Generation and Talbot effect of optical vortex lattices with high orbital angular momentum

Yidan ZHANG; Hao GUO; Zijing WANG; Hao LUO; Peng LI; Zhenkun WU

doi:10.3969/j.issn.1005-5630.202411050099

Journals >Optical Instruments >Volume 47 >Issue 1 >Page 14 > Article

Optical Instruments
Vol. 47, Issue 1, 14 (2025)

Generation and Talbot effect of optical vortex lattices with high orbital angular momentum

Yidan ZHANG¹, Hao GUO¹, Zijing WANG¹, Hao LUO¹..., Peng LI^1,2 and Zhenkun WU^1,2,*|Show fewer author(s)

Author Affiliations

¹School of Physics and Electronics, Henan University, Kaifeng 475004, China

²International Joint Research Laboratory of New Energy Materials and Devices of Henan Province, Henan University, Kaifeng 475004, China

show less

DOI: 10.3969/j.issn.1005-5630.202411050099 Cite this Article

Yidan ZHANG, Hao GUO, Zijing WANG, Hao LUO, Peng LI, Zhenkun WU. Generation and Talbot effect of optical vortex lattices with high orbital angular momentum[J]. Optical Instruments, 2025, 47(1): 14 Copy Citation Text

show less

Abstract

Optical vortex lattices (OVL) are gaining increased research attention owing to their unique features related to intensity and phase structure. Interference is a common method for generating an OVL. However, the topological charge (TC) carried in OVL is usually small and fixed and cannot be modulated, limiting its applications in many fields. This study applied phase multiplication to generate a high-order OVL to facilitate the arbitrary modulation of the TC. The generated high-order OVL exhibited the Talbot effect during transmission, and it transformed into a super-honeycomb lattice with specific fractional Talbot lengths. In addition, an orbital angular momentum was developed in the OVL. This has broad application prospects in optical micromanipulation. Furthermore, a method for generating super-honeycomb lattices was proposed. The findings of this study not only enhance understanding of the Talbot effect but also broaden the practical applications of OVL.

Keywords

high-order optical vortex lattices optical vortex lattices Talbot effect topological charge

\begin{aligned} E_{j} (x_{0}, y_{0}, z = 0) = & A \exp [- \frac{{(x_{0} - x_{j})}^{2} + {(y_{0} - y_{j})}^{2}}{w^{2}}] \times \\ \exp (i φ_{j}) \end{aligned}

(1)

View in Article

$ {E_{\mathrm{s}}}\left( {{x_0},{y_0},{\textit{z}} = 0} \right) = \sum\limits_{j = 1}^B {{E_j}\left( {{x_0},{y_0},{\textit{z}} = 0} \right)} $

(2)

View in Article

\begin{aligned} E_{f} (x, y) = & \frac{\exp (i k z)}{i λ z} \exp [i \frac{k}{2 z} (x^{2} + y^{2})] \times \\ \int \int_{- \infty}^{+ \infty} E_{0} (x_{0}, y_{0}, z = & 0) \exp [- i \frac{2 π}{λ z} (x_{0} x + y_{0} y)] d x_{0} d y_{0} \\ = & \frac{A}{i λ z} \exp [i k (z + \frac{x^{2} + y^{2}}{2 z})] \times \\ \sum_{j = 1}^{B} F [\exp (i φ_{j})] \otimes & F {\exp [- \frac{{(x_{0} - x_{j})}^{2} + {(y_{0} - y_{j})}^{2}}{w^{2}}]} \end{aligned}

(3)

View in Article

\begin{aligned} E_{f} (x, y) \propto & \sum_{j = 1}^{B} \exp (i φ_{j}) \times \\ \exp {i \frac{k ρ}{f} [x \cos (π j / 3) + y \sin (π j / 3)]} \end{aligned}

(4)

View in Article

\begin{aligned} E_{f}^{m = 1} (x, y) = & | 2 i [\sin (x) + \sin (\frac{1}{2} x) \cdot \cos (\frac{\sqrt{3}}{2} y)] - \\ {\sqrt{3} \cos (\frac{1}{2} x) \cdot \sin (\frac{\sqrt{3}}{2} y) |}^{2} \end{aligned}

(5)

View in Article

\begin{aligned} E_{f}^{m = 2} (x, y) = & | - 2 [\cos (\frac{1}{2} x) \cdot \cos (\frac{\sqrt{3}}{2} y) + \cos (x) \cdot \\ {\sqrt{3} i \cdot \sin (\frac{1}{2} x) \cdot \sin (\frac{\sqrt{3}}{2} y)] |}^{2} \end{aligned}

(6)

View in Article

\begin{aligned} E_{f}^{m = 0} (x, y) = & 2 \cos \frac{\sqrt{3} y}{2} (\cos \frac{x}{2} - i \sin \frac{x}{2}) + \\ \cos x + i \sin x \end{aligned}

(7)

View in Article

\begin{aligned} E_{f}^{m = 1} (x, y) = & \cos \frac{\sqrt{3} y}{2} [(\sqrt{3} i + 1) \cos \frac{x}{2} + \\ (\sqrt{3} i - 1) \sin \frac{x}{2}] - (\cos x + i \sin x) \end{aligned}

(8)

\begin{aligned} E (X, Y, Z) = & {F^{- 1} \exp [\frac{i}{2} (ω_{x}^{2} + ω_{y}^{2}) Z] \times \\ F [E (X, Y, Z = 0)]} \end{aligned}

(13)

View in Article

Yidan ZHANG, Hao GUO, Zijing WANG, Hao LUO, Peng LI, Zhenkun WU. Generation and Talbot effect of optical vortex lattices with high orbital angular momentum[J]. Optical Instruments, 2025, 47(1): 14

Download Citation

Tools

Save the article for my favorites

Paper Information

微信扫一扫：分享

微信扫一扫：分享