Clipping and saturation were investigated by the semi-analytical model. In the analysis, the waist radius of 20um at the micrometer position of 8mm is used.

1) Clipping

Firstly, the clipping loss was just geometrically calculated. Here the saturation issue was completely ignored.　The elements P6, P3, and P2 have the sizes of (500um)^2, (750um)^2m, and (1000um)^2, respectively. However, these numbers could not explain the clipping loss observed at the large spot sizes. Instead, empirically the effective sizes of (350um)^2, (610um)^2, and (860um)^2 were given to match the measurement and the calculation. This is equivalent to have 70um of an insensitive band at each edge of an element (Attachment 1). These effective element sizes are used for the calculation throughout this elog entry.

2) Saturation modeling

To incorporate the saturation effect, set a threshold power density. i.e. When the power density exceeds the threshold, the power density is truncated to this threshold. (Hard saturation)

Resulting loss was estimated using numerical integration using Mathematica. When the threshold power density was set to be 0.85W/mm^2, the drop of QE was approximately matched at the waist (Attachment 2). However, this did not explain the observed much-earlier saturation at the lower density. This suggests that the saturation is not such hard.

In order to estimate the threshold power density, look at the beam size where the first saturation starts. The earlier sagging of the QE was represented by the threshold density of 0.1W/mm^2. (Attachment 3)