Axicon

An axicon is a specialized optical element characterized by a conical surface on one side and typically a flat surface on the other, functioning as a type of prism that transforms a collimated laser beam into a non-diffracting Bessel beam or a ring-shaped intensity distribution along its optical axis.^[1]^[2] Invented in 1954 by John H. McLeod as a "universal-focus" lens capable of forming a continuous straight line of images from point sources without a definite focal point, the axicon derives its name from "axis image," emphasizing its ability to produce extended axial focus rather than a point-like convergence.^[3] Unlike conventional spherical lenses, which focus light to a point, axicons deflect rays at a constant angle determined by their apex angle (α) and the material's refractive index (n), creating interference patterns that approximate a Bessel–Gauss beam within a depth of focus (DOF) proportional to the input beam radius and α.^[4] Beyond this DOF, the beam evolves into a conical wavefront with a ring diameter that increases linearly with propagation distance, enabling applications requiring uniform intensity over extended paths.^[1]^[4] Axicons are fabricated from materials like UV fused silica or BK7 glass, with apex angles ranging from 0.5° to 40° to suit various beam characteristics, and they may be uncoated or antireflection-coated for specific wavelengths such as 245–1700 nm.^[2] Their non-diffracting properties make them valuable in laser processing, where they facilitate precise hole drilling, trepanning, and nano-channel formation in materials like glass without beam divergence.^[4]^[2] In biomedical contexts, axicons support optical trapping for manipulating particles, optical coherence tomography (OCT) for high-resolution imaging, and corneal surgery by generating focused lines of light for tissue ablation.^[1]^[2] Additionally, they find use in atom traps, medical instruments, and even telescopic systems for infinite-range focusing of point sources like illuminated pinholes.^[3]^[1]

Definition and Principles

Definition

An axicon is a specialized optical element characterized by a conical surface, typically comprising one flat face and one conical face, designed to refract or reflect incident light into a conical wavefront.^[3] Coined by J. H. McLeod in 1954, it functions as a universal-focus lens that converts a point source on its axis into a continuous line image along a portion of the optical axis.^[3]^[5] The basic geometry of an axicon is defined by its base angle α (the angle between the flat base and the conical surface), the base radius of the flat face, and, for refractive variants, the refractive index n of the material.^[6] This configuration enables precise control over the beam's divergence and focus properties.^[4] The primary purpose of an axicon is to transform a collimated parallel beam, such as a laser beam, into a conical beam that produces a ring-shaped intensity distribution propagating along the optical axis, yielding a line focus over an extended depth.^[6]^[4] Unlike standard spherical lenses, which focus light to a single point, axicons distribute the focus into a line or ring over a prolonged axial range, providing depth-invariant imaging capabilities.^[3]^[5]

Optical Principles

An axicon manipulates light through refraction or reflection at its conical surface, primarily described under the ray optics approximation for small apex angles. For a refractive axicon with refractive index n and small base angle \alpha, incident parallel rays deviate from the optical axis by an angle \theta \approx (n-1)\alpha. This deviation arises from Snell's law applied at the conical interface, where the rays are bent uniformly to form a converging or diverging conical wavefront depending on the axicon's orientation.^[7] When a collimated beam illuminates the axicon, the refracted rays create a hollow conical wavefront that propagates along the optical axis. Interference of these rays results in a line focus, where the beam intensity concentrates along the axis over an extended region rather than at a single point. This conical propagation leads to self-reconstruction properties, as the off-axis components can refill perturbations in the central intensity distribution.^[3]^[7] The depth of focus, or the length of the line focus z, is given by z = R / \tan\theta, where R is the radius of the input beam. This extended focus provides a non-diffracting propagation distance proportional to the beam size and inversely related to the cone angle, enabling applications requiring uniform axial intensity over significant lengths.^[7] In wave optics, the axicon imparts a linear phase shift proportional to the radial coordinate, transforming the incident plane wave into a quasi-Bessel beam. The transverse intensity profile is approximated by I(r) \propto [J_0(kr \sin\theta)]^2, where J_0 is the zeroth-order Bessel function, k = 2\pi/\lambda is the wavenumber, r is the radial distance, and \theta is the cone angle. This results in a central bright spot surrounded by concentric rings, with the approximation holding near the axis.^[7]^[8] The paraxial approximation underlying these descriptions assumes small angles and near-axis propagation, limiting accuracy for larger \alpha or high numerical apertures. Beyond this regime, aberrations such as spherical and chromatic effects degrade the beam quality, introducing deviations from the ideal Bessel profile and reducing the effective depth of focus. Vectorial treatments are required to account for polarization-dependent effects and off-axis distortions in such cases.^[7]

