Characterization of a refractive logarithmic axicon

Accelerating superluminal laser focus generated by a long-focal-depth mirror with high numerical aperture

The long-focal-depth mirror is a novel reflective element proposed in recent years. Due to the advantages of negligible dependence on wavelength and high damage threshold, it is suitable to focus ultra-short laser pulses with broadband spectra and high intensity with a focal depth of centimeter scale. To the best of our knowledge, the focusing properties of this mirror has been only studied under low numerical aperture (NA). In this paper, we extend it to the case of high NA and it is proved that an accelerating superluminal laser focus can be always generated by this extension, in which the degree of acceleration increases with the increase of NA. And the velocity of laser focus increases approximately linearly from c to 1.6c for NA = 0.707. Due to its properties of tight focusing, the Richards-Wolf integrals have been used to study the intensity distribution of each polarization component for different kinds of incident light. And these are linearly polarized light, radially polarized light, azimuthally polarized light, linearly polarized light with spiral phase, and linearly polarized light with ultrashort pulses. From comparisons of numerical results, the intensity distributions are obviously different for different kind of incident light, and accelerating superluminal laser focus with special structure (such as the hollow conical beam) can be produced under appropriate condition. We believe this study can expand the fields of application for the long-focal-depth mirror.

Miniature optoelectronic compound eye camera

Inspired by insect compound eyes (CEs) that feature unique optical schemes for imaging, there has recently been growing interest in developing optoelectronic CE cameras with comparable size and functions. However, considering the mismatch between the complex 3D configuration of CEs and the planar nature of available imaging sensors, it is currently challenging to reach this end. Here, we report a paradigm in miniature optoelectronic integrated CE camera by manufacturing polymer CEs with 19~160 logarithmic profile ommatidia via femtosecond laser two-photon polymerization. In contrast to μ-CEs with spherical ommatidia that suffer from defocusing problems, the as-obtained μ-CEs with logarithmic ommatidia permit direct integration with a commercial CMOS detector, because the depth-of-field and focus range of all the logarithmic ommatidia are significantly increased. The optoelectronic integrated μ-CE camera enables large field-of-view imaging (90°), spatial position identification and sensitive trajectory monitoring of moving targets. Moreover, the miniature μ-CE camera can be integrated with a microfluidic chip and serves as an on-chip camera for real-time microorganisms monitoring. The insect-scale optoelectronic μ-CE camera provides a practical route for integrating well-developed planar imaging sensors with complex micro-optics elements, holding great promise for cutting-edge applications in endoscopy and robot vision.

Refractive Bi-Conic Axicon (Volcone) for Polarization Conversion of Monochromatic Radiation

A new element is proposed for producing an azimuthally polarized beam with a vortex phase dependence. The element is formed by two conical surfaces in such a way that the optical element resembles a mountain with a crater on top, like a volcano (volcanic cone is volcone). The element in the form of a refractive bi-conic axicon is fabricated by diamond turning, in which an internal conical cavity is made. Polarization conversion in this optical element occurs on the inner surface due to the refraction of beams at the Brewster angle. The outer surface is used to collimate the converted beam, which significantly distinguishes the proposed element from previously proposed approaches. The paper describes a method for calculating the path of beams through a refractive bi-conic axicon, taking into account phase and polarization conversions. In the case of incident circularly polarized radiation, azimuthally polarized ring-shape beam radiation is generated at the output. The proposed element is experimentally made of polymethyl methacrylate on a CNC milling machine. The experiment demonstrates the effectiveness of the proposed element.

Transversal and axial modulation of axicon-generated Bessel beams using amplitude and phase masks for glass processing applications

The control of laser-induced microcracks in the volume of transparent materials is essential for scribing processes. In this paper, we investigate the effect of various amplitude and single-level phase masks on both transverse and axial intensity distribution of the conventional axicon-generated Bessel beams. Furthermore, we demonstrate the volumetric crack control induced by an asymmetrical central core with an appropriately selected intensity level to avoid the influence of peripheral intensity maxima. Proper alignment of cracks and intra-distance between the modifications results in the reduced separation stress of the scribed samples. Furthermore, the additional amplitude modulation of the incident Gaussian beam is introduced to flatten the axial intensity distribution of the axicon-generated Bessel beam.

