This paper proposes the method for generating a plane wave field using spherical harmonics with a non-spherical array. In sound field control, arbitrary sound fields can be expanded into plane waves; thus, the sound field construction requires the plane wave generation. In conventional studies using spherical harmonics, plane wave reproduction has mainly been examined with circular or spherical arrays. However, considering the practical constraints of room geometry, plane wave generation in rectangular-like arrays is also important because loudspeakers are located along walls to use the space exhaustively. In this paper, we propose formulating the distance between the center and each loudspeaker using the Lam function in a polar expression, by changing its order as well as the shape of spatial figures. This formulation allows us to reuse the same method applied to spherical arrays for configuring non-spherical arrays. As a result of the simulation experiment, it was confirmed that within the inscribed region, the proposed method using a higher-order Lam function achieved waveform reproduction accuracy comparable to that of a spherical array.
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