Magnitude-Controlled Phase Based on Euler's Formula

Phase manipulation plays a fundamental role in electromagnetic (EM) and optics research, i.e., the wavefront shaping depends heavily on phase modulation. However, the previous phase manipulation methods are limited to phase-angle dimensionality, and the magnitude and phase are generally deemed as two distinct characters that should be controlled separately. Herein, a phase manipulation method in which phase is modulated by magnitude is proposed that follows an EM expression of Euler's formula. A rotation phase of linearly-polarized waves is presented. Using this method, several unique applications in this research are demonstrated. First, a Hall effect of non-angular-momentum waves is obtained; second, an interdigital topology model with a unique topological-charge control strategy is presented; and finally, the method is applied to holographic imaging, of which information of the hologram is recorded as a distribution of magnitude. Furthermore, as this method is applicable to all forms of harmonic waves, it can be potentially applied to other areas of wave phenomena such as acoustics and mechanics.