Localized optical micromotors based on twin laser cavity solitons

It has recently been shown that vertical-cavity surface-emitting lasers with an intracavity saturable absorber are capable of forming binary localized structures called twin laser cavity solitons (LCSs). Apart from their asymmetric intensity distribution, they can spontaneously rotate about their center of mass with a frequency that is controllable via a bifurcation parameter representing the ratio of carrier lifetimes in the amplifier and in the absorber. Moreover, circles of maximum phase are found to form around the center of the binary structure which start rotation once the twin LCSs begin to do so. In this paper, we propose to use the fact that these phase circles continually shrink on the center of mass to trap microparticles at the center and subsequently rotate them through the dipole force provided by the asymmetric intensity distribution. This finding can be regarded as a first step in the realization of a localized microdimensional optical motor potentially useful in the manipulation of microparticles and nanofluids.

Figure 1

Energy bands available for switching single and twin LCSs versus pump current $\mu .r$ is fixed at 0.85. The vertical dashed line marks the boundary which separates only oscillating twin LCSs (to the right) from those of oscillating and rotating (to the left) LCSs.

Figure 2

The homogenous steady-state (H.S.S) solution and the single-twin LCS branches. $r=1$.

Figure 3

Entanglement of the two LCSs in the twin structure in terms of (a) intensity and (b) phase. The values on the vertical and horizontal axes in (b) are divided by $\pi$. Parameter values are as follows: $\mu =5.05,r=1$.

Figure 4

Frequency of (a) intensity oscillations $\nu$ and that of (b) rotation about the center of mass (in cycles per second) as a function of the pump current $\mu$. In (a) the frequencies are calculated for the regime of only oscillating LCSs. $r=0.85$.

Figure 5

(a) Phase structure of the transverse field taken from simulations and (b) the phase-field profiles along the line connecting the centers of the two peaks. A zero phase value is found almost at the intensity minimum between the two LCSs. $\mu =5.0,r=0.85$. See the Supplemental Material for a multimedia file (simulation movie) corresponding to this complex motion of the circles of the maximum phase [24].

Figure 6

The frequency at which circles of the maximum phase value shrink toward the center of mass of the binary structure versus the bifurcation parameter $r.\mu =5$.

Figure 7

Simultaneous injection of rotatory pulses (low in amplitude and short in time) in the vicinity of the peaks causing (a) clockwise and (b) counterclockwise rotation of the twin LCSs. The arrows are pointed at the locations where the rotatory pulses are injected. See the Supplemental Material for a multimedia file (simulation movie) corresponding to the counterclockwise rotation [24].

Figure 8

Force field experienced by the particle as the twin LCSs are in clockwise rotation. Intensity distributions (a), (c), (e), (g) and their respective force fields (b), (d), (f), and (h). The values are as follows: $\mathrm{\Gamma }=0.0621,\mathrm{\Omega }=-0.05\mathrm{GHz},\mu =5,r=0.72$. The time between consecutive snapshots is $\sim 90\mu \mathrm{s}$.

Figure 9

Change in the direction of the force lines for different signs of the detuning: (a) for $\mathrm{\Omega }=-0.015$ GHz the forces point to the center of the intensity maxima, (b) for $\mathrm{\Omega }=0$ the forces point to the center of the less intense LCS, and (c) for $\mathrm{\Omega }=0.015$ GHz the forces point outwards. Note that for $+0.010<\mathrm{\Omega }<+0.015\mathrm{GHz}$ the gradients from the field and phase almost cancel out. The values are the same as in Fig. 8.