pubs.acs.org/NanoLett
Optical Resonant Cavity in a Nanotaper Sang Hyun Lee,*,† Takenari Goto,† Hiroshi Miyazaki,‡ Jiho Chang,§ and Takafumi Yao† †
Center for Interdisciplinary Research and ‡ Department of Applied Physics, Tohoku University, Sendai 980-8579, Japan and § Major of Semiconductor Physics, Korea Maritime University, Pusan 606-791, Korea ABSTRACT The present study describes an optical resonant cavity in a nanotaper with scale reduction from micro to several nanometers. Both experimental results and a finite-difference time-domain (FDTD)-based simulation suggested that the nanometerscale taper with a diameter similar to the wavelength of light acted as a mirror, which facilitated the formation of a laser cavity and caused lasing in ZnO nanotapers. As the light inside the nanotaper propagated toward the apex, the lateral mode was reduced and reflection occurred. This report suggests that use of the resonant optical cavities in nanotapers might result in novel active and passive optical components, which will broaden the horizons of photonic technology. KEYWORDS ZnO, nanotaper, optical resonant cavity, lasing
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reported in nanotapers with a tip diameter of less than the wavelength of light. This letter reports the formation of a novel optical cavity that uses nanotapers rather than flat crystal facets. We discovered that the apex of the nanotaper acted as a distributed mirror, which facilitated a laser cavity. This laser cavity differed essentially from the configuration of previous optical cavities that are based on reflection at facets. The laser beam generated in the structure was strongly focused by the waveguide effect and finally diverged around the tip. The nanotaper could be regarded as a coherent light source point that homogeneously radiated coherent light into threedimensional (3D) space. To understand the distributed reflection phenomenon, the electromagnetic field distribution in a nanotaper with the geometry shown in Figure 1a was surveyed using the 3D finite-difference time-domain (FDTD) method. The nanotaper consisted of a hexagonal pyramid (lt) and a column (lc) with lengths of 7 and 2 µm, respectively. The internal diameter of the hexagonal pyramid decreased from 1.5 µm to 30 nm with a vertical angle of about 12°. A 3D uniform grid with spatial resolution of 10 nm was built to solve the time-dependent Maxwell equation. Figure 1 shows the electric field distribution of a traveling light pulse that was injected into the nanotaper from the bottom plane (Movie 1). The light pulse moved toward the tip due to the waveguide effect and was emitted at the apex of the nanotaper (Figure 1b,c). It is of interest that, in the next moment, a reflected wave was observed in the taper region, as shown in Figure 1d. To understand this result, one must consider the effective refractive index (neff) for light propagating in a parallel waveguide. The diameter of this waveguide is large enough to support multiple modes. When the light enters a tapered waveguide region, the taper diameter is reduced and highorder modes vanish first, since neff depends on both the wavelength and the guiding mode. At a particular taper diameter, the propagation mode will collapse, even for an
o date, several optical cavity structures have been reported, including Fabry-Perot, distributed feedback (DFB), distributed Bragg reflector (DBR), and ring resonators.1 These cavities have been realized in actual semiconductor lasers.2-6 Advances in nano/microfabrication technology permit the realization of variously shaped microcavities, such as micropillar, microdisk, microsphere, and microtoroid microcavities.7-10 These microcavity structures can form microscale ring resonator cavities or whispering gallery cavities. Recent advances in bottom-up nanotechnology have enabled further size reduction that does not require complex fabrication processes.11,12 The characteristics of variously shaped nanostructures, including nanorods, nanowires, and nanorings, have been investigated as building blocks of optical and electrical devices. It should be mentioned, however, that the optical cavities in these structures are essentially comprised of flat facets that act as cavity mirrors, thus imposing the need for a fabrication process. Lasing phenomena have been observed in nanostructures that have either conventional or exotic cavities. For example, the two end facets of a nanowire or a nanoribbon can form a Fabry-Perot cavity, and the side facets of a nanoring and a nanodisk act as optical mirrors in a whispering gallery cavity.13-16 Each of these cavities is also based on flat crystal facets that act as cavity mirrors. Random lasing is possible by the formation of an optical closed loop through coherent multiple scattering at facets,17,18 where the laser beam is efficiently confined and amplified in the nanocavity by reflection at more than two crystal facets. Lasing behavior from nanotetrapods has been previously observed using optical pumping,19-21 although no optical cavities have been * To whom correspondence should be addressed. Tel: +1-865-576-6690. Fax: +1865-576-5235. E-mail:
