4.4 CO2 laser compensation by scanning

By scanning the rear face with a powerful CO2 laser, it is possible, in principle, to obtain any given intensity profile. In particular, it is possible to obtain an intensity distribution giving a flat thermal lens over a large central part of the mirror. Consider an intensity profile of the form
cosh(r2∕w2 ) I (r ) = PC---2--------2C-2- (4.14 ) πw C sinh(a ∕w C )
depending on the only parameter wC and normalized to PC W (see Figure 33View Image for the case of w C = 16.9 cm).
View Image

Figure 33: Source of heat on the mirror rear face for a power mask according to Equation (4.14View Equation) with wC = 16.9 cm (normalized to 1 W)

The resulting thermal lens has a perfect flatness in the central region. The goal is to create a profile such that, combined with the readout beam heat source, it gives that ideal profile. Consider, for instance, an intensity mask of the form

I (r) = 2PL-[cosh(r2∕w2 ) − exp(− r2∕w2 )], (4.15 ) C πw2 C
see the profile on Figure 34View Image. This is nothing but the complement to a source of heat corresponding to a TEM00 mode dissipating PL W on the coating. The resulting global thermal lens (thus corrected) can be seen in Figure 35View Image.
View Image

Figure 34: Source of heat on the mirror rear face for a power mask according to Equation (4.15View Equation) with wC = 16.9 cm for 1 W dissipated by the readout beam
View Image

Figure 35: Corrected thermal lens by a power mask according to Equation (4.15View Equation) with wC = 16.9 cm for 100 mW dissipated by the readout LG00 beam (w = 2 cm)

The price to pay is to provide the correcting power. According to Equation (4.15View Equation), the integrated power of the mask is

∫ a [ 2 ] PC = 2π IC(r)rdr = 2PL wC-sinh(a2∕w2 ) − 1 . (4.16 ) 0 w2 C


Table 13: Thermal compensation with a scanning CO2 beam for LG00 mode (w = 2 cm)
dissipated power initial losses compensation power minimal losses wavefront curvature
10 mW 350 ppm 1.9 W 0.7 ppm ∞
20 mW 1,400 ppm 3.8 W 3 ppm ∞
30 mW 3,100 ppm 5.6 W 6.4 ppm ∞
100 mW 34,300 ppm 18.8 W 71 ppm ∞

We see in this rather academic case (Table 13) that the residual losses are much less than in the preceding case (by a factor of about 20), but at the price of higher TCS power. The expansion in terms of Zernike polynomials is given in Table 14.


Table 14: Zernike coefficients for three TCS systems compensating LG00 mode (w = 2 cm)
  heating ring Axicon CO2 scan
cn µm/W µm/W µm/W
0 0.759 0.018 0.774
1 0.016 –0.008 –0.058
2 –0.044 0.003 –0.016
3 –0.012 0.001 0.001
4 0.002 –0.001 –0.002
5 0.004 0.001 0.002
6 0.002 0 –0.001
7 0 0 0.001
8 –0.001 0 –0.001


  Go to previous page Go up Go to next page