Lightwave In The Dynamic Behavior Of Photonic Lattices

So-called photonic lattices, are optical dielectric structures with a spatial periodic modulation of their dielectric constant that are designed to affect the motion of light flow. These include photonic crystals, optical waveguide arrays, sonic crystals etc. In contrast to homogeneous bulk systems, the eigenmodes of photonic lattices can be cast into a photonic band structure. The existence of this multi-branch dispersion relation is the most important consequence of the Floquet-Bloch theorem. General speaking, the concept of lattices can be extended to all kinds of waves for the generality of Floquet-Bloch theorem. For example, semiconductor superlattice for electrons, optical lattices for cold atoms, sonic crystals for elastic waves, etc.In Chapter One, we basically introduce the concept of photonic lattices and cite some kinds of photonic lattices, including photonic crystals, waveguide arrays etc. These photonic lattices display different transport properties; however, they possess the common features because of the action of the spatial periodicity. That is photonic band gap derived from Bloch theorem. In Chapter Two, we focus on the graded pho-tonic crystal. We exploit theoretically the occurrence and tunability of photonic Bloch oscillations and dipole oscillations in one-dimensional photonic crystals. Photons un-dergo Bloch oscillations inside tilted photonic bands, which are achieved by the appli-cation of graded refractive index contrast between layers in photonic crystals, varying along the direction perpendicular to the surface of layers. With appropriate gradations, terahertz oscillations can appear and cover a terahertz band in an electromagnetic spec-trum. The tunability of photonic Bloch oscillations (including amplitude and period) is readily achieved by changing the gradient. Besides that, optical pulses can undergo oscillations inside the curved band structure, analogous to the dipole oscillations in ul-tracold gases. The implementation of numerical simulations shows that our proposed scheme can produce stable and long-living photonic dipole oscillations. The physical origin is explored to give a clear physical picture. Finally, the transition between the photonic Bloch oscillations and photonic dipole oscillations is discussed. Results of the present research also offer great potential applications for controlling wave propagation by means of graded materials.In Chapter Three, the waveguide arrays are introduced firstly. In such systems the band gaps come to appear due to the site coupling and discreteness, called discrete diffraction. This is different from photonic crystals, in which the gaps open owing to the phenomenon of Bragg reflection. For the graded waveguide arrays, the Bloch oscil-lations can appear. We investigate the all kinds of dynamic behavior of light, including the traditional Bloch oscillations in single lattices, Bloch-Zener oscillations in binary lattices. On the other hand, we design the configuration of the waveguide array itself to modulate the dispersion relations of lattice. For example, in zigzag waveguide arrays the next-nearest-neighbor interactions are enhanced, leading to the band alteration be-yond the nearest-neighbor model. Contrary to the behavior in the vanishing SOC, the Bloch oscillations exhibit new features, namely, a double turning-back occurs when the beam is approaching the band edge. We also design a system called optical waveguide ladder. In such ladder, the dispersion relation presents new features due to the coupling of inter-layer. Correspondingly, by imposing gradient in propagation constant on the waveguide ladders, some anomalies of Bloch-Zener oscillations are demonstrated. This study can offer viable applications in optical steering devices.In the last Chapter, we conclude the dynamical behavior of light in graded photonic lattices and give some remarks.