Flat top / Beam shaping application notes - Diffractive optics

• Introduction
• Principal of Operation
• Design Considerations
• Typical Set-Up
• Characteristics
• Sensitivity to Alignment and Beam Tolerances
• Effects of Tolerances on Beam shaping
• Comparison of Top-Hat and Stable Top-Hat
• Design Tool for MATLAB
• Beam shaper software
• Beam shaper standard products

• Laser Ablation
• Laser Welding
• Hole Drilling
• Laser Scribing
• Laser Displays
• Filters for cigarettes
• Medical and aesthetic laser applications

1. Wavelength
2. Input Beam Size (Din)
3. Working distance (WD)
4. Output Spot Size (Dout)

Design Considerations
For good quality Top-Hat beam shaper performance, the laser output should be Single Mode (TEM00) with an M2 value under 1.3. Even if the M2 is higher, it may still be possible to reduce the M2 value by inserting a spatial filter in between the laser and the DOE lens component.
The spatial filter consists of a focusing lens, a small aperture in the focal plane, and a collimating lens. The spatial filter aperture acts to reduce parasitic modes, whose presence in the laser output causes a high M2 value and degraded Top-Hat performance. The user must take care to use a small aperture, BUT no smaller than 2x the beam size at the aperture plane. Too small an aperture will give rise to a parasitic interference pattern or ripple in the beam shaper output spot. By manipulating the focal lengths of these two lenses, the spatial filter can also be used as a beam expander. See fig.2 below for visual aid of spatial filter set-up functioning also as a beam expander. Figure 2: Typical Set Up.

The advantage of working with a larger input beam is twofold. First, a larger beam reduces somewhat the sensitivity of the Top-Hat output to tolerances. Secondly, a larger input beam will enable achieving a smaller output spot, which is a desired outcome for many beam shaper applications.
The two translation stages in fig.2 above are meant to give the user precise control of elements' locations, to reduce tolerance effects. This is discussed further in the section on Tolerances.
As was mentioned regarding the spatial filter aperture, ALL apertures in the beam path must be at least 2x as large as the beam size (1/e^2) on the aperture plane (best over 2.5x). These often include mirrors (for beam folding), beam expander, beam splitter and filter/diaphragm.
All optics in the beam path should be of high quality, i.e. low irregularity figure, so as not to introduce wave-front errors which would degrade the Top-Hat performance. This includes mirrors which should have high flatness specification. Here, too, a larger beam size incident on the mirror will reduce its sensitivity to aberrations.
As was mentioned above, the beam shaper element requires that the input beam be collimated.
For this reason, as well as for purposes of stability, it is recommended to work with the beam shaper element in the waist of the laser. Nonetheless, if the beam has a small divergence angle (<1º), there should not be any noticeable effect on the Top-Hat output quality, but only on the exact working distance.
If, due to mechanical or other constraints, the diffractive optical element (DOE) will be located at a distance from the beam waist, it is important to take this distance into consideration, along with the beam divergence, in the designing of the DOE. Otherwise, the resultant wave-front aberration can generate an interference/ripple pattern over the output beam, whose intensity will grow as a function of the DOE's distance from waist and the divergence angle.
When designing the desired output Top-Hat size, it is important to be familiar with the physical limits of the minimum spot size. The formula for the diffraction-limited spot size:

L: Working Distance
λ:  Wavelength
D:  Input Beam Size
M2:  M2 value of input laser beam

As a rule of thumb, the minimum Top-Hat beam shaper spot size will be between 3 to 5 times the diffraction-limited spot size given by the above formula. The precise factor depends on the whether the element is a Top-Hat or Stable Top-Hat. See final section for comparison.

 
Characteristics          

• Uniform intensity profile: Typically +/-5%.
• Steep transition region: Typically similar to diffraction-limited spot with the same input diameter and working distance.
• High Power Threshold
• High Efficiency:  >95%
• Sensitivity to X-Y displacement: 5% of the input beam, in order to keep acceptable performance.
• Sensitivity to Input Beam diameter: 5% of the input beam in order to keep acceptable performance.
• Rotation insensitive: For round shape.
• Sensitivity to working distance: smaller than 50% of the spot size in order to keep acceptable performance.

Simulated Effects of Tolerances on Top-Hat beam shaper Profile
The best performance will be obtained for a well-positioned perfectly aligned part, located precisely in the plane of the nominal working distance. To illustrate the sensitivity of Top-Hat performance to different tolerance parameters, several graphs are included here for a standard beam shaper element (WD: 120mm, λ: 532nm, Din: 10mm).
Fig. 4: Effect of x-axis or y-axis de-centering of input beam on Top-Hat Profile

**Noteworthy in figure 4 above is the "tilted" Top-Hat profile due to de-centering; i.e. a slope in the intensity going from one side of spot to the other.

Fig. 5: Effect of Working Plane Defocus on Top-Hat Profile

**Note the different behavior of Top-Hat profile when located too close (red curve) as opposed to being too distant (green curve). The uniformity suffers a drop in both cases, while the extended distance gives rise to narrow peaks at the Top-Hat spot periphery (a.k.a "dog ears").

Fig. 6: Effect of Input Beam Size Tolerance on Top-Hat Profile

**Interesting to note in fig.6, a very similar effect as in fig.5. There is clear parallel between too large beam size and extended defocus. The "dog ears" effect is the same.
Comparison of Top-Hat and Stable Top-Hat
Holo-Or uses two slightly different algorithms for the Top-Hat diffractive pattern, each algorithm with its own advantages. The original Top-Hat algorithm produces a higher level of uniformity than its "ST" counterpart, and is also less sensitive to errors in manufacturing. On the other hand, the "ST" algorithm can achieve smaller spot size (3x diff. limit) than the "Top-Hat" (5x diff. limit), and smaller transition region.
Included below is a typical graph superposition of equivalent designs – same spot size.
Top-Hat design tool for MATLAB
Holo/Or published a Top-Hat design tool for MATLAB. This free of charge service provides intensity distribution for any Top-Hat. The designer is free to choose the wavelength, input diameter, spot size and working distance of his preference. A link will be provided to get a fast quotation for the design simulated.
Download P-code for Top-Hat design tool
Instructions:

• Unzip the downloaded file
• Change your MATLAB current folder to the unzipped folder
• Write "help TH" in the "Command Window" and click "Enter"
• Follow the instructions in order to simulate your custom Top-Hat design

• Installation of environment:
  • Windows 32 bit
  • Windows 64 bit
• Unzip and run the exe file:
  • Windows 32 bit
  • Windows 64 bit