Conversion of orbital angular momentum of light in chiral fiber gratings

Huaxing Xu; Li Yang

doi:10.1364/OL.38.001978

Optics Letters
Vol. 38,
Issue 11,
pp. 1978-1980
(2013)
•https://doi.org/10.1364/OL.38.001978

Conversion of orbital angular momentum of light in chiral fiber gratings

Huaxing Xu and Li Yang

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Huaxing Xu and Li Yang, "Conversion of orbital angular momentum of light in chiral fiber gratings," Opt. Lett. 38, 1978-1980 (2013)

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- Diffraction and Gratings
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About this Article
History
- Original Manuscript: February 20, 2013
- Revised Manuscript: April 30, 2013
- Manuscript Accepted: May 6, 2013
- Published: May 31, 2013

Abstract

We examine mode couplings in chiral fiber grating (CFG) with N-fold rotation symmetry in the cross section and show how the angular momentum matching condition in couplings determines the generation and conversion of orbital angular momentum (OAM) beams. Then we discuss interactions of OAM and spin angular momentum in single- and double-helix long-period CFGs excited by the fundamental core modes. Subsequently, taking right-handed elliptic-core long-period CFGs as example, we demonstrate a dual-OAM converter generating OAM beams with charge $+ 2$ and charge $+ 4$ at dual wavelengths, both with a conversion efficiency greater than 97%, as well as a broadband converter based on adiabatic coupling, with a bandwidth about 10 nm for a conversion efficiency greater than 95%.

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Modes	$H E_{m n}^{+}$	$H E_{m n}^{-}$	$E H_{m n}^{+}$	$E H_{m n}^{-}$	$V_{0 n}^{+}$	$V_{0 n}^{-}$
$s$	$+ 1$	$- 1$	$- 1$	$+ 1$	$+ 1$	$- 1$
$l$	$m - 1$	$1 - m$	$m + 1$	$- m - 1$	$- 1$	$+ 1$
$j$	$m$	$- m$	$m$	$- m$	0	0

Fiber Mode 2 Excited Mode	AM-Matching Condition	Fiber Mode 1 Generated Mode
$H E_{m n}^{+} (s = 1, l = m - 1, j = m)$	$M_{1} = \pm N + m \neq 0$	$H E_{\| \pm N + m \|, f}^{σ_{1}} (s = σ_{1}, l = \pm N + m - σ_{1}, j = \pm N + m)$ ,
$E H_{m n}^{+} (s = - 1, l = m + 1, j = m)$	$M_{1} = \pm N + m \neq 0$	$E H_{\| \pm N + m, f}^{σ_{1}} (s = - σ_{1}, l = \pm N + m + σ_{1}, j = \pm N + m)$ , $σ_{1} = sign (\pm N + m)$
$H E_{m n}^{-} (s = - 1, l = 1 - m, j = - m)$	$M_{1} = \pm N - m \neq 0$	$H E_{\| \pm N + m \|, f}^{σ_{2}} (s = σ_{2}, l = \pm N - m - σ_{2}, j = \pm N - m)$ ,
$E H_{m n}^{-} (s = 1, l = - 1 - m, j = - m)$	$M_{1} = \pm N - m \neq 0$	$E H_{\| \pm N - m, f}^{σ_{2}} (s = - σ_{2}, l = \pm N - m + σ_{2}, j = \pm N - m)$ , $σ_{2} = sign (\pm N - m)$

	Generated Cladding Modes in L-1-CFG		Generated Cladding Modes in L-N-CFG ( $N \geq 2)$
Core Modes	Left-Handed	Right-Handed	Left-Handed	Right-Handed
$H E_{11, co}^{+} (s = 1, l = 0, j = 1)$	$T M_{0 f, cl} (s = 0, l = 0, j = 0)$	$H E_{2 f, cl}^{+} (s = 1, l = 1, j = 2)$	$H E_{N - 1, f, cl}^{-} (s = - 1, l = 2 - N, j = 1 - N)$	$H E_{N + 1, f, cl}^{+} (s = 1, l = N, j = N + 1)$
$H E_{11, co}^{+} (s = 1, l = 0, j = 1)$	$T E_{0 f, cl} (s = 0, l = 0, j = 0)$	$E H_{2 f, cl}^{+} (s = - 1, l = 3, j = 2)$	$E H_{N - 1, f, cl}^{-} (s = 1, l = - N, j = 1 - N)$	$E H_{N + 1, f, cl}^{+} (s = - 1, l = N + 2, j = N + 1)$
$H E_{11, co}^{-} (s = - 1, l = 0, j = - 1)$	$H E_{2 f, cl}^{-} (s = - 1, l = - 1, j = - 2)$	$T M_{0 f, cl} (s = 0, l = 0, j = 0)$	$H E_{N + 1, f, cl}^{-} (s = - 1, l = - N, j = - 1 - N)$	$H E_{N - 1, f, cl}^{+} (s = 1, l = N - 2, j = N - 1)$
$H E_{11, co}^{-} (s = - 1, l = 0, j = - 1)$	$E H_{2 f, cl}^{-} (s = 1, l = - 3, j = - 2)$	$T E_{0 f, cl} (s = 0, l = 0, j = 0)$	$E H_{N + 1, f, cl}^{-} (s = 1, l = - 2 - N, j = - 1 - N)$	$E H_{N - 1, f, cl}^{+} (s = - 1, l = N, j = N - 1)$

Modes	$H E_{m n}^{+}$	$H E_{m n}^{-}$	$E H_{m n}^{+}$	$E H_{m n}^{-}$	$V_{0 n}^{+}$	$V_{0 n}^{-}$
$s$	$+ 1$	$- 1$	$- 1$	$+ 1$	$+ 1$	$- 1$
$l$	$m - 1$	$1 - m$	$m + 1$	$- m - 1$	$- 1$	$+ 1$
$j$	$m$	$- m$	$m$	$- m$	0	0

Fiber Mode 2 Excited Mode	AM-Matching Condition	Fiber Mode 1 Generated Mode
$H E_{m n}^{+} (s = 1, l = m - 1, j = m)$	$M_{1} = \pm N + m \neq 0$	$H E_{\| \pm N + m \|, f}^{σ_{1}} (s = σ_{1}, l = \pm N + m - σ_{1}, j = \pm N + m)$ ,
$E H_{m n}^{+} (s = - 1, l = m + 1, j = m)$	$M_{1} = \pm N + m \neq 0$	$E H_{\| \pm N + m, f}^{σ_{1}} (s = - σ_{1}, l = \pm N + m + σ_{1}, j = \pm N + m)$ , $σ_{1} = sign (\pm N + m)$
$H E_{m n}^{-} (s = - 1, l = 1 - m, j = - m)$	$M_{1} = \pm N - m \neq 0$	$H E_{\| \pm N + m \|, f}^{σ_{2}} (s = σ_{2}, l = \pm N - m - σ_{2}, j = \pm N - m)$ ,
$E H_{m n}^{-} (s = 1, l = - 1 - m, j = - m)$	$M_{1} = \pm N - m \neq 0$	$E H_{\| \pm N - m, f}^{σ_{2}} (s = - σ_{2}, l = \pm N - m + σ_{2}, j = \pm N - m)$ , $σ_{2} = sign (\pm N - m)$

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