arXiv subjects

Milivoj R. Belić

Publications and source records attributed to Milivoj R. Belić.

At least 19 recordsLinked to original sources

arXiv2026

Stable vortex soliton arrays in disclination-fractal systems

Vortex light fields carry orbital angular momentum and have attracted significant attention because of their wide applications in light field manipulations, optical communications, and quantum information processing. In nonlinear media, the balance between diffraction and self-action enables the formation of vortex solitons. However, achieving the stability of vortex solitons remains challenging due to radial and azimuthal modulation instabilities. Here, we report stable vortex solitons and vortex-soliton arrays in disclination-fractal configurations with different rotational symmetries, constructed by applying disclination operations to fractal lattice structures. The stable vortex-soliton arrays---composed of several vortex solitons---can exist along domain walls, resulting from the disclination operation applied to the topologically trivial phase. Their stability is verified through both linear stability analysis and direct simulations of perturbed propagation. For comparison, vortex-soliton arrays in conventional disclination configurations are found to be completely unstable, demonstrating the significance of the fractal configuration in stabilizing these nonlinear states. These findings reveal a new nonlinear excitation mechanism arising from the interplay between fractal geometry and disclination defects, thereby providing theoretical underpinnings for both the improved understanding of multi-field excitation phenomena in complex geometric systems and opening new avenues for the design of photonic devices based on fractal disclination structures.

physics.optics↗

arXiv2025

Self-Accelerating Topological Edge States

Edge states emerging at the boundaries of materials with nontrivial topology are attractive for many practical applications due to their remarkable robustness to disorder and local boundary deformations, which cannot result in scattering of the energy of the edge states impinging on such defects into the bulk of material, as long as forbidden topological gap remains open in its spectrum. The velocity of the such states traveling along the edge of the topological insulator is typically determined by their Bloch momentum. In contrast, here, using valley Hall edge states forming at the domain wall between two honeycomb lattices with broken inversion symmetry, we show that by imposing Airy envelope on them one can construct edge states which, on the one hand, exhibit \textit{self-acceleration} along the boundary of the insulator despite their fixed Bloch momentum and, on the other hand, \textit{do not diffract} along the boundary despite the presence of localized features in their shapes. We construct both linear and nonlinear self-accelerating edge states, and show that nonlinearity considerably affects their envelopes. Such self-accelerating edge states exhibit self-healing properties typical for nondiffracting beams. Self-accelerating valley Hall edge states can circumvent sharp corners, provided the oscillating tail of the self-accelerating topological state is properly apodized by using an exponential function. Our findings open new prospects for control of propagation dynamics of edge excitations in topological insulators and allow to study rich phenomena that may occur upon interactions of nonlinear envelope topological states.

physics.optics↗

arXiv2024

$\mathcal{PT}$-symmetric photonic lattices with type-II Dirac cones

The type-II Dirac cone is a special feature of the band structure, whose Fermi level is represented by a pair of crossing lines. It has been demonstrated that such a structure is useful for investigating topological edge solitons, and more specifically, for mimicking the Kline tunneling. However, it is still not clear what the interplay between type-II Dirac cones and the non-Hermiticity mechanism will result in. Here, this question is addressed; in particular, we report the $\mathcal{PT}$-symmetric photonic lattices with type-II Dirac cones for the first time. We identify a slope-exceptional ring and name it the type-II exceptional ring. We display the restoration of the $\mathcal{PT}$ symmetry of the lattice by reducing the separation between the sites in the unit cell. Curiously, the amplitude of the beam during propagation in the non-Hermitian lattice with $\mathcal{PT}$ symmetry only decays because of diffraction, whereas in the $\mathcal{PT}$ symmetry-broken lattice it will be amplified, even though the beam still diffracts. This work establishes the link between the non-Hermiticity mechanism and the violation of Lorentz invariance in these physical systems.

