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GaN Nanocolumns
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ScienceDirect Physics Procedia 76 (2015) 68 – 72
The 17th International Conference on Luminescence and Optical Spectroscopy of Condensed Matter (ICL2014)
Light localization and stimulated emission in InGaN/GaN nanocolumns Y. Inosea,*, H. Uedaa, N. Shimosakoa, K. Emaa,b, Y. Igawaa, and K. Kishinoa,b a Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan Sophia Nanotechnology Research Center, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan
b
Abstract We report the dependence of stimulated emission phenomena on randomness in a collection of regularly arranged InGaN/GaN nanocolumns. By comparing the stimulated emission behavior for two samples with different degrees of randomness, we found that localization effects are inevitable even in the almost perfect sample, and several modes partially overlapping in space will compete with each other. The ultrafast dynamics of stimulated emission under femtosecond pulsed laser excitation were also investigated, and the emission peaks were observed to change with time. ©©2015 Authors. Published by Elsevier B.V. B.V. This is an open access article under the CC BY-NC-ND license 2015The The Authors. Published by Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of The Organizing Committee of the 17th International Conference on Luminescence and Peer-review under responsibility of The Organizing Committee of the 17th International Conference on Luminescence and Optical Optical Spectroscopy of Condensed Matter. Spectroscopy of Condensed Matter Keywords: random lasing; Anderson localization; distributed feedback; photonic crystal; nanostructure; InGaN; indium gallium nitride; nanocolumn; nanorod;
1. Introduction In two-dimensional (2D) random dielectric systems, the combination of multiple-light scattering and opticalinterference effects induces Anderson localization of light [1]. Furthermore, the localized light can form closed loop paths, and lasing action may occur if a gain mechanism is introduced into the system [2]. In previous word with 2D samples composed of a disordered array of self-organized gallium nitride (GaN) nanocolumns [3], multiple strong emission peaks were detected, suggesting that we observed “random lasing” on the GaN nanocolumns [4]. On the other hand, in 2D periodic systems, photonic band structures are formed [5]. Lasing modes over a large periodic 2D area can be controlled using a multi-directional distributed feedback (DFB) mechanism [6]. However, it
1875-3892 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of The Organizing Committee of the 17th International Conference on Luminescence and Optical Spectroscopy of Condensed Matter doi:10.1016/j.phpro.2015.10.012
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Y. Inose et al. / Physics Procedia 76 (2015) 68 – 72
is difficult in practice to produce perfect photonic crystal samples. In a previous paper the authors reported a clear relationship between the strength of light localization and the occurrence of random laser action through numerical calculations [7]. We report here the dependence of stimulated emission on the randomness in the periodic nanocolumn samples. The samples consisted of parallel nano-sized columnar indium gallium nitride (InGaN) crystals. Since InGaN can emit at wavelengths over the full visible region, this semiconductor shows promise for use in novel light-emitting devices. However, in the case of film samples, internal electric fields and threading dislocation are formed because of the crystal lattice strain, leading to degraded luminescent properties with decreased emission photon energy. On the other hand, it has been found that semiconductor nanocolumns show strong photoluminescence (PL) due to their high crystal quality [8]. In addition, these columns have nano-scale structure as an important feature. We have thus focused on light propagation phenomena in periodic nanocolumn samples. 2. Samples and Experiment Setup Two different samples, labeled as sample-1 and sample-2, were prepared for this study. Figures 1 (a) and (b) show the top views of the scanning electron microscope (SEM) images of the samples. These samples consist of regularly arranged GaN nanocolumns produced using the selective area growth (SAG) method [9], and InGaN/GaN multiple quantum wells (MQWs) were integrated in the upper portions of the samples. The target thickness of the InGaN well layers and the GaN barrier layers in the MQWs were 3 and 12 nm, respectively. The resulting regular configuration is known as a photonic crystal, in which Bragg diffraction is the most dominant effect, producing photonic band structures and photonic lasers. Both samples seem to be neatly aligned, but they are not perfect photonic crystals.
(a)
(b)
1 μm
1 μm H~ k
(c)
100 (d)
10-5
Fig. 1. Top view SEM images for the nanocolumn arrays [(a) sample-1, (b) sample-2], and FT images [(c) sample-1, (d) sample-2].
