Development of the ultimate, smallest possible laser has long been a central topic in the laser and quantum-optics communities.1 Wavelength-scale cavity lasers are promising for nanophotonic integrated circuits that require minimal thermal overhead. In addition, such on-demand single-photon sources can be realized on a chip using ultrasmall cavities.2
Photonic-crystal (PhC) cavities promise a high quality (Q) factor as well as a small mode volume, which are both required for ultralow-threshold lasing. Accordingly, much effort has been expended in creating PhC cavities with these features.3–7 One particularly attractive prospect is to be able to couple all photons generated inside the cavity into a truly single mode by reducing the cavity-mode volume. In a PhC cavity this can be achieved merely by shifting several lattice points.
Figure 1. Three types of photonic-crystal zero-cell cavities. (a) Square-lattice two-hole-shifted, (b) square-lattice four-hole-shifted, and (c) triangular-lattice three-hole-shifted cavities. a: Lattice separation. s: Hole-shift distance.
Figure 2. Top view of the vertical magnetic-field (top) and electric-field |E|2(bottom, logarithmic scale) profiles of the monopole modes excited in (a) the square-lattice two-hole-shifted and (b) triangular-lattice three-hole-shifted cavities.
PhC zero-cell cavities with an ultrasmall mode volume close to the diffraction limit of light have recently been suggested, and lasing with ultralow thresholds was successfully demonstrated.5–7 Here, we present three types of PhC zero-cell cavities formed by shifting lattice points in square- and triangular-lattice structures (see Figure 1). We focus on optimizing the cavity's lattice constant and shift distance to reduce both mode volume and Q factor.
Figure 3. Q factors and mode volumes for the monopole mode as a function of the hole-shift distance in (a) the square-lattice two-hole-shifted, (b) the square-lattice four-hole-shifted, and (c) the triangular-lattice three-hole-shifted cavities.
To theoretically study the optical properties of the resonant modes occurring in the cavities, we performed 3D finite-difference time-domain simulations.8 Monopole and quadrupole modes are excited in the square-lattice two- and four-hole-shifted cavities, while monopole and dipole modes are excited in the triangular-lattice three-hole-shifted cavity. In all three cavities, the monopole mode has the highest Q factor and smallest mode volume. Figure 2 shows the magnetic- and electric-field profiles of the monopole mode in the square-lattice two-hole-shifted and triangular-lattice three-hole-shifted cavities.
We calculated Q factors and mode volumes for the monopole mode of the zero-cell cavities as a function of the hole-shift distance, s. The smallest mode volume, ~0.017μm3 or ~ 1.7(λ/2nslab)3 (Q ~ 4300), is obtained for s = 0.1a/ √2 (where a is the separation between lattice points and nslab the slab thickness)—see Figure 3(a)—in the square-lattice two-hole-shifted cavity. On the other hand, the highest Q factor, ~20,000—for a mode volume ~0.025μm3or ~ 2.1(Λ/2nslab)3—is obtained for s = 0.11a/ √2—see Figure 3(b)—in the square-lattice four-hole-shifted cavity. In the triangular-lattice three-hole-shifted cavity, we obtain a smaller mode volume of ~ 0.015μm3 or ~ 1.5(Λ/2nslab)3 (Q ∼ 1000) for s=0.12a/ √3: see Figure 3(c). This ultrasmall mode volume is close to the theoretical lower limit. However, the Q factor needs to be improved for efficient lasing operation.
To demonstrate lasing action, we fabricated the square-lattice two-hole-shifted cavities in a freestanding indium gallium arsenide phosphide slab with a thickness of 200nm using typical semiconductor fabrication techniques.4,7 A single quantum well embedded in the slab was used as active material. Figure 4 shows scanning-electron-microscopy images of the cavity. We optically pumped the cavities at room temperature using a pulsed laser diode with a wavelength of 980nm (10ns pulses of ~ 1% duty cycle). We measured a single-mode lasing peak with a wavelength of 1511nm: see the above-threshold photoluminescence spectrum in Figure 5 (inset). Figure 5 shows the collected power as a function of the peak pump power. The superlinear increase is clearly observed and the lasing threshold is ~ 130μW. The cavity's experimental Q factor is ~ 2400, which agrees well with the calculated value.
Figure 4. (a) Scanning-electron-microscope image of our fabricated square-lattice two-hole-shifted cavity. Scale-bar length: 3μm. (b) Magnified section of (a). Scale-bar length: 1μm.
Figure 5. Lasing peak intensity (in arbitrary units, a.u.) as a function of incident peak-pump power. (inset) Above-threshold photoluminescence spectrum at 240μW.
In summary, we have theoretically investigated the optical properties of three types of PhC zero-cell cavities. A monopole mode with ultrasmall mode volume of ~ 0.017μm3— ~ 1.7(Λ/2nslab)3—and high Q factor of ~ 4300 is excited in the square-lattice two-hole-shifted cavity. We successfully achieved single-mode lasing with a low threshold of ~ 130μW. We believe that the zero-cell PhC laser is a strong candidate for the ultimate thresholdless laser and a promising light source in nanophotonic integrated circuits. We will next work on decreasing the lasing threshold by improving the Qand confinement factors, without spoiling the cavity's ultrasmall mode volume.
Ho-Seok Ee, Hong-Gyu Park
Department of Physics
Ho-Seok Ee received his BS and MS degrees in 2006 and 2008, respectively, from Korea University. He is currently a PhD student, studying design, fabrication, and characterization of nanowire photonic devices.
3. O. Painter, R. K. Lee, A. Scherer, Y. Yariv, J. D. O'Brien, P. D. Dapkus, I. Kim, Two-dimensional photonic band-gap defect mode laser, Science 284, pp. 1819-1821, 1999.
4. H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, Y.-H. Lee, Electrically driven single-cell photonic crystal laser, Science 305, pp. 1444-1447, 2004.