Self-ordering and collective dynamics of transversely illuminated point-scatterers in a 1D trap

Abstract

We study point-like polarizable particles confined in a 1D very elongated trap within the evanescent field of an optical nano-fiber or nanostructure. When illuminated transversely by coherent light, collective light scattering into propagating fiber modes induces long range interactions and eventually crystallisation of the particles into regular order. We develop a simple and intuitive scattering-matrix based approach to study these long-range interactions by collective scattering and the resulting light-induced self-ordering. For few particles we derive explicit conditions for self-consistent stable ordering. In the purely dispersive limit with negligible back-scattering, we recover the prediction of an equidistant lattice as previously found for effective dipole-dipole interaction models. We generalize our model to experimentally more realistic configurations including backscattering, absorption and a directional scattering asymmetry. For larger particle ensembles the resulting self-consistent particle-field equations can be numerically solved to study the formation of long-range order and stability limits. arXiv:1409.5307v1 [physics.optics]

Optical Nanofibers

“…They study the possible phase transitions of the atomic spatial order as a function of the external pump intensity which can show self-sustained crystallization, similar to Domokos and Ritsch (2002), but the parameter space is rich and there can coexist multiple ordered states with distinct appearances. Similar studies have been carried for slightly different nanophotonic platforms Chang et al (2013);Holzmann et al (2014); Eldredge et al (2016). For a detailed discussion about the role of long-range interaction in self-organized systems see Ritsch et al (2013).…”

Collective scattering and oscillation modes of optically bound point particles trapped in a single mode waveguide field

“…They collectively scatter light into the fiber mode and self-trap in the optical potential generated by interference of the scattered light and the pump field [9]. Surprisingly we see that not only the light confines the particle motion but the particles also confine the light forming Bragg like atom mirrors at their outer edges.…”

“…1 [9] . For a given spatial arrangement of point scatterers in the field of a 1D waveguide the light field can be calculated by a scattering matrix approach [17][18][19][20].…”

“…The transmission and reflection coefficients are related to the coupling constant via t = 1/(1−iζ) and r = iζ/(1 − iζ). For symmetric scattering the coupling between the amplitudes left and right of a particle can then be expressed using the following beam splitter matrix M BS [9] where B j , C j , η are the incoming fields allowing to determine the outgoing fields A j , D j , cf. …”

“…In previous work we and others have seen that under quite general conditions stationary equilibrium positions can be found, where all particles are force free and feel a restoring force against small shifts. However, in contrast to a standard 1D optical lattice, the absence of a force does not enforce an unaltered propagation of the light [18] but just guarantees a balance between internal and external light scattering [9]. Following Ref.…”