Fig. 5

Orthogonality and multiplexing orbital-angular-momentum (OAM) modes. a The orthogonality with different OAM modes of write- and read-lasers. The cross and check marks in up/down equation shows the weak/strong correlation under the different (\(\vert {l}_{{\rm{W}}}\vert \ne \vert {l}_{{\rm{R}}}\vert\)) /same OAM orders (\(\vert {l}_{{\rm{W}}}\vert =\vert {l}_{{\rm{R}}}\vert\)). b The coincidence counts for the different situations of \(\vert {l}_{{\rm{W}}}\rangle=\vert 0\rangle/\vert 10\rangle\), \(\vert {l}_{{\rm{S1}}}\rangle=\vert 0\rangle/\vert 10\rangle\), \(\vert {l}_{{\rm{R}}}\rangle=\vert 0\rangle/\vert -10\rangle\), \(\vert {l}_{{\rm{S2}}}> =\vert 0\rangle/\vert -10\rangle\). c The memory decay function with different OAM modes (black for \(\vert {l}_{{\rm{W}}}\vert =0\), red for \(\vert {l}_{{\rm{W}}}\vert =10\)). The memory decays exponentially with storage lifetime of \(\tau =1655\ {\rm{ns}}\). The fitted functions are \(y={y}_{0}+A{e}^{-\frac{t}{\tau }}\) with parameters of \({y}_{0}=-3.3\), \(A=104.6\), \(\tau =1655\) for black data and \({y}_{0}=-7.6\), \(A=73.5\), \(\tau =1655\) for red data. d The multiplexing in radial direction with different OAM modes in inner and outer rings. When the OAM orders in the inner and outer rings are different (up equation), the correlation is weak; on the contrary, the correlation is strong when the OAM orders are same (down equation). e The normalized coincidence counts with \(\vert {l}_{{\rm{W}}}\rangle=\vert 0\rangle+\vert 10\rangle\), \(\vert {l}_{{\rm{R}}}\rangle=\vert -10\rangle+\vert 0\rangle\), and \(\vert {l}_{{\rm{W}}}\rangle=\vert 0\rangle+\vert 10\rangle,\vert {l}_{{\rm{R}}}\rangle=\vert 0\rangle+\vert -10\rangle\) in the left two bars. The right two bars are the corresponding OAM mode of \(\vert {l}_{{\rm{W}}}\rangle=\vert 0\rangle+\vert 9\rangle\), \(\vert {l}_{{\rm{R}}}\rangle=\vert -9\rangle+\vert 0\rangle\), and \(\vert {l}_{{\rm{W}}}\rangle=\vert 0\rangle+\vert 9\rangle\), \(\vert {l}_{{\rm{R}}}\rangle=\vert 0\rangle+\vert -9\rangle\). f The detected contrast of coincidence counts against different \(\Delta l\), here \(\Delta l={l}_{{\rm{W}}}-{l}_{{\rm{R}}}\). The storage time is set to be 500 ns. The different signs of OAM quanta set in (a) and (d) are required to maintain OAM conservation. Error bars represent \(\pm\) one standard deviation