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- Type of Document: Ph.D. Dissertation
- Language: Farsi
- Document No: 46917 (04)
- University: Sharif University of Technology
- Department: Physics
- Advisor(s): Langari, Abdollah; Bahrampour, Alireza; Mahdavi, Mohammad
- Abstract:
- In recent years, a strong interplay between quantum mechanics and the physics of waveguide arrays was established based on a formal analogy between atomic and photonic lattices. The study of light evolution in photonic lattices has provided deep insights into the physics of wave function dynamics and, hence, peculiar quantum mechanical features. Arrays of evanescently coupled waveguides is a very versatile model system for discrete physics. Anderson localization and Bloch oscillations are two examples of coherent quantum transport phenomena, which have been investigated in this thesis. In the first part of this thesis, we investigate numerically the effect of long-range interaction on the transverse localization of light, in nonlinear zigzag optical waveguide lattices. We find that localization is hindered by coupling between next-nearest lattice sites. Additionally, (focusing) nonlinearity facilitates localization with increasing disorder, as long as the nonlinearity is sufficiently weak. However, for strong nonlinearities, increasing disorder results in weaker localization. The threshold nonlinearity, above which this anomalous result is observed, grows with increasing second-order coupling. In the second part, the effect of higher order couplings on optical Bloch oscillations is investigated. The analytical results show that coupling between non-nearest lattice sites, leads to multiple partial turning-back of wave to its excited sites along to spatial Bloch period, while the value of this period is not affected by higher order interactions. Moreover, the existence of localized modes (Wannier–Stark states) with equidistant wave-number spacing (Wannier–Stark ladder), in the presence of longrange interaction, is analytically proved. In addition, according to our results, the symmetric properties of propagation pattern depend on the input profile. In the last part of thesis, we study the effect of absorption, which is an intrinsic feature of photonic systems, on the light dynamics in an optical wavegude array. Before our work, the gain or loss at the sites was commonly implemented into the theory by adding an imaginary part to the diagonal terms of the Hamiltonian only. In this work, we carefully derive the tight-binding model from the discretizing of Helmholtz wave equation. Astonishingly, we find the tight-binding model assumed so far to be incomplete. We prove that the effect of gain or loss results in an imaginary part of the off-diagonal terms of the Hamiltonian as well. We prove the necessity of incorporating imaginary parts into the coupling by measuring experimentally the variance of a wavepacket evolving on a photonic lattice with homogenous loss. We observe a transition from the ballistic to the diffusive transport regime that is impossible according to the conventional model. However, our extended model (including complex coupling coefficients) accurately predicts this behavior. Finally, in the last section, we have studied the impact of these complex coupling coefficients on the transverse localization of light
- Keywords:
- Transverse Localization ; Bloch Oscillations ; Optical Waveguides ; Long Range Interaction ; Absorption Discrepancy
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