Introduction
A Diffractive Axicon (DA) is a kind of Diffractive Optical Element (DOE) that transforms a laser beam into a ring shape (a Bessel intensity profile). An Axicon also images a point source into a line along the optical axis and increases the Depth of Focus (DOF).
Each Diffractive Axicon product is defined by its ring propagation angle.
The calculated ring's width (RW) is equal to ~1.75xDiffraction Limit (DLSM) at 1/e2 size of the input for Single Mode laser beam.
For multimode beam the Ring width will equal to:
Where:
EFL – effective focal length
λ  Wavelength
D  Input Beam Size
M^{2}  M^{2} value of input laser beam (beam quality)
Definitions of sizes for Diffractive Axicon:
General specifications of Diffractive Axicons
Materials:  Fused Silica, Sapphire, ZnSe, Plastics 
Wavelength range:  193[nm] to 10.6[um] 
DOE design:  Binary (2level) and up to 16levels 
Diffraction efficiency: 
75%  96% 
Element size: 
Few mm to 100[mm] 
Damage threshold:  >3 [J/cm2] in 7 [nS] pulse @ 1064 [nm] 
Coating (optional):  AR/AR Coating 
Custom Design:  Almost any ring diameter 
Typical applications
Atomic traps  Generating plasma in linear accelerators 
Axicon resonators in lasers  Laser Corneal Surgery 
Optical Coherence Tomography (OCT)  Laser Drilling/Optical Trepanning 
Telescopes  Solar concentrators 
Advantages of the Diffractive Axicon
Allows very small angles  Aberration free 
Positive and negative configurations  Compact solution for larger angles – (fab. on thin window) 
Exceptionally precise shape and angle  Plastic available for low power applications in low price 
Fab. on Fused Silica or ZnSe (for infrared app.)  Arrays of micro Axicons 
Can accept very small incident beams 
smaller loss caused by absorption in the material (especially in spectral ranges such as the UV, where absorption can be signi?cant)

Principle of operation and design considerations
The principal of operation is similar as for basic focus lens.
Unlike a Refractive Axicon (RA), which is defined with an apex angle or a cone angle, a Diffractive Axicon (DA) is defined by its divergence angle. The divergence angle defines ring diameter in specific distance.
The divergence angle ß can be calculated from the diffraction grating equation:
The ring diameter can be calculated from a geometrical point of view:
Where:
λ  Wavelength
Λ  Diffraction period
WD  Working distance
D  Ring Diameter
Example for finding the divergence angle:
 Wavelength: 355 [nm]
 EFL: 50 [mm]
 Desired Ring Diameter: 0.2 [mm]
Relation between Divergence Angle, and Cone Angle or Apex Angle of a Refractive Axicon:
Where:
n – Refractive index
α  Base angle
θ  Apex angle
Another example for finding the divergence angle (β =?):
 Wavelength: 355 [nm]
 Cone angle: 0.25 [deg]
 Material Fused Silica
Diffractive versus Refractive comparison:
Diffractive Axicon  Refractive Axicon 
Function defined by divergence angle  Defined by cone or apex angle 
Wavelength dependent  Polychromatic 
No apex "dead" area  Has a "dead" area in the center 
Accurately defined angle with no variation  Angle changes with production tolerances 
Comparison between binary and multilevel Diffractive Axicon:
A binary (or two levels) Diffractive Axicon can be an affordable alternative to a multilevel model or to a refractive element.
In the table below, we show simulation results corresponding to a specific example, with the following parameters:
 Wavelength: 1064 [nm]
 Beam diameter: 6 [mm]
 Laser: TEM_{00} Gaussian
 DOE clear aperture: 9.2 [mm]
 Ideal lens f=100 [mm]
Refractive or Multilevel Diffractive Axicon  Binary Diffractive Axicon 
 
 
Superposition of profiles:

Refractive or Multilevel Diffractive Axicon 
Binary Diffractive Axicon 
Ring width (@1/e2) 
~1.75 x diffraction limit 
~ 1 x diffraction limit 
Peak power 

x 1.56 relative to multilevel 
Efficiency 
97.5 %(~100 % refractive) 
80 % (including side ring)* 
*: Side ring vanishes for lasers with M^2 > 5.
Sensitivity to mechanical tolerances
Similar to other optical elements with axial symmetry, the Diffractive Axicon is sensitive to centration relative to the optical axis. The Diffractive Axicon is not sensitive to input beam size & M^{2} (beam quality) of the laser. Other mechanical tolerances have low effect on functionality.
Summary table of tolerances:
Tolerance 
Value 
Remark 
Tilt X,Y 
< 5 [deg] 
Small amount of energy goes to Zero Order 
Shift X,Y 
Sensitive 
Uniformity along ring 
Tilt Z 
No effect 

Shift Z 
Yes 
Depends on optical setup 
Beam size 
No Effect 

M^{2} 
No Effect 

Polarization 
No Effect 

Typical optical setups TBD
 Controlling ring width by placing Variable Beam Expander before Diffractive Axicon.
The diameter of the ring remains constant.
 Controlling Ring diameter by placing DA after focusing lens.
Ring diameter will reduce linearly with distance between diffractive pattern and image plane/ focal plane. Ring width will remain constant.
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