Modern Types of Axicons: New Functions and Applications

Axicon is a versatile optical element for forming a zero-order Bessel beam, including high-power laser radiation schemes. Nevertheless, it has drawbacks such as the produced beam's parameters being dependent on a particular element, the output beam's intensity distribution being dependent on the quality of element manufacturing, and uneven axial intensity distribution. To address these issues, extensive research has been undertaken to develop nondiffracting beams using a variety of advanced techniques. We looked at four different and special approaches for creating nondiffracting beams in this article. Diffractive axicons, meta-axicons-flat optics, spatial light modulators, and photonic integrated circuit-based axicons are among these approaches. Lately, there has been noteworthy curiosity in reducing the thickness and weight of axicons by exploiting diffraction. Meta-axicons, which are ultrathin flat optical elements made up of metasurfaces built up of arrays of subwavelength optical antennas, are one way to address such needs. In addition, when compared to their traditional refractive and diffractive equivalents, meta-axicons have a number of distinguishing advantages, including aberration correction, active tunability, and semi-transparency. This paper is not intended to be a critique of any method. We have outlined the most recent advancements in this field and let readers determine which approach best meets their needs based on the ease of fabrication and utilization. Moreover, one section is devoted to applications of axicons utilized as sensors of optical properties of devices and elements as well as singular beams states and wavefront features.

Bessel Beam: Significance and Applications-A Progressive Review

Diffraction is a phenomenon related to the wave nature of light and arises when a propagating wave comes across an obstacle. Consequently, the wave can be transformed in amplitude or phase and diffraction occurs. Those parts of the wavefront avoiding an obstacle form a diffraction pattern after interfering with each other. In this review paper, we have discussed the topic of non-diffractive beams, explicitly Bessel beams. Such beams provide some resistance to diffraction and hence are hypothetically a phenomenal alternate to Gaussian beams in several circumstances. Several outstanding applications are coined to Bessel beams and have been employed in commercial applications. We have discussed several hot applications based on these magnificent beams such as optical trapping, material processing, free-space long-distance self-healing beams, optical coherence tomography, superresolution, sharp focusing, polarization transformation, increased depth of focus, birefringence detection based on astigmatic transformed BB and encryption in optical communication. According to our knowledge, each topic presented in this review is justifiably explained.

Toric lens analysis as a focal ring and Bessel beam generator

We propose an analytical solution of the focal ring generated at the focus of a toric lens. The analytical field of the focal ring is used with a Fourier transform lens to generate a Bessel beam. A comparative analysis between the use of an illuminated annular aperture, an axicon, and a toric lens to generate a Bessel beam is performed, and the benefits and drawbacks of each are discussed. This highlights the advantages of using a toric lens with a Gaussian beam to produce a focal line of increasing intensity, which is advantageous for applications such as high depth-of-field microscopy.

Long focusing range and self-healing Bessel vortex beam generator

Here a continuous axial-spiral phase microplate (CAsPP), based on combining a logarithmic axicon and a spiral phase plate, was proposed for generating high-quality higher-order Bessel vortex beams. The novel optical component implemented via femtosecond laser direct writing possesses compact geometry and unique optical properties. The CAsPP with a diameter of 80 µm possesses a controllable long focus ranging from 50 to 600 µm and exhibits a good self-healing ability after free transmission of about 45 µm. Unique optical properties were demonstrated in both experiments and simulations, which were well matched to each other. This Letter provides new opportunities for applications in integrated optics, optical trapping, laser machining, and information reconstruction.

Propagation of fully and partially coherent flat-topped multi-Gaussian beams through axicons

Theoretically, we have investigated the propagation of fully and partially coherent flat-topped multi-Gaussian beams through classical and logarithmic axicons. The stationary phase method applied to the Fresnel diffraction integral for intensity distribution has led to applicable relationships. The influences of axicon base angle, beam width, beam flatness, and coherence length with intensity distribution were studied. A number of results have been analyzed and discussed revealing some important conclusions. During this investigation, a specific interest has been given toward producing uniform intensity and long focal depth.

