Laser trapping-induced reconfiguration

We should note that our observation on laser trapping properties of the radial

symmetric 5CB droplet at low laser powers are in accordance with those recently reported and

well documented in works by Murazawa et al. [25] and Brasselet et al. [24] Our important

experimental finding is that, actually, optically induced reconfiguration does exist in the

droplet under high laser powers with a sharp threshold, similarly to the cases of other LC

droplets with radial configurations [23,32,33].

To interpret the optically-induced reconfiguration in the radial nematic LC droplet,

we first consider optical reorientation of LCs, analogous to optical Fréederickscz transition

(OFT) in LC thin films. The optical reorientation should take place when the free-energy by

the light field exceeds Frank distortional energy. In a corresponding LC thin slab analog, in

which reorientation driven by optical nonlinearities has been accurately described, for

conventional light irradiations, the threshold of light density to induce molecular reorientation,

I_th, is given by [34,35]

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extraordinary and ordinary refractive index, and K is the average Frank elastic constant. If

one considers that the diameter of the droplet is approximately equal with the thickness of the

LC thin slab analog, with K ≅10 pN, Eqn. (1) gives the threshold light density for a droplet

of 2.5-μm-diameter to be approximately 2 MW/cm², corresponding to electric field strength of 2 V/μm. This calculated threshold power, however, is about two orders of magnitude lower

than the actual power to induce the reconfiguration throughout the inside of the droplet (the

threshold power density is ~360 MW/cm²). The striking difference between the calculation

and experimental value is due to that laser intensity of a focused beam is steeply distributed

around the diffraction limited size, not all inside the droplet volume. Nevertheless, with this

calculation, we proposed that the focused beam with laser powers slightly above OFT

threshold should not only generate gradient force, which confines stably the birefringent

droplet, but such a polarized laser beam propagating in the confined droplet can also induce

optical reorientation locally within the focal spot at the droplet center, although such local

reorientation is too small inside the droplet to be detected by the POM imaging.

As a self-organized structure, droplet-liquid interface energetic will also control the

molecular orientation inside the droplet through the interfacial anchoring effect. In this sense,

the interface can be considered to act as the anchoring layer. Under the optical trapping at

laser powers between the OFT and reconfiguration threshold, the reorientation propagates

from the focal spot to the close vicinity area through most probably cooperative effects, and

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thus, the droplet may adopt a kind of intermediate configuration. In this situation, the local

reorientations inside the droplet will induce non-symmetrical orientations, and such symmetry

breaking inside the droplet leads to spatially unequal torque. This is clearly indicated by

rotation of the droplet under circularly polarized beam. At higher powers, when optical

reorientation overcomes the anchoring effect, rotation of the droplet is coupled with its

reconfiguration. Thus, the rotation is induced as the result of local optical reorientations and it

can be considered as an early process or precursor of the reconfiguration, which most

probably is an equilibrium reorientation throughout the inside of the droplet. This means that,

when such an equilibrium configuration is formed, the local birefringence ultimately becomes

negligible, the torque is spatially balanced, and the rotation stops as observed with the

appearances of ring patterns.

The ring patterns of the optical transmission can be usually related to a far-field

intensity distribution of the transmitted light due to its spatial self-phase modulation and the

wave-front curvature, when the light passes through the nematic LC thin film [36,37]. In this

droplet case, the ring patterns may indicate that, in the equilibrium state, the LC molecules

inside the droplet is reoriented, but since both linearly and circularly polarized beams result in

the same POM images of the reconfigured droplet, we could draw a conclusion that their LC

orientations are not preferred along the laser polarization. This is an indication that

reconfiguration is not solely due to the laser polarization in the focal spot, but also involves

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cooperative effects throughout the inside of the droplet. Though the LC molecular

configuration inside the droplet is still an open question, we qualitatively interpreted that one

of possible structures is a kind of twisted configuration [29]. However, as the initial pattern is

immediately restored when the laser beam is switched off, we could consider that the

molecular alignment at the interfacial layer which acts as an anchoring surface should always

remain intact.

Upon the reconfiguration, the local refractive index inside the droplet should jump

between the extraordinary and ordinary refractive indices. As a consequence, the optical

forces exerting on the droplet should be also modified, resulting in a relocation of the droplet

slightly from the initial trapping center. This could be attributable to the change in droplet

diameter in the POM image. In comparison, the similar effect has been observed in

photo-induced molecular reorganization inside optically trapped cholesteric LC droplets

[21,22].