Linear and nonlinear optics in curved space

Batz, Sascha; Peschel, Ulf

doi:10.1103/physreva.78.043821

Cited by 95 publications

(87 citation statements)

References 19 publications

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“…In the fundamental level, this formalism help us to extend our knowledge about quantum mechanics in more general mathematical frameworks, as a coordinate free theory; in addition, the mathematical structures developed in geometric quantum mechanics have capacity for application in new domains of experimental [2][3][4]. This can be illustrated by the existence of Landau levels for motion of a charged particle under perpendicular magnetic fields which is extend to curve space [5].…”

Section: Introductionmentioning

confidence: 95%

Coherent States of Quantum Free Particle on the Spherical Space

et al. 2015

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In this paper, we study the quantum free particle on the spherical space by applying da costa approach for quantum particle on the curved space. We obtain the discrete energy eigenvalues and associated normalized eigenfunctions of the free particle on the sphere. In addition, we introduce the Gazeau-Klauder coherent states of free particle on the sphere. Then, the Gaussian coherent states is defined, which is used to describe the localized particle on the spherical space. Finally, we study the relation between the f -deformed coherent states and Gazeau-Klauder ones for this system.

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Section: Introductionmentioning

confidence: 95%

Coherent States of Quantum Free Particle on the Spherical Space

et al. 2015

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“…Recent years have witnessed plenty of physical systems designed to simulate GR phenomena in laboratory, including electromagnetic waves [20][21][22][23][24], flexural waves [25], etc. Among them, investigation of optics on curved surface is a burgeoning attempt [26]. By discarding one spatial dimension, researchers are able to fabricate the geometrical structure of two-dimensional space straightforwardly, while existence of massive body is not necessary.…”

Section: Introductionmentioning

confidence: 99%

“…In the latest decade various concepts have been reconsidered and reported, such as solitons [28], evolution of speckle pattern [29], spatially accelerating wave packets following nongeodesic trajectories [30,31], topological phases in curved space photonic lattices [32], phase and group velocity of wave packets [33], Wolf effect of light spectrum [34,35], etc. Specially, in a pioneering work [26], Schrödinger equation for linear propagation on curved space with constant Gaussian curvature is derived, which is in essence the wave equation under paraxial approximation, and one of whose solutions is the fundamental notion in optics, Gaussian beam.…”

Section: Introductionmentioning

confidence: 99%

Gouy and spatial-curvature-induced phase shifts of light in two-dimensional curved space

Wang

2019

New J. Phys.

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Gouy phase is the axial phase anomaly of converging light waves discovered over one century ago, and is so far widely studied in various systems. In this work, we have theoretically calculated Gouy phase of light beams in both paraxial and nonparaxial regime on two-dimensional curved surface by generalizing angular spectrum method. We find that curvature of surface will also introduce an extra phase shift, which is named as spatial curvature-induced (SCI) phase. The behaviors of both phase shifts are illustrated on two typical surfaces of revolution, circular truncated cone and spherical surface. Gouy phase evolves slower on surface with greater spatial curvature on circular truncated cone, which is however opposite on spherical surface, while SCI phase evolves faster with curvature on both surfaces. On circular truncated cone, both phase shifts approach to a limit value along propagation, which does not happen on spherical surface due to the existence of singularity on the pole. An interpretation is presented to explain this peculiar phenomenon. Finally we also provide the analytical expression of paraxial Gaussian beam on general SORs. By comparing the result with the exact method we find the analytical expression is valid under the approximation that beam waist and scale of surface are beyond order of wavelength. We expect this work will enhance the comprehension about the behavior of electromagnetic wave in curved space, and further contribute to the study of general relativity phenomena in laboratory.

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“…This concept was introduce into EM waves [3], where pioneering experiments were carried out with coherent light propagating in a film waveguide attached to the curved surface area of a three-dimensional body. Naturally, general wavepackets evolving in curved space would propagate along geodesics, which are the shortest optical path (analogous to straight lines in flat geometry).…”

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confidence: 99%

Linear and Nonlinear Accelerating Beams in Curved Space

et al. 2013

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We present the first study on linear and nonlinear accelerating beams in curved space. These shape-invariant wavepackets propagate along various trajectories arising from the interplay between the curvature of space and the interference effects.The complex dynamics of particles and of electromagnetic (EM) waves in curved space time is still inaccessible to laboratory experiments. Over the years, many physical systems have been suggested to demonstrate analogies to general relativity phenomena. Among these, optical systems have had a major success. For example, metamaterials enable creating artificial black holes, by engineering the (EM) properties of the material through which light is propagating [1]. Another intriguing suggestion was to use a moving dielectric medium that acts as an effective gravitational field on the light. This idea was demonstrated experimentally by employing ultrashort pulses in an optical fiber to create an artificial event horizon [2].However, it would certainly be intriguing to create curved space by engineering the geometry of the space itself. This concept was introduce into EM waves [3], where pioneering experiments were carried out with coherent light propagating in a film waveguide attached to the curved surface area of a three-dimensional body. Naturally, general wavepackets evolving in curved space would propagate along geodesics, which are the shortest optical path (analogous to straight lines in flat geometry). But, do wavepackets propagating in curved space have to follow special geodesic paths, or can they exhibit other kinds of propagation?Here, we show that wavepackets can exhibit shape-invariant evolution in curved space, propagating in trajectories reflecting interplay between the curvature of space and interference effects arising from initial conditions. We specifically present spatially-accelerating wavepackets that propagate on a general surface of revolution, but the concept is universal, applying to a general setting of curved space.Accelerating wavepackets were introduced into optics in 2007, demonstrating accelerating Airy beams [4]. This area has drawn extensive interest and initiated various new additional directions, such as accelerating ultrashort pulses and light bullets, [5] and accelerating beams in nonlinear media [6,7]. These ideas were followed by many applications ranging from manipulating micro-particles [8,9] to self-bending plasma channel.Here, we present the first study on linear and nonlinear accelerating beams in curved space. These beams, which are solutions to the paraxial equation in curved space, propagate on a general surface of revolution following a variety of trajectories with their intensity profile scaled in a self-similar fashion. These unique trajectories arise from the interplay between the curvature of space and the interference effect set by a proper initial condition. We show that these new solutions allow accelerating super-oscillations, whereby the local spatial frequency is considerably larger than the spatial frequencies carrie...

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Linear and nonlinear optics in curved space

Cited by 95 publications

References 19 publications

Coherent States of Quantum Free Particle on the Spherical Space

Coherent States of Quantum Free Particle on the Spherical Space

Gouy and spatial-curvature-induced phase shifts of light in two-dimensional curved space

Linear and Nonlinear Accelerating Beams in Curved Space

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