We report in-plane slotted patch antenna-coupled electro-optic phase modulators with a carrier-to-sideband ratio (CSR) of 22 dB under an RF power density of 120 W/m(2) and a figure of merit of 2.0 W(-1/2) at the millimeter wave frequencies of 36-37 GHz based on guest-host type of second-order nonlinear polymer SEO125. CSR was improved more than 20 dB by using a SiO(2) protection layer. We demonstrate detection of 3 GHz modulation of the RF carrier. We also derive closed-form expressions for the modulated phase of optical wave and carrier-to-sideband ratio. Design, simulation, fabrication, and experimental results are discussed.