Solitons in curved space of constant curvature

Batz, Sascha; Peschel, Ulf

doi:10.1103/physreva.81.053806

Cited by 35 publications

(41 citation statements)

References 15 publications

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“…Here H and K are extrinsic and intrinsic curvature, respectively, whose effects have been investigated in Ref. [30]. The term H 2 − K, which is known as geometric potential, shows influence of curved space on wave equation, however, in flat space both H and K are vanishing.…”

Section: Basic Theorymentioning

confidence: 99%

“…Dynamics of electromagnetic waves on curved surfaces was carried out in optics about a decade ago [29]. Since then light in curved space has been investigated in various systems [30][31][32][33][34][35][36][37][38][39][40]. For example, wave packets propagating along nongeodesic trajectories on surfaces of revolution (SOR), demonstrating the interaction between curvature and interference effect, is studied both theoretically and experimentally [32,33].…”

Section: Introductionmentioning

confidence: 99%

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Generalization of Wolf effect of light on arbitrary two-dimensional surface of revolution

Xu¹,

Abbas²,

Wang³

2018

Opt. Express

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Investigation of physics on two-dimensional curved surface has significant meaning in study of general relativity, inasmuch as its realizability in experimental analogy and verification of faint gravitational effects in laboratory. Several phenomena about dynamics of particles and electromagnetic waves have been explored on curved surfaces. Here we consider Wolf effect, a phenomenon of spectral shift due to the fluctuating nature of light fields, on an arbitrary surface of revolution (SOR).The general expression of the propagation of partially coherent beams propagating on arbitrary SOR is derived and the corresponding evolution of light spectrum is also obtained. We investigate the extra influence of surface topology on spectral shift by defining two quantities, effective propagation distance and effective transverse distance, and compare them with longitudinal and transverse proper lengths. Spectral shift is accelerated when the defined effective quantities are greater than real proper lengths, and vice versa. We also employ some typical SORs, cylindrical surfaces, conical surfaces, SORs generated by power function and periodic peanut-shell shapes, as examples to provide concrete analyses. This work generalizes the research of Wolf effect to arbitrary SORs, and provides a universal method for analyzing properties of propagation compared with that in flat space for any SOR whose topology is known.

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Section: Basic Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalization of Wolf effect of light on arbitrary two-dimensional surface of revolution

Xu¹,

Abbas²,

Wang³

2018

Opt. Express

View full text Add to dashboard Cite

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“…Experimentally it can be realized by covering a thin layer of waveguide on surface [27]. 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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“…The introduction of curved geometry allows to control and design lasing modes in the nonlinear regime.Studies on the effect of geometry on wave propagation can be tracked back to Lord Rayleigh in the early theory of sound [1], and extend to recent investigation as, for example, analogs of gravity in Bose-Einstein condensates [2], optical event horizon in fiber solitons [3,4], Anderson localization [5], random lasing [6] and celestial mechanics in metamaterials with transformation optics [7][8][9][10]. In addition to linear optics in curved space [11], geometrical constraints affect shape preserving wave packets, including localized solitary waves [12], extended Airy beams [13], and shock waves [14,15]. Curvature also triggers localization by trapping the wave in extremely deformed regions [16].The effect of geometry on nonlinear phenomena suggests that a confining structure may alter the conditions for observing spatial or temporal solitary waves, which are due to the nonlinear compensation of linear diffraction, or dispersion effects [17].…”

mentioning

confidence: 99%

Lasing on nonlinear localized waves in curved geometry

Hong¹,

Lin

Chang³

et al. 2018

Advanced Photonics 2018 (BGPP, IPR, NP, NOMA, Sensors, Networks, SPPCom, SOF)

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The use of geometrical constraints opens many new perspectives in photonics and in fundamental studies of nonlinear waves. By implementing surface structures in vertical cavity surface emitting lasers as manifolds for curved space, we experimentally study the impacts of geometrical constraints on nonlinear wave localization. We observe localized waves pinned to the maximal curvature in an elliptical-ring, and confirm the reduction in the localization length of waves by measuring near and far field patterns, as well as the corresponding dispersion relation. Theoretically, analyses based on a dissipative model with a parabola curve give good agreement remarkably to experimental measurement on the transition from delocalized to localized waves. The introduction of curved geometry allows to control and design lasing modes in the nonlinear regime.Studies on the effect of geometry on wave propagation can be tracked back to Lord Rayleigh in the early theory of sound [1], and extend to recent investigation as, for example, analogs of gravity in Bose-Einstein condensates [2], optical event horizon in fiber solitons [3,4], Anderson localization [5], random lasing [6] and celestial mechanics in metamaterials with transformation optics [7][8][9][10]. In addition to linear optics in curved space [11], geometrical constraints affect shape preserving wave packets, including localized solitary waves [12], extended Airy beams [13], and shock waves [14,15]. Curvature also triggers localization by trapping the wave in extremely deformed regions [16].The effect of geometry on nonlinear phenomena suggests that a confining structure may alter the conditions for observing spatial or temporal solitary waves, which are due to the nonlinear compensation of linear diffraction, or dispersion effects [17]. In general, self-localized nonlinear waves require an extra formation power to bifurcate from the linear modes [18], but geometrical constraints may reduce or cancel this threshold. In this work, we use the vertical cavity surface emitting lasers (VC-SELs) as a platform and fabricate a series of curved surfaces, including circular-ring and elliptical-ring cavities, as well as a reference "cold" device with no trapping potential. By introducing symmetry-breaking in geometry, i.e., passing from a circular-ring to an elliptical one, we realize experimentally lasing on nonlinear localized waves when the ellipticity of the ring is larger than a critical value [19]. With different curved geometries, we measure the corresponding lasing characteristics both in the near and far fields, as well as the dispersion relation, to verify the localized modes pinned at the maximal curvature. With state-of-the-art semiconductor technologies, microcavities in VCSELs have allowed small mode volumes and ultrahigh qualify factors, for applications from sensors, optical interconnects, printers, optical storages, FIG. 1. (a) Schematic diagram of our electrically driven GaAs-based vertical cavity surface emitting laser (VCSEL) with a curved potential on the emissio...

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Solitons in curved space of constant curvature

Cited by 35 publications

References 15 publications

Generalization of Wolf effect of light on arbitrary two-dimensional surface of revolution

Generalization of Wolf effect of light on arbitrary two-dimensional surface of revolution

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

Lasing on nonlinear localized waves in curved geometry

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