Exact dynamic localization in curved AlGaAs optical waveguide arrays.
ABSTRACT We present experimental observations of exact dynamic localization of an optical beam in a periodically curved AlGaAs waveguide array. The dynamic localization of the beam is "exact" in that it is observed even when the photonic band of the array is not well described in the nearest-neighbor tight-binding approximation. We present the spatial evolution of the beam around the two-period plane in the structure, explicitly demonstrating the delocalization and subsequent relocalization of the beam. We also emonstrate the strong wavelength dependence of the beam relocalization for a four period structure.
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ABSTRACT: We study nondiffracting accelerating paraxial optical beams in periodic potentials, in both the linear and the nonlinear domains. In particular, we show that only a unique class of z-dependent lattices can support a true accelerating diffractionless beam. Accelerating lattice solitons, autofocusing beams and accelerating bullets in optical lattices are systematically examined.Optics Letters 04/2014; 39(7):2129-32. · 3.39 Impact Factor
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ABSTRACT: We show that light tunneling inhibition may take place in suitable dynamically modulated waveguide arrays for light spots whose features are remarkably smaller than the wavelength of light. We found that tunneling between neighboring waveguides can be suppressed for specific frequencies of the out-of-phase refractive index modulation, affording undistorted propagation of the input subwavelength light spots over hundreds of Rayleigh lengths. Tunneling inhibition turns out to be effective only when the waveguide separation in the array is above a critical threshold. Inclusion of a weak focusing nonlinearity is shown to improve localization. We analyze the phenomenon in purely dielectric structures and also in arrays containing periodically spaced metallic layers.Optics Letters 08/2013; 38(15):2846-9. · 3.39 Impact Factor
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ABSTRACT: We present the experimental observation of three different optical localization schemes in curved coupled optical waveguide arrays. Exact and approximate dynamic localization are compared and a new type of localization, quasi-Bloch oscillations, is demonstrated.05/2009;
Exact Dynamic Localization in Curved AlGaAs Optical
Rajiv Iyer1, Jun Wan2, Marc M. Dignam2, C. Martijn de Sterke3, J. Stewart Aitchison1
1 Department of Electrical and Computer Engineering, University of Toronto, 10 King’s College Road, Toronto, Ontario, Canada, M5S 3G4.
2 Department of Physics, Queen’s University, Kingston, Ontario, Canada, K7L 3N6.
3 Centre for Ultrahigh bandwidth Devices for Optical Systems (CUDOS), University of Sydney, New South Wales 2006, Australia.
Abstract: We present the first experimental observations of exact dynamic localization of an
optical beam in periodically-curved strongly-coupled waveguide arrays. Spatial and spectral
measurements of two and four period devices agree well with theory.
©2007 Optical Society of America
OCIS codes: (130.3120) Integrated optics devices; (130.2790) Guided waves
The evolution of an electron wavepacket in a one-dimensional periodic spatial potential under the influence of a
time-dependent, ac electric field has attracted much recent attention [1-3]. Under special conditions, the interplay
between the potential and the ac electric field causes the wavepacket to exhibit dynamic localization (DL), the
periodic return of the wave packet to its original localized state, a phenomenon similar to Bloch oscillations in dc
fields. Because of the difficulties observing DL in electronic systems, we consider an alternative, but mathematically
equivalent, system: the Curved Coupled Optical Waveguide (CCOW) array [4-6], where the time-dependent ac field
is mimicked in the optical domain by a distance-dependent periodic curvature profile in the waveguides.
DL has been previously observed to arise for continuously varying ac fields in systems whose bandstructure
could be well described by the nearest-neighbor tight-binding (NNTB) approximation [1, 2, 3, 6]. This approximate
dynamic localization (ADL) was observed in a sinusoidally curved CCOW device by Longhi . In contrast, exact
dynamic localization (EDL) can only occur in general structures (e.g., non-NNTB) if the ac field is discontinuous
. Here we present an experimental demonstration of EDL in non-NNTB CCOWs with discontinuous curvature
profiles — the first demonstration of EDL in any system. We find that EDL persists for at least four periods, and
report excellent agreement of our measurements with theory for both DL evolution and wavelength dependence.
