Configuration optimization of off-axis parabolic mirror for enhancing the focusability of a laser beam

Xiahui Zeng

doi:10.3788/COL202119.032601

Journals >Chinese Optics Letters >Volume 19 >Issue 3 >Page 032601 > Article

Chinese Optics Letters
Vol. 19, Issue 3, 032601 (2021)

Configuration optimization of off-axis parabolic mirror for enhancing the focusability of a laser beam

Xiahui Zeng^*

Author Affiliations

Department of Physics & Electronic Information Engineering, Minjiang University, Fuzhou 350108, China

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DOI: 10.3788/COL202119.032601 Cite this Article Set citation alerts

Xiahui Zeng. Configuration optimization of off-axis parabolic mirror for enhancing the focusability of a laser beam[J]. Chinese Optics Letters, 2021, 19(3): 032601 Copy Citation Text

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Abstract

We demonstrate a configuration optimization process of an off-axis parabolic mirror to maximize the focused peak intensity based on a precise knowledge of the tight focusing properties by using a full vector-diffraction theory and obtain an optimum configuration scaling rule, which makes it possible to achieve the maximum peak intensity. In addition, we also carry out an assessment analysis of the offset and off-axis angle tolerances corresponding to a 5% drop of the maximum focused peak intensity and present scaling laws for the tolerances of the offset and off-axis angle. Understanding these scaling laws is important to enhance the focusability of a laser beam by an off-axis parabolic mirror in the optimum configuration, in particular, which is valuable for structural design and selection of an off-axis parabolic mirror in ultrashort and ultraintense laser–matter interaction experiments.

Keywords

configuration optimization laser focusing off-axis parabolic mirror vector-diffraction theory

E_{i} = (E_{0 x} \hat{x} + E_{0 y} \hat{y}) \exp (- i ω t - i k z_{i}),

(1)

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H_{i} = \frac{1}{η} (E_{0 y} \hat{x} - E_{0 x} \hat{y}) \exp (- i ω t - i k z_{i}),

(2)

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E_{x}^{'} (P) = D \iint_{S_{OAP}^{'}} J \exp [i k (u x_{P}^{'} + v y_{P}^{'} + γ z_{P}^{'})] \times [(\frac{1}{r} - \frac{x^{2}}{2 f r^{2}}) E_{0 x} - \frac{x y}{2 f r^{2}} E_{0 y}] d u d v,

(3)

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E_{y}^{'} (P) = D \iint_{S_{OAP}^{'}} J \exp [i k (u x_{P}^{'} + v y_{P}^{'} + γ z_{P}^{'})] \times [(\frac{1}{r} - \frac{y^{2}}{2 f r^{2}}) E_{0 y} - \frac{x y}{2 f r^{2}} E_{0 x}] d u d v,

(4)

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E_{z}^{'} (P) = D \iint_{S_{OAP}^{'}} J \exp [i k (u x_{P}^{'} + v y_{P}^{'} + γ z_{P}^{'})] \times \frac{1}{r^{2}} (x E_{0 x} + y E_{0 y}) d u d v,

(5)

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H_{x}^{'} (P) = D \iint_{S_{OAP}^{'}} \frac{J \exp [i k (u x_{P}^{'} + v y_{P}^{'} + γ z_{P}^{'})]}{η} \times [(- \frac{x y}{2 f r^{2}}) E_{0 x} + (\frac{x^{2} - y^{2}}{4 f r^{2}} - \frac{f}{r^{2}}) E_{0 y}] d u d v,

(6)

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H_{y}^{'} (P) = D \iint_{S_{OAP}^{'}} \frac{J \exp [i k (u x_{P}^{'} + v y_{P}^{'} + γ z_{P}^{'})]}{η} \times [(\frac{x^{2} - y^{2}}{4 f r^{2}} + \frac{f}{r^{2}}) E_{0 x} + (\frac{x y}{2 f r^{2}}) E_{0 y}] d u d v,

(7)

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H_{z}^{'} (P) = D \iint_{S_{OAP}^{'}} \frac{J \exp [i k (u x_{P}^{'} + v y_{P}^{'} + γ z_{P}^{'})]}{η} \times \frac{1}{r^{2}} (y E_{0 x} - x E_{0 y}) d u d v,

(8)

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J = \frac{4 f^{2}}{γ {(1 + u \sin ψ + γ \cos ψ)}^{2}} .

(9)

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\frac{h_{opt}}{R} = \frac{A}{1 + \exp [- B (f / #) + C]},

(10)

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\frac{h_{max-crit}}{f} = a + \frac{b}{(f / #)},

(11)

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ψ_{max-crit} (\deg) = α + \frac{m}{(f / #) + n} (\deg),

(12)

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Xiahui Zeng. Configuration optimization of off-axis parabolic mirror for enhancing the focusability of a laser beam[J]. Chinese Optics Letters, 2021, 19(3): 032601

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