Flexible rotation of transverse optical field for 2D self-accelerating beams with a designated trajectory

Lei Zhu; Xuesong Zhao; Chen Liu; Songnian Fu; Yuncai Wang; Yuwen Qin

doi:10.29026/oea.2021.200021

Journals >Opto-Electronic Advances >Volume 4 >Issue 3 >Page 200021-1 > Article

Opto-Electronic Advances
Vol. 4, Issue 3, 200021-1 (2021)

Flexible rotation of transverse optical field for 2D self-accelerating beams with a designated trajectory

Lei Zhu¹, Xuesong Zhao¹, Chen Liu¹, Songnian Fu^2,*..., Yuncai Wang² and Yuwen Qin²|Show fewer author(s)

Author Affiliations

¹Wuhan National Laboratory for Optoelectronics, and School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan 430074, China

²School of Information Engineering, Guangdong University of Technology, and Guangdong Provincial Key Laboratory of Photonics Information Technology, Guangzhou 510006, China.

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DOI: 10.29026/oea.2021.200021 Cite this Article

Lei Zhu, Xuesong Zhao, Chen Liu, Songnian Fu, Yuncai Wang, Yuwen Qin. Flexible rotation of transverse optical field for 2D self-accelerating beams with a designated trajectory[J]. Opto-Electronic Advances, 2021, 4(3): 200021-1 Copy Citation Text

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Abstract

Self-accelerating beams have the unusual ability to remain diffraction-free while undergo the transverse shift during the free-space propagation. We theoretically identify that the transverse optical field distribution of 2D self-accelerating beam is determined by the selection of the transverse Cartesian coordinates, when the caustic method is utilized for its trajectory design. Based on the coordinate-rotation method, we experimentally demonstrate a scheme to flexibly manipulate the rotation of transverse optical field for 2D self-accelerating beams under the condition of a designated trajectory. With this scheme, the transverse optical field can be rotated within a range of 90 degrees, especially when the trajectory of 2D self-accelerating beams needs to be maintained for free-space photonic interconnection.

Keywords

caustic optical field self-accelerating beams

\begin{aligned} E (X, Z) \\ = \frac{1}{2 π} \int A (k_{x}) e x p {i [k_{x} X + \sqrt{k^{2} - {k_{x}}^{2}} Z + φ (k_{x})]} d k_{x} \\ = \frac{1}{2 π} \int A (k_{x}) e x p [i ψ (k_{x})] d k_{x}, \end{aligned}

(1)

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$\frac{{{\rm{d}}\psi \left( {{k_x}} \right)}}{{{\rm{d}}{k_x}}} = X - \frac{{{k_x}}}{{\sqrt {{k^2} - {k_x}^2} }}Z + \phi '\left( {{k_x}} \right) = 0\;.$

(2)

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$\left[ {

\begin{matrix} X_{θ} \\ Y_{θ} \end{matrix}

} \right] = \left[ {

\begin{matrix} \cos θ & \sin θ \\ - \sin θ & \cos θ \end{matrix}

} \right]\left[ {

\begin{matrix} f (Z) \\ g (Z) \end{matrix}

} \right]\;.$

(3)

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$\left[ {

\begin{matrix} {x_{0,}}_{θ} \\ y_{0, θ} \end{matrix}

} \right] = \left[ {

\begin{matrix} \cos θ & \sin θ \\ - \sin θ & \cos θ \end{matrix}

} \right]\left[ {

\begin{matrix} f (Z) - Z f^{'} (Z) \\ g (Z) - Z g^{'} (Z) \end{matrix}

} \right]\;,$

(4)

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$\left[ {

\begin{matrix} k_{0, x, θ} \\ k_{0, y, θ} \end{matrix}

} \right] = k\left[ {

\begin{matrix} \cos θ & \sin θ \\ - \sin θ & \cos θ \end{matrix}

} \right]\left[ {

\begin{matrix} f^{'} (Z) \\ g^{'} (Z) \end{matrix}

} \right]\;.$

(5)

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\begin{aligned} W_{θ} (x_{θ}, y_{θ}, k_{x, θ}, k_{y, θ}) \\ = \int δ [x_{θ} - x_{0, θ}, y_{θ} - y_{0, θ}] δ [k_{x, θ} - k_{0, x, θ}, k_{y, θ} - k_{0, y, θ}] d Z, \end{aligned}

(6)

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${\varphi _\theta } = \int { - \frac{{\int {{x_\theta }{y_\theta }{W_\theta }{\rm{d}}{x_\theta }{\rm{d}}{y_\theta }} }}{{\int {{W_\theta }{\rm{d}}{x_\theta }{\rm{d}}{y_\theta }} }}{\rm{d}}{k_{x,\theta }}{\rm{d}}{k_{y,\theta }}} \;,$

(7)