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Chinese Optics Letters
Vol. 16, Issue 10, 103201 (2018)

Dynamical analysis of the effect of elliptically polarized laser pulses on molecular alignment and orientation

Jingsong Liu, Qiyuan Cheng, Daguang Yue, Xucong Zhou, and Qingtian Meng^*

Author Affiliations

School of Physics and Electronics, Shandong Normal University, Jinan 250358, China

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DOI: 10.3788/COL201816.103201 Cite this Article Set citation alerts

Jingsong Liu, Qiyuan Cheng, Daguang Yue, Xucong Zhou, Qingtian Meng. Dynamical analysis of the effect of elliptically polarized laser pulses on molecular alignment and orientation[J]. Chinese Optics Letters, 2018, 16(10): 103201 Copy Citation Text

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Abstract

In this Letter, we study the molecular alignment and orientation driven by two elliptically polarized laser pulses. It is shown that the field-free molecular alignment can be achieved in a three-dimensional (3D) case, while the field-free molecular orientation is only along the x and y directions, and that the field-free alignment and orientation along different axes are related to the populations of the rotational states. It is demonstrated that changing the elliptic parameter is efficient for controlling both in-pulse and post-pulse molecular alignment and orientation. The delay time also has an influence on the field-free molecular alignment and orientation.

{\vec{E}}_{i} (t) = E_{0} (t) {{\vec{e}}_{x} a_{i} \cos [ω_{i} (t - t_{i})] + {\vec{e}}_{y} b_{i} \sin [ω_{i} (t - t_{i})]}, (i = 1, 2),

(1)

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E_{0} (t) = E_{i} \exp [- {(t - t_{i})}^{2} / 2 σ_{i}^{2}],

(2)

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{\hat{H}}_{0} (t) = {\hat{H}}_{0} + {\hat{H}}_{pol} (t) + {\hat{H}}_{dip} (t) .

(3)

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{\hat{H}}_{pol} (t) = - \frac{1}{4} E_{0}^{2} (t) (α_{∥} - α_{⊥}) \sin^{2} θ [(a_{1}^{2} - b_{1}^{2}) \cos^{2} ϕ + b_{1}^{2}],

(4)

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{\hat{H}}_{dip} (t) = - μ E_{0} (t) a_{2} \sin θ \cos ϕ \cos [ω_{2} (t - t_{2})] + μ E_{0} (t) b_{2} \sin θ \sin ϕ \sin [ω_{2} (t - t_{2})],

(5)

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\frac{d \hat{ρ} (t)}{d t} = - \frac{i}{ℏ} [\hat{H}, \hat{ρ} (t)] .

(6)

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\frac{d ρ_{J M j^{'} M^{'} (t)}}{d t} = - \frac{i}{ℏ} {\sum_{J_{1} M_{1}} (ρ_{J_{1} M_{1} J^{'} M^{'}} (t) 〈 J M | B_{e} {\hat{J}}^{2} | J_{1} M_{1} 〉 - ρ_{J M J_{1} M_{1}} (t) 〈 J_{1} M_{1} | B_{e} {\hat{J}}^{2} | J^{'} M^{'} 〉) - \frac{1}{4} E_{0}^{2} (t) (α_{∥} - α_{⊥}) \sum_{J_{1} M_{1}} [(a_{1}^{2} - b_{1}^{2}) (ρ_{J_{1} M_{1} J^{'} M^{'}} (t) \cdot 〈 J M | \sin^{2} θ \cos^{2} ϕ | J_{1} M_{1} 〉 - ρ_{J M J_{1} M_{1}} (t) 〈 J_{1} M_{1} | \sin^{2} θ \cos^{2} ϕ | J^{'} M^{'} 〉)] - b_{1}^{2} (ρ_{J_{1} M_{1} J^{'} M^{'}} (t) 〈 J M | \cos^{2} θ | J_{1} M_{1} 〉 - ρ_{J M J_{1} M_{1}} (t) 〈 J_{1} M_{1} | \cos^{2} θ | J^{'} M^{'} 〉) - μ E_{0} (t) \sum_{J_{1} M_{1}} [a_{2} \cos (ω_{2} (t - t_{2})) (ρ_{J_{1} M_{1} J^{'} M^{'}} (t) \cdot 〈 J M | \sin^{} θ \cos ϕ J_{1} M_{1} 〉 - ρ_{J M J_{1} M_{1}} (t) 〈 J_{1} M_{1} | \sin θ \cos ϕ J^{'} M^{'} 〉) + b_{2} \sin (ω_{2} (t - t_{2})) (ρ_{} (t) \cdot 〈 J M | \sin θ \sin ϕ | J_{1} M_{1} 〉 - ρ_{J M J_{1} M_{1}} (t) 〈 J_{1} M_{1} | \sin θ \sin ϕ J^{'} M^{'} 〉)]} .

(7)

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ρ_{0} (T) = \frac{1}{Z} \sum_{J = 0}^{\infty} \sum_{J = 0}^{M = J} | J M 〉 〈 J M | e^{- ε / K_{B} T},

(8)

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\begin{matrix} 〈 \cos^{2} θ_{x} 〉 = T r {\sin^{2} θ \cos^{2} ϕ \hat{ρ} (t)} \\ 〈 \cos^{2} θ_{y} 〉 = T r {\sin^{2} θ \sin^{2} ϕ \hat{ρ} (t)} \\ 〈 \cos^{2} θ_{z} 〉 = T r {\cos^{2} θ \hat{ρ} (t)} \end{matrix}},

(9)

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\begin{matrix} 〈 \cos θ_{x} 〉 = T r {\sin θ \cos ϕ \hat{ρ} (t)} \\ 〈 \cos θ_{y} 〉 = T r {\sin θ \sin ϕ \hat{ρ} (t)} \\ 〈 \cos θ_{z} 〉 = T r {\cos θ \hat{ρ} (t)} \end{matrix}} .

(10)

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{〈 \cos^{2} θ_{y} 〉}_{a^{2}} (t) \approx b^{2} y_{1} + a^{2} x_{1} = (\frac{1 - 3 a^{2}}{2}) y_{1} + \frac{a^{2}}{2},

(11)

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{〈 \cos^{2} θ_{x} 〉}_{a^{2}} (t) \approx a^{2} y_{1} + b^{2} x_{1} = (\frac{3 a^{2} - 1}{2}) y_{1} - \frac{a^{2}}{2} + \frac{1}{2},

(12)

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Jingsong Liu, Qiyuan Cheng, Daguang Yue, Xucong Zhou, Qingtian Meng. Dynamical analysis of the effect of elliptically polarized laser pulses on molecular alignment and orientation[J]. Chinese Optics Letters, 2018, 16(10): 103201

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