With the use of a negative and positive axicon lens, ring diameter can be adjusted to fit the needs by manipulating the distance between the two axicons. What’s the tips to design it? We share it here.

An axicon lens, is a conical prism defined by its alpha (α) and apex angles, also known as a rotationally symmetric prism, is a lens that features one conical surface and one plano surface. They are commonly used to create a beam with a Bessel intensity profile or a conical, non-diverging beam.

Plano-concave axicons have a plano surface in combination with a concave conical surface. Concave axicon produces a ring shaped image along the axis from a point light source (e.g. Gaussian laser beam).

An axicon deflects light according to Snell’s Law, which can be used to find the deflection angle:

where n is the index of refraction of the glass, α is the physical angle of the prism, and ß is the angle the deflected beam creates with the optical axis. Here, the refractive index of air is assumed to be 1. This interaction is illustrated in the reference image to the right.

### About the Axicon Beams

- Bessel Beam: Non-Diffracting

The axicon can replicate the properties of a Bessel beam, a beam comprised of rings equal in power to one another. The Bessel beam region may be thought of as the interference of conical waves formed by the axicon. A Bessel beam is a non-diffracting beam of concentric rings, each having the same power as the central ring.

The absolute value of a 0^{th} order Bessel function. A true Bessel Beam requires each ring to have the same energy as the central peak, thus an infinite amount of energy is needed.

- Ring-Shaped Beam: Ideal for Laser Drilling

When the beam is projected further from the lens, a single ring-shaped beam is formed. The beam is actually conical (i.e., diameter increases with distance), but the rays are non-diverging so that the thickness of the ring remains constant. The ring’s thickness will be half of the input laser beam’s diameter. This type of beam is commonly used in laser-drilling applications. The thickness of the ring (t) remains constant and is equivalent to R( the beam entering the axicon)

The simplified equation again assumes small angles of refraction. The diameter of the ring is proportional to distance.

- Axicon’s depth of focus (DOF).

DOF is a function of the radius of the beam entering the axicon (R), the axicon’s index of refraction (n), and the alpha angle

- Problem of Manufacturing imperfection- Apex Rounding

The intensity distributions of the resulting Bessel and ring-shaped Gaussian beams are influenced by tip imperfections. The central lobe of the zero-order Bessel beam shows **intensity oscillations rather than spatial invariance** if the tip is rounded, while the hollow Gaussian beam features an asymmetric ring with a tail towards the center or secondary rings.

Please note that the non-zero peak at the center of the ring is an expected feature since only an ideal, perfect axicon will have high intensity edges and zero-intensity everywhere else. By improving the apex rounding diameter and reducing surface imperfections of the axicon, the contrast between the high intensity region and the nonzero center can be improved.

An Axicon example is attached here for your reference and study. Axicon Beam example