 ![(a) A schematic diagram of a Gedankenexperiment for the observation of localized modes in graphene waveguides, created by the top gate (V$_{\textrm{\scriptsize{TG}}}$). The Fermi level is set using the back gate (V$_{\textrm{\scriptsize{BG}}}$) to be at the Dirac point ($\varepsilon_{\textrm{\scriptsize{F}}}=0$). (b) The electrostatic potential created by the applied top gate voltage. The plane shows the Fermi level position at $\varepsilon_{\textrm{\scriptsize{F}}}=0$.[]{data-label="fig:Cosh_0/0"}](fig0a "fig:"){width="0.0cm"} ![(a) A schematic diagram of a Gedankenexperiment for the observation of localized modes in graphene waveguides, created by the top gate (V$_{\textrm{\scriptsize{TG}}}$). The Fermi level is set using the back gate (V$_{\textrm{\scriptsize{BG}}}$) to be at the Dirac point ($\varepsilon_{\textrm{\scriptsize{F}}}=0$). (b) The electrostatic potential created by the applied top gate voltage. The plane shows the Fermi level position at $\varepsilon_{\textrm{\scriptsize{F}}}=0$.[]{data-label="fig:Cosh_0/0"}](fig0b "fig:"){width="0.0cm"}  