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

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.

Figure 1

(a) Schematic view of PQCLs; (b) scanning electron micrographs; (c)–(f) emission spectra of samples with $a=540$, 560, 580, 600 nm.

Figure 2

Spot images of the out-of-plane emission. (a) measurement setup. (b)–(e) measured spot images. (f)–(i) spot images calculated from the reciprocal lattice. See also Fig. 4.

Figure 3

Reciprocal lattice representation of lasing condition. The diameter of spots is proportional to the Fourier amplitude. (a) An example of lasing condition. (b) $2k$ circles deduced experimentally are overlapped on the reciprocal lattice.

Figure 4

Reciprocal lattice representation of out-of-plane emission. (a) Lasing condition with $G_L$ induces out-of-plane emission in the $k_R$ direction as a result of diffraction coupling with $G_c$. (b) $2k$ circles and reciprocal lattice points shown in different colors according to their spot images.