Penrose-lattice Photonic Quasicrystal Laser
Masaya Notomi1, Hiroyuki Suzuki2, Toshiaki Tamamura3, and Keiichi Edagawa4
Physical Science Laboratory1, NTT Photonics Labs. 2, NTT Electronics3, Univ. of Tokyo4
Crystals have periodicity and translational symmetry. But there exist a certain class of structures called quasicrystals that do not posses periodicity nor translational symmetry, but have long-range order and rotational symmetry. Quasicrystals have bandgap and density of states in a similar way to crystals, but some important concepts such as band structures, Bloch theorem, Brillouin zone cannot be defined. Concerning crystals, it has been known that lasing action is possible in photonic crystals having optical gain because of some standing wave formation at the photonic band edges. Then, what happens if we introduce gain into photonic quasicrystals that do not have periodicity? Is coherent lasing possible?
From these backgrounds, we have fabricated photonic quasicrystal lasers with organic dye for the first time.  Our quasicrystals have so-called Penrose lattice (shown in Fig. 1(left)) exhibiting 10-fold rotational symmetry which is inhibited in periodic crystals. By optical pumping, we observed clear lasing action, and peculiar 10-fold rotationally symmetric spot patterns shown in Fig. 1(right). Both of lasing wavelengths and spot patterns sensitively depend on the quasilattice constant, indicating that lasing is due to the quasiperiodicity. Sharp spot patterns also indicate that lasing occurs by delocalized coherent modes inside the quasicrystal.
Since we cannot use conventional band theory for quasicrystal, we instead used their reciprocal lattice to analyze the lasing action, and successfully explained the observed lasing wavelengths and spot patterns quantitatively. The reciprocal lattice of quasicrystals are very unique comparing to crystals one. The reciprocal lattice of crystals have a Brillouin zone and any points outside it are equivalent to some points inside it. In the case for quasicrystals, all of them are basically non-equivalent, and thus a wide variety of lasing modes can exist. This uniqueness of the reciprocal lattice is most distinguishable feature of quasicrystal lasers. In fact, lasing action in periodic photonic crystals is restricted from the limitation of periodicity, but quasicrystal lasers are free from those restrictions.
 M. Notomi, H. Suzuki, T. Tamamura, K. Edagawa, Phys. Rev. Lett. 92 (2004) 123906.
Fig. 1. Electron microscope image of the Penrose-lattice photonic quasicrystals (left). The observed 10-fold rotationally symmetric spot pattern for photonic quasicrystal lasers (right).
Fig. 2. Reciprocal lattice of the fabricated Penrose-lattice photonic quasicrystals (calculation).
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