Observation of In-Band Lattice Solitons

Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA.
Physical Review Letters (Impact Factor: 7.51). 01/2008; 99(24):243901. DOI: 10.1103/PhysRevLett.99.243901
Source: PubMed


We report the first experimental and theoretical demonstrations of in-band (or embedded) lattice solitons. Such solitons appear in trains, and their propagation constants reside inside the first Bloch band of a square lattice, different from all previously observed solitons. We show that these solitons bifurcate from Bloch modes at the interior high-symmetry X points within the first band, where normal and anomalous diffractions coexist along two orthogonal directions. At high powers, the in-band soliton can move into the first band gap and turn into a gap soliton.

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    • "For instance, the onsite line solitons near the X-point (71), at angle θ = π/4 for defocusing nonlinearity and at angle θ = π/2 for focusing nonlinearity, have been numerically obtained and displayed in Fig. 7 (right panels); and their envelope locations agree with those predicted by the formulae (58). Our analytical results are consistent with the numerical and experimental reports of line solitons inside Bloch bands in [13] [14] [15] as well. "
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    ABSTRACT: As a first step toward a fully two-dimensional asymptotic theory for the bifurcation of solitons from infinitesimal continuous waves, an analytical theory is presented for line solitons, whose envelope varies only along one direction, in general two-dimensional periodic potentials. For this two-dimensional problem, it is no longer viable to rely on a certain recurrence relation for going beyond all orders of the usual multi-scale perturbation expansion, a key step of the exponential asymptotics procedure previously used for solitons in one-dimensional problems. Instead, we propose a more direct treatment which not only overcomes the recurrence-relation limitation, but also simplifies the exponential asymptotics process. Using this modified technique, we show that line solitons with any rational line slopes bifurcate out from every Bloch-band edge; and for each rational slope, two line-soliton families exist. Furthermore, line solitons can bifurcate from interior points of Bloch bands as well, but such line solitons exist only for a couple of special line angles due to resonance with the Bloch bands. In addition, we show that a countable set of multi-line-soliton bound states can be constructed analytically. The analytical predictions are compared with numerical results for both symmetric and asymmetric potentials, and good agreement is obtained.
    Full-text · Article · May 2013 · Studies in Applied Mathematics
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    • "trains as a collection of transverse dipoles, hence we may expect the soliton trains bifurcated from Γ and M points to be unstable. However, for soliton trains bifurcated from the X points (under either self-focusing or self-defocusing nonlinearity), adjacent transverse intensity peaks are out of phase under self-focusing nonlinearity, and are in-phase under self-defocusing nonlinearity (see Fig. 2 and [19]). Dipoles with such phase structures are stable in deep lattices [7, 24–27]. "
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    ABSTRACT: We report the existence of transversely stable soliton trains in optics. These stable soliton trains are found in two-dimensional square photonic lattices when they bifurcate from X-symmetry points with saddle-shaped diffraction inside the first Bloch band and their amplitudes are above a certain threshold. We also show that soliton trains with low amplitudes or bifurcated from edges of the first Bloch band (Gamma and M points) still suffer transverse instability. These results are obtained in the continuous lattice model and further corroborated by the discrete model.
    Preview · Article · Sep 2011 · Physical Review A
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    • "A distinctive feature of the periodic media is that it can support a wide variety of solitons residing in different band gaps. Examples include fundamental solitons [9] [11] [12] [13] [14] [15] [16] [17], dipole solitons [18] [19], vortex solitons [13] [20] [21] [22] [23], reduced-symmetry solitons [24], higher-band vortex solitons [25] [26] [27], embedded-soliton trains [28], and so on — many of which have been experimentally observed. Solitons in Besselring lattices have been reported too [29] [30]. "
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    ABSTRACT: Various families of charge-one vortex solitons in two-dimensional periodic media are reported. These vortices reside either in the semi-infinite gap or higher band gaps of the media. For both Kerr and saturable nonlinearities (either focusing or defocusing), infinite vortex families are found. All these families do not bifurcate from Bloch bands; rather, they turn around before reaching edges of Bloch bands. It is further revealed that vortices with drastically different topological shapes can belong to the same vortex family, which is quite surprising. Comment: To appear in Phys. Rev. A (with higher resolution figures)
    Preview · Article · Feb 2008 · Physical Review A
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