Topological Defect Lasers
Authors: Sebastian Knitter, Seng Fatt Liew, Wen Xiong, Hui Cao
Affiliation: Department of Applied Physics, Yale University, New Haven, Connecticut, USA.
Topological defects have been widely studied in liquid crystals and colloids. One important application of topological defects to photonics is the manipulation of the orbital angular momentum of optical beams. However, they have not been incorporated into lasers. Inspired by the topological defects existing in nematic liquid crystal, we recently designed and fabricated a new type of laser – a topological defect laser .
One essential component of a laser is a cavity that confines light. A microscale cavity can be made within a photonic crystal, e.g., a two-dimensional membrane containing a periodic array of circular air holes, as shown in Fig. 1(a). Light, of wavelength comparable to the lattice constant, may be confined in the central square region as a result of high reflectivity from the surrounding photonic crystal walls. Figure 1(b) shows a spatial field profile of a confined mode, and Fig. 1(c) is the spatial map of its energy flow .
Figure 1: Introducing topological defect to a photonic crystal with anisotropic unit cell. (a,c) A square lattice of air holes embedded in a dielectric membrane. In (a), the holes have circular cross-section. The 4×4 holes are removed from the center to from a cavity that confines light by high reflection from the surrounding photonic crystal walls. The lattice constant is a = 220nm, and the hole radius is 65nm. To introduce topological defect in (c), the air holes are deformed to ellipses. The major axis of each ellipse is rotated to an angle φ = kθ + c from the horizontal axis. θ is the polar angle of the center position of the ellipse. k = 1 and c = π/4. (b,d) Calculated spatial distribution of the magnetic field for a confined optical mode in (a,b). The wavelength of the mode is 880nm. The topological defect rotates the mode in (d). (c,e) The spatial map of the Poynting vector for the modes in (b,d). Each arrow points in the direction of local energy flux, and its length is proportional to the amplitude of the flux. In the photonic crystal structure, the energy flows out of the central defect region in all four directions. In the topological defect structure, the optical flux circulates in the central region.
To introduce the topological defect to this micro-cavity, we deform the air hole shape from circle to ellipse, and rotate the orientation of individual ellipses to form a vortex-like topological defect, as seen in Fig. 1(d). Light can still be confined in the central region, but the spatial field profile of confined mode is twisted as shown in Fig. 1(e). Figure 1(f) reveals an even more dramatic change in the energy flow: a tightly confined circulating flux pattern arises at the center, in contrast to the outward energy flow in Fig. 1(c). Such change is attributed to the spatial variation of the ellipse orientation in the topological defect structure, which creates the swirling vortex of light .
Experimentally we fabricated such structure in a free-standing gallium-arsenide membrane by molecular beam epitaxy, electron-beam lithography, reactive ion etching and wet chemical etching. Figure 2 is the scanning electron micrograph of a fabricated sample. The 190nm-thick membrane contains three layer of quantum dots made of indium arsenide. When pumped by an external laser, the quantum dots are excited to upper states. They subsequently decay to lower states by emitting photons to the confined modes such as the one shown in Fig. 1. When the amplification rate exceeds the leakage rate through the walls, lasing action starts. The laser light swirls around in a vortex.
Fig. 2: Scanning-electron micrograph (SEM) of a topological defect laser fabricated in a GaAs membrane. (a) Top-view SEM image of a square lattice of 32 × 32 air holes with elliptical shape. The ellipticity is ε = 1.4. The lattice constant is a = 220 nm. The air filling fraction is 0.27. At the array center, 4 × 4 air holes are removed. (b) Magnified SEM of a section in (a), highlighted by the gray rectangle. (c) Tilt-view SEM image showing the free-standing GaAs-membrane. Scale-bars in (b) and (c) represent a length of 500 nm.
The power-flow vortex persists beyond the membrane. Our calculation shows that the evanescent field above the top surface of the membrane possess circulating energy flows. These may transfer angular momentum to particles or molecules in the vicinity of the topological defect structure. Thus the optical vortex of the lasing mode may potentially be used for on-chip nanoparticle manipulation. Further experimental study is required to optimize the topological defect laser and exploit the unique potential for applications in areas such as microfluidics for particle sorting and separation. Finally, this work shows that the spatially inhomogeneous variation of the unit cell orientation adds another degree of freedom to the control of a lasing mode, enabling the manipulation of its field pattern and energy flow landscape.
 Sebastian Knitter, Seng Fatt Liew, Wen Xiong, Mikhael I. Guy, Glenn S Solomon, Hui Cao, “Topological defect lasers”, Journal of Optics, 18, 014005 (2015). Full Article.
 Seng Fatt Liew, Sebastian Knitter, Wen Xiong, Hui Cao, “Photonic crystals with topological defects”, Physical Review A, 91, 023811 (2015). Abstract.