FM-to-AM conversion in high-power lasers

Steve Hocquet; Denis Penninckx; Edouard Bordenave; Claude Gouédard; Yves Jaouën

doi:10.1364/AO.47.003338

Applied Optics
Vol. 47,
Issue 18,
pp. 3338-3349
(2008)
•https://doi.org/10.1364/AO.47.003338

FM-to-AM conversion in high-power lasers

Steve Hocquet, Denis Penninckx, Edouard Bordenave, Claude Gouédard, and Yves Jaouën

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Steve Hocquet, Denis Penninckx, Edouard Bordenave, Claude Gouédard, and Yves Jaouën, "FM-to-AM conversion in high-power lasers," Appl. Opt. 47, 3338-3349 (2008)

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Abstract

FM-to-AM conversion is an important issue that could prevent fusion ignition with high-power lasers, such as the Laser MegaJoule (LMJ). We first overview the whole problem of FM-to-AM conversion in high-power lasers and we explain why AM spectral content of FM-to-AM conversion is important, although this information was not used in previous studies. We then propose simple analytical models to simulate FM-to-AM conversion in the LMJ frequency conversion system. We succeed in isolating every cause of spectrum distortion and give, for each of them, FM-to-AM predictions that are in very good agreement with simulations of a complex propagation code. Finally, we show how the last grating filters most of the FM-to-AM conversion. We conclude that the FM-to-AM conversion distortion criterion will be, on LMJ, below 40% in the last optics and 10% on the target.

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	α value
Transfer Function	$\| f_{c} \| < m f_{m}$	$\| f_{c} \| > m f_{m}$
$1 + i σ (f - f_{c})$	$α = \frac{σ^{2} [\| f_{c} \| + m . f_{m}]^{2}}{1 - 1 / 2 σ^{2} [\| f_{c} \| + m . f_{m}]^{2}}$	$α = \frac{4 σ^{2} . m . f_{m} f_{c}}{1 - σ^{2} [{f_{c}}^{2} + (m . f_{m})^{2}]^{2}}$
$1 - σ (f - f_{c})^{2}$	$α = \frac{2 σ [\| f_{c} \| + m . f_{m}]^{2}}{1 - σ [\| f_{c} \| + m . f_{m}]^{2}}$	$α = \frac{8 σ . m . f_{m} f_{c}}{1 - 2 σ [{f_{c}}^{2} + (m . f_{m})^{2}]^{2}}$
$1 - i σ (f - f_{c})^{2}$	$α = 4 σ m {f_{m}}^{2}$

	$14.25 GHz$		$14.25 + 2 GHz$
	without grating	with grating	without grating	with grating
$α_{c}$	47%	17%	66%	24%
$α_{d}$	0%	26%	0%	27%
$α_{NF}$	47%	34%	66%	39%
$α_{FF}$	3%	8%	12%	9%

	α value
Transfer Function	$\| f_{c} \| < m f_{m}$	$\| f_{c} \| > m f_{m}$
$1 + i σ (f - f_{c})$	$α = \frac{σ^{2} [\| f_{c} \| + m . f_{m}]^{2}}{1 - 1 / 2 σ^{2} [\| f_{c} \| + m . f_{m}]^{2}}$	$α = \frac{4 σ^{2} . m . f_{m} f_{c}}{1 - σ^{2} [{f_{c}}^{2} + (m . f_{m})^{2}]^{2}}$
$1 - σ (f - f_{c})^{2}$	$α = \frac{2 σ [\| f_{c} \| + m . f_{m}]^{2}}{1 - σ [\| f_{c} \| + m . f_{m}]^{2}}$	$α = \frac{8 σ . m . f_{m} f_{c}}{1 - 2 σ [{f_{c}}^{2} + (m . f_{m})^{2}]^{2}}$
$1 - i σ (f - f_{c})^{2}$	$α = 4 σ m {f_{m}}^{2}$

	$14.25 GHz$		$14.25 + 2 GHz$
	without grating	with grating	without grating	with grating
$α_{c}$	47%	17%	66%	24%
$α_{d}$	0%	26%	0%	27%
$α_{NF}$	47%	34%	66%	39%
$α_{FF}$	3%	8%	12%	9%

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Applied Optics