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Photon Statistics in Disordered Lattices
 Date Issued:
 2015
 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 considered, namely, diagonal and offdiagonal disorders. The latter exhibits disorderimmune chiral symmetry  the appearance of the eigenmodes in skewsymmetric 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 disorderimmune chiral symmetry. In these systems, the span of subthermal photon statistics is inaccessible to the input coherent light, which  once the steady state is reached  always emerges with superthermal 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 photonstatistics interferometry: by exciting two lattice sites with a variable relative phase, as in a traditional twopath interferometer, the excitationsymmetry of the chiral mode pairs is judiciously broken and interferometric control over the photon statistics is exercised, spanning subthermal and superthermal 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 offdiagonal case: for evensited ring and linear lattices, the electromagnetic field evolves into a single quadrature component, so that the field takes discrete phase values and is noncircular in the complex plane. As a consequence, the statistics become superthermal. For oddsited ring lattices, the field becomes random in both quadratures resulting in subthermal 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.
Title:  Photon Statistics in Disordered Lattices. 
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Name(s): 
Kondakci, Hasan, Author Saleh, Bahaa, Committee Chair Abouraddy, Ayman, Committee Member Christodoulides, Demetrios, Committee Member Mucciolo, Eduardo, Committee Member University of Central Florida, Degree Grantor 

Type of Resource:  text  
Date Issued:  2015  
Publisher:  University of Central Florida  
Language(s):  English  
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 considered, namely, diagonal and offdiagonal disorders. The latter exhibits disorderimmune chiral symmetry  the appearance of the eigenmodes in skewsymmetric 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 disorderimmune chiral symmetry. In these systems, the span of subthermal photon statistics is inaccessible to the input coherent light, which  once the steady state is reached  always emerges with superthermal 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 photonstatistics interferometry: by exciting two lattice sites with a variable relative phase, as in a traditional twopath interferometer, the excitationsymmetry of the chiral mode pairs is judiciously broken and interferometric control over the photon statistics is exercised, spanning subthermal and superthermal 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 offdiagonal case: for evensited ring and linear lattices, the electromagnetic field evolves into a single quadrature component, so that the field takes discrete phase values and is noncircular in the complex plane. As a consequence, the statistics become superthermal. For oddsited ring lattices, the field becomes random in both quadratures resulting in subthermal 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.  
Identifier:  CFE0005968 (IID), ucf:50786 (fedora)  
Note(s): 
20151201 Ph.D. Optics and Photonics, Optics and Photonics Doctoral This record was generated from author submitted information. 

Subject(s):  photonic lattices  waveguide arrays  coherence photon statistics  disorder  disordered lattices  coupled waveguides  photonnumber distribution  diagonal disorder  offdiagonal disorder  photonic thermalization gap  discrete Anderson speckle  Anderson localization  transverse localization  topology  
Persistent Link to This Record:  http://purl.flvc.org/ucf/fd/CFE0005968  
Restrictions on Access:  campus 20161215  
Host Institution:  UCF 