Table 1 Criteria of the nine logic gates

From: All-in-one, all-optical logic gates using liquid metal plasmon nonlinearity

Gate

Focal position of control beam (with respect to the focal plane of signal beam)

\(\Delta {\varphi }_{{{{{\rm{L}}}}}}\)

Strength contrast of control beam

\(\Delta {\varphi }_{{{{{{\rm{NL}}}}}}}\)

AND

Behind

>0

\({I}_{{{{{{\rm{NL}}}}}}{,}^{{\prime} }{0}^{{\prime} }} > {I}_{{{{{{\rm{NL}}}}}}{,}^{{\prime} }{1}^{{\prime} }}\)

\({\pi > \Delta \varphi }_{{{{{{\rm{NL}}}}}},{\prime} 0{\prime} } > {\Delta \varphi }_{{{{{{\rm{NL}}}}}},{\prime} 1{\prime} } > 0\)

OR

Ahead

<0

\({I}_{{{{{{\rm{NL}}}}}}{,}^{{\prime} }{0}^{{\prime} }} < {I}_{{{{{{\rm{NL}}}}}}{,}^{{\prime} }{1}^{{\prime} }}\)

\({\pi > \Delta \varphi }_{{{{{{\rm{NL}}}}}},{\prime} 1{\prime} } > \Delta {\varphi }_{{{{{{\rm{NL}}}}}},{\prime} 0{\prime} } > 0\)

NOT

Ahead

<0

only \({I}_{{{{{{\rm{NL}}}}}}{,}^{{\prime} }{0}^{{\prime} }}\) (or only \({I}_{{{{{{\rm{NL}}}}}}{,}^{{\prime} }{1}^{{\prime} }}\))

\(2{\pi > \Delta \varphi }_{{{{{{\rm{NL}}}}}}{,}^{{\prime} }{0}^{{\prime} }}({{{{{\rm{or}}}}}}\Delta {\varphi }_{{{{{{\rm{NL}}}}}}{,}^{{\prime} }{1}^{{\prime} }}) > \pi\)

NAND

Ahead

<0

\({I}_{{{{{{\rm{NL}}}}}}{,}^{{\prime} }{0}^{{\prime} }} < {I}_{{{{{{\rm{NL}}}}}}{,}^{{\prime} }{1}^{{\prime} }}\)

\({\Delta \varphi }_{{{{{{\rm{NL}}}}}},{\prime} 1{\prime} } > \Delta {\varphi }_{{{{{{\rm{NL}}}}}},{\prime} 0{\prime} } > \pi\)

NOR

Ahead

<0

\({I}_{{{{{{\rm{NL}}}}}}{,}^{{\prime} }{0}^{{\prime} }} < {I}_{{{{{{\rm{NL}}}}}}{,}^{{\prime} }{1}^{{\prime} }}\)

\(\Delta {\varphi }_{{{{{{\rm{NL}}}}}},{\prime} 1{\prime} } > {\Delta \varphi }_{{{{{{\rm{NL}}}}}},{\prime} 0{\prime} } > \pi\)

XNOR

Ahead

<0

\({I}_{{{{{{\rm{NL}}}}}}{,}^{{\prime} }{0}^{{\prime} }} > {I}_{{{{{{\rm{NL}}}}}}{,}^{{\prime} }{1}^{{\prime} }}\)

\({\Delta \varphi }_{{{{{{\rm{NL}}}}}},{\prime} 0{\prime} } > \pi > {\Delta \varphi }_{{{{{{\rm{NL}}}}}},{\prime} 1{\prime} } > 0\)

XOR

Ahead

<0

\({I}_{{{{{{\rm{NL}}}}}}{,}^{{\prime} }{0}^{{\prime} }} < {I}_{{{{{{\rm{NL}}}}}}{,}^{{\prime} }{1}^{{\prime} }}\)

\(\Delta {\varphi }_{{{{{{\rm{NL}}}}}},{\prime} 1{\prime} } > \pi > \Delta {\varphi }_{{{{{{\rm{NL}}}}}},{\prime} 0{\prime} } > 0\)

IMP

Ahead

<0

\({I}_{{{{{{\rm{NL}}}}}}{,}^{{\prime} }{0}^{{\prime} }} > {I}_{{{{{{\rm{NL}}}}}}{,}^{{\prime} }{1}^{{\prime} }}\)

\({\pi > \Delta \varphi }_{{{{{{\rm{NL}}}}}},{\prime} 0{\prime} } > {\Delta \varphi }_{{{{{{\rm{NL}}}}}},{\prime} 1{\prime} } > 0\)

NIMP

Ahead

<0

\({I}_{{{{{{\rm{NL}}}}}}{,}^{{\prime} }{0}^{{\prime} }} > {I}_{{{{{{\rm{NL}}}}}}{,}^{{\prime} }{1}^{{\prime} }}\)

\({\Delta \varphi }_{{{{{{\rm{NL}}}}}},{\prime} 0{\prime} } > {\Delta \varphi }_{{{{{{\rm{NL}}}}}},{\prime} 1{\prime} } > \pi\)

  1. \(\Delta {\varphi }_{{{{{\rm{L}}}}}}\): linear phase-shift of signal beam, \(\Delta {\varphi }_{{{{{{\rm{NL}}}}}}}\) :nonlinear phase-shift of signal beam, \({\Delta \varphi }_{{{{{\rm{NL}}}}},{\prime} 0{\prime} }\) :\(\Delta {\varphi }_{{{{{{\rm{NL}}}}}}}\) to induce ‘0’ state of signal beam, \({\Delta \varphi }_{{{{{\rm{NL}}}}},{\prime} 1{\prime} }\) :\(\Delta {\varphi }_{{{{{{\rm{NL}}}}}}}\) to induce ‘1’ state of signal beam, \({I}_{{{{{\rm{NL}}}}}{,}^{{\prime} }{0}^{{\prime} }}\) :strength of control beam at ‘0’ state of control beam, \({I}_{{{{{\rm{NL}}}}}{,}^{{\prime} }{1}^{{\prime} }}\): strength of control beam at ‘1’ state of control beam.
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