Nikolaos Efremidis - Academia.edu (original) (raw)

Papers by Nikolaos Efremidis

Research paper thumbnail of Thermodynamic optical pressures in tight-binding nonlinear multimode photonic systems

Communications Physics

Optical forces are known to arise in a universal fashion in many and diverse physical settings. A... more Optical forces are known to arise in a universal fashion in many and diverse physical settings. As such, they are successfully employed over a wide range of applications in areas like biophotonics, optomechanics and integrated optics. While inter-elemental optical forces in few-mode photonic networks have been so far systematically analyzed, little is known, if any, as to how they manifest themselves in highly multimoded optical environments. In this work, by means of statistical mechanics, we formally address this open problem in optically thermalized weakly nonlinear heavily multimode tight-binding networks. The outlined thermodynamic formulation allows one to obtain in an elegant manner analytical results for the exerted thermodynamic pressures in utterly complex arrangements-results that are either computationally intensive or impossible to obtain otherwise. Thus, we derive simple closed-form expressions for the thermodynamic optical pressures displayed among elements, which dep...

Research paper thumbnail of Generation of Vortex Optical Pin-like Beams

We propose and demonstrate anti-difîracting vortex optical pin-like beams (VOPBs) generated by pr... more We propose and demonstrate anti-difîracting vortex optical pin-like beams (VOPBs) generated by properly modulating both the amplitude and phase of an initial laser beam in Fourier space. Such VOPBs feature an autofocusing dynamics and outperform conventional higher-order Bessel beams and abruptly autofocusing beams.

Research paper thumbnail of Demonstration of Vortex Optical Pin Beams

OSA Advanced Photonics Congress (AP) 2020 (IPR, NP, NOMA, Networks, PVLED, PSC, SPPCom, SOF), 2020

We report on vortex optical pin beams, obtained by spatially tailoring amplitude and phase profil... more We report on vortex optical pin beams, obtained by spatially tailoring amplitude and phase profile of a laser beam in Fourier space. Numerical and experimental results show controllable and anti-diffractive dynamics during long-distance propagation.

Research paper thumbnail of Coupled Circular Arrays of Optical Amplifiers

Nonlinear Guided Waves and Their Applications, 2004

ABSTRACT A circular array of optical amplifiers coupled with a central core is proposed. Nonlinea... more ABSTRACT A circular array of optical amplifiers coupled with a central core is proposed. Nonlinear losses and energy tunneling within the array elements and the core are present fascilitating the existence of highly localized modes.

Research paper thumbnail of Random-phase solitons in nonlinear periodic lattices

We predict the existence of random phase solitons in nonlinear periodic lattices. These solitons ... more We predict the existence of random phase solitons in nonlinear periodic lattices. These solitons exist when the nonlinear response time is much longer than the characteristic time of random phase fluctuations. The intensity profiles, power spectra, and statistical (coherence) properties of these stationary waves conform to the periodicity of the lattice. The general phenomenon of such solitons is analyzed in the context of nonlinear photonic lattices.

Research paper thumbnail of Controlled generation of pseudospin-mediated vortices in photonic graphene

2D materials, Jun 26, 2015

ABSTRACT We demonstrate controllable generation and destruction of pseudospin-mediated topologica... more ABSTRACT We demonstrate controllable generation and destruction of pseudospin-mediated topological charges (vortices) in the photonic analogy of graphene—optically induced honeycomb lattices (HCLs). When only one of the two sublattices is selectively excited by the probe beams that are momentum-matched onto the Dirac points, a singly-charged optical vortex emerges in the output of the symmetric conical diffraction pattern. Furthermore, flipping of the topological charge is observed as the excitation shifts from sublattice A to sublattice B. On the other hand, when both sublattices are simultaneously excited, the conical diffraction pattern becomes highly asymmetric, accompanied by interesting phenomena related to the generation of half-integer vortices and line singularities. We present four different cases of selective excitation using two different approaches; one with three input probe beams that are momentum-matched to the three K valleys, and the other with only two probe beams while the Bloch modes surrounding the third valley are excited due to Bragg reflection. Our experimental results are confirmed by numerical simulation of the paraxial wave equation with a HCL potential as well as by theoretical analysis of the two-dimensional Dirac─Weyl equations directly. These studies indicate that the lattice pseudospin is not just a mathematical formality, but rather it can manifest through its angular momentum transferred to probing optical beams.

