Ultra-stable nano-manipulation of mechanically-variable system : optical forces and beyond

Optical force and acoustic force have been intensively investigated over the past several decades in the applications ranging from the optical/acoustic trapping, high-resolution biomedical imaging, sensing technology, signal processing to acoustic levitation, ultrasonic calibration, etc. I started from the calculation of the optical force including both radiation pressure and electrostriction force in stimulated Brillouin scattering using finite-element method. Then I investigated the sufficient condition of creating conservative optical force field, which is hard to realize as the optical force generally contains inevitable rotational component in a multi-port system. To verify the conclusion, this condition has been subsequently applied to three scenarios, realizing auto-alignment of millimeter-scale photonic crystal slabs, simultaneously trapping and orientating nano-particles, and self-aligned topological photonic crystal. To overcome the material loss which breaks the conservativeness of the optical force, a compensating method using the gain media to recover the conservative optical force field is presented and verified by the vorticity ratio derived from Helmholtz-Hodge decomposition (HHD). As an analog to the optical radiation pressure but generally millions larger in magnitude, the acoustic radiation pressure calculation using the response theory is also proposed, which perfectly agrees with the traditional Reynold stress tensor integration and, more importantly, reveals the sufficient condition of conservative acoustic force. The contributions of this work are significant in four aspects in the area of numerical device simulation and parallel scientific computing: first of all, it paves the fundamental way to ultra-stable trapping by providing correct ways of numerically calculating optical/acoustic forces, which are corroborated by response theory developed in this work; secondly, the complete temporal coupled-mode theory unveils all spectral response of waveguide-resonator systems; thirdly, the parallel algorithm of HHD applied to periodic structure provides reliable metric to evaluate stability of trapping; finally, the newly developed weak-form formulation of topological photonic crystal with loss/gain helps design of novel photonic devices.