Figure 1: Optical micrographs of a R = 23.375 µm SiNx microdisk interacting with a 1.1 µm fiber taper waveguide. The stored optical energy in the resonator increases from right to left.

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Overview:

Cavity-Enhanced Optical Dipole Force (CEODF)

Although light is usually thought of as imponderable, carrying energy but relatively little momentum, light can exert a large force per photon if confined to small structures. Such forces have recently been proposed[1,2] as a means to construct novel optomechanical components such as tunable filters, couplers, and lasers. Other theoretical studies of the nonlinear dynamics of these systems have shown them to be useful for performing optical wavelength conversion and efficient optical-to-mechanical energy conversion[3,4]. In the field of quantum physics, there has also been recent interest in using radiation pressure forces within micro-optomechanical resonators to help cool macroscopic mechanical oscillators to their quantum-mechanical ground state[5-8].

Figure 2: Schematic diagrams of two different optomechanical cavity systems. Blue arrows indicate the propagation of light, with the resulting intensity profiles in the resonators shown as red lines. a, Fabry-Perot cavity system with the position of the back mirror behaving as a mechanical oscillator. Radiation pressure from the stored cavity field pushes on the reflective back mirror, causing a power-dependent nonlinearity in the length of the cavity. b, Evanescently-coupled cavity system. The position of the input waveguide acts as a mechanical oscillator in this case. A CEODF from the stored internal field of the resonator attracts the input waveguide, causing a power-dependent nonlinearity in the coupling of the waveguide to the cavity.

The ponderomotive effects of light within optical resonators have long been considered in the field of high-precision measurement[9]. The canonical system, shown in Fig. 2a, consists of a Fabry-Perot (FP) resonant cavity formed between a rigid mirror and a movable mirror attached to a spring or hung as a pendulum[10]. A nearly resonant optical field builds up in amplitude as it bounces back-and-forth between the mirrors and pushes on the movable mirror with each reflection, which detunes the FP cavity. The nonlinear dynamics associated with the displacement of the mirror and the build-up of internal cavity energy result in an “optical spring” effect[11]. Under conditions in which the optical field cannot adiabatically follow the mirror movement, the radiation pressure force can drive or dampen oscillations of the position of the movable mirror[12–14]—this effect is the basis for some optomechanical cooling schemes[5,7,8].

In contrast to the FP optomechanical system, the system studied here consists of a monolithic, whispering-gallery-mode (WGM) resonator coupled to an external waveguide. The waveguide is suspended (secured at two distant points) and behaves as if attached to a spring. Light evanescently couples into the resonator from the waveguide, as illustrated in Fig. 2b. The intra-cavity light intensity changes the waveguide position via an all-optical force on the waveguide due to the field of the resonator. The resulting movement changes the waveguide-resonator coupling-rate—rather than the cavity resonance condition as in the FP system—which is sensitive to the distance between the waveguide and resonator. Unlike the FP system, the optical force is derived from the gradient force, a result of intensity-dependent light shifts of electronic states in the dielectric external waveguide[15,16]. No complete correspondence between the FP system and the system in Fig. 1b can be made due to the external nature of the waveguide (the FP would require a mirror that could change its reflectivity in response to changing optical power[17]). This non-trivial difference also applies to a wide class of cavity geometries in which a non-resonant dielectric object loads the cavity.

[1] M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, Opt. Lett. 30, 3042 (2005).

[2] M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, Opt. Express 13, 8287 (2005).

[3] M. Notomi and S. Mitsugi, Phys. Rev. A 73, 051803(R) (2006).

[4] M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, Phys. Rev. Lett. 97, 023903 (2006).

[5] S. Gigan, H. R. B¨ ohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. B¨ auerle, M. Aspelmeyer, and A. Zeilinger, Nature 444, 67 (2006).

[6] D. Kleckner and D. Bouwmeester, Nature 444, 75 (2006).

[7] O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, Nature 444, 71 (2006).

[8] A. Schliesser, P. Del’Haye, N. Nooshi, K. Vahala, and T. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).

[9] V. B. Braginsky and A. B. Manukin, Measurements of Weak Forces in Physics Experiments (The University of Chicago Press, Chicago, IL, 1977).

Questions?

Please contact Matt Eichenfield or Oskar Painter if there are any questions.