Types of Axicons

Refractive Axicons

Refractive axicons are constructed as conical prisms featuring a polished conical surface on one side and a flat base on the opposite side, enabling beam deviation through refraction at the conical interface. These devices are typically fabricated from transparent materials such as glass, fused silica, or polymers, which provide the necessary refractive index contrast for light bending while minimizing scattering losses. Positive refractive axicons converge incident beams into a line focus along the optical axis, whereas negative variants diverge them, with the choice of material influencing the overall optical performance and wavelength compatibility.^[9] Fabrication of refractive axicons demands high precision to achieve accurate conical profiles, commonly employing methods like diamond turning for smooth surfaces on glass or fused silica substrates, molding for polymer replicas, and grinding followed by polishing to refine the apex. These techniques allow for apex angles typically ranging from 0.1° to 10°, which determine the beam deflection and focal line length, with tolerances below 0.1° essential to maintain beam quality and avoid aberrations. Advanced variants, such as micro-axicons, may incorporate laser-assisted wet etching in fused silica for sub-millimeter features, followed by CO₂ laser polishing to reduce surface roughness to approximately 1 nm RMS.^[10] Refractive axicons offer advantages including broadband operation across visible and infrared wavelengths due to their material-based refraction, which exhibits lower chromatic dispersion compared to diffractive alternatives, and relatively low cost for basic designs produced via standard machining. However, they suffer from wavelength-dependent deflection caused by dispersion in the refractive index, leading to beam profile variations, as well as potential absorption losses in thicker elements or at longer wavelengths. Fused silica axicons exhibit high transmittance in the visible and near-infrared, which can be further improved with antireflection coatings.^[9]^[10] Standard conical prism axicons, often made from fused silica with apex angles of 1° to 5°, serve as common examples in laboratory setups for generating nondiffracting beams in optical experiments and prototyping. These are readily integrated into beam delivery systems for initial testing of axicon-based applications, providing a cost-effective means to explore refraction-induced focusing without the complexities of custom fabrication.^[9]

Reflective Axicons

Reflective axicons, also known as reflaxicons, are optical elements that utilize reflection from a conical mirror surface to generate non-diffracting beams, such as Bessel beams, by redirecting incoming light rays into a conical wavefront. The term "reflaxicon" was coined by W. R. Edmonds in 1973 to describe this reflective variant of the axicon, distinguishing it from refractive designs.^[11] In design, reflective axicons consist of either hollow or solid conical mirrors, with a reflective coating applied to the inner or outer surface to achieve high reflectivity. Common coatings include metallic layers such as aluminum or advanced dielectric multilayers, which can be optimized for specific wavelengths or broadband operation.^[11]^[12] The geometry features a conical apex angle denoted as \alpha, where the angle of reflection \theta for incoming rays is approximately \theta \approx 2\alpha for small angles, making the beam propagation independent of the input beam's wavelength. This contrasts with refractive axicons, where beam deviation depends on the material's refractive index.^[11] Reflective axicons offer several advantages, including achromatic performance due to the absence of dispersion in reflection-based ray redirection, making them suitable for broadband or polychromatic light sources. Their compact form factor and high damage threshold—often exceeding that of transmissive optics—enable use with high-power lasers without thermal lensing or ablation risks. However, they are sensitive to misalignment, which can distort the output beam, and may introduce stray light from imperfect coatings or surface irregularities.^[12]^[11] Fabrication of reflective axicons involves precision machining of the conical substrate, typically from metals or ceramics for durability, followed by deposition of the reflective coating via techniques like evaporation or sputtering. Apex angles are often engineered below 1° to produce extended focal lines, with lengths scaling inversely with \alpha, allowing for applications requiring long-depth-of-focus propagation.^[11]^[12]

