Theoretical investigation on nonlinear optical effects in laser trapping of dielectric nanoparticles with ultrafast pulsed excitation

Abstract

The use of low-power high-repetition-rate ultrafast pulsed excitation in stable optical trapping of dielectric nanoparticles has been demonstrated in the recent past; the high peak power of each pulse leads to instantaneous trapping of a nanoparticle with fast inertial response and the high repetition-rate ensures repetitive trapping by successive pulses However, with such high peak power pulsed excitation under a tight focusing condition, nonlinear optical effects on trapping efficiency also become significant and cannot be ignored. Thus, in addition to the above mentioned repetitive instantaneous trapping, trapping efficiency under pulsed excitation is also influenced by the optical Kerr effect, which we theoretically investigate here. Using dipole approximation we show that with an increase in laser power the radial component of the trapping potential becomes progressively more stable but the axial component is dramatically modulated due to increased Kerr nonlinearity. We justify that the relevant parameter to quantify the trapping efficiency is not the absolute depth of the highly asymmetric axial trapping potential but the height of the potential barrier along the beam propagation direction. We also discuss the optimal excitation parameters leading to the most stable dipole trap. Our results show excellent agreement with previous experiments.

Nonlinear Optical Tweezers As an Optical Method for Controlling Particles with High Trap Efficiency

“…The stable degree of trapped particle or stiffness of optical tweezers depends on the magnitude of force peaks [33] and the spatial distance between them [34], i.e., depends on height and diameter of the distribution of F grd,ρ (grd,z) , which is similar to the OT's potential bell, U ρ(z) = − P ρ(z) • E , where P ρ(z) is the radial (or axial) polarization and E is the electric field of laser ( Fig. 1d) [21].…”

“…As well-known, since the nonlinearity of convenient fluid and interesting particles are very low, for example the nonlinear refractive index of water, polystyrene and silica is just n w = 2.7 × 10 −20 m 2 /W [18], n p = 5.9 × 10 −17 m 2 /W [19] and n s = 2.0 × 10 −20 m 2 /W [20], respectively, so the nonlinear effect in OT should be observed only if using the high-repetition ultrafast pulsed laser [21][22][23]. Consequently, the nonlinear effect is very weak and then practically to enhance optical trap efficiency (OTE) it needs a high laser intensity [6].…”

Theory and practice of simulation of optical tweezers

“…• Nonlinear particles. Particles with non-linear electromagnetic properties have the potential for many interesting behaviours in optical traps Saloma, 1997, 2006;Devi and De, 2016).…”

Optical forces of focused femtosecond laser pulses on nonlinear optical Rayleigh particles

“…Alternatively, researchers directly modified the Rayleigh scattering formulae by replacing the refractive index n p 0 with n p 0 + n 2 I [19-21], where I is the optical intensity, n p 0 and n 2 are the linear and third-order nonlinear refractive indexes of particle, respectively. This phenomenological theory could interpret the self-focusing effect that increases the trapping force strength and improves the confinement of Rayleigh particles [19][20][21].In this work, for the first time, we establish the timeaveraged optical forces on a nonlinear optical Rayleigh particle using high-repetition-rate ultrafast laser pulses, based on the linear and nonlinear polarization effects.For time-harmonic electromagnetic waves with a Gaussian temporal envelope, we havewhere E 0 ( r) is the complex function of position in space, ω is the circular frequency, c is the speed of light in vacuum, and τ F is the full width at half maximum for a Gaussian pulse. Now we consider a spherical dielectric particle immersed in liquid (e.g.…”

“…In this case, the third-order nonlinear optical susceptibility χ 3 is related to the third-order nonlinear refractive index n 2 through the conversion formula Re[χ 3 ] = n 2 ε 0 2 ε 0 c/(3ε 0 1 ). In this work, the nonlinear refractive indexes are taken to be n 2 = 5.9 × 10 −17 and −5.9 × 10 −17 m 2 /W, which corresponds to the self-focusing and self-defocusing effects of the trapped particle, respectively [21]. Without loss of generality, the particle is assumed to be immersed in water.…”