Research paper thumbnail of Asymmetric conical diffraction and generation of non-integer phase singularities in photonic graphene

We demonstrate asymmetric conical diffraction accompanied by pseudospin-mediated non-integer phas... more We demonstrate asymmetric conical diffraction accompanied by pseudospin-mediated non-integer phase singularities when two sublattices of photonic graphene are equally excited near the Dirac points. Experimental and numerical results agree with analysis of the Dirac equation.

Research paper thumbnail of Thermodynamic optical pressures in tight-binding nonlinear multimode photonic systems

arXiv (Cornell University), Oct 13, 2022

Optical forces are known to arise in a universal fashion in many and diverse physical settings. A... more Optical forces are known to arise in a universal fashion in many and diverse physical settings. As such, they are successfully employed over a wide range of applications in areas like biophotonics, optomechanics and integrated optics. While inter-elemental optical forces in few-mode photonic networks have been so far systematically analyzed, little is known, if any, as to how they manifest themselves in highly multimoded optical environments. In this work, by means of statistical mechanics, we formally address this open problem in optically thermalized weakly nonlinear heavily multimode tight-binding networks. The outlined thermodynamic formulation allows one to obtain in an elegant manner analytical results for the exerted thermodynamic pressures in utterly complex arrangements-results that are either computationally intensive or impossible to obtain otherwise. Thus, we derive simple closed-form expressions for the thermodynamic optical pressures displayed among elements, which depend only on the internal energy as well as the coupling coefficients involved. In all cases, our theoretical results are in excellent agreement with numerical computations. Our study may pave the way towards a deeper

Research paper thumbnail of Demonstration of turbulence-resistant propagation of anti-diffracting optical beams beyond kilometer distances

Conference on Lasers and Electro-Optics, 2019

We demonstrate robust propagation of anti-diffracting optical beams through atmosphere turbulence... more We demonstrate robust propagation of anti-diffracting optical beams through atmosphere turbulence beyond kilometer distances. Such Airy-Bessel-like light beams surpass conventional Bessel beams and can, in principle, exhibit “self-focusing” in free space without any optical nonlinearity. © 2019 The Author(s)

Research paper thumbnail of Excitation spectrum of a mixture of two Bose gases confined in a ring potential with interaction asymmetry

New Journal of Physics, 2018

We study the rotational properties of a two-component Bose-Einstein condensed gas of distinguisha... more We study the rotational properties of a two-component Bose-Einstein condensed gas of distinguishable atoms which are confined in a ring potential using both the mean-field approximation, as well as the method of diagonalization of the many-body Hamiltonian. We demonstrate that the angular momentum may be given to the system either via single-particle, or 'collective' excitation. Furthermore, despite the complexity of this problem, under rather typical conditions the dispersion relation takes a remarkably simple and regular form. Finally, we argue that under certain conditions the dispersion relation is determined via collective excitation. The corresponding many-body state, which, in addition to the interaction energy minimizes also the kinetic energy, is dictated by elementary number theory.

Research paper thumbnail of Fragility of the bosonic Laughlin state

Physical Review A, 2019

When a Bose-Einstein condensate rotates in a purely harmonic potential with an angular frequency ... more When a Bose-Einstein condensate rotates in a purely harmonic potential with an angular frequency which is close to the trap frequency, its many-body state becomes highly correlated, with the most well-known being the bosonic Laughlin state. To take into account that in a real experiment no trapping potential is ever exactly harmonic, we introduce an additional weak, quartic potential and demonstrate that the Laughlin state is highly sensitive to this extra potential. Our results imply that achieving these states experimentally is essentially impossible, at least for a macroscopic atom number.

Research paper thumbnail of Valley Vortex States and Degeneracy Lifting via Photonic Higher-Band Excitation

Physical Review Letters, 2019

We demonstrate valley-dependent vortex generation in a photonic graphene. Without breaking the in... more We demonstrate valley-dependent vortex generation in a photonic graphene. Without breaking the inversion symmetry, excitation of two equivalent valleys leads to formation of an optical vortex upon Bragg-reflection to the third valley, with its chirality determined by the valley degree of freedom. Vortex-antivortex pairs with valley-dependent topological charge flipping are also observed and corroborated by numerical simulations. Furthermore, we develop a three-band effective Hamiltonian model to describe the dynamics of the coupled valleys, and find that the commonly used two-band model is not sufficient to explain the observed vortex degeneracy lifting. Such valley-polarized vortex states arise from high-band excitation without inversion symmetry breaking or synthetic-field-induced gap opening. Our results from a photonic setting may provide insight for the study of valley contrasting and Berry-phase mediated topological phenomena in other systems.