Diffractive and Other Variants

Diffractive axicons are phase-only diffractive optical elements (DOEs) that replicate the conical phase profile of conventional axicons through patterned gratings, such as spiral or conical zone plates, to generate nondiffracting Bessel-like beams. These elements are typically fabricated by etching microstructures onto transparent substrates like fused silica using photolithography to define the pattern followed by reactive ion etching to transfer the phase structure. The design process often employs iterative Fourier transform algorithms, such as the Gerchberg-Saxton method, to optimize the phase distribution for desired beam characteristics while minimizing unwanted diffraction orders.^[13] Efficiency of diffractive axicons can reach up to 90% for blazed gratings in metasurface implementations, though binary-phase versions typically achieve 75-81%, with performance being highly sensitive to the design wavelength due to the dispersive nature of diffraction. This wavelength dependence limits broadband operation, as deviations from the optimized wavelength reduce efficiency and introduce aberrations. Despite these drawbacks, diffractive axicons offer advantages in compactness and lightweight construction compared to bulk refractive or reflective counterparts, and they can be dynamically tuned by integrating with spatial light modulators (SLMs) to adjust the cone angle in real time.^[12]^[14] A prominent diffractive variant is the meta-axicon, an ultrathin flat metasurface using nanopatterned dielectric or metallic structures to impart the conical phase profile. Fabricated via electron-beam lithography or nanoimprint, meta-axicons enable high numerical apertures (NA up to ~1), polarization control, and reduced thickness compared to traditional DOEs. Recent developments include tunable meta-axicons using phase-change materials or liquid crystals for dynamic beam shaping, as demonstrated in 2023 studies for multifunctional optics.^[12]^[15] Other variants include hybrid elements combining refractive and diffractive features, as well as computer-generated holograms (CGHs) on SLMs for programmable axicon-like phases. These facilitate structured light generation for applications such as optical trapping.^[12]

Beam Characteristics and Features

For a refractive axicon, the deflection half-angle θ (the angle refracted rays make with the optical axis) is related to the apex half-angle α and refractive index n by θ ≈ (n - 1) α for small α; more precisely, θ = arcsin(((n - 1)/n) sin α).^[7]

Bessel Beam Generation

Axicons generate non-diffracting Bessel beams by imparting a linear phase ramp to an incident collimated beam, such as a Gaussian beam, which results in a conical superposition of plane waves that interfere to form a transverse intensity profile described by the zeroth-order Bessel function J_0. This phase ramp arises from the conical geometry of the axicon, transforming the input wavefront into a converging conical wave that maintains its structure during propagation. The electric field of the resulting beam can be approximated as

E(r, z) \approx A J_0(k r \sin \theta) \exp(i k z \cos \theta),

where k = 2\pi / \lambda is the wavenumber, \theta is the deflection half-angle, r is the radial coordinate, z is the propagation distance, and A is a constant amplitude.^[16] This formulation captures the invariant transverse profile along the propagation axis, with the central intensity lobe exhibiting non-diffracting behavior. The central lobe propagates without significant diffraction over a maximum distance z_{\max} \approx R / \tan \theta, where R is the radius of the incident beam, providing an extended depth of field. The transverse resolution of this lobe is on the order of \lambda / \sin \theta, determined by the deflection angle and wavelength, enabling subwavelength focusing in appropriate configurations. In practice, axicons produce finite approximations known as Bessel-Gauss beams, as ideal Bessel beams require infinite energy and extent, whereas real beams incorporate a Gaussian envelope that leads to gradual decay beyond z_{\max}.^[16] These quasi-Bessel beams exhibit self-healing properties, reconstructing their central lobe after encountering obstacles, due to the continuous interference of the surrounding conical wave components. However, energy conservation imposes fundamental limits on the propagation length, as the beam's total power is distributed across the conical rings, constraining the intensity and duration of non-diffracting behavior.^[16]