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Y. Inose et al. / Physics Procedia 76 (2015) 68 – 72
In order to investigate the degree of randomness of the samples, we first converted the SEM images to spatial images to simply the analysis of the spatial information at the single-bit level. Next, we computed the Fourier transform (FT) of the spatial images, and obtained FT images in wave-number space, as shown in Figs. 1 (c) and (d). It can be seen that the column configuration of sample-1 is somewhat imperfect, while that of sample-2 is almost perfect. We performed optical experiments using a microspectroscopy system because the area of each sample was a square as small as 150 μm on a side. We measured the PL from the samples at liquid nitrogen temperature, namely 77 K. The center photon energy of the incident pulsed laser was 3.1 eV, the pulse width was about 200 fs, and the repetition rate was 10 kHz. The pump pulse was focused onto the samples using a lens with a focal length of 200 mm to excite a wide area for investigating light propagation phenomena. The spot-size at the sample surface was about 60 μm in diameter. In this experiment, the objective lens of the microspectroscopy system was used to identify the precise position of the samples and collect the emission from the samples. 3. Experiment Results and Discussion A previous study found that in periodic InGaN/GaN nanocolumn samples, strong emission peaks were observed under nanosecond-pulsed laser excitation [11]. The single-shot spectrum changed randomly from one pump pulse to another, and it was found that several sharp peaks were localized at different areas. These results are typical behavior for random lasing, suggesting that these sharp emissions were not coming from the photonic effect, but from random lasing. Since our sample does not have a completely perfect lattice, the localization effect is inevitable. In this paper, we report the stimulated emission dynamics observed using a femtosecond pulsed laser, and the dependence of stimulated emission on the randomness of the periodic samples. We have observed excitation-density dependence of the PL spectra from the nanocolumns, as shown in Figs. 2 (a) and (b). In these figures, the horizontal axes are shifted gradually to the right with increasing excitation density to make them more visible. As the pump power was increased, stimulated emission peaks appeared in both samples. We performed numerical calculations based on plane-wave expansion methods [10], and the results indicated that the selectivity of photon energy for light propagation phenomena is derived from the Bragg diffraction effect. Figures 3 (a) and (b) show the spatial distribution of the stimulation emission. The white ellipses show the beam waist of the excitation laser. One can see that the brightness is inhomogeneous in sample-1, while the brightness is almost homogeneous in sample-2. These results are consistent with the FT images in Figs. 1 (c) and (d). Spectra in Fig. 2 seem to indicate perfect photonic laser action from the nanocolumn ensemble. However, we found that a slight fluctuation of the sample configuration has a large effect on the spatial distribution of the stimulated emission. We presume that the stimulated emission occurs in small areas corresponding to each different photon energy in sample1 as discussed in Ref. [11].
Wavelength (nm)
PL Intensity (arb. units)
600
550
Excitation Density 2 (MW/cm ) 20812 6547 2092 1468 659 205 66
2.0
2.2 2.4 2.6 Photon Energy (eV)
Wavelength (nm)
(b)
500
650 600
PL Intensity (arb. units)
(a)
550
500
450
Excitation Density 2 (MW/cm ) 20245 6441 2028 1357 669 202 65
1.8
2.0
2.2 2.4 2.6 2.8 Photon Energy (eV)
3.0
Fig. 2. Spontaneous emission and stimulated emission spectra [(a) sample-1, (b) sample-2].
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Y. Inose et al. / Physics Procedia 76 (2015) 68 – 72
(a)
(b)
100
524
Wavelength (nm) 522 520
(d)
518
Intensity (arb. units)
Intensity (arb. units)
(c) 80 60 40 20 0
2.36
2.37 2.38 2.39 Photon Energy (eV)
2.40
100
538
Wavelength (nm) 536 534
532
530
80 60 40 20 0
2.30
2.31 2.32 2.33 Photon Energy (eV)
2.34
Fig. 3. Spatial distribution of stimulated emission [(a) sample-1, (b) sample-2], and spatial dependence of stimulated emission spectra over areas with a diameter of 2.5μm [(c) sample-1, (d) sample-2] at 6.5 GW/cm2. In order to test this presumption, we observed the spatial dependence of the stimulated emission spectra for the lowest threshold modes in Fig. 2. Figures 3 (c) and (d) show the stimulated emission spectra at eight different areas, where each spectrum is detected from an area 2.5 μm in diameter on the samples. These spectral shapes from the small areas are quite different from each other in sample-1, while the shapes are nearly identical among the different points in sample-2. These results indicate that sample-1 is apparently random lasing because of the configuration fluctuation. While sample-2 also shows some configuration fluctuation, it is very close to nearly perfect photonic lasing. This experiment verifies that slight fluctuations of the sample configuration have a large effect on the stimulated emission. In the case of nanosecond pulsed laser excitation, the spectral shape changes randomly because only a few modes can survive for the relatively long excitation time. On the other hand, the spectral line width under femtosecond pulsed laser excitation seems large for a single DFB mode. We postulate that the stimulated emission occurs for all the localization modes under the short excitation time, and many modes compete with each other under the femtosecond pulsed laser even in the almost perfect sample-2. Finally, we show time-resolved spectra of the stimulated emission on sample-2 measured using a high-speed streak camera in Fig. 4. This result indicates that the stimulated emission dynamics occur on an ultrafast time scale. We found that the photon energy of each emission peak changed slightly over time, and the amount of the shift was different among the three peaks. In the DFB phenomenon, the spatial pattern of the standing wave differs from one mode to another, thus the non-linear optical effects may vary a great deal depending on the DFB modes. With our high-speed streak camera, we cannot resolve this fast relaxation process because the relaxation time is less than the time resolution. In order to clarify this, we are planning to perform ultrafast time-resolved measurements, using the Kerr-gate method.
