Ultrasmall photonic-crystal zero-cell laser cavities

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/2n_slab)³ (Q ~ 4300), is obtained for s = 0.1a/ √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 ~0.025μm³or ~ 2.1(Λ/2n_slab)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/2n_slab)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/2n_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 Qand confinement factors, without spoiling the cavity's ultrasmall mode volume.