Research paper thumbnail of Spatiotemporal diffraction-free pulsed beams in free-space of the Airy and Bessel type

Optics Letters, 2017

We investigate the dynamics of spatiotemporal optical waves with one transverse dimension that ar... more We investigate the dynamics of spatiotemporal optical waves with one transverse dimension that are obtained as the intersections of the dispersion cone with a plane. We show that, by appropriate spectral excitations, the three different types of conic sections (elliptic, parabolic, and hyperbolic) can lead to optical waves of the Bessel, Airy, and modified Bessel type, respectively. We find closed form solutions that accurately describe the wave dynamics and unveil their fundamental properties.

Research paper thumbnail of Mean-field yrast spectrum and persistent currents in a two-component Bose gas with interaction asymmetry

Physical Review A, 2015

We analyze the mean-field yrast spectrum of a two-component Bose gas in the ring geometry with ar... more We analyze the mean-field yrast spectrum of a two-component Bose gas in the ring geometry with arbitrary interaction asymmetry. Of particular interest is the possibility that the yrast spectrum develops local minima at which persistent superfluid flow can occur. By analyzing the mean-field energy functional, we show that local minima can be found at plane-wave states and arise when the system parameters satisfy certain inequalities. We then go on to show that these plane-wave states can be yrast states even when the yrast spectrum no longer exhibits a local minimum. Finally, we obtain conditions which establish when the plane-wave states cease to be yrast states. Specific examples illustrating the roles played by the various interaction asymmetries are presented.

Research paper thumbnail of Specially shaped Bessel-like self-accelerating beams along predesigned trajectories

Science Bulletin, 2015

Over the past several years, spatially shaped self-accelerating beams along different trajectorie... more Over the past several years, spatially shaped self-accelerating beams along different trajectories have been studied extensively. Due to their useful properties such as resistance to diffraction, self-healing, and selfbending even in free space, these beams have attracted great attention with many proposed applications. Interestingly, some of these beams could be designed with controllable spatial profiles and thus propagate along various desired trajectories such as parabolic, snake-like, hyperbolic, hyperbolic secant, three-dimensional spiraling, and even self-propelling trajectories. Experimentally, such beams are realized typically by using a spatial light modulator so as to imprint a desired phase distribution on a Gaussian-like input wave front propagating under paraxial or nonparaxial conditions. In this paper, we provide a brief overview of our recent work on specially shaped self-accelerating beams, including Bessel-like, breathing Bessellike, and vortex Bessel-like beams. In addition, we propose and demonstrate a new type of dynamical Bessel-like beams that can exhibit not only self-accelerating but also self-propelling during propagation. Both theoretical and experimental results are presented along with a brief discussion of potential applications.

Research paper thumbnail of Stabilization of dark solitons in the cubic Ginzburg-Landau equation

Physical Review E, 2000

The existence and stability of exact continuous-wave and dark-soliton solutions to a system consi... more The existence and stability of exact continuous-wave and dark-soliton solutions to a system consisting of the cubic complex Ginzburg-Landau ͑CGL͒ equation linearly coupled with a linear dissipative equation is studied. We demonstrate the existence of vast regions in the system's parameter space associated with stable darksoliton solutions, having the form of the Nozaki-Bekki envelope holes, in contrast to the case of the conventional CGL equation, where they are unstable. In the case when the dark soliton is unstable, two different types of instability are identified. The proposed stabilized model may be realized in terms of a dual-core nonlinear optical fiber, with one core active and one passive.

