Indoor optical wireless communication with optical beamsteering capability is currently attracting a lot of attention. One major two-dimensional (2D) optical beamsteering scheme is realized by 2D grating or its active counterpart, which is usually based on a spatial light modulator (SLM). However, there is a fundamental trade-off between the field of view (FoV) and power efficiency due to the inherent feature of gratings. In this Letter, we propose a new class of 2D beamsteering, named cyclically arranged optical beamsteering (CAO-BS), which can break that trade-off. Traditional 2D gratings extend the optical beam in the Cartesian coordinates (1D grating in horizontal + 1D grating in vertical), while CAO-BS extends the optical beam in the polar coordinates (1D grating + angular rotation). Since only 1D grating is engaged, the power efficiency increases with the number of grating lobes reduced. In the polar coordinates, the angle rotation tuning in a SLM is quasi-continuous in a full 2π range. The CAO-BS is demonstrated at the receiving end in an indoor experimental system. The FoV is 18° by 360° in polar coordinates without any additional mechanical parts. Based on the CAO-BS, 40 Gbit/s on-off keying data is also successfully transmitted over 1 km single-mode fiber and 0.5 m free space.