Topological Aharonov-Bohm Suppression of Optical Tunneling in Twisted Nonlinear Multicore Fibers

Optical mode stability and dynamics in nonlinear twisted 𝒫𝒯-symmetric structures

“…Adding twist to this optical system induces a phase factor in the nearest neighbor coupling constants, thus adding a new degree of freedom to a system that has nonlinearity and loss/gain strength representing a discrete PT property. As one can intuitively notice, twist is a topological property, so this optical configuration was recently considered [2] to show that Aharonov-Bohm-like suppression of optical tunneling in twisted multi-core fibers can persist under highly nonlinear conditions.…”

Spatiotemporal dynamics in a twisted, circular waveguide array

“…i.e. the order of the remainder term is one order higher in k. Since the formulas (19) involve the products, a n θ n , of the amplitudes and phases, Figure 7b plots the log of the L 2 error of (a n (θ n − nφ) num − a n (θ n − nφ) asymp L 2 vs. the log of coupling parameter k, where the true value is obtained from numerical parameter continuation, and the approximate value is computed using a n (θ n − nφ) asymp = k N −n a n θ n and (19). The slopes of least squares regressions lines for the error in a 1 θ 1 and a 2 θ 2 are within 2.5% of 5 and 4 (respectively), which suggests that the order of the remainder term in k is correct in the asymptotic expansions ( 14) for θ n .…”

“…Specifically, an asymptotic analysis of the optical intensity in a six-core twisted optical fiber [5] showed that if the bulk of the optical intensity is confined to a single fiber in the ring, then the intensity in the opposite fiber in the ring is suppressed, to leading order, when φ = π/6. This phenomenon can be interpreted as an optical analogue of Aharonov-Bohm (AB) suppression of tunneling in [15,19,18], in which the fiber twist plays the role of the magnetic flux in the quantum mechanical system [13]. This suppression effect was established analytically for a four-core optical fiber when φ = π/4 in [18].…”

“…The complex amplitudes, c n (z), represent the localized field amplitude in each waveguide, the independent variable, z, is along the axis of propagation, and k is the non-dimensional strength of the nearest-neighbor coupling of the waveguides in the ring. The entire fiber structure is twisted along the propagation axis with a spatial period, Λ, and the twist parameter, φ = 4π 2 ǫn s R 2 /N λ, is the Peierls phase introduced by the twist [12,20], where ǫ = 2π/Λ is the frequency of the twist, n s the refractive index of the substrate, R is the radius of the circular ring, and λ is the wavelength of the propagating field [5,19]. We note that this model only considers standing wave modes in each waveguide.…”

Optical vortices in waveguides with discrete and continuous rotational symmetry

“…In terms of the mathematical model, the twist adds a Pierels phase to the coupling constant amongst nearest neighbors [68]. For twisted arrays, recent works have shown what is interpreted as an optical Aharonov-Bohm suppression of tunneling, both in the linear [69] and the nonlinear [70,71] regime. Since the twist creates an orbital angular momentum (OAM), twisted multi-core arrays presents opportunities to explore novel dynamics [72] and find nonlinear modes including stable discrete light bullets [73] and vortices carrying an additional degree of freedom.…”