arXiv subjects

Milivoj R. Belić

Publications and source records attributed to Milivoj R. Belić.

33 records · Page 2Linked to original sources

arXiv2015

Photonic Floquet Topological Insulator in an Atomic Ensemble

We demonstrate the photonic Floquet topological insulator (PFTI) in an atomic vapor with nonlinear susceptibilities. The interference of three coupling fields splits the energy levels periodically to form a periodic refractive index structure with honeycomb symmetry that can be adjusted by the choice of frequency detunings and intensities of the coupling fields, which all affect the appearance of Dirac cones in the momentum space. When the honeycomb lattice sites are helically ordered along the propagation direction, we obtain a PFTI in the atomic vapor in which an obliquely incident beam moves along the zigzag edge without scattering energy into the PFTI, due to the confinement of the edge states. The appearance of Dirac cones and the formation of PFTI is strongly affected by the nonlinear susceptibilities; i.e. the PFTI can be shut off by the third-order nonlinear susceptibility and re-opened up by the fifth-order one.

physics.optics↗

arXiv2015

Propagation dynamics of a light beam in fractional Schr\"odinger equation

Dynamics of wavepackets in fractional Schrodinger equation is still an open problem. The difficulty stems from the fact that the fractional Laplacian derivative is essentially a nonlocal operator. We investigate analytically and numerically the propagation of optical beams in fractional Schr\"odinger equation with a harmonic potential. We find that the propagation of one- and two-dimensional (1D, 2D) input chirped Gaussian beams is not harmonic. In 1D, the beam propagates along a zigzag trajectory in the real space, which corresponds to a modulated anharmonic oscillation in the momentum space. In 2D, the input Gaussian beam evolves into a breathing ring structure in both real and momentum spaces, which forms a filamented funnel-like aperiodic structure. The beams remain localized in propagation, but with increasing distance display increasingly irregular behavior, unless both the linear chirp and the transverse displacement of the incident beam are zero.

physics.optics↗

arXiv2015

Modulation of the photonic band structure topology of a honeycomb lattice in an atomic vapor

In an atomic vapor, a honeycomb lattice can be constructed by utilizing the three-beam interference method. In the method, the interference of the three beams splits the dressed energy level periodically, forming a periodic refractive index modulation with the honeycomb profile. The energy band topology of the honeycomb lattice can be modulated by frequency detunings, thereby affecting the appearance (and disappearance) of Dirac points and cones in the momentum space. This effect can be usefully exploited for the generation and manipulation of topological insulators.

physics.optics↗

arXiv2015

Self-Fourier transform and self-Fourier beams due to parabolic potential

We investigate the propagation of light beams including Hermite-Gauss, Bessel-Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams -- that is, the beams whose Fourier transforms are the beams themselves.

physics.optics↗

arXiv2015

Two-dimensional linear and nonlinear Talbot effect from rogue waves

We introduce two-dimensional (2D) linear and nonlinear Talbot effects. They are produced by propagating periodic 2D diffraction patterns and can be visualized as 3D stacks of Talbot carpets. The nonlinear Talbot effect originates from 2D rogue waves and forms in a bulk 3D nonlinear medium. The recurrences of an input rogue wave are observed at the Talbot length and at the half-Talbot length, with a πphase shift; no other recurrences are observed. Different from the nonlinear Talbot effect, the linear effect displays the usual fractional Talbot images as well. We also find that the smaller the period of incident rogue waves, the shorter the Talbot length. Increasing the beam intensity increases the Talbot length, but above a threshold this leads to a catastrophic self-focusing phenomenon which destroys the effect. We also find that the Talbot recurrence can be viewed as a self-Fourier transform of the initial periodic beam that is automatically performed during propagation. In particular, linear Talbot effect can be viewed as a fractional self-Fourier transform, whereas the nonlinear Talbot effect can be viewed as the regular self-Fourier transform. Numerical simulations demonstrate that the rogue wave initial condition is sufficient but not necessary for the observation of the effect. It may also be observed from other periodic inputs, provided they are set on a finite background. The 2D effect may find utility in the production of 3D photonic crystals.

physics.optics↗

arXiv2015

Dual accelerating Airy-Talbot recurrence effect

We demonstrate the dual accelerating Airy-Talbot recurrence effect, i.e., the self-imaging of accelerating optical beams, by propagating a superposition of Airy beams with successively changing transverse displacements. The dual Airy-Talbot effect is a spontaneous recurring imaging of the input and of the input with alternating component signs. It results from the constructive interference of Airy wave functions, which is also responsible for other kinds of Airy beams, for example, Airy breathers. An input composed of finite-energy Airy beams also displays the dual Airy-Talbot effect, but it demands a large transverse displacement and diminishes fast along the propagation direction.

physics.optics↗

arXiv2014

Beam splitter and combiner based on Bloch oscillations in spatially modulated waveguide arrays

We numerically investigate the light beam propagation in periodic waveguide arrays which are elaborately modulated with certain structures. We find that the light beam may split, coalesce, deflect, and be localized during propagation in these spatially modulated waveguide arrays. All the phenomena originate from Bloch oscillations, and supply possible method for fabricating on-chip beam splitters and beam combiners.

physics.optics↗

arXiv2014

Variational approach to multidimensional solitons in highly nonlocal nonlinear media

We apply the variational approach to solitons in highly nonlocal nonlinear media in $D=1,2,3$ dimensions. We compare results obtained by the variational approach with those obtained in the accessible soliton approximation, by considering the same system of equations in the same spatial region and under the same boundary conditions. To assess the accuracy of these approximations, we also compare them with the numerical solution of the equations. We discover that the variational highly nonlocal approximation provides more accurate results and as such is more appropriate solution than the accessible soliton approximation.

