Dynamic trapping of light in modulated waveguide lattices
Open accessAbstract
A discrete analogue of the dynamic (Kapitza) trapping effect, known for classical and quantum particles in rapidly oscillating potentials, is proposed for light waves in modulated graded-index waveguide lattices. In particular, it is shown that, while a graded-index potential in a nonmodulated waveguide lattice can confine light at either normal or Bragg angle incidence, periodic modulation of the potential in the longitudinal direction enables one to trap optical beams at both normal and Bragg incidence angles.
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Klein tunneling arises from the existence of negative-energy solutions of the Dirac equation and requires a potential step height ΔV of the order of twice the rest energy mc2 of the electron.
“Such a transparency effect, originally predicted by Klein [26] and referred to as Klein tunneling (KT), arises from the existence of negative-energy solutions of the Dirac equation and requires a potential step height ∆V of the order of twice the rest energy mc 2 of the electron [49].”
From Classical simulation of relativistic quantum mechanics in periodic optical structures (2011) · cites this paper as [49]
The discussion of dynamical trapping (pp. 1–3) concerns light in modulated waveguide lattices; its negative quasienergies are those of Floquet states, not negative-energy solutions of the Dirac equation. Searches for Klein tunneling, the Dirac equation, and a potential step of roughly twice the electron rest energy found no passage addressing the attributed claim. (LLM, conf=0.76)
Experimental — accuracy not yet measuredEq.(16) is formally analogous to the one-dimensional Dirac equation with ħ=c=1 in presence of an external electrostatic potential V(z), m playing the role of a dimensionless and generally space-dependent rest mass.
“In its present form, Eq.(16) is formally analogous to the one-dimensional Dirac equation with ¯ h = c = 1 in presence of an external electrostatic potential V ( z ), m playing the role of a dimensionless (and generally space-dependent) rest mass (see, for instance, [49,51]).”
From Classical simulation of relativistic quantum mechanics in periodic optical structures (2011) · cites this paper as [49]
The discussion on p. 2 describes a Schrödinger-type equation for a modulated waveguide lattice, not a one-dimensional Dirac analogy. Searches of our copy for “Dirac equation,” “rest mass,” and “Eq. (16)” found no passage addressing the claimed analogy or the role of m. (LLM, conf=0.75)
Experimental — accuracy not yet measuredSauter showed that to observe barrier transparency the potential increase ΔV ≃ eEl should occur over a distance l of the order or smaller than the Compton wavelength λC, the transmission probability rapidly decaying toward zero for a smoother potential increase.
“Sauter showed that to observe barrier transparency the potential increase ∆V ≃ eEl should occur over a distance l of the order or smaller than the Compton wavelength λ C = ¯ h/ ( mc ), the transmission probability rapidly decaying toward zero for a smoother potential increase [49,50,51].”
From Classical simulation of relativistic quantum mechanics in periodic optical structures (2011) · cites this paper as [49]
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Cites
Quantum-optical analogies using photonic structures
Longhi, S. (2009) · Laser & Photonics Reviews · doi:10.1002/lpor.200810055 · Cited by 725 · see citing works
Self-citationObservation of Dynamic Localization in Periodically Curved Waveguide Arrays
Longhi, S., Marangoni, M., Lobino, M., Ramponi, R., Laporta, P., Cianci, E., & Foglietti, V. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.243901 · Cited by 357 · see citing works
Self-citationAnomalous Refraction and Diffraction in Discrete Optical Systems
Pertsch, T., Zentgraf, T., Peschel, U., Bräuer, A., & Lederer, F. (2002) · Physical Review Letters · doi:10.1103/physrevlett.88.093901 · Cited by 323 · see citing works
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Research works printed but not linked: 1
- [18]18. L.D. Landau and E.M. Lifshitz, Mechanics (Pergamon, Oxford, 1960), pp. 93-95.
Cited by
Sorted by citations
Classical simulation of relativistic quantum mechanics in periodic optical structures
Longhi, S. (2011) · Applied Physics B · doi:10.1007/s00340-011-4628-7 · Cited by 72 · see citing works
Self-citation
- Authors
- Longhi, S.
- Affiliations
- Politecnico di Milano (IT)
- Corresponding author
- Longhi, Stefano
- ORCID
- Longhi, Stefano
- Venue
- Optics Letters
- Publisher
- Optica Publishing Group
- Published
- 2011-03-08
- Volume
- 36
- Issue
- 6
- Pages
- 819
- ISSN
- 0146-9592 (ISSN-L)
- 1539-4794
- OpenAlex
- W2003051976
- Cited by
- 10
- References
- 3
- Citations by year
- 2026: 1 · 2022: 1 · 2019: 1 · 2017: 1 · 2016: 1 · 2015: 1 · 2013: 2
- FWCI
- 0.98
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Optics Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Virtual Community of Pathological Anatomy (University of Castilla La Mancha) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Ministero dell’Istruzione , dell’Università e della Ricerca (MIUR) (PRIN-2008-YCAAK)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Nonlinear Photonic Systems
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Orbital Angular Momentum in Optics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
- Keywords
- dynamic trapping, graded-index waveguides, normal incidence, periodic potential modulation, optical waveguide arrays
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