APPLIED PHYSICS LETTERS
VOLUME 80, NUMBER 21
27 MAY 2002
Square-lattice photonic band-gap single-cell laser operating in the lowest-order whispering gallery mode Han-Youl Ryu,a) Se-Heon Kim, Hong-Gyu Park, Jeong-Ki Hwang,b) and Yong-Hee Lee Department of Physics, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea
Jeong-Soo Kim Telecommunication Basic Research Laboratory, Electronics and Telecommunications Research Institute, Taejon 305-600, Korea
共Received 10 September 2001; accepted for publication 1 April 2002兲 Square-lattice photonic band-gap lasers are realized at room temperature from single-cell photonic crystal slab microcavities fabricated in InGaAsP quantum-well materials emitting at 1.5 m. This single-cell photonic band-gap laser operates in a class of two-dimensional mode to be classified as the smallest possible whispering gallery mode with genuine energy null at the center. The low-loss nondegenerate mode with modal volume of 0.1 共/2兲3 demonstrates a spectrometer-limited below-threshold quality factor ⬎2000 and a theoretical quality factor ⬎10 000. The other class of photonic crystal lasers is also observed outside the photonic band gap of the square lattice, operating in the dipole mode. © 2002 American Institute of Physics. 关DOI: 10.1063/1.1480103兴
Photonic crystals offer various ways to modify spontaneous emission by forming a low-loss wavelength-size cavity.1,2 It has been shown, theoretically, that spontaneous emission can be strongly modified in two-dimensional 共2D兲 photonic crystal slab structures.3–5 Recently, photonic crystal single-cell lasers were reported from triangular lattices of air holes suspended in air.6,7 The triangular lattice of air holes has been a natural choice for photonic band-gap lasers6 – 8 since a large photonic band gap for in-plane polarization 共TE polarization兲 exists. In slab-type 2D photonic crystal cavities, however, one should consider out-of-plane coupling as well as in-plane mode confinement. In fact, vertical radiation out of the slab is strongly related to the mode pattern of a photonic crystal cavity.9 A microdisk cavity10,11 offers valuable insight into the low-loss modes to be achieved in photonic crystal slabs. Whispering gallery modes formed by use of total internal reflection in the microdisk cavity radiate mostly in the radial direction and show low intensity in the normal direction.11–13 If this radial radiation can somehow be suppressed, whispering gallery modes with high-quality factors (Q) and smaller mode numbers would be realized. In this sense, we expect that, if the whispering-gallery-like modes can be formed in a photonic crystal slab cavity, these modes could have high Q since both in-plane and out-of-plane radiation are suppressed at the same time. It is interesting to note that the C 4 v symmetry of a single-cell cavity formed in a 2D square-lattice photonic crystal allows for the existence of the whispering gallery mode with a lowest azimuthal mode number of 2. However, square-lattice air–hole structures have been hardly investigated because the size of the band gap for TE-polarization is much smaller than the band-gap size of a triangular lattice. To start, we investigate resonant frequencies, mode profiles, a兲
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b兲
and Q of single-cell cavity modes in a free-standing squarelattice photonic crystal slab by using the three-dimensional 共3D兲 finite-difference time-domain 共FDTD兲 method.3–5 The refractive index of the slab material is chosen to be 3.4. The thickness of the slab is 0.4 a, where a is periodicity of the square lattice. A single-cell cavity is introduced by removing one hole in the square lattice. Two types of resonant modes appear in this cavity. The first one is nondegenerate and has a square symmetry, as shown in Figs. 1共a兲–1共c兲. The electric- and magnetic-field intensity profiles are shown in Figs. 1共a兲 and 1共b兲, respectively. The maximum intensity of the electric fields exists around four nearest-neighbor holes, whereas that of the magnetic fields exists in the diagonal direction around the center. Both electric and magnetic fields have a node at the center. These features are reminiscent of the whispering gallery mode in the microdisk cavity. In addition, as shown in Fig. 1共c兲, electric fields at four intensity maxima are directed radially in and out, alternatively, which is also the characteristic of the lowest-order whispering gallery mode with the azimuthal mode number of 2. In this sense, we label this mode the lowest-order whispering gallery 共LWG兲 mode. The other resonant mode is the dipole mode, which is doubly degenerate. The electric-field intensity profile of the dipole mode, which oscillates in the y direction, is shown in Fig. 1共d兲. Resonant frequencies and Q of both cavity modes are calculated varying the radius of air holes. The resonant frequencies are plotted in Fig. 2共a兲 along with band-gap positions. The gray area represents a full in-plane band-gap frequency region. Hatched areas below and above the gray region indicate the band gap in the ⌫–X and ⌫–M directions, respectively. The resonant frequency of the LWG mode is within the full band gap in most cases. However, it is interesting to note that the resonant frequency of the dipole mode lies outside the full in-plane band gap for all air–hole radius. Since both of the degenerate dipole modes oscillate predominantly in the ⌫–X direction, the band gap for the ⌫–X direction plays an important role.
