I. Moulanier, L. T. Dickson, F. Massimo, G. Maynard, and B. Cros, "Fast laser field reconstruction method based on a Gerchberg–Saxton algorithm with mode decomposition," J. Opt. Soc. Am. B 40, 2450-2461 (2023)
Knowledge of the electric field of femtosecond, high intensity laser pulses is of paramount importance to study the interaction of this class of lasers with matter. A hybrid method to reconstruct the laser field from fluence measurements in the transverse plane at multiple positions along the propagation axis is presented, combining a Hermite–Gauss mode decomposition (MD) and elements of the Gerchberg–Saxton algorithm (GSA). The proposed GSA-MD takes into account the pointing instabilities of high intensity laser systems by tuning the centers of the HG modes. Furthermore, it quickly builds a field description by progressively increasing the number of modes and thus the accuracy of the field reconstruction. The results of field reconstruction using the GSA-MD are shown to be in excellent agreement with experimental measurements from two different high peak power laser facilities.
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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Algorithm to find the coefficients of the HG modes from experimental fluence images measured at planes , with . HG mode centers are set at the start of the algorithm and kept fixed. Steps 6–9 are repeated for each of the mode indices , . This algorithm corresponds to the yellow rectangle of Fig. 3
Carrier wavelength ${\lambda _0}$, peak power ${P_0}$, mean energy per laser shot, shot-to-shot relative pulse centroid position fluctuations $\delta \bar x/{w_{0,{\rm Gauss}}}$ and $\delta \bar y/{w_{0,{\rm Gauss}}}$, position $z$ of the fluence measurement planes ($z = 0$ is the focal plane), number of pixels in the fluence images, pixel size, estimated Gaussian fit’s waist ${w_{0,{\rm Gauss}}}$, uncertainty of the focal plane position ${\Delta _z}$, waists ${w_{0,x}} = {w_{0,y}}$ for HG modes, number of modes ${N_m}$ and ${N_n}$ in $x$ and $y$ directions for the EG (RS) phase ${N_{m,{\rm EG}}}$, ${N_{n,{\rm EG}}}$ (${N_{m,{\rm RS}}}$, ${N_{n,{\rm RS}}})$, search area ${S_{\rm{EG}}}$ (${S_{\rm{RS}}}$) for the centers of the EG (RS) phase, number of iterations ${N_{\rm{iter}}}$ for Algorithm 1, number of center tuning iterations for the EG (RS) phase ${N_{\rm tuning,EG}}$ (${N_{\rm tuning,RS}}$), computing time for EG and RS phases.
Table 2.
Performances on the Apollon Dataset of the GSA and GSA-MD without and with Origin Tuninga
Parameter
GSA
GSA-MD (, without Origin Tuning)
GSA-MD (, with Origin Tuning)
50
50
50
Total time
3.8 s
13.6 s
1 h 15 min
()
2.50
2.28
1.61
()
1.94
2.76
1.98
()
3.89
2.48
1.52
()
1.67
1.60
1.35
The value $\chi _k^2$ is the value of the reconstruction error in plane ${z_k}$.
Tables (3)
Algorithm 1.
Algorithm to find the coefficients of the HG modes from experimental fluence images measured at planes , with . HG mode centers are set at the start of the algorithm and kept fixed. Steps 6–9 are repeated for each of the mode indices , . This algorithm corresponds to the yellow rectangle of Fig. 3
Carrier wavelength ${\lambda _0}$, peak power ${P_0}$, mean energy per laser shot, shot-to-shot relative pulse centroid position fluctuations $\delta \bar x/{w_{0,{\rm Gauss}}}$ and $\delta \bar y/{w_{0,{\rm Gauss}}}$, position $z$ of the fluence measurement planes ($z = 0$ is the focal plane), number of pixels in the fluence images, pixel size, estimated Gaussian fit’s waist ${w_{0,{\rm Gauss}}}$, uncertainty of the focal plane position ${\Delta _z}$, waists ${w_{0,x}} = {w_{0,y}}$ for HG modes, number of modes ${N_m}$ and ${N_n}$ in $x$ and $y$ directions for the EG (RS) phase ${N_{m,{\rm EG}}}$, ${N_{n,{\rm EG}}}$ (${N_{m,{\rm RS}}}$, ${N_{n,{\rm RS}}})$, search area ${S_{\rm{EG}}}$ (${S_{\rm{RS}}}$) for the centers of the EG (RS) phase, number of iterations ${N_{\rm{iter}}}$ for Algorithm 1, number of center tuning iterations for the EG (RS) phase ${N_{\rm tuning,EG}}$ (${N_{\rm tuning,RS}}$), computing time for EG and RS phases.
Table 2.
Performances on the Apollon Dataset of the GSA and GSA-MD without and with Origin Tuninga
Parameter
GSA
GSA-MD (, without Origin Tuning)
GSA-MD (, with Origin Tuning)
50
50
50
Total time
3.8 s
13.6 s
1 h 15 min
()
2.50
2.28
1.61
()
1.94
2.76
1.98
()
3.89
2.48
1.52
()
1.67
1.60
1.35
The value $\chi _k^2$ is the value of the reconstruction error in plane ${z_k}$.
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