physics.optics↗

arXiv2021

Higher-order Breathers as Quasi-rogue Waves on a Periodic Background

We investigate higher-order breathers of the cubic nonlinear Schrödinger equation on an elliptic background. We find that, beyond first-order, any arbitrarily constructed breather is a single-peaked solitary wave on a disordered background. These "quasi-rogue waves" are also common on periodic backgrounds. We assume the higher-order breather is constructed out of constituent first-order breathers with commensurate periods (i.e., higher-order harmonic waves). In that case, one obtains "quasi-periodic" breathers with distorted side-peaks. Fully periodic breathers are obtained when their wavenumbers are harmonic multiples of the background and each other. They are truly rare, requiring finely-tuned parameters. Thus, on a periodic background, we arrive at the paradoxical conclusion that the apparent higher-order rogue waves are rather common, while the truly periodic breathers are exceedingly rare.

nlin.PS↗

arXiv2020

Rabi oscillation of azimuthons in weakly nonlinear waveguides

Rabi oscillation, an inter-band oscillation, depicts the periodic flopping between two states that belong to different energy levels in the presence of an oscillatory driving field. In photonics, Rabi oscillation can be mimicked by applying a weak longitudinal periodic modulation to the refractive index change of the system. However, the Rabi oscillation of nonlinear states has yet to be discussed. We report Rabi oscillations of azimuthons---spatially modulated vortex solitons---in weakly nonlinear waveguides with different symmetries, both numerically and theoretically. The period of Rabi oscillation can be determined by applying the coupled mode theory, which largely depends on the modulation strength. Whether the Rabi oscillation between two states can be obtained or not is determined by the spatial symmetry of the azimuthons and the modulating potential. In this paper we succeeded in obtaining the Rabi oscillation of azimuthons in the weakly nonlinear waveguides with different symmetries. Our results not only enrich the Rabi oscillation phenomena, but also provide a new avenue in the study of pattern formation and spatial field manipulation in nonlinear optical systems.

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arXiv2019

Vortex soliton in a cold atomic gas via electromagnetically induced transparency

We investigate the formation and propagation of vector vortex solitons (VS) and unipolar soliton (US) in a cold atomic gas with Bessel lattices (BLs). The system we consider is a cold, coherent atomic gas with a tripod or multipod level configuration. Dueing to the giant enhancement of Kerr nonlinearity contributed by electromagnetically induced transparency (EIT), a vector weak vortex soliton can be effectively formed with ultraslow propagating velocity. Furthermore, we demonstrate that the characteristics of 2D VS and US can be controlled and manipulated via adjusting BLs. The results predicted here may be used to design all-optical switching at very low light level.

nlin.PS↗

arXiv2017

PT-symmetry in nonlinear twisted multi-core fibers

We address propagation of light in nonlinear twisted multi-core fibers with alternating amplifying and absorbing cores that are arranged into the PT - symmetric structure. In this structure, the coupling strength between neighboring cores and global energy transport can be controlled not only by the nonlinearity strength, but also by gain and losses and by the fiber twisting rate. The threshold level of gain/losses, at which PT -symmetry breaking occurs, is a non-monotonic function of the fiber twisting rate and it can be reduced nearly to zero or, instead, notably increased just by changing this rate. Nonlinearity usually leads to the monotonic reduction of the symmetry breaking threshold in such fibers.

physics.optics↗

arXiv2017

Edge states in dynamical superlattices

We address edge states and rich localization regimes available in the one-dimensional (1D) dynamically modulated superlattices, both theoretically and numerically. In contrast to conventional lattices with straight waveguides, the quasi-energy band of infinite modulated superlattice is periodic not only in the transverse Bloch momentum, but it also changes periodically with increase of the coupling strength between waveguides. Due to collapse of quasi-energy bands dynamical superlattices admit known dynamical localization effect. If, however, such a lattice is truncated, periodic longitudinal modulation leads to appearance of specific edge states that exist within certain periodically spaced intervals of coupling constants. We discuss unusual transport properties of such truncated superlattices and illustrate different excitation regimes and enhanced robustness of edge states in them, that is associated with topology of the quasi-energy band.

physics.optics↗

arXiv2016

Peak-height formula for higher-order breathers of the nonlinear Schrödinger equation on non-uniform backgrounds

