Conical Diffraction and Gap Solitons in Honeycomb Photonic Lattices

Abstract

We study wave dynamics in honeycomb photonic lattices, and demonstrate the unique phenomenon of conical diffraction around the singular diabolical (zero-effective-mass) points connecting the first and second bands. This constitutes the prediction and first experimental observation of conical diffraction arising solely from a periodic potential. It is also the first study on k space singularities in photonic lattices. In addition, we demonstrate "honeycomb gap solitons" residing in the gap between the second and the third bands, reflecting the special properties of these lattices.

Geometric stabilization of extendedS=2vortices in two-dimensional photonic lattices: Theoretical analysis, numerical computation, and experimental results

“…However, more recently both in optics [28,29] and in BEC [30,31] (so far in the absence of the lattice for the latter case), the study of higher charge vortices has been of interest. In particular, in the emerging area of hexagonal [21,32] and honeycomb [20] lattices, it has been predicted [33,34] and experimentally observed [35] very recently that a higher-order vortex with topological charge S = 2 is more stable than a fundamental vortex with unit charge (S = 1) when self-trapped with a focusing nonlinearity.…”

“…Indeed, the theoretical proposal [5] of such lattice solitons was followed quickly by their experimental realization in 2D induced lattices [9,10], subsequently leading to the observation of a host of novel solitons in this setting, including dipole [11], multipole [12], necklace [13], and rotary [14] solitons as well as discrete [15,16] and gap [17] vortices. In addition to lattice solitons, photonic lattices have enabled observations of other intriguing phenomena such as higher order Bloch modes [18], Zener tunneling [19], and localized modes in honeycomb [20], hexagonal [21] and quasi-crystalline [22] lattices, and Anderson localization [23] (see, e.g., the recent review [24] for additional examples). In parallel, experimental development in the area of BECs closely follows, with prominent recent results including the observation of bright, dark and gap solitons in quasi-onedimensional settings [25], with the generation of similar structures in higher dimensions being experimentally feasible for BECs trapped in optical lattices [26,27].…”

Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices

“…This phenomenon, termed conical diffraction, was observed later by Lloyd [2]. Conical diffraction is possible in crystals with dispersion surfaces that intersect at a singular point where the group velocity is not uniquely defined [3]. This is often referred to as the Dirac point or diabolical point.…”

“…It has been shown in various contexts that conical diffraction is possible in systems with Dirac cones in the dispersion relation [1,3,9]. A suitable initial condition in order to observe the relevant phenomenology is a localized function (such as a Gaussian) that is modulating a Bloch wave with a wavenumber near the Dirac point.…”

“…a honeycomb symmetry and indeed emerges due to the special symmetry of the lattice. This has led to a burst of activity towards the study of Dirac points in other physical systems with the honeycomb and hexagonal symmetries, e.g., in photonics [3,[9][10][11][12][13][14][15][16][17] -giving also rise to the term "photonic graphene"-, where it has been shown that conical diffraction is possible [3,9]. More recently, Dirac points have started to be explored in phononic systems, where pressure waves are manipulated rather than light waves [18][19][20].…”