Full vectorial feature of second-harmonic generation with full Poincar&#233; beams

Li Zhang; Fei Lin; Xiaodong Qiu; Lixiang Chen

doi:10.3788/COL201917.091901

Journals >Chinese Optics Letters >Volume 17 >Issue 9 >Page 091901 > Article

Chinese Optics Letters
Vol. 17, Issue 9, 091901 (2019)

Full vectorial feature of second-harmonic generation with full Poincaré beams | On the Cover

Li Zhang^1、2, Fei Lin², Xiaodong Qiu², and Lixiang Chen^2、*

Author Affiliations

¹School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China

²Department of Physics, Collaborative Innovation Center for Optoelectronic Semiconductors and Efficient Devices, and Jiujiang Research Institute, Xiamen University, Xiamen 361005, China

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DOI: 10.3788/COL201917.091901 Cite this Article Set citation alerts

Li Zhang, Fei Lin, Xiaodong Qiu, Lixiang Chen. Full vectorial feature of second-harmonic generation with full Poincaré beams[J]. Chinese Optics Letters, 2019, 17(9): 091901 Copy Citation Text

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Abstract

We demonstrate the full vectorial feature of second-harmonic generation (SHG), i.e., from infrared full Poincaré beams to visible full Poincaré beams, based on two cascading type I phase-matching beta barium borate crystals of orthogonal optical axes. We visualize the structured features of the vectorial SHG wave by using Stokes polarimetry and show the interesting doubling effect of the polarization topological index, i.e., a low-order full Poincaré beam is converted to a high-order one. However, the polarization singularities of both C points and L lines are found to keep invariant during the SHG process. Our scheme could offer a deeper understanding on the interaction of vectorial light fields with media and can be generalized to other nonlinear optical effects.

E (r, φ) = A \cdot {LG}_{0}^{0} (r, φ) e_{1} + B \cdot {LG}_{0}^{l} (r, φ) e_{2}

(1)

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{LG}_{0}^{l} (r, φ) = E_{0} r^{| l |} L_{0}^{| l |} (\frac{2 r}{w^{2}}) \exp (- \frac{r^{2}}{w^{2}}) \exp (i l φ),

(2)

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{LG}_{0}^{0} (r, φ) (\begin{matrix} 1 \\ 0 \end{matrix}) \to \frac{(1 + i) \cos (2 α)}{2} {LG}_{0}^{0} (r, φ) (\begin{matrix} 1 \\ i \end{matrix}) + \frac{(1 - i) \sin (2 α)}{2} {LG}_{0}^{2} (r, φ) (\begin{matrix} 1 \\ - i \end{matrix}),

(3)

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{LG}_{0}^{0} (r, φ) (\begin{matrix} 1 \\ 0 \end{matrix}) \to i \cos (2 α) {LG}_{0}^{0} (r, φ) (\begin{matrix} 1 \\ 0 \end{matrix}) - i \sin (2 α) {LG}_{0}^{2} (r, φ) (\begin{matrix} 0 \\ 1 \end{matrix}) .

(4)

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\frac{d E_{S H}^{V}}{d z} = \frac{i ω_{S H}^{2} d_{eff}}{k_{S H} c^{2}} E_{H}^{2}, \frac{d E_{S H}^{H}}{d z} = \frac{i ω_{S H}^{2} d_{eff}}{k_{S H} c^{2}} E_{V}^{2},

(5)

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{LG}_{0}^{0} (r, φ) (\begin{matrix} 1 \\ 0 \end{matrix}) \to - \cos^{2} (2 α) {[{LG}_{0}^{0} (r, φ)]}^{2} (\begin{matrix} 1 \\ i \end{matrix}) + \sin^{2} (2 α) {[{LG}_{0}^{2} (r, φ)]}^{2} (\begin{matrix} 1 \\ - i \end{matrix}),

(6)

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{\begin{matrix} s_{0} = I_{H} + I_{V} \\ s_{1} = I_{H} - I_{V} \\ s_{2} = I_{D} - I_{A} \\ s_{3} = I_{R} - I_{L} \end{matrix},

(7)

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Li Zhang, Fei Lin, Xiaodong Qiu, Lixiang Chen. Full vectorial feature of second-harmonic generation with full Poincaré beams[J]. Chinese Optics Letters, 2019, 17(9): 091901

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