[email protected]. Present address: Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831. Received for review: 1/12/2010 Published on Web: 05/04/2010 © 2010 American Chemical Society
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DOI: 10.1021/nl100100z | Nano Lett. 2010, 10, 2038–2042
be regarded as a distributed mirror. To observe considerable distributed reflection, the neff gradient must be small; otherwise, the distributed reflection effect becomes meaningless. Consequently, the distributed reflection phenomenon has rarely been observed in conventional tapers. Figure 2 shows the distribution of the electric field intensity of a continuous wave (λ ) 390 nm, see Figure 2a and Movie 2) that moved in and out of the nanotaper under steady-state conditions. The periodic distribution of the electric field intensity indicates the formation of standing waves due to interference between the injected and reflected waves. This longitudinal spatial period (i.e., the distance between adjacent local maxima) is an important fingerprint of cavity formation by reflection. Two longitudinal modes were found, one for x > 0.7 µm and another for x < 0.7 µm, where x denotes the distance from the apex of the taper, as shown in Figure 2b. For the x > 0.7 µm region, the longitudinal spatial period was estimated to be ∼85 nm. It should be noted that the diameter of the taper at x ∼ 0.7 µm was ca. 170 nm, which was close to the wavelength of incident light. This spatial period agreed well with one-half of the wavelength (µ/2nZnO ∼ 84 nm) of incident light, which implied Fabry-Perot interference. It is interesting, however, that the longitudinal spatial period abruptly changed to ca. 130 nm in the x < 0.7 µm region, where the diameter of the taper was less than the wavelength of light. These results suggest phase retardation due to reflection. Strong localization of electric fields due to a reduction in the diameter of the hexagonal structures was observed at eight points from the bottom to the apex (Figure 2c, Movie 3). Multiple transverse modes were observed at the edge of the hexagonal pillar region (the right-most picture in Figure 2c). These
FIGURE 1. Three-dimensional FDTD calculation. (a) Schematic illustration of a nanotaper. The distribution of the electric field intensity in a nanotaper as determined by a traveling pulsed light wave (λ ) 390 nm) toward the tip (b), emission (c), and bottom (d). The maximal electric field intensities of (b-d) was 11.678, 1.708, and 0.017, respectively. The scale bar represents 1 µm.
eigen-mode, after which light propagation is not allowed, but radiation or reflection is permitted. Generally, reflection occurs because of the discontinuity of neff. Thus, a reflection plane can be defined where neff varies abruptly. However, in the case of a nanotaper with an extremely small neff gradient, determination of the reflection plane becomes difficult and sometimes meaningless, because reflection occurs where the taper diameter is less than the wavelength of light. Hence, the nanotaper should
FIGURE 2. Distribution of the electric field intensity in a nanotaper. (a) Longitudinal mode in a nanotaper under steady-state conditions. The wavelength of the injected light was 390 nm. (b) Profile of the electric field intensity near the tip (denoted by the bar in Figure 2a). (c) Evolution of the transverse mode at selected positions in the nanotaper. The intensity increased from black to bright red, and the maximal intensity (corresponding diameter of hexagon, µm) of each image from left to right was 170(0.24), 72(0.45), 45(0.66), 22(0.87), 12(1.08), 20(1.29), 26(1.5), and 10(1.5), respectively. © 2010 American Chemical Society
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FIGURE 3. Morphology of ZnO nanotapers. (a) Typical SEM image of ZnO nanotapers grown on a Si substrate. (b) TEM images of a ZnO nanowire with a diameter of about 35 nm. The inset shows a high-resolution TEM image of the ZnO nanowire with (0001) lattice fringe. (c) The surface morphology of the tapered part and (inset) the corresponding electron diffraction pattern. (d) ZnO nanotaper dispersed on Si substrate for optical evaluation. Insets show the morphology of the tip and of the bottom of the ZnO nanotaper.
