The energy-based methods as the Dispersion Relation (DR) and Response Theory of Optical Forces (RTOF) have been largely applied to obtain the optical forces in the nano-optomechanical devices, in contrast to the Maxwell Stress Tensor (MST). In this work, we apply first principles to show explicitly why these methods must agree with the MST formalism in linear lossless systems. We apply the RTOF multi-port, to show that the optical force expression on these devices can be extended to analyze multiple light sources, broadband sources, and multimode devices, with multiple degrees of freedom. We also show that the DR method, when expressed as a function of the derivative of the effective index performed at a fixed wave vector, may be misinterpreted and lead to overestimated results. Optical (transverse gradient) forces between two adjacent dielectric structures, due to the overlap of the evanescent field of the guided modes, were proposed by Povinelli et al. [1]. The optical forces can be rigorously calculated using the Maxwell Stress Tensor (MST) formalism [2] or, alternatively, in linear lossless dielectric materials, it may be obtained directly from the device's dispersion relation as a function of one of the structure's degrees of freedom (gap) [1,3,4]. Due to its computational simplicity and physical insights, the latter method has been more used than the former [3,4]. Furthermore, the Dispersion Relation (DR) method can be further simplified to express the optical force as a function of the mode effective (refractive) index derivative, with respect to the gap, leading to two expressions: one where the derivative must be performed at a fixed wave vector [5], and another where it must be performed at a fixed angular frequency [6][7][8]. The latter expression version can also be obtained in an alternative formal manner, by using the recently developed Response Theory of Optical Force (RTOF) method, proposed by Rakich et al. [9,10]. Besides that, all these expressions must agree with the MST formalism [1,9].In this letter, we apply first principles to explicitly show why these energy-based methods must agree with the MST formalism. We analyze a typical nano-optomechanical device to show that the DR method, expressed in terms of the effective index with derivative performed at a fixed wave vector, may overestimate the optical force if the correct transformations are not used, thus disagreeing with the MST. We also use the RTOF theory to extend the correct expression to more general cases.For a nano-optomechanical system composed of pure dielectric materials, the conservation of linear momentum states that [2,11]:where EM is the electromagnetic momentum density, ME is the mechanical momentum (or the force) density, and ⃡ is the Maxwell Stress Tensor (MST), which represents the momentum flux, given by [2,11]: where ( , ) and ( , ) are the electric and magnetic field, respectively, 0 and 0 are the vacuum electric permittivity and magnetic permeability, respectively, and the symbol * denotes their complex conjugate, an...

Nano-optomechanical devices have enabled a lot of interesting scientific and technological applications. However, due to their nanoscale dimensions, they are vulnerable to the action of Casimir and van der Waals (dispersion) forces. This work presents a rigorous analysis of the dispersion forces on a nano-optomechanical device based on a silicon waveguide and a silicon dioxide substrate, surrounded by air and driven by optical forces. The dispersion forces are calculated using a modified Lifshitz theory with experimental optical data and validated by means of a rigorous 3D FDTD simulation. The mechanical nonlinearity of the nanowaveguide is taken into account and validated using a 3D FEM simulation. The results show that it is possible to attain a no pull-in critical point due to only the optical forces; however, the dispersion forces usually impose a pull-in critical point to the device and establish a minimal initial gap between the waveguide and the substrate. Furthermore, it is shown that the geometric nonlinearity effect may be exploited in order to avoid or minimize the pull-in and, therefore, the device collapse.

Abstract In this work, we describe dynamic modeling and simulation of a capacitive silicon bulk-micromachined microaccelerometer. The modeling of the mechanical part is done through equivalent stiffness and equivalent damping coefficients analyses using the Euler-Bernoulli equation and the Modified Reynolds equation, respectively. A dynamic model is obtained taking into account the electric force influence between the electrodes. Nonlinear and linear models are compared. The analytical results are compared with numerical results obtained by computational method in both time-domain and frequencydomain and it show a quite good agreement.

This work presents a rigorous analysis of optical forces between planar waveguides immersed in an arbitrary background medium. This approach exploits the Minkowski stress tensor formulation, which is compared with a normalized version of the dispersion relation method, showing excellent results agreement for different dielectric fluid media. Due to slot-waveguide effect, optical forces from TM modes are more sensitive to changes in the fluid refractive index than the TE counterparts. Furthermore, the repulsive optical force from the antisymmetric TM1 mode becomes stronger for higher refractive indexes, whereas the attractive force of the symmetric TM0 mode becomes weaker. The methodology and results presented in this work provide a rigorous analysis of nano-optomechanical devices actuated by optical forces in a broad range of materials and applications. Therefore, this study may impact areas of light-induced interactions presenting novel optofluidic and optomechanical functionalities, thus finding applications in nanoscale transport, sensing and manipulation. Rigorous analysis of optical forces between two dielectric planar