Superposition causes nonlinear consequence

KUAN-REN CHEN^1*, Alex E. Chen², Jian-Shiung Hong¹

¹Department of Physics, National Cheng Kung University, Tainan, Taiwan
²Department of Electrical Engineering, The Pennsylvania State University, University Park, PA, USA

* Presenter:KUAN-REN CHEN, email:chenkr@phys.ncku.edu.tw

The principle of superposition applies to any linear system while the multiplication of oscillations causes nonlinear consequences. We find that superposition, as linear addition, can surprisingly induce the multiplication and thus nonlinearity during transient dynamics. When a light pulse is being transmitted through a subwavelength metallic slit, a portion exits as a sub-pulse. The rest is reflected at the exit interface to travel a roundtrip within the slit, and then attempts to exit again. This process repeats. The superposition of the exiting sub-pulses is rigorously shown in mathematics to cause nonlinear consequence even with all materials and individual processes considered here are linear. The wave is manipulated in space to induce a discrete phase effect in time. The resultant nonlinear consequence is proportional to the wave amplitude; not to a high order. This finding is fundamental in sciences and its meaning is far beyond the electromagnetics or optics studied.

Keywords: plasmonic, superposition, nonlinear