CONTENT

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:

multimode beam the Ring width

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:

axicon ring size

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 significant)

Principle of operation and design considerations

axicon principle of operation illustration 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 (defined from peak to peak in intensity) 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 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

axicon - multilevel
axicon - ml profile

Binary Diffractive Axicon

axicon - binary
axicon - binary profile

Superposition of profiles:

axicon - ml+bin superposition
 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:
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
M2 No Effect
Polarization No Effect

Typical optical setups TBD

  1. Controlling ring width by placing Variable Beam Expander before Diffractive Axicon.
    The diameter of the ring remains constant.
    axicon - typical setup
  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.
    axicon - controlling beam diameter