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DISCRETE WAVE PROPAGATION IN QUADRATICALLY NONLINEAR MEDIA
Title
DISCRETE WAVE PROPAGATION IN QUADRATICALLY NONLINEAR MEDIA.
Creator
Iwanow, Robert, Stegeman, George, University of Central Florida
Abstract / Description
Discrete models are used in describing various microscopic phenomena in many branches of science, ranging from biology through chemistry to physics. Arrays of evanescently coupled, equally spaced, identical waveguides are prime examples of optical structures in which discrete dynamics can be easily observed and investigated. As a result of discretization, these structures exhibit unique diffraction properties with no analogy in continuous systems. Recently nonlinear discrete optics has...
Show moreDiscrete models are used in describing various microscopic phenomena in many branches of science, ranging from biology through chemistry to physics. Arrays of evanescently coupled, equally spaced, identical waveguides are prime examples of optical structures in which discrete dynamics can be easily observed and investigated. As a result of discretization, these structures exhibit unique diffraction properties with no analogy in continuous systems. Recently nonlinear discrete optics has attracted a growing interest, triggered by the observation of discrete solitons in AlGaAs waveguide arrays reported by Eisenberg et al. in 1998. So far, the following experiments involved systems with third order nonlinearities. In this work, an experimental investigation of discrete nonlinear wave propagation in a second order nonlinear medium is presented. This system deserves particular attention because the nonlinear process involves two or three components at different frequencies mutually locked by a quadratic nonlinearity, and new degrees of freedom enter the dynamical process. In the first part of dissertation, observation of the discrete Talbot effect is reported. In contrast to continuous systems, where Talbot self-imaging effect occurs irrespective of the pattern period, in discrete configurations this process is only possible for a specific set of periodicities. The major part of the dissertation is devoted to the investigation of soliton formation in lithium niobate waveguide arrays with a tunable cascaded quadratic nonlinearity. Soliton species with different topology (unstaggered – all channels in-phase, and staggered – neighboring channels with a pi relative phase difference) are identified in the same array. The stability of the discrete solitons and plane waves (modulational instability) are experimentally investigated. In the last part of the dissertation, a phase-insensitive, ultrafast, all-optical spatial switching and frequency conversion device based on quadratic waveguide array is demonstrated. Spatial routing and wavelength conversion of milliwatt signals is achieved without pulse distortions.
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Date Issued
2005
Identifier
CFE0000420, ucf:46382
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0000420
OPTICAL WAVE PROPAGATION IN DISCRETE WAVEGUIDE ARRAYS
Title
OPTICAL WAVE PROPAGATION IN DISCRETE WAVEGUIDE ARRAYS.
Creator
Hudock, Jared, Christodoulides, Demetrios, University of Central Florida
Abstract / Description
The propagation dynamics of light in optical waveguide arrays is characteristic of that encountered in discrete systems. As a result, it is possible to engineer the diffraction properties of such structures, which leads to the ability to control the flow of light in ways that are impossible in continuous media. In this work, a detailed theoretical investigation of both linear and nonlinear optical wave propagation in one- and two-dimensional waveguide lattices is presented. The ability to...
Show moreThe propagation dynamics of light in optical waveguide arrays is characteristic of that encountered in discrete systems. As a result, it is possible to engineer the diffraction properties of such structures, which leads to the ability to control the flow of light in ways that are impossible in continuous media. In this work, a detailed theoretical investigation of both linear and nonlinear optical wave propagation in one- and two-dimensional waveguide lattices is presented. The ability to completely overcome the effects of discrete diffraction through the mutual trapping of two orthogonally polarized coherent beams interacting in Kerr nonlinear arrays of birefringent waveguides is discussed. The existence and stability of such highly localized vector discrete solitons is analyzed and compared to similar scenarios in a single birefringent waveguide. This mutual trapping is also shown to occur within the first few waveguides of a semi-infinite array leading to the existence of vector discrete surface waves. Interfaces between two detuned semi-infinite waveguide arrays or waveguide array heterojunctions and their possible applications are also considered. It is shown that the detuning between the two arrays shifts the dispersion relation of one array with respect to the other. Consequently, these systems provide spatial filtering functions that may prove useful in future all-optical networks. In addition by exploiting the unique diffraction properties of discrete arrays, diffraction compensation can be achieved in a way analogous to dispersion compensation in dispersion managed optical fiber systems. Finally, it is demonstrated that both the linear (diffraction) and nonlinear dynamics of two-dimensional waveguide arrays are significantly more complex and considerably more versatile than their one-dimensional counterparts. As is the case in one-dimensional arrays, the discrete diffraction properties of these two-dimensional lattices can be effectively altered depending on the propagation Bloch k-vector within the first Brillouin zone. In general, this diffraction behavior is anisotropic and as a result, allows the existence of a new class of discrete elliptic solitons in the nonlinear regime. Moreover, such arrays support two-dimensional vector soliton states, and their existence and stability are also thoroughly explored in this work.