0003-6951/2002/80(21)/3883/3/$19.00 3883 © 2002 American Institute of Physics Downloaded 10 Jun 2002 to 143.248.117.5. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/aplo/aplcr.jsp
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Appl. Phys. Lett., Vol. 80, No. 21, 27 May 2002
FIG. 1. 共Color兲 Resonant mode profiles of a free-standing square-lattice single-cell cavity calculated by the 3D FDTD method. 共a兲 Electric-field intensity profile of the lowest-order whispering gallery 共LWG兲 mode calculated at the center of the slab. 共b兲 Magnetic-field intensity profile of the LWG mode. 共c兲 Electric-field directions of the LWG mode. 共d兲 Electric-field intensity profile of the y-dipole mode. Side-view electric-field intensity profile of the LWG mode 共e兲 and the dipole mode 共f兲 are calculated along the ⌫–X direction through the defect center. The color map of relative intensity scales is shown for reference.
The computational domain for Q calculations contains 11⫻11 unit cells in the photonic crystal plane. As shown in Fig. 2共b兲, the total Q of the LWG mode are usually several thousand and the Q of about 13 000 is observed when the air-hole radius is about 0.38 a. The total Q is decomposed into vertical and the horizontal Q. The boundary for separating vertical radiation from laterally guided modes is positioned at 0.5 a from the surface of the slab. Below this vertical boundary position, the contribution of the evanescent tail of the resonant mode becomes significant. Considering that the Q of the resonant mode is ultimately limited by vertical Q, 5 Q of the LWG mode can be as large as 40 000. As mentioned previously, the high Q values of the LWG mode originate from the low vertical radiation of whispering-gallery-like modes and the strong in-plane photon confinement achieved by the photonic band gap. The effective mode volume of the LWG mode is calculated to be 0.04 m,3 which corresponds to 0.1 共/2兲.3 This value is about 30% larger than the mode volume of the dipole mode in the triangular lattice single-cell cavity. This increase of the mode volume is partly responsible for the improvement of Q. 6,9 Due to the large Q and the small mode volume, this microcavity mode can lead to very large Purcell factors or even Rabi oscillations. Q of the dipole mode are smaller than those of the LWG mode by more than an order of magnitude. The largest Q obtained for the dipole mode is only about 550. In the dipole
Ryu et al.
FIG. 2. 共a兲 Resonant frequencies and band-gap positions as a function of air–hole radius. Gray area represents a full in-plane band-gap region. Horizontally and obliquely hatched areas below and above the gray area indicate the band gap in the ⌫–X and ⌫–M directions, respectively. 共b兲 Quality factors (Q) of the LWG mode. 共c兲 Q of the dipole mode. Total Q 共square兲 are decomposed to the vertical 共triangle兲 and the horizontal 共circle兲 components.
