Systems and methods for bandwidth reduction in polar modulation systems are described. The first and second substrates are bonded to one another so that the second layer of the second substrate covers the concave portion of the first substrate. The banks and the black matrix enclose a plurality of spaces for respectively accommodating the R, G and B color portions. A compiling unit compiles the source generated for each policy and generates an emulator for each policy. More preferably, the free magnetic layer is composed of an alloy or a stacked film containing at least one element selected from Co, Ni, Fe, and B.