Multiplication and division of orbital angular momentum beams by Fermat’s spiral transformation

Zishuai Zeng; Zihao Pang; Keming Pan; Jia Xu; Daomu Zhao

doi:10.1364/PRJ.477439

Journals >Photonics Research >Volume 11 >Issue 2 >Page 165 > Article

Photonics Research
Vol. 11, Issue 2, 165 (2023)

Multiplication and division of orbital angular momentum beams by Fermat’s spiral transformation

Zishuai Zeng, Zihao Pang, Keming Pan, Jia Xu, and Daomu Zhao^*

Author Affiliations

Zhejiang Province Key Laboratory of Quantum Technology and Device, School of Physics, Zhejiang University, Hangzhou 310058, China

show less

DOI: 10.1364/PRJ.477439 Cite this Article Set citation alerts

Zishuai Zeng, Zihao Pang, Keming Pan, Jia Xu, Daomu Zhao. Multiplication and division of orbital angular momentum beams by Fermat’s spiral transformation[J]. Photonics Research, 2023, 11(2): 165 Copy Citation Text

EndNote(RIS)

BibTex

Plain Text

show less

Abstract

Optical geometrical transformation is a novel and powerful tool to switch orbital angular momentum (OAM) states in modern optics. We demonstrate a scheme to operate multiplication and division in OAM by Fermat’s spiral transformation. The characteristics of the output beams in the case of integer and fraction OAM operations are presented in detail. Additionally, the power weight of the output OAM modes and the interference patterns of the output beams are reported to confirm the expected ability of OAM mode conversion by Fermat’s spiral transformation. We further investigate the evolution of OAM beams in operations theoretically and experimentally. This work provides a practical way to perform an optical transformation mapping on OAM beams. It can find application in optical communications with larger OAM mode numbers as well as quantum information in high-dimensional systems.

ρ = a {(\frac{r}{b})}^{- 1 / n}, φ = \frac{θ}{n},

(1)

View in Article

r = \frac{g}{{(\sqrt{h θ})}^{n}},

(2)

View in Article

θ = θ_{0} + 2 m π, m = ⌈ \frac{1}{2 π} (\frac{g^{2 / n}}{h r} - θ_{0}) ⌉, θ_{0} \in [0, 2 π),

(3)

View in Article

ρ = a h^{1 / 2} \sqrt{φ},

(4)

View in Article

φ = θ_{0} + 2 t π, t = ⌈ \frac{1}{2 π} (\frac{ρ^{2}}{a^{2} h} - θ_{0}) ⌉, θ_{0} \in [0, 2 π) .

(5)

View in Article

{LG}_{0}^{ℓ} (r, θ) = \frac{1}{w_{0}} {(\frac{r \sqrt{2}}{w_{0}})}^{| ℓ |} \exp (- \frac{r^{2}}{w_{0}^{2}}) \exp (i ℓ θ),

(6)

View in Article

ϕ_{1} (r, θ) = \frac{k a b^{1 / n}}{d (1 - 1 / n)} r^{1 - 1 / n} \cos (θ - \frac{θ}{n}) - \frac{k r^{2}}{2 d},

(7)

View in Article

U_{2}^{'} (ρ, φ) = \frac{- i k}{2 π d} \exp (i k d) \int_{0}^{2 π} \int_{0}^{+ \infty} U_{1} (r, θ) \times \exp {\frac{i k}{2 d} [r^{2} + ρ^{2} - 2 r ρ \cos (θ - φ)]} r d r d θ,

(8)

View in Article

ϕ_{2} (ρ, φ) = \frac{k b a^{n}}{d (1 - n)} r^{1 - n} \cos (φ - n φ) - \frac{k ρ^{2}}{2 d} .

(9)

View in Article

U_{2} (ρ, φ) = U_{2}^{'} (ρ, φ) \exp [i ϕ_{2} (ρ, φ)] .

(10)

View in Article

Zishuai Zeng, Zihao Pang, Keming Pan, Jia Xu, Daomu Zhao. Multiplication and division of orbital angular momentum beams by Fermat’s spiral transformation[J]. Photonics Research, 2023, 11(2): 165

Download Citation

EndNote(RIS)

BibTex

Plain Text

Set citation alerts for the article

Tools

Set citation alerts for the article

Save the article for my favorites

Paper Information