mode, vertical and horizontal Q have similar values ⬃1000. Q of the dipole mode could be improved by changing the cavity design as the Caltech group demonstrated for the triangular lattice dipole mode.5,14 Figures 1共e兲 and 1共f兲 show the side view of the electric-field intensity profiles for the LWG and dipole modes, respectively. The electric field of the LWG mode is well confined inside the slab. Note, especially, the large difference of vertical coupling between the two modes. The square-lattice single-cell slab structures were fabricated in InGaAsP/InP materials by using electron-beam lithography, Cl2 -assisted Ar-beam etching, and selective wet etching.6,7 Six 6 nm strain-compensated InGaAsP quantum wells were used as active materials. The thickness of the InGaAsP slab is 200 nm. A top-view scanning electron micrograph of a fabricated single-cell square lattice cavity is shown in Fig. 3. The square-lattice single-cell structures were optically pumped by a 980 nm laser diode with 10 ns pulses at a repetition rate of 500 kHz. The pump spot size was about 3.5 m. All measurements were performed at room temperature. Lasing actions have been observed from many samples with various lattice parameters. Lasing from both the LWG and dipole modes in a wide spectral range between 1340 and 1610 nm was observed and identified. The mode profile of the LWG mode laser is taken from an infrared camera and shown in the inset of Fig. 4共a兲. The mode image shows a clear four-lobe shape and a nodal point at the center, which is
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Ryu et al.
Appl. Phys. Lett., Vol. 80, No. 21, 27 May 2002
FIG. 3. Top-view scanning electron micrograph of a fabricated free-standing square-lattice single-cell cavity. Lattice constant a is 525 nm, and air–hole radius is about 0.38 a.
the characteristic of the lowest-order whispering gallery mode. Each laser mode was also identified by polarization measurements. The dipole mode is nearly linearly polarized, whereas the LWG mode does not have definite polarization directions. The threshold peak pump power is estimated to be about 0.8 mW for the laser shown in Fig. 4共a兲, which operates in the LWG mode. The lowest threshold of the dipole mode laser is about 1.0 mW, which is 20% higher than that of the LWG mode laser. This reflects the higher Q of the LWG mode. To determine the Q of the mode experimentally, the spectral linewidth of the LWG mode is measured near the transparency pumping condition. Figure 4共b兲 shows the spectrum of the LWG mode when the pump power is 0.4 mW. From measurement of the full width at half maximum, Q of the LWG mode is estimated to be about 2000. This Q value is limited by the resolution of the spectrometer. In real situations, Q will be limited by scattering at etched air–hole interfaces although the theoretical Q is very high. The single-mode operation is observed from the LWG mode. No splitting of the emission wavelength indicates that the LWG mode is nondegenerate. In summary, resonant modes in the square-lattice air– hole photonic crystal slab single-cell cavity has been studied in this letter. The LWG mode in the square lattice has the characteristics of the fundamental whispering gallery mode. Theoretical Q⬎10 000 and the Purcell factor ⬎1000 are achieved from this mode. This LWG mode shows roomtemperature lasing actions with threshold pump power of about 0.8 mW. The other resonant mode, the dipole mode, also shows a lasing action even though the mode exists outside the in-plane band gap of the square lattice. The LWG mode has other favorable properties for photonic crystal microcavity devices. The nondegeneracy of this LWG mode will result in a large spontaneous emission factor,15 which implies that this mode has a high potential for realization of a thresholdless laser. And, since there is an intensity node at
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FIG. 4. Characteristics of the LWG mode laser shown in Fig. 3. 共a兲 Collected output power measured at the lasing wavelength is plotted as a function of peak pump power. In the inset, the infrared camera image of the mode pattern is shown. 共b兲 Below-threshold spectrum measured at the peak pump power of 0.4 mW.
the center of the cavity, electrical pumping can be achieved without degrading mode properties by placing a current flow path at the cavity center as has been realized in microdisk lasers. Using these properties, the LWG mode of a squarelattice single-cell cavity will find potential applications to low-threshold microcavity lasers and miniaturized photonic integrated circuits. This work was supported by the National Research Laboratory Project of Korea.
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