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This paper describes a new type of couplers which has small size and enables power transmission through Two-Dimensional Communication (2DC) Sheet. Our 2DC system allows non-contact power transmission using microwaves. The power transmission capacity is limited because of the risk of human exposure to microwaves. Our goal is supplying 1 W/cm power and satisfying two criteria as follows. First, localized specific absorption rate (SAR) must conform to a regulation based on the International Commission on Non-Ionizing Radiation Protection (ICNIRP) Safety Guidelines. Second, the coupler size should be less than 100 mm in length and width for convenient use. To achieve the goal, we propose coupler which has a capacitive impedance layer on its surface. We verify the validity of the proposal through theoretical analysis of electromagnetic fields in the sheet and coupler. Moreover, a three-dimensional simulation result also supports applicability to real systems. Finally we confirm the feasibility of the new coupler through a verification experiment.