Esther Brainin (Ruppin Academic Center), Efrat Neter (Ruppin Academic Center) Assessing the reada... more Esther Brainin (Ruppin Academic Center), Efrat Neter (Ruppin Academic Center) Assessing the readability and cultural sensitivity of health information on the Web Hadas Weinberger (Holon Institute of Technology), Boaz Tadmor (Beilinson Hospital), Pierre Singer (Beilinson Hospital) Healthcare Decision-making: the generative dance between chaos and control at the point of care for the complex-patient 12:20-13:45 Lunch 4 13:45-15:15 Parallel sessions D-F
We propose complex networks constructed from interacting vector solitons. Within soliton-based ne... more We propose complex networks constructed from interacting vector solitons. Within soliton-based networks, we demonstrate memory effects that are greatly enhanced by noise, as well as spontaneous entire network self-synchronization effects.
We present the spatially accelerating solutions of the Maxwell equations. Such nonparaxial beams ... more We present the spatially accelerating solutions of the Maxwell equations. Such nonparaxial beams accelerate in a circular trajectory, thus generalizing the concept of Airy beams.
We present a general theory of three-dimensional nonparaxial spatiallyaccelerating waves of the M... more We present a general theory of three-dimensional nonparaxial spatiallyaccelerating waves of the Maxwell equations. These waves constitute a two-dimensional structure exhibiting shape-invariant propagation along semicircular trajectories. We provide classification and characterization of possible shapes of such beams, expressed through the angular spectra of parabolic, oblate and prolate spheroidal fields. Our results facilitate the design of accelerating beams with novel structures, broadening scope and potential applications of accelerating beams.
Optics InfoBase is the Optical Society's online library for flagship journals, partnered and... more Optics InfoBase is the Optical Society's online library for flagship journals, partnered and copublished journals, and recent proceedings from OSA conferences.
ABSTRACT We present a new approach for optimizing a 3D non-paraxial volume for multiphoton flores... more ABSTRACT We present a new approach for optimizing a 3D non-paraxial volume for multiphoton florescence microscopy. Our optimized solutions demonstrate volume reduction of up to 6.5, compared to the best current design for three-photon microscopy.
ABSTRACT In 1958, a revolutionary paper by Aharonov and Bohm predicted a phase difference between... more ABSTRACT In 1958, a revolutionary paper by Aharonov and Bohm predicted a phase difference between two parts of an electron wavefunction even when being confined to a regime with no EM field. The Aharonov-Bohm effect was groundbreaking: proving that the EM vector potential is a real physical quantity, affecting the outcome of experiments not only through the EM fields extracted from it. But is the EM potential a real necessity for an Aharonov-Bohm-type effect? Can it exist in a potential-free system such as free-space? Here, we find self-accelerating wavepackets that are solutions of the free Dirac equation, for massive/massless fermions/bosons. These accelerating Dirac particles mimic the dynamics of a free-charge moving under a ``virtual'' EM field, even though no field is acting and there is no charge: the entire dynamics is a direct result of the initial conditions. We show that such particles display an effective Aharonov-Bohm effect caused by exactly the same ``virtual'' potential that also ``causes'' the acceleration. Altogether, along the trajectory, there is no way to distinguish between a real force and the self-induced force - it is real by all measurable quantities. This proves that one can create all effects induced by EM fields by only controlling the initial conditions of a wave pattern, while the dynamics is in free-space. These phenomena can be observed in various settings: e.g., optical waves in honeycomb photonic lattices or in hyperbolic metamaterials, and matter waves in honeycomb interference structures.
We study networks made up of interacting solitons (solitonets), and find that their dynamics exhi... more We study networks made up of interacting solitons (solitonets), and find that their dynamics exhibits stochastic recurrent behavior, independent of the topology, where the interaction rule at the single-node level can be used to predict the dynamics of the entire network. The ideas are general, not specific to solitonets: they apply to many kinds of networks whose dynamics converges to a recurrent structure.
We show that optical nonlinearities allow sub-wavelength beams to propagate in circular trajector... more We show that optical nonlinearities allow sub-wavelength beams to propagate in circular trajectories without being attenuated in spite of their partially evanescent spectrum. Such beams are exact solutions to Maxwell's equations with Kerr or saturable nonlinearity.
