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Lasers & Sources

Development of large-aperture diffractive optical elements for beam smoothing

A multi-step diffractive optical element (MDOE), developed using a hybrid algorithm, has been shown to perform laser-beam smoothing well.
19 May 2006, SPIE Newsroom. DOI: 10.1117/2.1200602.0007

Uniform illumination has become a popular topic in recent years.1 For example, improvement in laser-irradiation uniformity is now an important issue for those developing high-power-laser output systems.2–3 Diffractive optical elements (DOEs) have been widely used to solve this problem,4 but the manufacture of these elements—especially large DOES—is very difficult.

In our group, we used a DOE with an axisymmetric continuous profile5 because of its relatively-high design index and because it can be fabricated using a rotary etching facility.6 However, in practice, it is very difficult to match the design of this kind of continuous profile using this kind of fabrication. The accumulation of etching errors can make the experimental DOE far worse than the design index. However, this problem can be solved using a multi-step diffractive optical element (MDOE) that has a stepped phase structure that can be fabricated easily using multiple-mask etching.

To improve the design index and save computing time, we have developed a mixed algorithm for MDOE design that inserts a quasi-optimum process in every GS (Gerchberg-Saxton)7 iterative loop. Initially, though we could quickly get a convergent result by using the GS algorithm, the illumination uniformity was not as good as we expected. This was because the feedback was too limited to carry enough information to control the change of phase distribution. Also, occasionally, self-trapping and oscillation would prevent the GS algorithm from working properly.8

We decided to solve these problems by making the feedback carry more effective information in each loop. We did this by adding two adjustable parameters and using a quasi-optimum process to set their value in each iteration. This reformative mixed method can be described using the equations below.

Here, ak is the output-amplitude feedback coefficient and βk is the input-phase feedback coefficient. In every iterative loop, quantities are randomly generated for a and β, and each set of values gives a different U(k+1)i. We choose the best values for ak and βk as those that give the minimum deviation from the ideal.

In practice, the self-trapping and oscillation effects can be effectively suppressed using this reformative method. Furthermore, it is faster (in terms of computing time) and produces a better design result than the GS and I-O algorithms shown in Figure 2.

In Figure 1, the top profile error (TPE) is that defined in Equation 2 to evaluate the quality of the output distribution. Iavg is the average flat-top intensity, and N and Ireal are the number of samples and the flat-top intensity distribution, respectively.


 
Figure 1. The phase distribution of an MDOE: (a) phase distribution in two-dimensions, (b) phase distribution in one-dimension along the diametric.
 

 
Figure 2. The output-beam pattern on the focal plane: (a) simulated result, (b) experimental result.
 

To prove the validity of our new method, a large-aperture MDOE was designed for beam smoothing using the reformative mixed algorithm. The MDOE has a 70mm diameter and the uniform illumination area is a 600μm spot at the focal plane. We set phase values with 16 steps ranging from π/8rad to 2πrad (see Figure 2).

This kind of structure can easily be realized using multiple-mask etching. The simulated intensity of the output beam is shown in Figure 2a. The TPE of the MDOE in our design was 8.34%. We fabricated the MDOE with K9 glass, and there were 10-80nm depth-etch errors during fabrication (as measured by a step-depth meter, see Table 1).

 
Mask 1 Mask 2 Mask 3 Mask 4
Etch Depth (nm) 1040 520 260 130
Min Etch Error (nm) +14 -16 +13 +7
Max Etch Error (nm)   +59 -62 +13 +7
 
Table 1. Etch depth and error for each mask step: for positive values the actual etch depth is deeper than the ideal, for negative values it is shallower.
  
The focal-plane pattern is shown in Figure 2b. The spot diameter is about 600μm, matching our design data well. We again used TPE to evaluate the uniformity of the flat top, and the experimental result is about 19%: a little inferior to the design because of high etch errors. We can see that, although the actual depth errors of the first two etches are much more than 20nm, the MDOE still smooths the beam effectively at the focal plane.

The simulated and experimental results show that the new reformative algorithm is indeed useful for MDOE design. In practice, the stepped phase structure of MDOEs are easily realized with multiple-mask etching. Although the etching error makes the experimental TPE inferior to that of design, the error can be dealt with within the design process.


Authors
Yong-Ping Li, Xiao-BoZhang, Wei Zhang, Fang-Jie Shu, and Rong Wu
University of Science and Technology of China
HeFei, China