Diffraction control in periodically curved two-dimensional waveguide arrays

Garanovich, Ivan L.; Szameit, Alexander; Sukhorukov, Andrey A.; Pertsch, Thomas; Królikowski, Wiesław; Nolte, Stefan; Neshev, Dragomir N.; Tuennermann, Andreas; Kivshar, Yuri S.

doi:10.1364/oe.15.009737

Cited by 49 publications

(38 citation statements)

References 32 publications

(53 reference statements)

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“…Finally, the third class of optical analogues is related to solid-state physics and include Bloch oscillations [85][86][87][88][89][90][91][92][93][94], Zener tunnelling [95][96][97][98][99], Anderson localization [100][101][102], dynamic localization [103][104][105][106][107][108][109][110][111][112][113], surface physics [114][115][116][117][118][119][120][121][122][123][124][125], and others [126][127][128]. One should perhaps also mention that the research on photonic crystals, started in the late of 1980's, borrowed many ideas and concepts from solidstate physics.…”

Section: Overview On Quantum-optical Analogiesmentioning

confidence: 99%

Quantum‐optical analogies using photonic structures

Longhi¹

2009

Laser & Photonics Reviews

672

579

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Engineered photonic waveguides have provided in the past decade an extremely rich laboratory tool to visualize with optical waves the classic analogues of a wide variety of coherent quantum phenomena encountered in atomic, molecular or condensed-matter physics. As compared to quantum systems, optics offers the rather unique advantage of a direct mapping of the wave function evolution in coordinate space by simple fluorescence imaging or scanning tunneling optical microscopy techniques. In this contribution recent theoretical and experimental advances in the field of quantum-optical analogies are reviewed. Special attention is devoted to some relevant optical analogies based on the use of curved photonic structures, including: coherent destruction of tunneling in driven bistable potentials; coherent population transfer and adiabatic passage in laser-driven multilevel atomic systems; quantum decay control and Zeno dynamics; electronic Bloch oscillations and Zener tunneling, Anderson localization and dynamic localization in crystalline potentials. Curvilinear Propagation distance (cm) u u ( m) m 8 6 4 2 0 0 20 40 60 Curvilinear Propagation distance (cm) u Beam Center of Mass n > > 0 2 4 6 8 0 2 4 6 8 10 u u 0 Input Beam R a Optical analogue of quantum particle bouncing on a lattice under the gravitational field. A light wave packet periodically bounces the edge of a circularly-curved waveguide array, showing collapses and revivals.

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Section: Overview On Quantum-optical Analogiesmentioning

confidence: 99%

Quantum‐optical analogies using photonic structures

Longhi¹

2009

Laser & Photonics Reviews

672

579

View full text Add to dashboard Cite

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“…Using the approach developed for onedimensional periodically curved waveguide arrays which has been outlined in Sec. 2, we show that after the full bending period [ → + L], the beam diffraction in the periodically curved hexagonal waveguide array is the same as in a straight hexagonal waveguide array with the effective coupling coefficients [21] …”

Section: Periodically Curved Twodimensional Waveguide Arraysmentioning

confidence: 94%

“…On the other hand, it is important to explore the potential of periodic photonic structures for tunable spatial shaping of the polychromatic light beams. In this paper, we overview our recent theoretical results [20][21][22] on shaping and switching of polychromatic light beams in arrays of coupled optical waveguides, which axes are periodically curved in the propagation direction as schematically shown in Fig. 1.…”

Section: Introductionmentioning

confidence: 99%

Shaping and switching of polychromatic light in arrays of periodically curved nonlinear waveguides

2008

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Abstract:We overview our recent theoretical results on spatio-spectral control, diffraction management, and broadband all-optical switching of polychromatic light in periodically curved one and two dimensional arrays of coupled optical waveguides. In particular, we show that polychromatic light beams and patterns produced by white-light and supercontinuum sources can experience wavelength-independent normal, anomalous, or zero diffraction in specially designed structures. We also demonstrate that in the nonlinear regime, it is possible to achieve broadband all-optical switching of polychromatic light in a directional waveguide coupler with special bending of the waveguide axes. Our results suggest novel opportunities for creation of all-optical logical gates and switches which can operate in a very broad frequency region, e.g., covering the entire visible spectrum. PACS

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“…In particular, waveguide arrays with a curved axis provide a particularly interesting set up to manage discrete diffraction for both monochromatic and polychromatic light [9,[12][13][14][15]. It is therefore of major interest to have general laws describing the global behavior of beam propagation in curved waveguide arrays.…”

Section: Beam Propagation In Curved Waveguide Arraysmentioning

confidence: 99%

Discrete diffraction and shape-invariant beams in optical waveguide arrays

Longhi

2009

Phys. Rev. A

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General properties of linear propagation of discretized light in homogeneous and curved waveguide arrays are comprehensively investigated and compared to those of paraxial diffraction in continuous media. In particular, general laws describing beam spreading, beam decay and discrete far-field patterns in homogeneous arrays are derived using the method of moments and the steepest descend method. In curved arrays, the method of moments is extended to describe evolution of global beam parameters. A family of beams which propagate in curved arrays maintaining their functional shape -referred to as discrete Bessel beams-is also introduced. Propagation of discrete Bessel beams in waveguide arrays is simply described by the evolution of a complex q parameter similar to the complex q parameter used for Gaussian beams in continuous lensguide media. A few applications of the q parameter formalism are discussed, including beam collimation and polygonal optical Bloch oscillations.

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Diffraction control in periodically curved two-dimensional waveguide arrays

Cited by 49 publications

References 32 publications

Quantum‐optical analogies using photonic structures

Quantum‐optical analogies using photonic structures

Shaping and switching of polychromatic light in arrays of periodically curved nonlinear waveguides

Discrete diffraction and shape-invariant beams in optical waveguide arrays

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