of severe perturbations imposed. Both the Airy beam and the Bessel beam exhibit self-healing properties during propagation. And non-diffraction beams have potential applications in many fields. In atmosphere, such as in optical communication, non-diffracting beam exhibits more resilience against perturbations. Finally, brief summary and outlook of non-diffraction beams playing important roles in future study, and their application prospects are presented. In addition to Airy beam and Bessel beam, for other non-diffraction beams due to the complexity of the beams themselves, by comparison, their applications are investigated very little, so the applications in Mathieu beam, cosine beam, and parabolic beam will be a hot research spot.

Partially coherent diffraction-free vortex beams with a Bessel-mode structure.

A new family of partially coherent beams carrying optical vortices is introduced. Any member of this family represents an incoherent superposition of fully coherent orthogonal Bessel modes with the same helical wavefront and is notable for its diffraction-free propagation. It is shown analytically and experimentally that such beams can be approximately generated in the Fourier-transforming optical system with a computer-controlled liquid-crystal spatial light modulator.

Spatiotemporal diffraction-free pulsed beams in free-space of the Airy and Bessel type.

We investigate the dynamics of spatiotemporal optical waves with one transverse dimension obtained as the intersections of the dispersion cone with a plane. We show that, by appropriate spectral excitations, the three different types of conic sections (elliptic, parabolic, and hyperbolic) can lead to optical waves of the Bessel, Airy, and modified Bessel types, respectively. We find closed form solutions that accurately describe the wave dynamics and unveil their fundamental properties.

Diffraction-free space–time light sheets

Diffraction-free optical beams propagate freely without change in shape and scale. Monochromatic beams that avoid diffractive spreading require two-dimensional transverse profiles, and there are no corresponding solutions for profiles restricted to one transverse dimension. Here, we demonstrate that the temporal degree of freedom can be exploited to efficiently synthesize one-dimensional pulsed optical sheets that propagate self-similarly in free space. By introducing programmable conical (hyperbolic, parabolic, or elliptical) spectral correlations between the beam's spatio-temporal degrees of freedom, a continuum of families of axially invariant pulsed localized beams is generated. The spectral loci of such beams are the reduced-dimensionality trajectories at the intersection of the light-cone with spatio-temporal spectral planes. Far from being exceptional, self-similar axial propagation is a generic feature of fields whose spatial and temporal degrees of freedom are tightly correlated. These one-dimensional `space-time' beams can be useful in optical sheet microscopy, nonlinear spectroscopy, and non-contact measurements.

Straightening light sheets

Diffraction-free light-sheet beams, strongly confined in one axis, are typically thought to self-bend during propagation in free space and cannot be made flat. Now, diffraction-free planar light sheets in air have been realized by exploiting polychromatic pulsed beams.

Controlling nonlinear instabilities in Bessel beams through longitudinal intensity shaping.

During ultrafast laser pulse propagation in dielectrics, the nonlinear generation of new spatial frequencies can be deleterious to reach high intensities and to generate uniform plasma channels. In this context, diffraction-free Bessel beams have attracted major recent interest because of their enhanced stability when compared to conventional Gaussian beams. However, Bessel beams can still suffer from significant modulation instability arising from noise-induced nonlinear four-wave mixing (FWM). In this Letter we report control of the nonlinear instability growth by shaping the longitudinal intensity profile of the incident field. Our results show that tailored longitudinal intensity shaping of a nondiffracting Bessel beam can strongly reduce FWM-induced oscillations and stabilize nonlinear propagation at ablation-level intensities.

Unraveling beam self-healing.

We show that, contrary to popular belief, diffraction-free beams may not only reconstruct themselves after hitting an opaque obstacle but also, for example, Gaussian beams. We unravel the mathematics and the physics underlying the self-reconstruction mechanism and we provide for a novel definition for the minimum reconstruction distance beyond geometric optics, which is in principle applicable to any optical beam that admits an angular spectrum representation. Moreover, we propose to quantify the self-reconstruction ability of a beam via a newly established degree of self-healing. This is defined via a comparison between the amplitudes, as opposite to intensities, of the original beam and the obstructed one. Such comparison is experimentally accomplished by tailoring an innovative experimental technique based upon Shack-Hartmann wave front reconstruction. We believe that these results can open new avenues in this field.

Tunable diffraction-free array in nonlinear photonic crystal

Diffraction-free beams have attracted increasing research interests because of their unique performances and broad applications in various fields. Although many methods have been developed to produce such beams, it is still challenging to realize a tunable non-diffracting beam. Here, we report the generation of a tunable diffraction-free array through second-harmonic generation in a nonlinear photonic crystal, i.e., a 2D periodically-poled LiTaO3 crystal. In such a crystal, the second-harmonic wave is engineered by properly designing the domain structure based on the Huygens-Fresnel principle. The characteristics of the generated diffraction-free array including its period, propagation length, and wavelength can be tuned by simply changing the input wavelength. Our observation not only enriches the diffraction-free optics, but also has potential applications for photolithography and imaging.

Generation of Bessel beam by manipulating Pancharatnam-Berry phase

Bessel beam is one of diffraction-free beams and has some peculiar properties. Varieties of its applications have been found, such as microparticle manipulating, material processing and biological studies. In this work, we propose a method of creating a Bessel beam by manipulating Pancharatnam-Berry phase. Using femtosecond laser, nano waveplatelets are written on a fused silicon glass to form a metasurface. The optical axis of waveplatelets rotating in the radial direction can produce the space-varying Pancharatnam-Berry phase. The designed metasurface acts as a planar axicon to generate Bessel beams by replacing the traditional one. A Jones calculation is employed to analyze the transformation of the metasurface. The theoretical results indicate that a left-handed circularly polarized light passing through the planar axicon is convergent, while a right-handed circularly polarized one is divergent. The intrinsic physical reason is that Pancharatnam-Berry phase is spin-dependent. Therefore, Bessel beams are generated by the planar axicon only when a left-handed circularly polarized light inputs the system. It is notable that the maximum nondiffracting distance is determined by the rate of rotation of the metasurface microstructure. By reducing the rate of rotation, we can easily obtain a longer nondiffracting distance, thus avoiding the problem that the base angle of the traditional axicon is too small to fabricate. According to the Fresnel diffraction integral, we simulate the propagation of the field emerging from the planar axicon and obtain the intensity distributions behind the planar axicon with different distances. The results show that the intensity pattern remains unchanged in the propagating process and possesses the propagation properties of Bessel beam. It implies that approximate nondiffraction Bessel beams can be achieved by employing the planar axicon with metasurface. Finally, we set up an experimental system with the Pancharatnam-Berry phase metasurface with period d=1000 upm to verify the theoretical analysis. Theoretically, the maximum nondiffraction distance is 7.9 m. In the shaded region, we measure the intensity distributions at different distances. The experimental results are in good agreement with the simulation results, so the planar axicon based on Pancharatnam-Berry phase can be an effective Bessel beam generator. We believe that these results are helpful for developing more spin-dependent photonic devices.