Refractive twisted microaxicons

Complex-shaped light fields with specially designed intensity, phase, and polarization distributions are highly demanded for various applications including optical tweezers, laser material processing, and lithography. Here, we propose a novel (to the best of our knowledge) optical element formed by the twisting of a conic surface, a twisted microaxicon, allowing us to controllably generate high-quality spiral-shaped intensity patterns. Performance of the proposed element was analyzed both analytically and numerically using ray approximation and the rigorous finite difference time domain (FDTD) solution of Maxwell's equation. The main geometric parameters, an apex cone angle and a degree of twisting, were considered to control and optimize the generated spiral-shaped intensity patterns. The three-dimensional structure of such a microaxicon cannot be described by an unambiguous height function; therefore, it has no diffraction analogue in the form of a thin optical element. Such an element can be produced via direct laser ablation of transparent targets with structured laser beams or direct laser writing via two-photon photopolymerization and can be used in various micro- and nano-optical applications.

Generalization of the axicon shape: the gaxicon

We generalize the shape of the traditional axicon by analytically finding the function of the output surface when the input surface is not flat but an arbitrary continuous function that possesses rotational symmetry. Several illustrative examples are presented and tested using ray tracing techniques without the paraxial approximation.

Volumetric chemical imaging by stimulated Raman projection microscopy and tomography

Volumetric imaging allows global understanding of three-dimensional (3D) complex systems. Light-sheet fluorescence microscopy and optical projection tomography have been reported to image 3D volumes with high resolutions and at high speeds. Such methods, however, usually rely on fluorescent labels for chemical targeting, which could perturb the biological functionality in living systems. We demonstrate Bessel-beam-based stimulated Raman projection (SRP) microscopy and tomography for label-free volumetric chemical imaging. Our SRP microscope enables fast quantitation of chemicals in a 3D volume through a two-dimensional lateral scan. Furthermore, combining SRP and sample rotation, we demonstrate the SRP tomography that can reconstruct the 3D distribution of chemical compositions with optical spatial resolution at a higher speed than the Gaussian-beam-based stimulated Raman scattering sectioning imaging can. We explore the potential of our SRP technology by mapping polymer particles in 3D volumes and lipid droplets in adipose cells.

Recent advances have enabled high-speed three-dimensional optical imaging through the use of fluorescent markers. Here, Chen et al. integrate stimulated Raman imaging into those methods, enabling the label-free and chemically specific volumetric imaging of complex samples.

Toward the optical "magic carpet": reducing the divergence of a light sheet below the diffraction limit

In 3D, diffraction-free or Bessel beams are well known and have found applications in diverse fields. An analog in 2D, or pseudonondiffracting (PND) beams, is a nontrivial problem, and existing methods suffer from deficiencies. For example, Airy beams are not highly localized, some PND beams have significant side lobes, and a cosine beam has to be truncated by a very narrow aperture thus discarding most of the energy. We show, both theoretically and experimentally, that it is possible to generate a quasi-nondiffracting 2D light beam in a simple and efficient fashion. This is achieved by placing a mask consisting of a pair of double slits on a cylindrical lens. The applications include light sheet microscopy/optical sectioning and particle manipulation.

Development of spot size and lateral intensity distribution generated by exponential, logarithmic, and linear axicons

Axicons are known to produce a nearly Bessel beam transverse intensity distribution. It has been previously recognized that linear axicons and logarithmic axicons with a predefined distant depth of field (DOF) and no blocking present a development region characterized by an enlarged central spot size. In this paper, we aim to obtain a better insight on the formation of lateral light distribution in this development region. We also examine the spot size and transverse intensity distribution of the recently developed exponential axicon. We present experiments and detailed nonparaxial numerical simulations for a plane wave passing through these optical elements and show that the lateral intensity distribution they generate differs from that of a Bessel beam for a significant part of their DOF. This anomaly/irregularity in the formation of nondiffracting Bessel beams has to be taken into account in applications of these axicons, such as imaging or optical trapping.

Liquid Crystal Lensacons, Logarithmic and Linear Axicons

Until now, several attempts have been made to obtain axicons by using liquid crystals. Previous results had always a considerable deviation from the linear response and the resulting aperture is square. In addition, classical fabrications methods are expensive and only produce fixed phase profiles. In this study, a novel structure to obtain tunable axicons with a perfect conical shape and a circular aperture is proposed and theoretically studied. The proposed optical device is based on nematic liquid crystal and phase shifted electrical signals. A simulation program consisted of Finite Elements Method to solve the voltage distribution combined with the Frank-Oseen equation to solve the molecular position of the nematic liquid crystal is employed. This device is totally reconfigurable by using low voltage signals. The focus depth and the position of this one can be controlled electrically.