Device Design and Simulation
A schematic of our CCOW system is shown in Fig. 1. The single mode, polarization independent waveguides were
designed to have width, dw = 4.0 μm. The CCOW array was designed with period, d = 6.7 μm at the resonant
wavelength, λR = 1550 nm. We used the simplest discontinuous ac curvature profile, the square-wave, with a
distance dependent radius of curvature, R(v), which varied between +R0 to –R0 over one full period, Λ. For our
design, R0 = 35.238 mm, and Λ = 5 mm.
The beam evolution over two periods through the CCOW structure was simulated at λR = 1550 nm using the
Schrödinger equation in the one-band approximation (Fig. 2). At v=0, an initially localized beam begins to spread
(with a slight asymmetry in the u-dimension) to an oscillation amplitude of ΨDL ≈ 4d (i.e., the maximum beam
divergence is ±4 waveguides), and relocalizes at v=Λ, and v=2Λ, remaining localized over a length, ΔvDL ≈ 300 μm.
Fig. 1. Schematic of CCOW structure Fig. 2. Simulation results of beam propagation. (Log scale)
The chips were fabricated on an AlGaAs wafer using photolithography and dry etching . A polarized CW beam
was coupled into each chip using a microscope objective; the output beam was captured using a traditional
waveguide imaging system. Only TM-launch results are presented below.
We tracked the beam propagation through our CCOW device to obtain a spatial map around the 2-period EDL
plane at 1550 nm (Fig. 3(a)). The measured performance agrees very well with the theoretical predictions from the
one-band Schrödinger model (using experimentally measured parameters), shown in Fig. 3(b). After 2 periods of
oscillation, we see the following expected behavior: (1) DL was clearly observed, (2) the beam remains localized for
ΔvDL ≈ 300 μm, (3) the oscillation amplitude, ΨDL ≈ 4d, and (4) the beam propagation was slightly asymmetric in
The wavelength dependence of our 4-period EDL device was conducted between 1480 and 1600 nm, shown in
Fig. 4(a). From the measurements, we see that after 4 periods, the beam has fully relocalized at a wavelength of
1555 nm, i.e., the actual resonant wavelength of the fabricated device. For comparison, the simulation result from
the one-band Schrödinger model (using experimentally measured parameters) is shown in Fig. 4(b). DL occurs only
close to the resonant wavelength; hence, the beam is seen to spread to ±3d at 1480 nm, and to ±2d at 1600 nm.
Because of this wavelength dependence, this device has been proposed for optical filtering applications .
Fig. 3(a). Measured beam propagation.
Fig. 3(b). Simulation results of beam
propagation. (Logarithmic scale)
Fig. 4. Wavelength dependency.
(a) Measured, and (b) Simulation results
(Both on a logarithmic scale)
This is the first time in any system, to the authors’ knowledge, that exact dynamic localization has been
experimentally observed, or that the evolution of DL of any kind has been experimentally mapped. We
demonstrated EDL over four periods in the optical domain, using closely coupled CCOW arrays, driven by an
equivalent ac square-wave field; we find excellent agreement with theory and with the design targets. We have
shown that the CCOW array serves as an ideal alternative system in which to test quantum electronic phenomena.
This device has applications in broadband optical filtering.
Review B 34, 3625-3633 (1986).
2. M. Holthaus, "Collapse of minibands in far-infrared irradiated superlattices," Physical Review Letters 69, 351-354 (1992).
3. M. M. Dignam, and C. M. de Sterke, "Conditions for dynamic localization in generalized ac electric fields," Physical Review Letters 88,
4. G. Lenz, R. Parker, M. C. Wanke, and C. M. de Sterke, "Dynamic localization and AC Bloch oscillations in periodic optical waveguide
arrays," Optical Communications 218, 87-92 (2003).
5. J. Wan, M. Laforest, C. M. de Sterke, and M. M. Dignam, "Optical filters based on dynamic localization in curved coupled optical
waveguides," Optical Communications 247, 353-365 (2005).
6. S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in
periodically curved waveguide arrays," Physical Review Letters 96, 243901-243901 (2006).
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Bloch oscillations," Physical Review Letters 83, 4756-4759 (1999).
D. H. Dunlap, and V. M. Kenkre, "Dynamic localization of a charged-particle moving under the influence of an electric-field," Physical