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 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.
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 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.
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