Characterization of a refractive linear axicon with distant depth of field and no central blocking

We report the manufacturing and characterization of a refractive linear axicon producing a linearly increasing axial intensity Bessel-type beam over a predetermined range starting away from the axicon and without central blocking when illuminated by a plane wave. This is in contrast to a classical axicon that generates a diffraction-free beam starting from the axicon tip and extending to a range limited by the input beam aperture. The measured characteristics of the beam produced by the linear axicon, including its intensity distribution and spot size, are in good agreement with the theoretical predictions. Together with logarithmic axicon and exicon, this is another element of the axicon family that can generate a prescribed intensity distribution over a chosen range/depth of field.

Imaging properties of three refractive axicons

The imaging properties of three types of refractive axicons are examined by using them in an imaging system. A linear axicon, a logarithmic axicon, and a Fresnel axicon are characterized by determining their point spread functions (PSFs) experimentally and by numerical simulation. The PSFs, which vary along the depth of field for the cases considered in the present investigation, are used in digital filters to denoise the images. A comparison of the imaging performance of these three optical elements is presented.

Phase-only shaping algorithm for Gaussian-apodized Bessel beams

Gaussian-apodized Bessel beams can be used to create a Bessel-like axial line focus at a distance from the focusing lens. For many applications it is desirable to create an axial intensity profile that is uniform along the Bessel zone. In this article, we show that this can be accomplished through phase-only shaping of the wavefront in the far field where the beam has an annular ring structure with a Gaussian cross section. We use a one-dimensional transform to map the radial input field to the axial Bessel field and then optimized the axial intensity with a Gerchberg-Saxton algorithm. By separating out the quadratic portion of the shaping phase the algorithm converges more rapidly.

Logarithmic axicon characterized by scanning optical probe system

A scanning optical probe system is proposed to measure a logarithmic axicon (LA) with subwavelength resolution. Multiple plane intensity profiles measured by a fiber probe are interpreted by solving an optimization problem to get the phase retardation function (PRF) of the LA. Experimental results show that this approach can accurately obtain the PRF with which the optical path difference of the generated quasi-nondiffracting beam in the propagation is calculated.

The taming of absorption: generating a constant intensity beam in a lossy medium

We report the first observation (to our best knowledge) of a constant intensity, quasi-Bessel/nondiffracting beam in an absorbing medium generated by a novel optical element, "exicon," or exponential intensity axicon. Such absorption-compensated and diffraction-resistant beams can find applications in illumination, remote sensing, free-space communications, imaging in biological tissues, nonlinear optics, and other situations where absorption and diffraction hinder light propagation.

Influences of twist phenomenon of partially coherent field with uniform-intensity diffractive axicons

The effects of twist phenomenon (beam rotation) of a partially coherent field are studied on the operation of two classes of uniform-intensity diffractive axicons. A general theory of axicon image formation is developed, discussed, and examined. We show that the intensity of the diffracted field is a multiple Bessel field, and only the energy of the zero-order Bessel field diffracts along the propagation axes. We also show that, at any twist strength in all correlation levels, the images can be evaluated by using the stationary-phase method. The three-dimensional stationary-phase formula of axicon images is derived. Such formula may be used in fast image evaluation, for designing diffractive axicons that perform a uniform axial intensity in a twisted partially coherent field.

Diffraction of a Gaussian beam by a logarithmic axicon

We derive an explicit analytical relationship to describe the axial light intensity when a Gaussian beam is diffracted by the logarithmic axicon (LA). An evaluation formula for the effective radius of the diffraction pattern that we deduce shows the said radius to be in inverse proportion to the LA "force" parameter. The finite-difference time-domain-based simulation has shown that using the LA makes it possible to go beyond the diffraction limit: in the LA vicinity, the FWHM of the light beam can be as small as one fifth of the illumination wavelength.

Demonstration of a Fresnel axicon

We design and manufacture a Fresnel axicon (fraxicon) that generates a quasi-diffraction-free/Bessel beam with a large depth of field. The novel optical element is characterized with both coherent and incoherent light, and its behavior is compared with that of a classical axicon. While the fraxicon exhibits a strong interference pattern in the on-axis intensity distribution, it can be smoothed out when using broadband light, partial spatial coherence light, or by period randomization. As inexpensive, compact/lightweight, and low-absorption elements, fraxicons may find applications in imaging, illumination, and situations where low absorption and dispersion are important.