nlin.PS↗

arXiv2014

Interactions of incoherent localized beams in a photorefractive medium

We investigate numerically interactions between two bright or dark incoherent localized beams in an strontium barium niobate photorefractive crystal in one dimension, using the coherent density method. For the case of bright beams, if the interacting beams are in-phase, they attract each other during propagation and form bound breathers; if out-of-phase, the beams repel each other and fly away. The bright incoherent beams do not radiate much and form long-lived well-defined breathers or quasi-stable solitons. If the phase difference is $π/2$, the interacting beams may both attract or repel each other, depending on the interval between the two beams, the beam widths, and the degree of coherence. For the case of dark incoherent beams, in addition to the above the interactions also depend on the symmetry of the incident beams. As already known, an even-symmetric incident beam tends to split into a doublet, whereas an odd-symmetric incident beam tends to split into a triplet. When launched in pairs, the dark beams display dynamics consistent with such a picture and in general obey soliton-like conservation laws, so that the collisions are mostly elastic, leading to little energy and momentum exchange. But they also radiate and breathe while propagating. In all the cases, the smaller the interval between the two interacting beams, the stronger the mutual interaction. On the other hand, the larger the degree of incoherence, the weaker the interaction.

nlin.PS↗

arXiv2014

Three-dimensional nonparaxial accelerating beams from the transverse Whittaker integral

We investigate three-dimensional nonparaxial linear accelerating beams arising from the transverse Whittaker integral. They include different Mathieu, Weber, and Fresnel beams, among other. These beams accelerate along a semicircular trajectory, with almost invariant nondiffracting shapes. The transverse patterns of accelerating beams are determined by their angular spectra, which are constructed from the Mathieu functions, Weber functions, and Fresnel integrals. Our results not only enrich the understanding of multidimensional nonparaxial accelerating beams, but also display their real applicative potential -- owing to the usefulness of Mathieu and Weber functions, and Fresnel integrals in describing a wealth of wave phenomena in nature.

physics.optics↗

arXiv2014

Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media

We investigate numerically interactions between two in-phase or out-of-phase Airy beams and nonlinear accelerating beams in Kerr and saturable nonlinear media in one transverse dimension. We discuss different cases in which the beams with different intensities are launched into the medium, but accelerate in opposite directions. Since both the Airy beams and nonlinear accelerating beams possess infinite oscillating tails, we discuss interactions between truncated beams, with finite energies. During interactions we see solitons and soliton pairs generated that are not accelerating. In general, the higher the intensities of interacting beams, the easier to form solitons; when the intensities are small enough, no solitons are generated. Upon adjusting the interval between the launched beams, their interaction exhibits different properties. If the interval is large relative to the width of the first lobes, the generated soliton pairs just propagate individually and do not interact much. However, if the interval is comparable to the widths of the maximum lobes, the pairs strongly interact and display varied behavior.

nlin.PS↗

arXiv2014

The Nonlinear Talbot Effect of Rogue Waves

Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the nonlinear Schrödinger equation (NLSE). Talbot effect (TE) is an image recurrence phenomenon in the diffraction of light waves. We report the nonlinear TE of rogue waves in a cubic medium. It is different from the linear TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE. Periodic rogue waves impinging on a NL medium exhibit recurrent behavior, but only at the TE length and at the half-TE length with a π-phase shift; the fractional TE is absent. The NL TE is the result of the NL interference of the lobes of rogue wave breathers. This interaction is related to the transverse period and intensity of breathers, in that the bigger the period and the higher the intensity, the shorter the TE length.

nlin.PS↗

arXiv2013

Fresnel diffraction patterns as accelerating beams

We demonstrate that beams originating from Fresnel diffraction patterns are self-accelerating in free space. In addition to accelerating and self-healing, they also exhibit parabolic deceleration property, which is in stark contrast to other accelerating beams. We find that the trajectory of Fresnel paraxial accelerating beams is similar to that of nonparaxial Weber beams. Decelerating and accelerating regions are separated by a critical propagation distance, at which no acceleration is present. During deceleration, the Fresnel diffraction beams undergo self-smoothing, in which oscillations of the diffracted waves gradually focus and smooth out at the critical distance.

physics.optics↗

arXiv2013

Variational approach vs accessible soliton approximation in nonlocal nonlinear media

We discuss differences between the variational approach to solitons and the accessible soliton approximaion in a highly nonlocal nonlinear medium. We compare results of both approximations by considering the same system of equations in the same spatial region, under the same boundary conditions. We also compare these approximations with the numerical solution of the equations. We find that the variational highly nonlocal approximation provides more accurate results and as such is more appropriate solution than the accessible soliton approximation. The accessible soliton model offers a radical simplification in the treatment of highly nonlocal nonlinear media, with easy comprehension and convenient parallels to quantum harmonic oscillator, however with a hefty price tag: a systematic numerical discrepancy of up to 100% with the numerical results.

nlin.PS↗

arXiv2012

Ground state of nonlinear Schrodinger systems with saturable nonlinearity

We prove the existence of ground state in a multidimensional nonlinear Schrodinger model of paraxial beam propagation in isotropic local media with saturable nonlinearity. Such ground states exist in the form of bright counterpropagating solitons. From the proof, a general threshold condition on the beam coupling constant for the existence of such fundamental solitons follows.

math-ph↗