Research paper thumbnail of Multichannel pulse dynamics in a stabilized Ginzburg-Landau system

Physical Review E, 2002

We study the stability and interactions of chirped solitary pulses in a system of nonlinearly cou... more We study the stability and interactions of chirped solitary pulses in a system of nonlinearly coupled cubic Ginzburg-Landau (CGL) equations with a group-velocity mismatch between them, where each CGL equation is stabilized by linearly coupling it to an additional linear dissipative equation. In the context of nonlinear fiber optics, the model describes transmission and collisions of pulses at different wavelengths in a dual-core fiber, in which the active core is furnished with bandwidth-limited gain, while the other, passive (lossy) one is necessary for stabilization of the solitary pulses. Complete and incomplete collisions of pulses in two channels in the cases of anomalous and normal dispersion in the active core are analyzed by means of perturbation theory and direct numerical simulations. It is demonstrated that the model may readily support fully stable pulses whose collisions are quasi-elastic, provided that the group-velocity difference between the two channels exceeds a critical value. In the case of quasi-elastic collisions, the temporal shift of pulses, predicted by the analytical approach, is in semi-quantitative agrement with direct numerical results in the case of anomalous dispersion (in the opposite case, the perturbation theory does not apply). We also consider a simultaneous collision between pulses in three channels, concluding that this collision remains quasi-elastic, and the pulses remain completely stable. Thus, the model may be a starting point for the design of a stabilized wavelength-division-multiplexed (WDM) transmission system.

Research paper thumbnail of Diffraction management and elliptic discrete solitons in two-dimensional waveguide arrays

Nonlinear Guided Waves and Their Applications, 2004

We demonstrate that the linear and nonlinear dynamics of two-dimensional waveguide arrays are sig... more We demonstrate that the linear and nonlinear dynamics of two-dimensional waveguide arrays are significantly more complex than their one-dimensional counterparts. Their diffraction behavior is anisotropic allowing the existence of discrete elliptic solitons in nonlinear arrays.

Research paper thumbnail of Bloch oscillations and solitons in Discrete Ginzburg-Landau lattices

Nonlinear Guided Waves and Their Applications, 2004

We demonstrate that Bloch oscillations and discrete solitons are possible in laser arrays describ... more We demonstrate that Bloch oscillations and discrete solitons are possible in laser arrays described by Ginzburg-Landau lattices.

Research paper thumbnail of One-Dimensional Massless Dirac-Particles in Waveguide Arrays with Alternating Coupling

Conference on Lasers and Electro-Optics 2012, 2012

ABSTRACT We experimentally realized a waveguide device with alternating positive and negative cou... more ABSTRACT We experimentally realized a waveguide device with alternating positive and negative coupling and show that this geometry is an optical simulator of the conditions found for a massless relativistic particle described by the one-dimensional Dirac-equations.

Research paper thumbnail of Thermodynamic optical pressures in tight-binding nonlinear multimode photonic systems

Communications Physics

Optical forces are known to arise in a universal fashion in many and diverse physical settings. A... more Optical forces are known to arise in a universal fashion in many and diverse physical settings. As such, they are successfully employed over a wide range of applications in areas like biophotonics, optomechanics and integrated optics. While inter-elemental optical forces in few-mode photonic networks have been so far systematically analyzed, little is known, if any, as to how they manifest themselves in highly multimoded optical environments. In this work, by means of statistical mechanics, we formally address this open problem in optically thermalized weakly nonlinear heavily multimode tight-binding networks. The outlined thermodynamic formulation allows one to obtain in an elegant manner analytical results for the exerted thermodynamic pressures in utterly complex arrangements-results that are either computationally intensive or impossible to obtain otherwise. Thus, we derive simple closed-form expressions for the thermodynamic optical pressures displayed among elements, which dep...

Research paper thumbnail of Generation of Vortex Optical Pin-like Beams

We propose and demonstrate anti-difîracting vortex optical pin-like beams (VOPBs) generated by pr... more We propose and demonstrate anti-difîracting vortex optical pin-like beams (VOPBs) generated by properly modulating both the amplitude and phase of an initial laser beam in Fourier space. Such VOPBs feature an autofocusing dynamics and outperform conventional higher-order Bessel beams and abruptly autofocusing beams.

Research paper thumbnail of Demonstration of Vortex Optical Pin Beams

OSA Advanced Photonics Congress (AP) 2020 (IPR, NP, NOMA, Networks, PVLED, PSC, SPPCom, SOF), 2020

We report on vortex optical pin beams, obtained by spatially tailoring amplitude and phase profil... more We report on vortex optical pin beams, obtained by spatially tailoring amplitude and phase profile of a laser beam in Fourier space. Numerical and experimental results show controllable and anti-diffractive dynamics during long-distance propagation.