ture of 900 °C without a metal catalyst. Graphite was used as a substrate support and source boat. The typical morphology of ZnO nanotapers grown on the Si substrate is shown in Figure 3. The ZnO nanotaper consisted of a taper (with length lt) and a hexagonal pillar (with length lp). The length of the nanotaper (l ) lt + lp), tip angle (θt), and taper diameter, d, were 9-24 µm, 10-18°, and 1.5-2 µm, respectively. The hexagonal pillars were 2-5 µm in length. TEM images of the tapered region (Figure 3b,c) revealed the crystal-structure and surface morphology. A high-resolution TEM image (inset of Figure 3b) showed (0001) lattice fringe. In addition, the TEM image and electron-diffraction pattern recorded along the [011¯0] zone axis from the surface of the tapered parts (Figure 3c) clearly indicated that a single crystal ZnO grew along the c-axis and was tapered by repetition of facets with angles of ∼62 and 90° between the (0001) plane, respectively. From the crystallographic point of view, these facets corresponded to (101¯1) and (101¯0) facets. The connected part was easily detached by the microcracks that existed between structures. The morphology of the nanotaper was controlled by varying both the growth temperature and the gas flow. Higher growth temperatures resulted in smaller tip angles and a longer nanotaper. Figure 3d shows a ZnO nanotaper with an extremely small tip angle (about 1-2°) and a length of 77 µm grown at 930 °C. The photoluminescence (PL) properties of a single taper were observed using a He-Cd laser (325 nm line) at room temperature. To explore the PL characteristics of the single ZnO nanotaper shown in the inset of Figure 4a, a laser beam was focused onto a 1 µm diameter spot using an objective lens. At room temperature, a broad band-edge emission peak with a full width at half the maximum of ∼135 meV was observed at ∼382 nm, as shown in Figure 4c. An optical pumped lasing experiment was performed using the pulsed laser excitation (repetition frequency of 10 Hz) of a frequencytripled line of a Nd:YAG laser at room temperature. Figure 4a shows the PL spectra as a function of excitation power
multiple modes could be easily described by guided wave theory.1 The relationship between diameter and total transverse mode number (Ntotal ≈ 4d/λ02(nZnO2 -1), where d is the diameter, λ0 is the wavelength in vacuum, and nZnO is the effective refractive index) indicates that multiple modes can exist when d is above 132 nm. Since higher-order modes have small effective refractive indices, that is, small propagation constants in comparison with those of a fundamental mode, a reduction in the waveguide diameter caused the higher-order modes to disappear first. The higher-order transverse modes disappeared as the diameter decreased, and when the taper diameter was less than 240 nm (the leftmost picture in Figure 2c), almost all higher-order modes had degenerated. Subsequently, the surviving fundamental mode was reflected by the distributed mirror at the apex of the nanotaper. The tip angle will affect optical gain by changing the cavity length, hence the quality factor of a resonator, the Q-factor, will increase rapidly in the small tip angle region, due to an increase in cavity length (see Figure S1 in Supporting Information).The results of the simulation described above clearly indicate that lasing from the novel optical cavity is possible. Zinc oxide (ZnO) nanotapers obtained by bottom-up growth were used22 to explore the formation of the exotic optical cavity. ZnO is a good candidate for the study of optical phenomena and for application in optoelectronic devices due to its large direct bandgap (3.37 eV) and exciton binding energy (60 meV).23,24 ZnO supports stable excitonic emission, even at room temperature. The geometric properties of the as-grown ZnO structures were characterized by scanning electron microscopy (SEM, Hitachi S-4300E at 5 kV) and transmission electron microscopy (TEM, JEM-3000F at 300 kV). ZnO nanotaper structures were grown on a SiO2 (400 nm)-coated Si (100) substrate by a vapor-solid reaction using carbothermic reduction of ZnO powder in a flowing gas mixture (95% Ar, O2 5%, 50 sccm) at a local tempera© 2010 American Chemical Society
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FIGURE 4. Lasing action from a single ZnO nanotaper. (a) Excitation-power-dependent PL recorded from a ZnO nanotaper at room temperature. The inset shows a typical SEM image of a ZnO nanotaper. (b) Plot of PL intensity and fwhm as a function of excitation power. (c) PL of a ZnO nanotaper under excitation by a He-Cd laser and laser emission under an excitation power of 3 MW/cm2 (Nd:YAG). (d) Excitation-powerdependent PL intensity recorded from a thin nanotaper. The inset of Figure 4d shows an optical image of lasing from the nanotaper under excitation of 0.4 MW/cm2. Scale bar represents 20 µm.
could be resolved. For example, for nanotapers 17 µm in length, the LM was determined to be 2.26 nm. When the Fabry-Perot interference condition was applied to the LM, a cavity with a length of 11.4 µm was obtained.26 The cavity length calculated from LM was considerably less than the actual length of the nanotaper. The threshold excitation power (160 kW/cm2) for lasing was considerably smaller than that (400 kW/cm2) of the nanotaper with a larger tip angle (10-18°), as shown in Figure 4b. Direct observation of the optical field distribution during lasing was attempted using a CCD camera under an excitation power of ∼3 MW/ cm2, as shown in Supporting Information Figure S2a. The far-field pattern of the sharp nanotaper during lasing is shown in the inset of Figure 4d and Supporting Information Figure S3. The resonator cavity was confirmed by the bright emissions in tapered regions with diameters of less than 100 nm and at the end of the nanotaper. The emission characteristics were consistent with the simulated radiation at the tapered region. In summary, a laser cavity formed in a nanotaper due to the inherent geometric properties of nanotapers. In the present study, the nanometer-scale geometry of the apex acted as a reflector, which led to optical gain in the ZnO
density. At low excitation power, the luminescence intensity increased almost linearly with the excitation power. However, above a threshold power of ∼0.4 MW/cm2, the intensity rapidly increased and line-width abruptly decreased from 120 to 30 meV, as shown in Figure 4b (and in the spectra in Figure 4a,c,d). All lasing spectra revealed a considerable red shift. Under weak excitation conditions, a dominant peak was observed at 380-388 nm. However, even with a low excitation energy (
