Ultrahigh-Performance ENZ Modulator Based on a Stack of Three-Layer Graphene and ITO
Mohsen Heidari, Shahram Bahadori-Haghighi, Babak Janjan, Mohammad R. Khosravi, Derek Abbott
Abstract
A high-performance electro-absorption optical modulator based on the epsilon-near-zero (ENZ) effect is proposed. The structure consists of a waveguide with a silicon (Si) core over which a stack of graphene/HfO <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_2$</tex-math></inline-formula> /graphene/ITO/HfO <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_2$</tex-math></inline-formula> /graphene is grown, covered by a Si cladding. An external voltage is applied across the graphene layers to change the carrier concentration in the indium tin oxide (ITO) layers. Using a self-consistent theory, the required voltage to achieve the ENZ points in the ITO layers is calculated up to 3.42 V for an ITO thickness of 5 nm. The operation of the modulator is investigated using a three-dimensional finite-difference time-domain (FDTD) method, resulting in a modulation depth as high as 5.23 dB/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{\mu}$</tex-math></inline-formula> m (5.36 dB/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{\mu }$</tex-math></inline-formula> m) at a wavelength of 1.55 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{\mu }$</tex-math></inline-formula> m for the TE (TM) polarization, which ensures the polarization-insensitivity of our proposed modulator. It is also calculated that the insertion loss of the modulator is in the order of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{ 2.5 \times 10^{-3}}$</tex-math></inline-formula> dB/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{\mu }$</tex-math></inline-formula> m that yields the figure of merit (FOM) of more than 1800. The outstanding features of our proposed modulator are mainly attributed to using the Si cladding layer instead of metal cladding. Furthermore, in contrast to the previously studied structures with metal electrodes, graphene layers significantly reduce the insertion loss.