Pis’ma v ZhETF, vol. 112, iss. 2, pp. 79 - 80

Dynamics of particles trapped by dissipative domain walls

D. A. Dolinina¹⁾, A. S. Shalin, A. V. Yulin

ITMO University, 197101 St. Petersburg, Russia

Submitted 26 April 2020

Resubmitted 29 May 2020

Accepted 30

May 2020

DOI: 10.31857/S1234567820140025

1. Introduction. Nonlinear localized structures

ity and existence of bright solitons and domain walls,

have been attracting much attention in recent time be-

see [10-15]. A particle on the surface of resonator is at-

cause of the two reasons. The first one is fundamental

tracted in the area of higher intensity because of the gra-

interest to their rich variety in physical systems of differ-

dient force [16] and in [8, 9] it is demonstrated that dissi-

ent natures, including hydrodynamics, plasma physics,

pative solitons in considered system are able to steadily

biology and nonlinear optics, see [1-4]. And the second

capture particles and transport them in desirable direc-

reason of high interest in nonlinear localized structures

tion.

is their potential applications in many fields, including

The optical field of the considered resonator is de-

information optical processing [5, 6], optical fiber com-

scribed in the slow varying amplitude approach by the

munications [7], and optical manipulation [8, 9].

Schrödinger equation with the nonlinearity of saturable

One of the most interesting localized structures

type, dissipation and pumping:

are switching waves, or alternatively “domain walls”,

∂

∂²

connecting different stationary spatially homogeneous

E - iC

E + (γ + iδ + i

)E =

∂t

∂x²

1 + |E|²

states. The direction and the velocity of the domain

wall motion strongly depends on the pumping intensity.

= (1 - fe-(x-ǫ)2/ω2 )P,

(1)

But there is a special value of pumping intensity char-

acterized by zero velocity of the domain wall and it is

where C is diffraction coefficient, E is a complex ampli-

called Maxwell point. Near the Maxwell point the do-

tude of optical field in the resonator, P is an amplitude

main walls are able to create different bound states, such

of laser pumping, γ is decay rate, α is the nonlinearity

as bright or dark solitons [10-12].

coefficient; δ is laser detuning from resonant frequency,

Another important effect of domain walls is reported

ǫ is coordinate of the nanoparticle. Parameter ω defines

in [13]. It is demonstrated that under biharmonical

width of the particle shadow located at x = ǫ, f relates

pumping the direction and the velocity of the domain

to the transparency of a particle: if f = 0, then the par-

wall can be controlled by changing only the mutual

ticle is transparent and if f = 1, then the particle is

phase between the harmonics, it is so called “ratchet

opaque. The viscous motion of particle under the gradi-

effect”.

ent force is described by the following equation for the

In this Letter we suggest a new strategy of optical

particles’ coordinate:

manipulation of small particles by dissipative domain

∂

walls. This problem is closely related to the manipula-

ǫ=η

|E(ǫ)|².

(2)

∂t

∂x

tion of the particles by dissipative bright solitons consid-

ered in [8, 9]. This Letter is devoted to the formation,

In our model we use the typical assumption that the

stability and the dynamics of the bound states of the

dragging force acting on the particle is proportional to

particles and the domain walls. Special attention is paid

the gradient of the intensity of the optical field, the co-

to the influence of the ratchet effect on the processes of

efficient η accounts for the interaction strength. Let us

particle capturing and on the possibility to use ratchet

note that for mathematical convenience we use the di-

effect for nanoparticles manipulation.

mensionless variables.

We considered a nonlinear Fabry-Perot resonator

We performed numerical simulations with the pa-

pumped by the coherent light with a dielectric particle,

rameters insuring the existence of the domain wall.

located in the surface. Such resonators provide bistabil-

We focus on the dynamics of the domain walls with

particle under uniform and time-independent pumping

¹⁾e-mail: d.dolinina@metalab.ifmo.ru

P (x, t) = P₀. Since the uniform states connected by the

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2020

D. A. Dolinina, A. S. Shalin, A. V. Yulin

domain walls are not equivalent in the terms of intensi-

of the domain wall, but also its direction of propagation.

ties, the particle location relative to the wall is impor-

In case if θ ≈ 0 the domain wall propagates in the direc-

tant. In dependence of particles transparency and lo-

tion of extension of the area of higher intensity, and in

cation several scenarios of interaction are possible, from

case if θ ≈ π/2 the domain wall moves in the opposite

successful particle trapping as in Fig. 1a, to the full stop

direction, see Fig. 1c, d.

of the domain wall by the particle as in Fig.1b.

From Fig. 1c, d it is seen that trapping of particles

by oscillating front is also possible. The domain walls

moving because of the ratchet effect have very slow ve-

locities what makes it possible to achieve high accuracy

of particle manipulation.

This work was supported by the Ministry of Sci-

ence and Higher Education of Russian Federation

(Goszadanie # 2019-1246). Also the work was partially

supported by the Russian Foundation for Basic Re-

search (Projects #18-02-00414). The calculations of the

fronts dynamics were supported by the Russian Science

Foundation (Project # 18-72-10127).

Full text of the paper is published in JETP Letters

journal. DOI: 10.1134/S0021364020140027

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