Research paper thumbnail of Coupled Circular Arrays of Optical Amplifiers

Nonlinear Guided Waves and Their Applications, 2004

ABSTRACT A circular array of optical amplifiers coupled with a central core is proposed. Nonlinea... more ABSTRACT A circular array of optical amplifiers coupled with a central core is proposed. Nonlinear losses and energy tunneling within the array elements and the core are present fascilitating the existence of highly localized modes.

Research paper thumbnail of Random-phase solitons in nonlinear periodic lattices

We predict the existence of random phase solitons in nonlinear periodic lattices. These solitons ... more We predict the existence of random phase solitons in nonlinear periodic lattices. These solitons exist when the nonlinear response time is much longer than the characteristic time of random phase fluctuations. The intensity profiles, power spectra, and statistical (coherence) properties of these stationary waves conform to the periodicity of the lattice. The general phenomenon of such solitons is analyzed in the context of nonlinear photonic lattices.

Research paper thumbnail of Controlled generation of pseudospin-mediated vortices in photonic graphene

2D materials, Jun 26, 2015

ABSTRACT We demonstrate controllable generation and destruction of pseudospin-mediated topologica... more ABSTRACT We demonstrate controllable generation and destruction of pseudospin-mediated topological charges (vortices) in the photonic analogy of graphene—optically induced honeycomb lattices (HCLs). When only one of the two sublattices is selectively excited by the probe beams that are momentum-matched onto the Dirac points, a singly-charged optical vortex emerges in the output of the symmetric conical diffraction pattern. Furthermore, flipping of the topological charge is observed as the excitation shifts from sublattice A to sublattice B. On the other hand, when both sublattices are simultaneously excited, the conical diffraction pattern becomes highly asymmetric, accompanied by interesting phenomena related to the generation of half-integer vortices and line singularities. We present four different cases of selective excitation using two different approaches; one with three input probe beams that are momentum-matched to the three K valleys, and the other with only two probe beams while the Bloch modes surrounding the third valley are excited due to Bragg reflection. Our experimental results are confirmed by numerical simulation of the paraxial wave equation with a HCL potential as well as by theoretical analysis of the two-dimensional Dirac─Weyl equations directly. These studies indicate that the lattice pseudospin is not just a mathematical formality, but rather it can manifest through its angular momentum transferred to probing optical beams.

Research paper thumbnail of Asymmetric conical diffraction and generation of non-integer phase singularities in photonic graphene

We demonstrate asymmetric conical diffraction accompanied by pseudospin-mediated non-integer phas... more We demonstrate asymmetric conical diffraction accompanied by pseudospin-mediated non-integer phase singularities when two sublattices of photonic graphene are equally excited near the Dirac points. Experimental and numerical results agree with analysis of the Dirac equation.

Research paper thumbnail of Thermodynamic optical pressures in tight-binding nonlinear multimode photonic systems

arXiv (Cornell University), Oct 13, 2022

Optical forces are known to arise in a universal fashion in many and diverse physical settings. A... more Optical forces are known to arise in a universal fashion in many and diverse physical settings. As such, they are successfully employed over a wide range of applications in areas like biophotonics, optomechanics and integrated optics. While inter-elemental optical forces in few-mode photonic networks have been so far systematically analyzed, little is known, if any, as to how they manifest themselves in highly multimoded optical environments. In this work, by means of statistical mechanics, we formally address this open problem in optically thermalized weakly nonlinear heavily multimode tight-binding networks. The outlined thermodynamic formulation allows one to obtain in an elegant manner analytical results for the exerted thermodynamic pressures in utterly complex arrangements-results that are either computationally intensive or impossible to obtain otherwise. Thus, we derive simple closed-form expressions for the thermodynamic optical pressures displayed among elements, which depend only on the internal energy as well as the coupling coefficients involved. In all cases, our theoretical results are in excellent agreement with numerical computations. Our study may pave the way towards a deeper

Research paper thumbnail of Demonstration of turbulence-resistant propagation of anti-diffracting optical beams beyond kilometer distances

Conference on Lasers and Electro-Optics, 2019

We demonstrate robust propagation of anti-diffracting optical beams through atmosphere turbulence... more We demonstrate robust propagation of anti-diffracting optical beams through atmosphere turbulence beyond kilometer distances. Such Airy-Bessel-like light beams surpass conventional Bessel beams and can, in principle, exhibit “self-focusing” in free space without any optical nonlinearity. © 2019 The Author(s)

Research paper thumbnail of Excitation spectrum of a mixture of two Bose gases confined in a ring potential with interaction asymmetry