We present shape-preserving self-accelerating beams of Maxwell's equations with optical nonlinear... more We present shape-preserving self-accelerating beams of Maxwell's equations with optical nonlinearities. Such beams are exact solutions to Maxwell's equations with Kerr or saturable nonlinearity. The nonlinearity contributes to self-trapping and causes backscattering. Those effects, together with diffraction effects, work to maintain shape-preserving acceleration of the beam on a circular trajectory. The backscattered beam is found to be a key issue in the dynamics of such highly non-paraxial nonlinear beams. To study that, we develop two new techniques: projection operator separating the forward and backward waves, and reverse simulation. Finally, we discuss the possibility that such beams would reflect themselves through the nonlinear effect, to complete a 'U' shaped trajectory.
Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences, 2009
We propose complex networks made with interacting fields, where the interaction dynamics at each ... more We propose complex networks made with interacting fields, where the interaction dynamics at each individual node in the system has infinite degrees of freedom. We construct networks, based on the interactions between vector solitons, whose dynamics are governed by conservation laws. Hence, the dimensionality of the dynamics at each node is determined by the initial conditions, making the problem tractable. We present examples of small and large soliton-based networks, and demonstrate memory effects within them that are enormously enhanced by noise. Finally, we demonstrate that such networks, with infinite-dimensional dynamics, can exhibit spontaneous self-synchronization effects.
We present self-accelerating self-trapped beams in self-focusing and self-defocusing Kerr and sat... more We present self-accelerating self-trapped beams in self-focusing and self-defocusing Kerr and saturable media. Such beams are stable under self-defocusing and weak self-focusing, whereas for strong self focusing they off-shoot solitons while their main lobe continues accelerating.
In this note we give a new upper bound for the Laplacian eigenvalues of an unweighted graph. Let ... more In this note we give a new upper bound for the Laplacian eigenvalues of an unweighted graph. Let $G$ be a simple graph on $n$ vertices. Let $d_{m}(G)$ and $\lambda_{m+1}(G)$ be the $m$-th smallest degree of $G$ and the $m+1$-th smallest Laplacian eigenvalue of $G$ respectively. Then $ \lambda_{m+1}(G)\leq d_{m}(G)+m-1 $ for $\bar{G} \neq K_{m}+(n-m)K_1 $. We also introduce upper and lower bound for the Laplacian eigenvalues of weighted graphs, and compare it with the special case of unweighted graphs.
We show that new families of diffraction-free nonparaxial accelerating optical beams can be gener... more We show that new families of diffraction-free nonparaxial accelerating optical beams can be generated by considering the symmetries of the underlying vectorial Helmholtz equation. Both two-dimensional transverse electric and magnetic accelerating wave fronts are possible, capable of moving along elliptic trajectories. Experimental results corroborate these predictions when these waves are launched from either the major or minor axis of the ellipse. In addition, three-dimensional spherical nondiffracting field configurations are presented along with their evolution dynamics. Finally, fully vectorial self-similar accelerating optical wave solutions are obtained via oblate-prolate spheroidal wave functions. In all occasions, these effects are illustrated via pertinent examples.
We study accelerating and decelerating shape-preserving temporal Airy wave-packets propagating in... more We study accelerating and decelerating shape-preserving temporal Airy wave-packets propagating in dispersive media. We explore the effects of causality, and find that, whereas decelerating pulses can asymptotically reach zero group velocity, pulses that accelerate towards infinite group velocity inevitably break up, after a specific critical point. The trajectories and the features of causal pulses are analyzed, along with the requirements for the existence of the critical point and experimental schemes for its observation. Finally, we show that causality imposes similar effects on accelerating pulses in the presence of local Kerr-like nonlinearities.
We present the experimental observation of 1D and 2D self-accelerating nonlinear beams in quadrat... more We present the experimental observation of 1D and 2D self-accelerating nonlinear beams in quadratic media, which are also the first nonlinear self-accelerating beams in any symmetric nonlinearity. Notably, we show that the intensity peaks of the first and second harmonics are asynchronous with respect to one another, but the coupled harmonics exhibit joint acceleration within the nonlinear medium. Finally, we demonstrate the impact of self-healing effects on the jointly accelerating first and second harmonics.
We identify periodic solitons in nonlocal nonlinear media: multi-hump soliton solutions propagati... more We identify periodic solitons in nonlocal nonlinear media: multi-hump soliton solutions propagating in a fully periodic fashion. We also demonstrate recurrences and breathers whose evolution is statistically periodic and discuss why some systems support periodic solitons while others do not.