Given any background (or seed) solution of the nonlinear Schrödinger equation, the Darboux transformation can be used to generate higher-order breathers with much greater peak intensities. The Darboux transformation is generic in iterating a pair of generating solutions of the Lax-pair equation which preserves the solution of the nonlinear Schrödinger equation as a consistency condition. The Darboux transformation itself knows nothing about the background solution except through the initial pair of Lax solutions. Because of this, in this work, we can prove in an unified manner, and without knowing the analytical form of the background solution, that the peak-height of a high-order breather, is just a sum of peak-heights of first-order breathers plus that of the background, {\it irrespective} of the specific choice of the background. Detailed results are verified for breathers on a cnoidal background. Generalizations to more extended nonlinear Schrödinger equations are also indicated.

nlin.PS↗

arXiv2016

Unveiling the link between fractional Schrödinger equation and light propagation in honeycomb lattice

We establish a link between the fractional Schrödinger equation (FSE) and light propagation in the honeycomb lattice (HCL) - the Dirac-Weyl equation (DWE). The fractional Laplacian in FSE causes a modulation of the dispersion relation of the system, which in the limiting case becomes linear. In the HCL, the dispersion relation is already linear around the Dirac point, suggesting a possible connection with the FSE. Here, we demonstrate this connection by describing light propagation in both FSE and HCL, using DWE. Thus, we propagate Gaussian beams according to FSE, HCL around the Dirac point, and DWE, to discover very similar behavior - the conical diffraction. However, if an additional potential is brought into the system, the link between FSE and HCL is broken, because the added potential serves as a perturbation, which breaks the translational periodicity of HCL and destroys Dirac cones in the dispersion relation.

physics.optics↗

arXiv2016

Transport properties in the photonic super-honeycomb lattice - a hybrid fermionic and bosonic system

We report on transport properties of the super-honeycomb lattice, the band structure of which possesses a flat band and Dirac cones, according to the tight-binding approximation. This super-honeycomb model combines the honeycomb lattice and the Lieb lattice and displays the properties of both. The super-honeycomb lattice also represents a hybrid fermionic and bosonic system, which is rarely seen in nature. By choosing the phases of input beams properly, the flat-band mode of the super-honeycomb will be excited and the input beams will exhibit strong localization during propagation. On the other hand, if the modes of Dirac cones of the super-honeycomb lattice are excited, one will observe conical diffraction. Furthermore, if the input beam is properly chosen to excite a sublattice of the super-honeycomb lattice and the modes of Dirac cones with different pseudospins, e.g., the three-beam interference pattern, the pseudospin-mediated vortices will be observed.

physics.optics↗

arXiv2016

Spatiotemporal accessible solitons in fractional dimensions

We report solutions for solitons of the "accessible" type in globally nonlocal nonlinear media of fractional dimension (FD), viz., for self-trapped modes in the space of effective dimension $2<D\le3$ with harmonic-oscillator potential whose strength is proportional to the total power of the wave field. The solutions are categorized by a combination of radial, orbital and azimuthal quantum numbers $(n,l,m)$. They feature coaxial sets of vortical and necklace-shaped rings of different orders, and can be exactly written in terms of special functions that include Gegenbauer polynomials, associated Laguerre polynomials, and associated Legendre functions. The validity of these solutions is verified by direct simulation. The model can be realized in various physical settings emulated by FD spaces; in particular, it applies to excitons trapped in quantum wells.

nlin.PS↗

arXiv2016

Coherent and incoherent nonparaxial self-accelerating Weber beams

We investigate the coherent and incoherent nonparaxial Weber beams, theoretically and numerically. We show that the superposition of coherent self-accelerating Weber beams with transverse displacement cannot display the nonparaxial accelerating Talbot effect. The reason is that their lobes do not accelerate in unison, which is a requirement for the appearance of the effect. While for the incoherent Weber beams, they naturally cannot display the accelerating Talbot effect but can display the nonparaxial accelerating properties, although the transverse coherence length is smaller than the beam width, based on the second-order coherence theory. Our research method directly applies to the nonparaxial Mathieu beams as well, and one will obtain similar conclusions as for the Weber beams, although this is not discussed in the paper. Our investigation identifies families of nonparaxial accelerating beams that do not exhibit the accelerating Talbot effect, and in addition broadens the understanding of coherence properties of such nonparaxial accelerating beams.

