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 lens 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
M2 – M2 value of input laser beam (beam quality)

Definitions of sizes for Diffractive Axicon:

General specifications of Diffractive Axicon LENSES

Materials:Fused Silica, Sapphire, ZnSe, Plastics
Wavelength range:193[nm] to 10.6[um]
DOE design:Binary (2-level) and up to 16-levels
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 trapsGenerating plasma in linear accelerators
Axicon resonators in lasersLaser Corneal Surgery
Optical Coherence Tomography (OCT)Laser Drilling/Optical Trepanning
TelescopesSolar concentrators

Advantages of the Diffractive Axicon LENS

Allows very small anglesAberration free
Positive and negative configurationsCompact solution for larger angles – (fab. on thin window)
Exceptionally precise shape and anglePlastic 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]

 

Diffractive versus Refractive comparison:

Diffractive AxiconRefractive Axicon
Function defined by divergence angleDefined by cone or apex angle
Wavelength dependentPolychromatic
No apex “dead” areaHas a “dead” area in the center
Accurately defined angle with no variationAngle changes with production tolerances

Comparison between binary and multilevel Diffractive Axicon:

A binary (or two levels) Diffractive Axicon lens 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: TEM00 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 AxiconBinary Diffractive Axicon
Ring width (@1/e2)~1.75 x diffraction limit~ 1 x diffraction limit
Peak power x 1.56 relative to multilevel
Efficiency97.5 %(~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 lens is sensitive to centration relative to the optical axis. The Diffractive Axicon is not sensitive to input beam size & M2 (beam quality) of the laser. Other mechanical tolerances have low effect on functionality. 

Summary table of tolerances:

ToleranceValueRemark
Tilt X,Y< 5 [deg]Small amount of energy goes to Zero Order
Shift X,YSensitiveUniformity along ring
Tilt ZNo effect 
Shift ZYesDepends on optical setup
Beam sizeNo Effect 
M2No Effect 
PolarizationNo Effect

Typical optical setups TBD

  1. Controlling ring width by placing Variable Beam Expander before Diffractive Axicon.
    The diameter of the ring remains constant.
  2. 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.