Ring and Line Focusing

When a collimated beam of radius R illuminates an axicon, it generates a conical wavefront producing a ring-shaped transverse intensity profile that propagates along the optical axis, with ring radius given by r = z \tan \theta at distance z from the element, where \theta is the deflection angle determined by the axicon's geometry and material refractive index. The distance f = R / \tan \theta corresponds to the maximum depth of focus, over which the central Bessel-like lobe is maintained; the ring thickness remains approximately constant and equal to the input beam radius beyond this point as the beam diverges conically.^[4]^[1] For an ideal uniform input beam, the ring exhibits uniform azimuthal intensity distribution, though Gaussian beam inputs lead to apodization, softening the edges and reducing peak intensity uniformity.^[7] In contrast, when a point source is imaged through an axicon, it produces a continuous line focus along the optical axis, extending the depth of field compared to traditional point imaging. This line focus maintains a narrow transverse profile over the propagation distance f, leveraging the conical refraction to distribute light linearly rather than spherically. The axial intensity along this line remains relatively constant within the focal region, but beyond f, it decays proportionally to $1/z^2, where z is the distance past the focus, due to the geometric divergence of the conical beam.^[1] Axicons enable beam shaping by converting a collimated Gaussian beam into a ring profile with relatively uniform intensity, ideal for applications requiring annular illumination, such as uniform processing over circular areas. This transformation exploits the axicon's phase modulation to redistribute Gaussian energy radially, achieving higher efficiency than flat-top beam shapers in ring configurations.^[7] Unlike spherical lenses, which concentrate light to a single point focus with limited depth of field, axicons provide an extended line or ring focus, enabling higher energy density along the axial path for improved uniformity in extended volumes. This geometric advantage stems from the conical surface, which avoids the spherical aberration issues of curved lenses while supporting non-diffracting propagation characteristics over longer distances.

Applications

Medical and Biomedical Uses

Axicons play a significant role in laser corneal surgery by generating ring-shaped beams that enhance precision in tissue ablation and smoothing, particularly in refractive procedures like photorefractive keratectomy, which shares similarities with LASIK in correcting vision. These beams improve uniformity by distributing energy evenly along a circular path, reducing irregularities in corneal reshaping. For instance, early designs incorporated axicons for controllable surface ablation and trephination, allowing surgeons to tailor the beam for specific incision depths and patterns. In hyperopic correction using excimer lasers, axicons create blend zones up to 1.50 mm in diameter to ensure smooth transitions between treated and untreated areas, minimizing visual aberrations. In optical coherence tomography (OCT), axicons extend the depth-of-field through Bessel beam generation, enabling high-resolution retinal imaging without mechanical scanning adjustments. Dual-axicon configurations produce beams with small transverse focal spots over extended ranges, facilitating three-dimensional visualization of retinal layers with reduced motion artifacts. This approach has been demonstrated in spectral domain OCT systems, where axicon lenses achieve ultrahigh transverse resolution suitable for clinical diagnosis of ocular conditions. Biomedical applications leverage axicons in optical tweezers for cell manipulation, utilizing non-diffracting Bessel beams to enable stable three-dimensional trapping of micron-sized biological particles with low heating effects. Zeroth-order Bessel beams formed by axicons allow for prolonged manipulation of samples like dielectric microspheres and living cells, such as lymphocytes isolated from lymph nodes, supporting studies in biophysics and cellular mechanics. Advancements in the 2010s have integrated axicons with femtosecond lasers for corneal surgery, enabling adjustable ring diameters via tunable systems like spatial light modulators or dual-axicon zoom setups, which facilitate precise curved incisions for customized refractive corrections. These developments build on earlier axicon beam delivery concepts, enhancing ablation control and incision geometry in procedures targeting complex corneal profiles.

