Detailed theoretical analysis of the effect of the carrier density disorder on the optical conductivity of graphene-based vertical-cavity optical modulator is presented. Analytical expression for the optical conductivity of disordered graphene is derived by assuming Gaussian distribution for the carrier density variation. We theoretically demonstrate a simple ultrafast optical modulator using graphene-based vertical-cavity and double dielectric DBR mirrors. Two graphene flakes connected to a gate voltage are placed inside a resonant cavity to control the optical conductivity of graphene and to detune the resonant wavelength of the optical cavity. The bandpass spectrum of the device can be tuned by varying the gate voltage at an ultrahigh speed. Switching speed as high as 63 GHz is predicted for two flakes structures separated by a 100 nm SiO2 layer with a wavelength range as high as similar to 5 nm around the resonant wavelength. The transmission characteristics of the modulator are studied for different disorder levels. Our analysis reveals that disorder significantly reduces both the contrast ratio and the insertion loss of the modulator.
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