Esther Brainin (Ruppin Academic Center), Efrat Neter (Ruppin Academic Center) Assessing the reada... more Esther Brainin (Ruppin Academic Center), Efrat Neter (Ruppin Academic Center) Assessing the readability and cultural sensitivity of health information on the Web Hadas Weinberger (Holon Institute of Technology), Boaz Tadmor (Beilinson Hospital), Pierre Singer (Beilinson Hospital) Healthcare Decision-making: the generative dance between chaos and control at the point of care for the complex-patient 12:20-13:45 Lunch 4 13:45-15:15 Parallel sessions D-F
We propose complex networks constructed from interacting vector solitons. Within soliton-based ne... more We propose complex networks constructed from interacting vector solitons. Within soliton-based networks, we demonstrate memory effects that are greatly enhanced by noise, as well as spontaneous entire network self-synchronization effects.
We present the spatially accelerating solutions of the Maxwell equations. Such nonparaxial beams ... more We present the spatially accelerating solutions of the Maxwell equations. Such nonparaxial beams accelerate in a circular trajectory, thus generalizing the concept of Airy beams.
We present a general theory of three-dimensional nonparaxial spatiallyaccelerating waves of the M... more We present a general theory of three-dimensional nonparaxial spatiallyaccelerating waves of the Maxwell equations. These waves constitute a two-dimensional structure exhibiting shape-invariant propagation along semicircular trajectories. We provide classification and characterization of possible shapes of such beams, expressed through the angular spectra of parabolic, oblate and prolate spheroidal fields. Our results facilitate the design of accelerating beams with novel structures, broadening scope and potential applications of accelerating beams.
Optics InfoBase is the Optical Society's online library for flagship journals, partnered and... more Optics InfoBase is the Optical Society's online library for flagship journals, partnered and copublished journals, and recent proceedings from OSA conferences.
ABSTRACT We present a new approach for optimizing a 3D non-paraxial volume for multiphoton flores... more ABSTRACT We present a new approach for optimizing a 3D non-paraxial volume for multiphoton florescence microscopy. Our optimized solutions demonstrate volume reduction of up to 6.5, compared to the best current design for three-photon microscopy.
ABSTRACT In 1958, a revolutionary paper by Aharonov and Bohm predicted a phase difference between... more ABSTRACT In 1958, a revolutionary paper by Aharonov and Bohm predicted a phase difference between two parts of an electron wavefunction even when being confined to a regime with no EM field. The Aharonov-Bohm effect was groundbreaking: proving that the EM vector potential is a real physical quantity, affecting the outcome of experiments not only through the EM fields extracted from it. But is the EM potential a real necessity for an Aharonov-Bohm-type effect? Can it exist in a potential-free system such as free-space? Here, we find self-accelerating wavepackets that are solutions of the free Dirac equation, for massive/massless fermions/bosons. These accelerating Dirac particles mimic the dynamics of a free-charge moving under a ``virtual'' EM field, even though no field is acting and there is no charge: the entire dynamics is a direct result of the initial conditions. We show that such particles display an effective Aharonov-Bohm effect caused by exactly the same ``virtual'' potential that also ``causes'' the acceleration. Altogether, along the trajectory, there is no way to distinguish between a real force and the self-induced force - it is real by all measurable quantities. This proves that one can create all effects induced by EM fields by only controlling the initial conditions of a wave pattern, while the dynamics is in free-space. These phenomena can be observed in various settings: e.g., optical waves in honeycomb photonic lattices or in hyperbolic metamaterials, and matter waves in honeycomb interference structures.
We study networks made up of interacting solitons (solitonets), and find that their dynamics exhi... more We study networks made up of interacting solitons (solitonets), and find that their dynamics exhibits stochastic recurrent behavior, independent of the topology, where the interaction rule at the single-node level can be used to predict the dynamics of the entire network. The ideas are general, not specific to solitonets: they apply to many kinds of networks whose dynamics converges to a recurrent structure.
We show that optical nonlinearities allow sub-wavelength beams to propagate in circular trajector... more We show that optical nonlinearities allow sub-wavelength beams to propagate in circular trajectories without being attenuated in spite of their partially evanescent spectrum. Such beams are exact solutions to Maxwell's equations with Kerr or saturable nonlinearity.
