  We present an electro-optic modulator exploiting an array of Vanadium dioxide
nanorods operating in the epsilon near regime as the active switching material
integrated in a silicon waveguide. The modulator takes advantage of the
insulator-to-metal transition of Vanadium dioxide to achieve a robust
modulation depth of 19.7 dB/micron with a broad wavelength of operation. Using
simulations, we demonstrate how the effective permittivity of the metamaterial
can be tuned to a near-zero value by varying the nanorod geometry. The paper
also proposes a novel hexagonal array design which achieves low insertion
losses while retaining a strong modulation depth. The results provide insight
into the design of ultra-compact modulators with high operation frequencies and
low insertion losses.