New Journal of Physics, 2018

We study the rotational properties of a two-component Bose-Einstein condensed gas of distinguisha... more We study the rotational properties of a two-component Bose-Einstein condensed gas of distinguishable atoms which are confined in a ring potential using both the mean-field approximation, as well as the method of diagonalization of the many-body Hamiltonian. We demonstrate that the angular momentum may be given to the system either via single-particle, or 'collective' excitation. Furthermore, despite the complexity of this problem, under rather typical conditions the dispersion relation takes a remarkably simple and regular form. Finally, we argue that under certain conditions the dispersion relation is determined via collective excitation. The corresponding many-body state, which, in addition to the interaction energy minimizes also the kinetic energy, is dictated by elementary number theory.

Research paper thumbnail of Fragility of the bosonic Laughlin state

Physical Review A, 2019

When a Bose-Einstein condensate rotates in a purely harmonic potential with an angular frequency ... more When a Bose-Einstein condensate rotates in a purely harmonic potential with an angular frequency which is close to the trap frequency, its many-body state becomes highly correlated, with the most well-known being the bosonic Laughlin state. To take into account that in a real experiment no trapping potential is ever exactly harmonic, we introduce an additional weak, quartic potential and demonstrate that the Laughlin state is highly sensitive to this extra potential. Our results imply that achieving these states experimentally is essentially impossible, at least for a macroscopic atom number.

Research paper thumbnail of Valley Vortex States and Degeneracy Lifting via Photonic Higher-Band Excitation

Physical Review Letters, 2019

We demonstrate valley-dependent vortex generation in a photonic graphene. Without breaking the in... more We demonstrate valley-dependent vortex generation in a photonic graphene. Without breaking the inversion symmetry, excitation of two equivalent valleys leads to formation of an optical vortex upon Bragg-reflection to the third valley, with its chirality determined by the valley degree of freedom. Vortex-antivortex pairs with valley-dependent topological charge flipping are also observed and corroborated by numerical simulations. Furthermore, we develop a three-band effective Hamiltonian model to describe the dynamics of the coupled valleys, and find that the commonly used two-band model is not sufficient to explain the observed vortex degeneracy lifting. Such valley-polarized vortex states arise from high-band excitation without inversion symmetry breaking or synthetic-field-induced gap opening. Our results from a photonic setting may provide insight for the study of valley contrasting and Berry-phase mediated topological phenomena in other systems.

Research paper thumbnail of Spatiotemporal diffraction-free pulsed beams in free-space of the Airy and Bessel type

Optics Letters, 2017

We investigate the dynamics of spatiotemporal optical waves with one transverse dimension that ar... more We investigate the dynamics of spatiotemporal optical waves with one transverse dimension that are obtained as the intersections of the dispersion cone with a plane. We show that, by appropriate spectral excitations, the three different types of conic sections (elliptic, parabolic, and hyperbolic) can lead to optical waves of the Bessel, Airy, and modified Bessel type, respectively. We find closed form solutions that accurately describe the wave dynamics and unveil their fundamental properties.

Research paper thumbnail of Mean-field yrast spectrum and persistent currents in a two-component Bose gas with interaction asymmetry

Physical Review A, 2015

We analyze the mean-field yrast spectrum of a two-component Bose gas in the ring geometry with ar... more We analyze the mean-field yrast spectrum of a two-component Bose gas in the ring geometry with arbitrary interaction asymmetry. Of particular interest is the possibility that the yrast spectrum develops local minima at which persistent superfluid flow can occur. By analyzing the mean-field energy functional, we show that local minima can be found at plane-wave states and arise when the system parameters satisfy certain inequalities. We then go on to show that these plane-wave states can be yrast states even when the yrast spectrum no longer exhibits a local minimum. Finally, we obtain conditions which establish when the plane-wave states cease to be yrast states. Specific examples illustrating the roles played by the various interaction asymmetries are presented.

