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The tight-binding electronic structure of two-dimensional quasicrystals is studied numerically for three patterns of Penrose tiling with up to 426 vertices. According to the range of interactions, three different models are considered. For the simplest model, two different interactions are assigned to long and short edges of the Penrose tile. Energy spectra show several significant gaps whose width and position depend on the relative strength of the interactions. The cumulative density of states is linear in energy at the band edge, indicating the existence of the Van Hove singularities. The energy spectra for other models show similar band gaps and singularities, though the density of states is asymmetric. Participation ratios are examined. %hen the relative strength of interactions becomes small, significant numbers of states become localized. Lattice vibration perpendicular to the plane is studied in the harmonic approximation for the simplest model. The vibrational spectra show gaps and singularities similar to the electronic spectra.

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We have developed a compact and stable all-fiber fundamentally mode-locked 12 GHz laser system. The passively mode-locked laser centered at 1535 nm has temporal pulse width of ∼2  ps and average power of 5 mW. The timing jitter, which is cumulative from pulse-to-pulse, has been measured using an optical cross-correlation method and found to be 44  fs/pulse. The self-starting, mode-locked laser consists of a semiconductor-based saturable absorber with high modulation depth and a high gain per unit length, polarization-maintaining 0.8 cm long Er/Yb phosphate fiber as a gain medium.

Quantum walk is a key operation in quantum computing, simulation, communication and information. Here, we report for the first time the demonstration of quantum walks and localized quantum walks in a new type of optical fibers having a ring of cores constructed with both periodic and quasiperiodic Fibonacci sequences, respectively. Good agreement between theoretical and experimental results have been achieved. The new multicore ring fibers provide a new platform for experiments of quantum effects in low-loss optical fibers which is critical for scalability of real applications with large-size problems. Furthermore, our new quasiperiodic Fibonacci multicore ring fibers provide a new class of quasiperiodic photonics lattices possessing both on-and offdiagonal deterministic disorders for realizing localized quantum walks deterministically. The proposed Fibonacci fibers are simple and straightforward to fabricate and have a rich set of properties that are of potential use for quantum applications. Our simulation and experimental results show that, in contrast with randomly disordered structures, localized quantum walks in new proposed quasiperiodic photonics lattices are highly controllable due to the deterministic disordered nature of quasiperiodic systems.

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Early applications driving the development of single photon sensitive detectors, such as fluorescence and photoluminescence spectroscopy, simply required low noise performance with kiloHertz and lower count rate requirements and minimal or no timing resolution. Newer applications, such as high data rate photon starved free space optical communications require photon counting at flux rates into megaphoton or gigaphoton per second regimes coupled with sub-nanosecond timing accuracy. With deep space optical communications as our application driver, we have developed and implemented systems to both characterize gigaHertz bandwidth single photon detectors as well as process photon count signals at rates beyond 100 megaphotons per second to implement communications links at data rates exceeding 100 megabits per second with efficiencies greater than two bits per detected photon. With these systems, we have implemented high bandwidth real-time systems using intensified photodiodes, visible light photon counter detectors, superconducting nanowire detectors, Geiger-mode semiconductor avalanche photodiodes, and negative avalanche feedback photon counters.