Lasing Action due to the Two-Dimensional Quasiperiodicity of Photonic Quasicrystals with a Penrose Lattice

Abstract

We have fabricated photonic quasicrystal lasers with a Penrose lattice that does not possess translational symmetry but has long-range order, and observed coherent lasing action due to the optical feedback from quasiperiodicity, exhibiting a variety of 10-fold-symmetric lasing spot patterns. The lattice constant dependence of lasing frequencies and spot patterns show complicated features very different from photonic crystal/random lasers, and we have quantitatively explained them by considering their reciprocal lattice. Unique diversity of their reciprocal lattice opens up new possibilities for the form of lasers.

Anomalous properties of the band-edge states in large two-dimensional photonic quasicrystals

“…[11][12][13][14][15] Recently, a wide interest has been attracted to the bandedge states in quasiperiodic composites. 4,[16][17][18][19][20][21][22][23] Firstly, the property of wave functions at band edges in quasiperiodic structures remains an interesting and unresolved topic. 24 By observing the liquid surface wave on a quasiperiodically drilled bottom, the wave function at the band edge is shown to be a plane wave with quasiperiodic modulation.…”

“…[25][26][27][28][29] However, recent studies showed that the band-edge states in photonic quasicrystals can support various applications with novel and promising properties that are unrealizable by using the band-edge states in photonic crystals. [17][18][19][20][21] For example, lasing action of tenfold rotational symmetry at the band-edge states has been observed in photonic quasicrystals with a Penrose lattice. 17 Higher-order harmonic generations with more flexibility, [18][19][20] even simultaneous phase matching of arbitrary optical frequencyconversion processes, 21 have been investigated in nonlinear photonic quasicrystals.…”

“…[17][18][19][20][21] For example, lasing action of tenfold rotational symmetry at the band-edge states has been observed in photonic quasicrystals with a Penrose lattice. 17 Higher-order harmonic generations with more flexibility, [18][19][20] even simultaneous phase matching of arbitrary optical frequencyconversion processes, 21 have been investigated in nonlinear photonic quasicrystals.…”

“…16,17 Thus, how the properties of the band-edge states evolve with sample size were not studied, and the effects due to the quasiperiodic long-range order were not fully manifested in these studies. In order to fully explore these effects, large-sized samples are required.…”

“…The Born approximation which is valid for small systems may become invalid. 17,22 In this work, we study the properties of the band-edge states for electromagnetic waves in large-sized twodimensional photonic quasicrystals by using the multiplescattering theory ͑MST͒ in conjunction with the sparsematrix canonical-grid ͑SMCG͒ method. 30 On the one hand, the SMCG method allows us to do large-scale calculations efficiently so that the quasiperiodic long-range order effects can be studied, as in the study of acoustic waves in largesized phononic quasicrystals; 23 on the other hand, the MST method allows us to calculate the wave functions of the band-edge states.…”