Theory of photon Bloch oscillations in photonic crystals

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Abstract
We study photonic Bloch oscillations (PBO’s) in various quasiperiodic dielectric structures. Photons, like electrons, may experience confinement within inclined allowed optical bands of photonic structures, which results in a characteristic photonic Wannier-Stark ladder (PWSL) and PBO’s analogous to electronic Bloch oscillations in crystals subjected to an electric field. In the photonic case the role of the electric field is played by a gradient of the size of the elementary cell of the optical crystal. The photonic band structure for laterally confined Bragg mirrors with circular cross section varying along the longitudinal axis is calculated analytically by means of the coupled-mode theory for structures surrounded laterally either by a metal or by air. Using the scattering state technique, we demonstrate that in porous silicon metallic Bragg reflectors the scattering states form a series of discrete levels with a constant interlevel spacing of about 5 meV, and show that PBO’s occur in these structures with a period of about 1 ps at room temperature. PBO’s and a PWSL with a comparable period and interlevel spacing are demonstrated in planar multiple-microcavity structures based on III-V semiconductors with cavity length varying along the growth axis. These structures are very promising, since they do not require any lateral confinement, thus avoiding dephasing mechanisms introduced by etching at the lateral sidewalls that can hinder the observation of PBO’s.

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