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, ~0.017μ*m*^{3} or ~ 1.7(λ/2*n*_{slab})^{3} (*Q* ~ 4300), is obtained for *s* = 0.1*a*/ √2 (where *a* is the separation between lattice points and *n*_{slab} 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 ~0.025μm^{3}or ~ 2.1(Λ/2*n*_{slab})^{3}—is obtained for *s* = 0.11*a*/ √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 ~ 0.015μ*m*^{3} or ~ 1.5(Λ/2*n*_{slab})^{3} (*Q* ∼ 1000) for *s*=0.12*a*/ √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 ~ 0.017μ*m*^{3}— ~ 1.7(Λ/2*n*_{slab})^{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 *Q*and confinement factors, without spoiling the cavity's ultrasmall mode volume.

Ho-Seok Ee, Hong-Gyu Park

Department of Physics

Korea University

Seoul, Korea

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.

References:

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.