We present shape-preserving self-accelerating beams of Maxwell's equations with optical nonlinear... more We present shape-preserving self-accelerating beams of Maxwell's equations with optical nonlinearities. Such beams are exact solutions to Maxwell's equations with Kerr or saturable nonlinearity. The nonlinearity contributes to self-trapping and causes backscattering. Those effects, together with diffraction effects, work to maintain shape-preserving acceleration of the beam on a circular trajectory. The backscattered beam is found to be a key issue in the dynamics of such highly non-paraxial nonlinear beams. To study that, we develop two new techniques: projection operator separating the forward and backward waves, and reverse simulation. Finally, we discuss the possibility that such beams would reflect themselves through the nonlinear effect, to complete a 'U' shaped trajectory.
Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences, 2009
We propose complex networks made with interacting fields, where the interaction dynamics at each ... more We propose complex networks made with interacting fields, where the interaction dynamics at each individual node in the system has infinite degrees of freedom. We construct networks, based on the interactions between vector solitons, whose dynamics are governed by conservation laws. Hence, the dimensionality of the dynamics at each node is determined by the initial conditions, making the problem tractable. We present examples of small and large soliton-based networks, and demonstrate memory effects within them that are enormously enhanced by noise. Finally, we demonstrate that such networks, with infinite-dimensional dynamics, can exhibit spontaneous self-synchronization effects.
We present self-accelerating self-trapped beams in self-focusing and self-defocusing Kerr and sat... more We present self-accelerating self-trapped beams in self-focusing and self-defocusing Kerr and saturable media. Such beams are stable under self-defocusing and weak self-focusing, whereas for strong self focusing they off-shoot solitons while their main lobe continues accelerating.
In this note we give a new upper bound for the Laplacian eigenvalues of an unweighted graph. Let ... more In this note we give a new upper bound for the Laplacian eigenvalues of an unweighted graph. Let $G$ be a simple graph on $n$ vertices. Let $d_{m}(G)$ and $\lambda_{m+1}(G)$ be the $m$-th smallest degree of $G$ and the $m+1$-th smallest Laplacian eigenvalue of $G$ respectively. Then $ \lambda_{m+1}(G)\leq d_{m}(G)+m-1 $ for $\bar{G} \neq K_{m}+(n-m)K_1 $. We also introduce upper and lower bound for the Laplacian eigenvalues of weighted graphs, and compare it with the special case of unweighted graphs.
We show that new families of diffraction-free nonparaxial accelerating optical beams can be gener... more We show that new families of diffraction-free nonparaxial accelerating optical beams can be generated by considering the symmetries of the underlying vectorial Helmholtz equation. Both two-dimensional transverse electric and magnetic accelerating wave fronts are possible, capable of moving along elliptic trajectories. Experimental results corroborate these predictions when these waves are launched from either the major or minor axis of the ellipse. In addition, three-dimensional spherical nondiffracting field configurations are presented along with their evolution dynamics. Finally, fully vectorial self-similar accelerating optical wave solutions are obtained via oblate-prolate spheroidal wave functions. In all occasions, these effects are illustrated via pertinent examples.
We study accelerating and decelerating shape-preserving temporal Airy wave-packets propagating in... more We study accelerating and decelerating shape-preserving temporal Airy wave-packets propagating in dispersive media. We explore the effects of causality, and find that, whereas decelerating pulses can asymptotically reach zero group velocity, pulses that accelerate towards infinite group velocity inevitably break up, after a specific critical point. The trajectories and the features of causal pulses are analyzed, along with the requirements for the existence of the critical point and experimental schemes for its observation. Finally, we show that causality imposes similar effects on accelerating pulses in the presence of local Kerr-like nonlinearities.
We present the experimental observation of 1D and 2D self-accelerating nonlinear beams in quadrat... more We present the experimental observation of 1D and 2D self-accelerating nonlinear beams in quadratic media, which are also the first nonlinear self-accelerating beams in any symmetric nonlinearity. Notably, we show that the intensity peaks of the first and second harmonics are asynchronous with respect to one another, but the coupled harmonics exhibit joint acceleration within the nonlinear medium. Finally, we demonstrate the impact of self-healing effects on the jointly accelerating first and second harmonics.
We identify periodic solitons in nonlocal nonlinear media: multi-hump soliton solutions propagati... more We identify periodic solitons in nonlocal nonlinear media: multi-hump soliton solutions propagating in a fully periodic fashion. We also demonstrate recurrences and breathers whose evolution is statistically periodic and discuss why some systems support periodic solitons while others do not.
Uploads
Papers by Ido Kaminer