Radiation pressure force

A force that is as large as the gravitational force can be used to suspend a particle against gravity, provided that it can be controlled and directed upward to balance gravity. One such force is the radiation pressure force or radiometric force. Ashkin and Dziedzic (1977), whose work is discussed in the next section, were the first to use the radiation pressure to levitate a microsphere stably. It was demonstrated by Allen et ai (1991) that the radiometric force can be measured with the electrodynamic balance, and they used the technique to determine the absolute intensity of the laser beam illuminating a suspended particle. This was accomplished in the apparatus displayed in Fig. 13. The laser illuminated the microparticle from below, and... 

Fig. 13. The double-ring electrodynamic balance used by Allen et al. (1991) to measure the radiation pressure force on a microparticle.

Ashkin and Dziedzic (1977) used the radiation pressure force of a laser beam to levitate microdroplets with the apparatus presented in Fig. 15. A polarized and electro-optically modulated laser beam illuminated the particle from below. The vertical position of the particle was detected using the lens and split photodiode system shown. When the particle moved up or down a difference signal was generated then a voltage proportional to the difference and its derivative were added, and the summed signal used to control an electro-optic modulator to alter the laser beam intensity. Derivative control serves to damp particle oscillations, while the proportional control maintains the particle at the null point. 

We note that since Q involves the scattering coefficients, the radiation pressure force has resonance or near-resonance behavior. This first was observed and analyzed by Ashkin and Dziedzic (1977) in their study of microparticle levitation by radiation pressure. They made additional measurements (Ashkin and Dziedzic, 1981) of the laser power required to levitate a microdroplet, and Fig. 19 presents their data for a silicone droplet. The morphological resonance spectrum for the 180° backscattered light shows well-defined peaks at wavelengths corresponding to frequencies close to natural frequencies of the sphere. The laser power shows the same resonance structures in reverse, that is, when the scattered intensity is high the laser power required to levitate the droplet is low. 

Calculating the. electromagnetic field near the focus of a very large aperture beam, and around a particle itself which is neither very small nor very large compared to the wavelength of the radiation, is notoriously very difficult and hence the exact analysis of the radiation pressure force acting on the nanorods becomes nearly intractable. Hence we try to understand the trend of the observed rotational motion by a simple dimensional analysis. 

The direct photophoretic force Tph for geometrically small particles can be written as a sum of the radiation pressure force and the gradient force F ... 

Not only can the radiation pressure force lead to ion cooling through the Doppler-effect, but it can be used further to exert a periodic force on the atomic ions. By modulating the intensity of one of the two laser-cooling beams propagating along... 

Doppler laser-cooling is an essential ingredient in the SCSI-MS technique. First, it provides the necessary damping force to cool directly and sympathetically the atomic and molecular ions, respectively, such that a cold and strongly-coupled two-ion system is formed. Second, it gives rise to the fluorescence photons used in the detection process. Third, the radiation pressure force can be modulated to excite the common motion of the ions. 

Acoustic waves in liquids can give rise to so-called radiation pressure forces that can in turn drive acoustic streaming flows, deform fluid-fluid interfaces to generate droplets, or exert levitation forces on suspended drops or particles. This contribution reviews three technologically relevant examples of these effects acoustic droplet ejection, droplet transport along a solid surface using surface acoustic waves, and acoustic levitation of droplets. 

The motion of a two-level atom in a spatially inhomogeneous laser field is generally governed by the dipole gradient force, the radiation pressure force, and the diffusion of momentmn. A detailed and consistent analysis of the motion of two-level atoms in light fields can be foimd in Minogin and Letokhov (1987) and Kazantsev et al. (1990), and here I shall restrict myself to a brief amvey of the basic formulas. 

In the above, /(r) = (c/87r) o( ) the intensity of the laser beam at the point r Is = cl4n) h yld) is the saturation intensity d=d- e is the projection of the dipole moment matrix element of the polarization vector e of the laser beam A is the detuning of the laser field frequency cu with respect to the atomic transition frequency tuo, that is, A = lo — loo, and the quantity 27 defines the rate of spontaneous decay of the atom from the upper level e) to the lower level g), that is, the Einstein coefficient A. Figure 5.6 shows the dependence of the radiation pressure force and the gradient force on the projection v =v of the atomic velocity on the propagation direction of a Gaussian laser beam for the case of strong saturation of the D-line of Na. 

The effects of the radiation pressure force and the gradient force on an atom are essentially different. The radiation pressure force (5.10) always accelerates the atom in the direction of the wave vector k. The gradient force (5.11) pulls the atom into the laser beam or pushes it out of the beam, depending on the sign of the Doppler shift detuning Z - k v. Both the radiation pressure force and the gradient force have a resonance at a velocity such that k v = Z, when the detuning A is compensated by the Doppler shift k v. 

Fig. 5.8 (a) Scheme of the longitudinal slowing and cooling of a thermal atomic beam by a counterpropagating laser beam, (b) Radiation pressure force as a function of the longitudinal atom velocity, (c) Evolution of the atomic velocity distribution at times t2>ti>to. 

Radiation pressure from continuous wavelength (cw) visible laser light is known to accelerate freely suspended particles in the direction of the light The magnitude of the radiation pressure force, has been given as (Ashkin, 1970)... 

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