We present a concise method for the design of arrayed waveguide gratings (AWGs) with a minimum number of arrayed waveguides and polarization independence. As an example to demonstrate the effectiveness of the proposed method, a 16×16 AWG using silica-based sol-gel material is optimally designed with the following practical specifications: central wavelength of 1.554 µm, channel spacing of 100 GHz or 0.8 nm, crosstalk between adjacent channels of <–30 dB, insertion loss of <3 dB, and nonuniform power level of the channels of <1.75 dB. We present, to our knowledge, for the first time, a simple criterion for determining the minimum number of arrayed waveguides with polarization independence. The criterion ensures that lights diffracted in the first slab are transferred into the second slab without loss of the image information. The criterion is perfectly verified by simulating the design of the AWG using a beam propagation method of analysis. In addition, the design procedure also allows the optimization of the parameters and structure of the AWG to achieve the required performance specifications.