We report the fabrication and characterization of metal-insulator-metal diodes incorporating vertically aligned carbon nanotube (VACNT) arrays encased in polymer for applications in high frequency optoelectronics. Polydimethylsiloxane (PDMS) and epoxy infiltrating media are used in this study. VACNT forests are embedded with polymer to form a planarized surface over which an array of tunneling diodes is fabricated. Diodes comprising Al2O3 and HfO2 dielectric multilayers achieve highly nonlinear and asymmetric current-voltage characteristics. Results show that asymmetry in excess of 92 can be achieved with multi-insulator barrier tuning, though there is a strong correlation between asymmetry, resistance, and device longevity. With our best performing and most stable device structure (PDMS-VACNT/Al2O3-HfO2-Al2O3-HfO2/PEDOT:PSS), we provide a demonstration of optical-to-d.c. rectification at 638 nm, realizing a current responsivity of 0.65 µA W-1. Our approach to fabricating these VACNT diode arrays is facile and highly scalable. It is capable of being integrated with solution-processed materials and soft lithography techniques to create flexible devices for optical and infrared detection.