Industrial and Laser Processing

Axicons play a pivotal role in industrial laser processing by enabling the generation of non-diffracting Bessel beams and ring-shaped intensity profiles, which facilitate precise material ablation, welding, and deposition without the need for beam repositioning. These beam characteristics allow for uniform energy delivery over extended depths, enhancing efficiency in manufacturing processes such as micromachining and additive fabrication.^[4] In laser micromachining, axicons produce line foci via Bessel beams, ideal for drilling high-aspect-ratio vias in printed circuit boards (PCBs) and scribing substrates like FR4 composites. For instance, customized quasi-Bessel beams generated by axicons and lenses enable through-hole drilling in 200-μm-thick FR4 with diameters from 10 to 95 μm and taper ratios up to 0.5, minimizing heat-affected zones and scattering effects compared to Gaussian beams. This approach supports aspect ratios exceeding 10:1 in via drilling, allowing single-pass processing without mechanical repositioning, which boosts throughput in PCB fabrication.^[17]^[18] For welding and cutting, axicon-generated ring beams provide uniform circumferential energy distribution, reducing defects in keyhole welding of metals and enabling clean cuts in brittle materials. Reflective axicons, such as the CANUNDA-AXICON, form stable ring profiles that achieve 5x faster cutting speeds in glass while maintaining sharp transitions 3x better than conventional methods, with minimal taper in ultrafast laser systems. In femtosecond laser welding of transparent-to-non-transparent materials like borosilicate glass to silicon, axicon-produced Bessel beams extend the focal-position tolerant zone to 410 μm—5.5 times that of Gaussian beams—yielding shear strengths up to 16.5 MPa through uniform material mixing.^[18]^[19]^[4] In additive manufacturing, Bessel beams from axicons enhance deep penetration and optothermal control in laser powder bed fusion of metals, such as stainless steel 316L. These beams provide a depth of focus (Rayleigh range) of approximately 240 μm compared to 120 μm for Gaussian beams, enabling more stable and deeper melt pools while reducing porosity to ~0.04% and keyhole defects. This results in parts with relative densities near 99.5% and smoother surfaces (surface roughness Sa < 10 μm on tops), minimizing spatter and enabling denser builds in metal 3D printing. For polymers, similar non-diffracting properties support precise layer deposition, though metal applications dominate due to higher power handling. As of 2025, advances in femtosecond Bessel beam generation from mode-locked lasers have further improved precision in ultrafast additive processes.^[20]^[21]

Optical Imaging and Trapping

Axicons play a pivotal role in optical imaging by generating Bessel beams that extend the depth of field (DOF), enabling high-resolution visualization of thick, volumetric samples without mechanical scanning. In light-sheet fluorescence microscopy (LSFM), axicons facilitate the creation of non-diffracting illumination sheets that maintain uniform intensity over extended axial distances, reducing phototoxicity and photobleaching in live specimens. For instance, a lens-axicon triplet configuration produces elongated Bessel beams for two-photon excitation, achieving a DOF of several hundred micrometers while preserving lateral resolution below 1 μm, as demonstrated in imaging Drosophila embryos where dynamic developmental processes are captured across multiple planes.^[22] Similarly, axicon-based two-photon scanned LSFM extends the DOF to over 200 μm, allowing rapid volumetric acquisition of biological tissues like cleared mouse brains with minimal aberrations.^[23] In optical trapping, axicons generate Bessel beams that exert long-range gradient and scattering forces on particles, enabling precise manipulation over distances far exceeding those of Gaussian beam traps. These beams support accelerated transport of microparticles along the optical axis, with propagation lengths up to millimeters, due to their self-reconstructing properties that mitigate diffraction losses. In microfluidic devices, double-axicon setups create interference patterns of multiple Bessel beams for selective sorting of nanoparticles by size and refractive index, achieving separation efficiencies above 90% in flow channels without physical contact.^[24] Such configurations have been used to assemble dielectric particles into stable arrays, leveraging the beams' ability to confine high- and low-index objects simultaneously.^[25] Holographic imaging benefits from axicons integrated with spatial light modulators (SLMs), where programmable axicon phases generate Bessel-like profiles for simultaneous multi-plane focusing in digital holography. This approach reconstructs 3D images at multiple depths by modulating the phase to form extended foci, enhancing axial resolution in off-axis setups without symmetric optics. For example, SLM-encoded axicon holograms produce tilted Bessel beams for conformal light sheets, enabling depth-multiplexed imaging of dynamic scenes with reduced computational overhead.^[26] Leveraging the non-diffracting features of these beams, such systems achieve uniform illumination across planes separated by tens of micrometers.^[9] Axicons enable resolution enhancement in sub-diffraction imaging through self-healing Bessel beams that propagate through scattering media while preserving beam integrity. In turbid environments, these beams reconstruct after obstructions, maintaining spot sizes below the diffraction limit (e.g., ~0.3λ) over propagation distances exceeding 1 mm, which is crucial for deep-tissue observation. This property facilitates structured illumination microscopy (SIM) variants where Bessel profiles reduce aberrations, yielding effective resolutions of 100-200 nm in inhomogeneous samples.^[27] In the 2020s, axicon-generated Bessel beams in two-photon LSFM have advanced super-resolution live-cell imaging, capturing subcellular dynamics in organoids with isotropic resolutions around 300 nm and minimal motion artifacts. As of 2025, dielectric metasurface axicons have enabled compact near-infrared systems for improved bottle beam trapping in advanced biomedical applications.^[22]^[28]

