Abstract
The fundamental switching energy limitations for waveguide coupled graphene-on-graphene optical modulators are described. The minimum energy is calculated under the constraints of fixed insertion loss and extinction ratio. Analytical relations for the switching energy both for realistic structures and in the quantum capacitance limit are derived and compared with numerical simulations. The results show that sub-femtojoule per bit switching energies and peak-to-peak voltages less than 0.1 V are achievable in graphene-on-graphene optical modulators using the constraint of 3 dB extinction ratio and 3 dB insertion loss. The quantum-capacitance limited switching energy for a single TE-mode modulator geometry is found to be < 0.5 fJ/bit at λ = 1.55 μm, and the dependences of the minimum energy on the waveguide geometry, wavelength, and graphene location are investigated. The low switching energy is a result of the very strong optical absorption in graphene, and the extremely-small operating voltages needed as the device approaches the quantum capacitance regime.
Highlights
Graphene is a promising material for optoelectronic applications, due to its relatively high absorption coefficient, broad spectral range of absorption, and excellent transport properties
Graphene integrated with silicon photonics is especially interesting, since Si photonics can provide an outstanding platform for integration with CMOS circuits [9]
Its total energy consumption can be analyzed using a similar analysis to other types of optical modulators that can be integrated with silicon photonics [12]
Summary
Graphene is a promising material for optoelectronic applications, due to its relatively high absorption coefficient, broad spectral range of absorption, and excellent transport properties. A interesting device to investigate is the graphene-ongraphene optical modulator described both theoretically [10] and experimentally [11]. Such a device lends itself well to theoretical treatment due to its simple parallel plate geometry, and the fact that under ideal circumstances, no DC current flows in the device. The fundamental energy limits of graphene-on-graphene optical modulators are analyzed. An analytical treatment for the device operation is provided, leading to an open form expression of the fundamental limit of the switching energy. A discussion of the implications and restrictions of this analysis is provided
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