Comparative study of different optimization methods for single attosecond pulse generation with a two- or three-color gating scheme

Ke Yang; Jin-Xu Du; Guo-Li Wang; Zhi-Hong Jiao; Song-Feng Zhao; Xiao-Xin Zhou; Xiao-Xin Zhou

doi:10.1364/JOSAB.444007

Journal of the Optical Society of America B
Vol. 39,
Issue 3,
pp. A75-A82
(2022)
•https://doi.org/10.1364/JOSAB.444007

Comparative study of different optimization methods for single attosecond pulse generation with a two- or three-color gating scheme

Ke Yang, Jin-Xu Du, Guo-Li Wang, Zhi-Hong Jiao, Song-Feng Zhao, and Xiao-Xin Zhou

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Ke Yang, Jin-Xu Du, Guo-Li Wang, Zhi-Hong Jiao, Song-Feng Zhao, and Xiao-Xin Zhou, "Comparative study of different optimization methods for single attosecond pulse generation with a two- or three-color gating scheme," J. Opt. Soc. Am. B 39, A75-A82 (2022)

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Abstract

The shaping of the waveform of a two- or three-color driving laser pulse is essential for generating an ultrashort isolated attosecond pulse (IAP) from high-order harmonic generation, which can be implemented in two different ways, i.e., direct coherent synthesizing of electric fields with appropriate parameters (wavelength, intensity, carrier envelope phase, time delay), and superposition of fields undergoing a spectral phase shaping in frequency space view, which additionally results in a chirp and pulse-width broadening. In this work, we perform a comparative study on the IAP generation with these two schemes by virtue of a genetic algorithm, and two very meaningful conclusions are clarified. First, weighing the advantages and disadvantages of the two methods, the width and strength of IAPs optimized from two schemes are basically the same. More optimization parameters in the second method of laser shaping do not show an advantage in shortening width or enhancing the intensity of the IAP compared with the first one. Second, in each case, one can get the shortest IAP when the carrier envelope phases for each spectral component are not required to be precisely controlled. This study provides useful theoretical guidance for generating a shorter IAP with multicolor gating in the experiment.

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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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	$I = 10 I_{0}$		$I = 14 I_{0}$
	Two-Color		Two-Color			Three-Color
Parameter	$C_{2, 10}^{1}$	$C_{2, 10}^{2}$	$C_{2, 14}^{1}$	$C_{2, 14}^{2}$	$C_{2, 14}^{3}$	$C_{3, 14}^{1}$	$C_{3, 14}^{2}$	$C_{3, 14}^{3}$	$C_{3, 14}^{4}$
$I_{1} (I_{0})$	5.347	5.377	7.014	8.996	7.269	6.316	9.000	7.529	6.366
$I_{2} (I_{0})$	4.653	4.623	6.986	5.004	6.731	2.502	2.191	4.137	3.902
$I_{3} (I_{0})$						5.182	2.809	2.334	3.732
$λ_{1} (n m)$	800.0	800.0	800.0	800.0	800.0	800.0	800.0	800.0	800.0
$λ_{2} (n m)$	459.3	461.1	462.6	400.0	474.5	530.0	400.0	490.4	408.0
$λ_{3} (n m)$						400.1	266.7	400.1	545.6
$τ_{1} (f s)$	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
$τ_{2} (f s)$	−0.271	0.066	−0.290	0.191	0.117	0.630	0.387	0.513	0.817
$τ_{3} (f s)$						−0.993	−0.369	0.750	0.539
$φ_{1} (π)$	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
$φ_{2} (π)$	0.434	0.0	0.505	1.969	0.0	1.229	1.622	0.0	0.9
$φ_{3} (π)$						1.484	1.438	0.0	1.6

	$I = 10 I_{0}$			$I = 14 I_{0}$
	Two-Color			Two-Color				Three-Color
Parameter	$C_{2, 10}^{1}$	$C_{2, 10}^{2}$	$C_{2, 10}^{3}$	$C_{2, 14}^{1}$	$C_{2, 14}^{2}$	$C_{2, 14}^{3}$	$C_{2, 14}^{4}$	$C_{3, 14}^{1}$	$C_{3, 14}^{2}$	$C_{3, 14}^{3}$	$C_{3, 14}^{4}$
$I_{1} (I_{0})$	5.469	5.722	5.362	7.014	11.078	7.219	7.246	6.609	8.063	6.033	6.206
$I_{2} (I_{0})$	4.531	4.278	4.638	6.986	2.923	6.781	6.754	3.428	3.032	2.641	4.596
$I_{3} (I_{0})$								3.963	2.906	5.327	3.198
$λ_{1} (n m)$	800.0	800.0	800.0	800.0	800.0	800.0	800.0	800.0	800.0	800.0	800.0
$λ_{2} (n m)$	461.7	464.0	467.7	466.4	400.0	467.3	474.9	524.7	400.0	583.1	511.0
$λ_{3} (n m)$								401.6	266.7	414.1	407.1
$ϕ_{01} (π)$	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
$ϕ_{02} (π)$	1.330	0.0	0.0	1.713	1.869	0.0	0.0	0.832	0.581	0.0	0.0
$ϕ_{03} (π)$								0.068	1.648	0.0	0.0
$α_{1} (f s)$	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
$α_{2} (f s)$	−2.63	−3.37	0.07	2.95	−2.1	0.07	0.12	1.56	−0.24	0.007	−2.12
$α_{3} (f s)$								0.45	−1.03	1.44	−0.60
$β_{1} (f s^{2})$	−0.14	−0.43	0.0	−0.28	0.23	0.25	0.0	0.46	0.04	0.39	0.0
$β_{2} (f s^{2})$	0.32	0.07	0.0	−0.44	0.48	0.29	0.0	0.28	0.02	0.27	0.0
$β_{3} (f s^{2})$								0.27	0.09	−0.11	0.0