History and Developments

Invention and Early Work

The axicon was first proposed in 1953 by John H. McLeod, an engineer at Eastman Kodak Company in Rochester, New York, as a novel optical element designed to generate a uniform line focus from a point source along its axis, with a detailed publication in 1954. McLeod coined the term "axicon," derived from "axis image," to describe this class of rotationally symmetric lenses or reflectors that produce extended depth-of-field imaging, initially explored for applications like universal-focus telescopes where a conical surface replaces a traditional spherical objective.^[3] In 1956, McLeod formalized his invention through U.S. Patent 2,759,393, which detailed the use of conical lenses—axicons—in optical alignment systems, such as combining them with spherical elements to create precise straight-line images for industrial alignment tasks.^[29] This patent emphasized the axicon's ability to form continuous line images from small sources, distinguishing it from conventional lenses and highlighting its potential in machinery setup, like paper mills or photographic equipment.^[29] McLeod expanded on the axicon's properties in his 1960 publication in the Journal of the Optical Society of America, where he analyzed various axicon configurations, including refractive and reflective types, and demonstrated their utility in beam shaping.^[30] These works laid the groundwork for initial applications in the 1960s, particularly in optical alignment and rudimentary beam manipulation setups. Following the invention of the laser in 1960, axicons saw rapid adoption in the emerging field of coherent optics, enabling the generation of non-diffracting beam profiles akin to Bessel beams for extended propagation without spreading, which proved valuable in early laser experiments for precise focusing and illumination.

Modern Research and Advances

In the 2000s, significant progress was made in integrating axicons with spatial light modulators (SLMs) to enable tunable beam generation, allowing dynamic adjustment of the conical angle and nondiffracting propagation length for applications like micro-hole drilling.^[31] Diffractive axicons emerged as compact alternatives to refractive ones, leveraging phase-only holograms to produce Bessel beams with high numerical apertures approaching 1, facilitating polarization conversion and sharp focusing in miniaturized optical systems.^[12] From 2010 to 2025, metasurface-based axicons advanced flat optics by achieving subwavelength thicknesses (typically under 1 μm) and efficiencies exceeding 80% across broadband visible to near-infrared wavelengths (690–1050 nm), enabling aberration-free beam shaping without bulky refractive elements.^[32] These meta-axicons, composed of nanostructured antenna arrays, support multifunctional wavefront control, such as generating twisted nondiffracting beams for enhanced depth of focus. Ongoing research explores nonlinear axicons for second-harmonic generation, where hybrid metasurface designs convert fundamental Bessel-Gaussian beams into their harmonics while preserving nondiffracting properties, achieving conversion efficiencies on the order of 10^{-6} in tungsten disulfide-based structures.^[33] In quantum optics, axicons shape entangled photon pairs via spontaneous parametric down-conversion, producing spatially correlated Bessel beams with adjustable orbital angular momentum for quantum information processing.^[34] Key challenges include boosting efficiency in ultraviolet and extreme ultraviolet regimes, where metasurface absorption limits performance to below 50%, and scaling designs for high-power fiber lasers (multi-kilowatt levels), where thermal damage and mode instability degrade beam quality.^[12] A seminal 2021 review synthesized these advancements, highlighting axicons' expanded roles in integrated photonics and beam multiplexing.^[12]