Research paper thumbnail of Specially shaped Bessel-like self-accelerating beams along predesigned trajectories

Science Bulletin, 2015

Over the past several years, spatially shaped self-accelerating beams along different trajectorie... more Over the past several years, spatially shaped self-accelerating beams along different trajectories have been studied extensively. Due to their useful properties such as resistance to diffraction, self-healing, and selfbending even in free space, these beams have attracted great attention with many proposed applications. Interestingly, some of these beams could be designed with controllable spatial profiles and thus propagate along various desired trajectories such as parabolic, snake-like, hyperbolic, hyperbolic secant, three-dimensional spiraling, and even self-propelling trajectories. Experimentally, such beams are realized typically by using a spatial light modulator so as to imprint a desired phase distribution on a Gaussian-like input wave front propagating under paraxial or nonparaxial conditions. In this paper, we provide a brief overview of our recent work on specially shaped self-accelerating beams, including Bessel-like, breathing Bessellike, and vortex Bessel-like beams. In addition, we propose and demonstrate a new type of dynamical Bessel-like beams that can exhibit not only self-accelerating but also self-propelling during propagation. Both theoretical and experimental results are presented along with a brief discussion of potential applications.

Research paper thumbnail of Stabilization of dark solitons in the cubic Ginzburg-Landau equation

Physical Review E, 2000

The existence and stability of exact continuous-wave and dark-soliton solutions to a system consi... more The existence and stability of exact continuous-wave and dark-soliton solutions to a system consisting of the cubic complex Ginzburg-Landau ͑CGL͒ equation linearly coupled with a linear dissipative equation is studied. We demonstrate the existence of vast regions in the system's parameter space associated with stable darksoliton solutions, having the form of the Nozaki-Bekki envelope holes, in contrast to the case of the conventional CGL equation, where they are unstable. In the case when the dark soliton is unstable, two different types of instability are identified. The proposed stabilized model may be realized in terms of a dual-core nonlinear optical fiber, with one core active and one passive.

Research paper thumbnail of Multichannel pulse dynamics in a stabilized Ginzburg-Landau system

Physical Review E, 2002

We study the stability and interactions of chirped solitary pulses in a system of nonlinearly cou... more We study the stability and interactions of chirped solitary pulses in a system of nonlinearly coupled cubic Ginzburg-Landau (CGL) equations with a group-velocity mismatch between them, where each CGL equation is stabilized by linearly coupling it to an additional linear dissipative equation. In the context of nonlinear fiber optics, the model describes transmission and collisions of pulses at different wavelengths in a dual-core fiber, in which the active core is furnished with bandwidth-limited gain, while the other, passive (lossy) one is necessary for stabilization of the solitary pulses. Complete and incomplete collisions of pulses in two channels in the cases of anomalous and normal dispersion in the active core are analyzed by means of perturbation theory and direct numerical simulations. It is demonstrated that the model may readily support fully stable pulses whose collisions are quasi-elastic, provided that the group-velocity difference between the two channels exceeds a critical value. In the case of quasi-elastic collisions, the temporal shift of pulses, predicted by the analytical approach, is in semi-quantitative agrement with direct numerical results in the case of anomalous dispersion (in the opposite case, the perturbation theory does not apply). We also consider a simultaneous collision between pulses in three channels, concluding that this collision remains quasi-elastic, and the pulses remain completely stable. Thus, the model may be a starting point for the design of a stabilized wavelength-division-multiplexed (WDM) transmission system.

Research paper thumbnail of Diffraction management and elliptic discrete solitons in two-dimensional waveguide arrays

Nonlinear Guided Waves and Their Applications, 2004

We demonstrate that the linear and nonlinear dynamics of two-dimensional waveguide arrays are sig... more We demonstrate that the linear and nonlinear dynamics of two-dimensional waveguide arrays are significantly more complex than their one-dimensional counterparts. Their diffraction behavior is anisotropic allowing the existence of discrete elliptic solitons in nonlinear arrays.

Research paper thumbnail of Bloch oscillations and solitons in Discrete Ginzburg-Landau lattices

Nonlinear Guided Waves and Their Applications, 2004

We demonstrate that Bloch oscillations and discrete solitons are possible in laser arrays describ... more We demonstrate that Bloch oscillations and discrete solitons are possible in laser arrays described by Ginzburg-Landau lattices.

Research paper thumbnail of One-Dimensional Massless Dirac-Particles in Waveguide Arrays with Alternating Coupling

Conference on Lasers and Electro-Optics 2012, 2012

ABSTRACT We experimentally realized a waveguide device with alternating positive and negative cou... more ABSTRACT We experimentally realized a waveguide device with alternating positive and negative coupling and show that this geometry is an optical simulator of the conditions found for a massless relativistic particle described by the one-dimensional Dirac-equations.