P. A. Maia Neto

Theory of optical tweezers

We derive an exact partial-wave (Mie) expansion of the axial force exerted on a transparent sphere by a laser beam focused through a high numerical aperture objective. The results hold throughout the range of interest for practical applications, as well as in the Rayleigh and geometrical optics limits. They allow, in principle, an absolute calibration of optical tweezers. Starting from the Mie result, we derive a closed analytic representation for the size-averaged short-wavelength limit that takes into account the Abbe sine condition. Numerical plots show large deviations from geometrical optics near the focal region and around the edge of the sphere, and oscillatory behavior of the force as a function of the size parameter. The oscillations are explained in terms of a simple interferometer picture derived from the Mie expansion. The few existing experimental data look more consistent with the present model than with previous ones.

Roughness correction to the Casimir force: Beyond the Proximity Force Approximation

We calculate the roughness correction to the Casimir effect in the parallel plates geometry, for metallic plates described by the plasma model. The calculation is perturbative in the roughness amplitude, with otherwise arbitrary values for the plasma wavelength, the plate separation and the roughness correlation length. The correction is found to be always larger than the result obtained in the Proximity Force Approximation.

Vacuum induced torque between corrugated metallic plates

We study the torque arising between two corrugated metallic plates due to the interaction with electromagnetic vacuum. This Casimir torque can be measured with torsion pendulum techniques for separation distances as large as 1 μm. It allows one to probe the non-trivial geometry dependence of the Casimir energy in a configuration which can be evaluated theoretically with accuracy. In the optimal experimental configuration, the commonly used proximity force approximation turns out to overestimate the torque by a factor 2 or larger.

Characterization of objective transmittance for optical tweezers.

We have measured the overall transmittance of a laser beam through an oil immersion objective as a function of the transverse size of the laser beam, using the dual-objective method. Our results show that the objective transmittance is not uniform and that its dependence on the radial beams position can be modeled by a Gaussian function. This property affects the intensity distribution pattern in the sample region and should be taken into account in theoretical descriptions of optical tweezers. Moreover, one must consider this position dependence to determine the local laser power delivered at the sample region by the dual-objective method, especially when the beam overfills the objectives back entrance. If the transmittance is assumed to be uniform, the local power is overestimated.

Modeling electrostatic patch effects in Casimir force measurements

Electrostatic patch potentials give rise to forces between neutral conductors at distances in the micrometer range and must be accounted for in the analysis of Casimir force experiments. In this paper we develop a quasilocal model for describing random potentials on metallic surfaces. In contrast to some previously published results, we find that patches may provide a significant contribution to the measured signal and thus may be a more important systematic effect than was previously anticipated. Additionally, patches may render the experimental data at distances below 1 μm compatible with theoretical predictions based on the Drude model.

Quantum radiation in a plane cavity with moving mirrors

We consider the electromagnetic vacuum field inside a perfect plane cavity with moving mirrors, in the nonrelativistic approximation. We show that low frequency photons are generated in pairs that satisfy simple properties associated to the plane geometry. We calculate the photon generation rates for each polarization as functions of the mechanical frequency by two independent methods: on one hand from the analysis of the boundary conditions for moving mirrors and with the aid of Green functions; and on the other hand by an effective Hamiltonian approach. The angular and frequency spectra are discrete, and emission rates for each allowed angular direction are obtained. We discuss the dependence of the generation rates on the cavity length and show that the effect is enhanced for short cavity lengths. We also compute the dissipative force on the moving mirrors and show that it is related to the total radiated energy as predicted by energy conservation.

Probing the Casimir force with optical tweezers

We propose to use optical tweezers to probe the Casimir interaction between microspheres inside a liquid medium for geometric aspect ratios far beyond the validity of the widely employed proximity force approximation. This setup has the potential for revealing unprecedented features associated to the non-trivial role of the spherical curvatures. For a proof of concept, we measure femtonewton double-layer forces between polystyrene microspheres at distances above 400 nm by employing very soft optical tweezers, with stiffness of the order of fractions of a fN/nm. As a future application, we propose to tune the Casimir interaction between a metallic and a polystyrene microsphere in saline solution from attraction to repulsion by varying the salt concentration. With those materials, the screened Casimir interaction may have a larger magnitude than the unscreened one. This line of investigation has the potential for bringing together different fields including classical and quantum optics, statistical physics and colloid science, while paving the way for novel quantitative applications of optical tweezers in cell and molecular biology.

Vacuum radiation pressure on moving mirrors

We consider a perfectly reflecting plane mirror moving in the vacuum of the electromagnetic field. The motional modification of the Maxwell stress tensor is computed up to first order in the displacement of the mirror. The resulting dissipative force is shown to be related to the creation of travelling-wave low-frequency photons and to obey the fluctuation-dissipation theorem.

Polarization effects in optical tweezers

We extend the MDSA (Mie–Debye spherical aberration) theory of trapping forces in optical tweezers, previously developed for circularly polarized trapping beams, to linear polarization. Although it does not significantly affect the trap stiffness, linear polarization may introduce a strong axial asymmetry of the optical forces near the edge of a trapped microsphere, arising from Mie resonance effects.

Dynamical Casimir effect with Dirichlet and Neumann boundary conditions

We derive the radiation pressure force on a nonrelativistic moving plate in 1 + 1 dimensions. We assume that a massless scalar field satisfies either Dirichlet or Neumann boundary condition (BC) at the instantaneous position of the plate. We show that when the state of the field is invariant under time translations, the results derived for Dirichlet and Neumann BC are equal. We discuss the force for a thermal field state as an example for this case. On the other hand, a coherent state introduces a phase reference, and the two types of BC lead to different results.