physics.optics↗

arXiv2016

Nonparaxial accelerating Talbot effect

We demonstrate the fractional Talbot effect of nonpraxial accelerating beams, theoretically and numerically. It is based on the interference of nonparaxial accelerating solutions of the Helmholtz equation in two dimensions. The effect originates from the interfering lobes of a superposition of the solutions that accelerate along concentric semicircular trajectories with different radii. Talbot images form along certain central angles, which are referred to as the Talbot angles. The fractional nonparaxial Talbot effect is obtained by choosing the coefficients of beam components properly. A single nonparaxial accelerating beam possesses duality --- it can be viewed as a Talbot effect of itself with an infinite or zero Talbot angle. These results improve the understanding of nonparaxial accelerating beams and the Talbot effect among them.

physics.optics↗

arXiv2016

New face-centered photonic square lattices with flat bands

We report two new classes of face-centered photonic square lattices with flat bands which we call the Lieb-I and the Lieb-II lattices. There are 5 and 7 sites in the corresponding unit cells of the simplest Lieb-I and Lieb-II lattices, respectively. The number of flat bands $m$ in the new Lieb lattices is related to the number of sites $N$ in the unit cell by $m=(N-1)/2$. Physical properties of the lattices with even and odd number of flat bands are different. We also consider localization of light in such Lieb lattices. If the input beam excites the flat-band mode, it will not diffract during propagation, owing to the strong localization in the flat-band mode. For the Lieb-II lattice, we also find that the beam will oscillate and still not diffract during propagation, because of the intrinsic oscillating properties of certain flat-band modes. The period of oscillation is determined by the energy difference between the two flat bands. This study provides a new platform for the investigation of flat-band modes.

physics.optics↗

arXiv2016

$\mathcal{PT}$ symmetry in a fractional Schrödinger equation

We investigate the fractional Schrödinger equation with a periodic $\mathcal{PT}$-symmetric potential. In the inverse space, the problem transfers into a first-order nonlocal frequency-delay partial differential equation. We show that at a critical point, the band structure becomes linear and symmetric in the one-dimensional case, which results in a nondiffracting propagation and conical diffraction of input beams. If only one channel in the periodic potential is excited, adjacent channels become uniformly excited along the propagation direction, which can be used to generate laser beams of high power and narrow width. In the two-dimensional case, there appears conical diffraction that depends on the competition between the fractional Laplacian operator and the $\mathcal{PT}$-symmetric potential. This investigation may find applications in novel on-chip optical devices.

physics.optics↗

arXiv2016

Controllable circular Airy beams via dynamic linear potential

We investigate controllable spatial modulation of circular autofocusing Airy beams, under action of different dynamic linear potentials, both theoretically and numerically. We introduce a novel treatment method in which the circular Airy beam is represented as a superposition of narrow azimuthally-modulated one-dimensional Airy beams that can be analytically treated. The dynamic linear potentials are appropriately designed, so that the autofocusing effect can either be weakened or even eliminated when the linear potential exerts a "pulling" effect on the beam, or if the linear potential exerts a "pushing" effect, the autofocusing effect can be greatly strengthened. Numerical simulations agree with the theoretical results very well.

physics.optics↗

arXiv2016

Diffraction-free beams in fractional Schrödinger equation

We investigate the propagation of one-dimensional and two-dimensional (1D, 2D) Gaussian beams in the fractional Schrödinger equation (FSE) without a potential, analytically and numerically. Without chirp, a 1D Gaussian beam splits into two nondiffracting Gaussian beams during propagation, while a 2D Gaussian beam undergoes conical diffraction. When a Gaussian beam carries linear chirp, the 1D beam deflects along the trajectories $z=\pm2(x-x_0)$, which are independent of the chirp. In the case of 2D Gaussian beam, the propagation is also deflected, but the trajectories align along the diffraction cone $z=2\sqrt{x^2+y^2}$ and the direction is determined by the chirp. Both 1D and 2D Gaussian beams are diffractionless and display uniform propagation. The nondiffracting property discovered in this model applies to other beams as well. Based on the nondiffracting and splitting properties, we introduce the Talbot effect of diffractionless beams in FSE.

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