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Date Issued
2005
Identifier
CFE0000833, ucf:46687
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0000833
Photon Statistics in Disordered Lattices
Title
Photon Statistics in Disordered Lattices.
Creator
Kondakci, Hasan, Saleh, Bahaa, Abouraddy, Ayman, Christodoulides, Demetrios, Mucciolo, Eduardo, University of Central Florida
Abstract / Description
Propagation of coherent waves through disordered media, whether optical, acoustic, or radio waves, results in a spatially redistributed random intensity pattern known as speckle -- a statistical phenomenon. The subject of this dissertation is the statistics of monochromatic coherent light traversing disordered photonic lattices and its dependence on the disorder class, the level of disorder and the excitation configuration at the input. Throughout the dissertation, two disorder classes are...
Show morePropagation of coherent waves through disordered media, whether optical, acoustic, or radio waves, results in a spatially redistributed random intensity pattern known as speckle -- a statistical phenomenon. The subject of this dissertation is the statistics of monochromatic coherent light traversing disordered photonic lattices and its dependence on the disorder class, the level of disorder and the excitation configuration at the input. Throughout the dissertation, two disorder classes are considered, namely, diagonal and off-diagonal disorders. The latter exhibits disorder-immune chiral symmetry -- the appearance of the eigenmodes in skew-symmetric pairs and the corresponding eigenvalues in opposite signs. When a disordered photonic lattice, an array of evanescently coupled waveguides, is illuminated with an extended coherent optical field, discrete speckle develops. Numerical simulations and analytical modeling reveal that discrete speckle shows a set of surprising features, that are qualitatively indistinguishable in both disorder classes. First, the fingerprint of transverse Anderson localization -- associated with disordered lattices, is exhibited in the narrowing of the spatial coherence function. Second, the transverse coherence length (or speckle grain size) freezes upon propagation. Third, the axial coherence depth is independent of the axial position, thereby resulting in a coherence voxel of fixed volume independently of position.When a single lattice site is coherently excited, I discovered that a thermalization gap emerges for light propagating in disordered lattices endowed with disorder-immune chiral symmetry. In these systems, the span of sub-thermal photon statistics is inaccessible to the input coherent light, which -- once the steady state is reached -- always emerges with super-thermal statistics no matter how small the disorder level. An independent constraint of the input field for the chiral symmetry to be activated and the gap to be observed is formulated. This unique feature enables a new form of photon-statistics interferometry: by exciting two lattice sites with a variable relative phase, as in a traditional two-path interferometer, the excitation-symmetry of the chiral mode pairs is judiciously broken and interferometric control over the photon statistics is exercised, spanning sub-thermal and super-thermal regimes. By considering an ensemble of disorder realizations, this phenomenon is demonstrated experimentally: a deterministic tuning of the intensity fluctuations while the mean intensity remains constant.Finally, I examined the statistics of the emerging light in two different lattice topologies: linear and ring lattices. I showed that the topology dictates the light statistics in the off-diagonal case: for even-sited ring and linear lattices, the electromagnetic field evolves into a single quadrature component, so that the field takes discrete phase values and is non-circular in the complex plane. As a consequence, the statistics become super-thermal. For odd-sited ring lattices, the field becomes random in both quadratures resulting in sub-thermal statistics. However, this effect is suppressed due to the transverse localization of light in lattices with high disorder. In the diagonal case, the lattice topology does not play a role and the transmitted field always acquires random components in both quadratures, hence the phase distribution is uniform in the steady state.
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Date Issued
2015
Identifier
CFE0005968, ucf:50786
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0005968