High-Q enhancement of attractive and repulsive optical forces between coupled whispering-gallery-mode resonators

Abstract

We have calculated the optically-induced force between coupled high-Q whispering gallery modes of microsphere resonators. Attractive and repulsive forces are found, depending whether the bi-sphere mode is symmetric or antisymmetric. The magnitude of the force is linearly proportional to the total power in the spheres and consequently linearly enhanced by Q. Forces on the order of 100 nN are found for Q=108, large enough to cause displacements in the range of 1mum when the sphere is attached to a fiber stem with spring constant 0.004 N/m.

Observation of thermal feedback on the optical coupling noise of a microsphere attached to a low-spring-constant cantilever

“…The field of optomechanics has expanded rapidly in the last decade due to the development of optical devices which are small enough to react to the minute forces created by photon radiation pressure [1,2] or intense optical gradients (i.e., dipole forces) [3][4][5][6][7]. Microscopic optical devices, such as whispering gallery resonators [8][9][10][11], tapered optical fibers [12], and photonic crystal cavities [13], enhance the strength of the electric field gradient due to high-optical-Q factors and small mode volumes [14,15].…”

“…When another dielectric device, such as another microresonator or waveguide, is brought into this intense field both devices feel a force due to the interaction of the dipoles in the material [3][4][5][6][7]. The sign of this force depends on the phase relationship between the electromagnetic fields connecting the two devices.…”

“…The phase can be adjusted by simply varying the gap between the devices, or by optically pumping the appropriate coupled cavity resonance, i.e., a symmetric (attractive dipole force) or antisymmetric mode (repulsive dipole force) [6]. The dipole or gradient force from one microresonator can be used to amplify or dampen the mechanical motion of another microscopic device, such as a nanostring [21] or a microdisk [22], as well as provide a way to precisely control the gap between them [3,4,6,7]. For example, Eichenfield et al [23] have shown how the cavity-enhanced optical dipole force from a microdisk can be used to control the relative position of a movable, tapered optical fiber.…”

“…For example, Eichenfield et al [23] have shown how the cavity-enhanced optical dipole force from a microdisk can be used to control the relative position of a movable, tapered optical fiber. Povinelli et al [3] discussed the possibility of observing both positive and negative optical forces between two evanescently coupled microspheres, sometimes termed a "photonic molecule." To date, both positive and negative forces have been observed in some optical microcavity systems [22], but not between microspheres.…”

“…We call this microsphere on a flexible stem a micropendulum, which is essentially a low-spring-constant microcantilever with a microsphere on one end. A micropendulum with a stem spring constant of 10 −3 N/m has been proposed [3] to observe an optical force displacement of 1 μm between two similarly sized spheres with Q factors of 10 6 . It has been suggested that microsphere pendulums with very low mechanical spring constants could prove to be useful tools for studying nanoscopic optical and mechanical forces, or optical cooling [24][25][26].…”