	$I = 10 I_{0}$		$I = 14 I_{0}$
	Two-Color		Two-Color			Three-Color
Parameter	$C_{2, 10}^{1}$	$C_{2, 10}^{2}$	$C_{2, 14}^{1}$	$C_{2, 14}^{2}$	$C_{2, 14}^{3}$	$C_{3, 14}^{1}$	$C_{3, 14}^{2}$	$C_{3, 14}^{3}$	$C_{3, 14}^{4}$
$I_{1} (I_{0})$	5.347	5.377	7.014	8.996	7.269	6.316	9.000	7.529	6.366
$I_{2} (I_{0})$	4.653	4.623	6.986	5.004	6.731	2.502	2.191	4.137	3.902
$I_{3} (I_{0})$						5.182	2.809	2.334	3.732
$λ_{1} (n m)$	800.0	800.0	800.0	800.0	800.0	800.0	800.0	800.0	800.0
$λ_{2} (n m)$	459.3	461.1	462.6	400.0	474.5	530.0	400.0	490.4	408.0
$λ_{3} (n m)$						400.1	266.7	400.1	545.6
$τ_{1} (f s)$	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
$τ_{2} (f s)$	−0.271	0.066	−0.290	0.191	0.117	0.630	0.387	0.513	0.817
$τ_{3} (f s)$						−0.993	−0.369	0.750	0.539
$φ_{1} (π)$	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
$φ_{2} (π)$	0.434	0.0	0.505	1.969	0.0	1.229	1.622	0.0	0.9
$φ_{3} (π)$						1.484	1.438	0.0	1.6

	$I = 10 I_{0}$			$I = 14 I_{0}$
	Two-Color			Two-Color				Three-Color
Parameter	$C_{2, 10}^{1}$	$C_{2, 10}^{2}$	$C_{2, 10}^{3}$	$C_{2, 14}^{1}$	$C_{2, 14}^{2}$	$C_{2, 14}^{3}$	$C_{2, 14}^{4}$	$C_{3, 14}^{1}$	$C_{3, 14}^{2}$	$C_{3, 14}^{3}$	$C_{3, 14}^{4}$
$I_{1} (I_{0})$	5.469	5.722	5.362	7.014	11.078	7.219	7.246	6.609	8.063	6.033	6.206
$I_{2} (I_{0})$	4.531	4.278	4.638	6.986	2.923	6.781	6.754	3.428	3.032	2.641	4.596
$I_{3} (I_{0})$								3.963	2.906	5.327	3.198
$λ_{1} (n m)$	800.0	800.0	800.0	800.0	800.0	800.0	800.0	800.0	800.0	800.0	800.0
$λ_{2} (n m)$	461.7	464.0	467.7	466.4	400.0	467.3	474.9	524.7	400.0	583.1	511.0
$λ_{3} (n m)$								401.6	266.7	414.1	407.1
$ϕ_{01} (π)$	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
$ϕ_{02} (π)$	1.330	0.0	0.0	1.713	1.869	0.0	0.0	0.832	0.581	0.0	0.0
$ϕ_{03} (π)$								0.068	1.648	0.0	0.0
$α_{1} (f s)$	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
$α_{2} (f s)$	−2.63	−3.37	0.07	2.95	−2.1	0.07	0.12	1.56	−0.24	0.007	−2.12
$α_{3} (f s)$								0.45	−1.03	1.44	−0.60
$β_{1} (f s^{2})$	−0.14	−0.43	0.0	−0.28	0.23	0.25	0.0	0.46	0.04	0.39	0.0
$β_{2} (f s^{2})$	0.32	0.07	0.0	−0.44	0.48	0.29	0.0	0.28	0.02	0.27	0.0
$β_{3} (f s^{2})$								0.27	0.09	−0.11	0.0

Abstract

Data Availability

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Tables (2)

Equations (6)

Journal of the Optical Society of America B