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We have proposed and demonstrated a low-power consumption thermooptic variable optical attenuator incorporating a membrane-type asymmetric branch waveguide in polymers. The membrane structure has been introduced by partially removing the silicon substrate with a bulk micromachining technique of backside etching. As a result, the heat flow in the polymer layers has been appropriately adjusted to increase the temperature gradient between the two arms of the branch and thus to enhance the attenuation efficiency. The measured electrical power consumption of the proposed attenuator was as small as 25 mW at 1550 nm, which was reduced by about 50% compared to that of the conventional device. Further improvement is achieved by a more optimized design of the area to be etched away.