Ermakov–Lewis symmetry in photonic lattices

Rodríguez-Lara, B. M.; Aleahmad, Parinaz; Moya‐Cessa, H.; Christodoulides, Demetrios N.

doi:10.1364/ol.39.002083

Cited by 31 publications

(56 citation statements)

References 19 publications

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“…This symmetry based approach allowed us to analyzed the characteristics of these photonic lattices straight from the impulse functions; in particular, their periodicity or lack of it. We want to emphasize the fact that the propagator for any given tight-binding array of photonic waveguides may be calculated in this way as long as the dynamical group is found, even in the case of arrays were the parameters depend on the propagation distance [11,12]. Furthermore, these photonic lattices can be seen as optical simulators of a class of Gilmore-Perelomov generalized coherent states.…”

Section: Discussionmentioning

confidence: 99%

Gilmore-Perelomov symmetry based approach to photonic lattices

Vergara

Rodríguez-Lara

2015

Opt. Express

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We revisit electromagnetic field propagation through tight-binding arrays of coupled photonic waveguides, with properties independent of the propagation distance, and recast it as a symmetry problem. We focus our analysis on photonic lattices with underlying symmetries given by three well-known groups, SU (2), SU (1, 1) and Heisenberg-Weyl, to show that disperssion relations, normal states and impulse functions can be constructed following a Gilmore-Perelomov coherent state approach. Furthermore, this symmetry based approach can be followed for each an every lattice with an underlying symmetry given by a dynamical group.

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Section: Discussionmentioning

confidence: 99%

Gilmore-Perelomov symmetry based approach to photonic lattices

Vergara

Rodríguez-Lara

2015

Opt. Express

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“…3) serve as testbed for observing some intriguing phenomena that were first predicted theoretically in the context of condensed matter such as Bloch oscillations [75][76][77][78], dynamic localization [79,80], Anderson localization [81] and more recently topological insulators [82][83][84][85]. Additionally, the mathematical analogy between discrete arrays and quantum optics has been also recently investigated [86,87].…”

Section: Symmetries In Discrete Photonic Systemsmentioning

confidence: 99%

Symmetry in optics and photonics: a group theory approach

Rodríguez-Lara¹,

El‐Ganainy²,

Guerrero³

2018

Science Bulletin

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Group theory (GT) provides a rigorous framework for studying symmetries in various disciplines in physics ranging from quantum field theories and the standard model to fluid mechanics and chaos theory. To date, the application of such a powerful tool in optical physics remains limited. Over the past few years however, several quantum-inspired symmetry principles (such as parity-time invariance and supersymmetry) have been introduced in optics and photonics for the first time. Despite the intense activities in these new research directions, only few works utilized the power of group theory. Motivated by this status quo, here we present a brief overview of the application of GT in optics, deliberately choosing examples that illustrate the power of this tool in both continuous and discrete setups. We hope that this review will stimulate further research that exploits the full potential of GT for investigating various symmetry paradigms in optics, eventually leading to new photonic devices. arXiv:1803.00121v1 [physics.optics]

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“…Photonic lattices provide a solid platform for the simulation of relativistic and quantum physics [1][2][3][4]. The use of finite or pseudo-infinite arrays, with an adequate set of effective refractive indices and coupling parameters, allows the optical realization of compact, SU (N ), and non-compact groups, SU (1, 1), for example [5][6][7]. The ability to classify photonic lattices by their underlying symmetry opens the door to the simulation of a large class of quantum phenomena and the use of symmetries to design integrated photonic devices.…”

Section: Introductionmentioning

confidence: 99%

Optical finite representation of the Lorentz group

Rodríguez-Lara¹,

Guerrero²

2015

Opt. Lett.

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We present a class of photonic lattices with an underlying symmetry given by a finite-dimensional representation of the 2+1D Lorentz group. In order to construct such a finite-dimensional representation of a non-compact group, we have to design a PT -symmetric optical structure. Thus, the array of coupled waveguides may keep or break PT -symmetry, leading to a device that behaves like an oscillator or directional amplifier, respectively. We show that the so-called linear PT -symmetric dimer belongs to this class of photonic lattices. * bmlara@inaoep.mx 1 arXiv:1508.05419v1 [physics.optics]

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Ermakov–Lewis symmetry in photonic lattices

Cited by 31 publications

References 19 publications

Gilmore-Perelomov symmetry based approach to photonic lattices

Gilmore-Perelomov symmetry based approach to photonic lattices

Symmetry in optics and photonics: a group theory approach

Optical finite representation of the Lorentz group

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