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Y. Inose et al. / Physics Procedia 76 (2015) 68 – 72
Fig. 4. Time-resolved spectra of stimulated emission on sample-2 at 6.5 GW/cm2. 4. Conclusion We have observed the randomness dependence of stimulated emission phenomena in regularly-arranged InGaN/GaN nanocolumns. We estimated the randomness of the sample configurations by computing the Fourier transform of the spatial images of the samples, and compared the stimulated emission behavior for two samples with different degrees of randomness. This work showed that several modes are present in different areas of an imperfect sample, and a distributed feedback effect is prominently visible in the almost perfect sample. However, we found that several modes which partially overlapped in the same space appeared to compete with each other, even in the almost perfect sample. These results indicate that localization effects are inevitable in any sample because there is no such thing as a perfect lattice. We also investigated the ultrafast time response of stimulated emission under femtosecond pulsed laser excitation. We observed that the emission peaks changed with time, and that the shift amounts differed from each other because the several modes present had diverse spatial patterns. Acknowledgements This work was supported by JSPS KAKENHI Grant Numbers 25800180, 24000013. References [1] John, S., 1984. Electromagnetic Absorption in a Disordered Medium near a Photon Mobility Edge. Physical Review Letters 53, 2169. [2] Cao, H., Xu, J. Y., Zhang, D. Z., Chang, S.-H., Ho, S. T., Seelig, E. W., Liu, X., Chang, R. P. H., 2000, Spatial Confinement of Laser Light in Active Random Media. Physical Review Letters 84, 5584. [3] Yoshizawa, M., Kikuchi, A., Mori, M., Fujita, N., Kishino, K., 1997. Growth of Self-Organized GaN Nanostructures on Al2O3(0001) by RFRadical Source Molecular Beam Epitaxy. Japanise Journal of Applied Physics, Part2 36, L459. [4] Sakai, M., Inose, Y., Ema, K., Ohtsuki, T., Sekiguchi, H., Kikuchi, A., Kishino, K., 2010. Random laser action in GaN nanocolumns. Applied Physics Retters 97, 151109. [5] Yablonovitch, E., 1987. Inhibited Spontaneous Emission in Solid-State Physics and Electrons. Physical Review Letters 58, 2059. [6] Imada, M., Chutinan, A., Noda, S., Mochizuki, M., 2002. Multidirectionally distributed feedback photonic crystal lasers. Physical Review B 65, 195306. [7] Inose, Y., Sakai, M., Ema, K., Kikuchi, A., Kishino, K., Ohtsuki, T., 2010. Light localization characteristics in a random configuration of dielectric cylindrical columns. Physical Review B 82, 205328. [8] Kikuchi, A., Yamano, K., Tada, M., Kishino, K., 2004. Stimulated emission from GaN nanocolumns. Physica Status Solidi (b) 241, 2754. [9] Kishino, K., Sekiguchi, H., Kikuchi, A., 2009. Improved Ti-mask selective-area growth (SAG) by rf-plasma-assisted molecular beam epitaxy demonstrating extremely uniform GaN nanocolumn arrays. Journal of Crystal Growth 311, 2063. [10] Plihal, M., Maradudin, A. A., 1991. Photonic band structure of two-dimensional systems: The triangular lattice. Physical Review B 44, 8565. [11] Ishizawa, S., Kishino, K., Araki, R., Kikuchi, A., Sugimoto, S., 2011. Optically Pumped Green (530–560 nm) Stimulated Emissions from InGaN/GaN Multiple-Quantum-Well Triangular-Lattice Nanocolumn Arrays. Applied Physics Express 4, 055001.
ScienceDirect Physics Procedia 76 (2015) 68 – 72
The 17th International Conference on Luminescence and Optical Spectroscopy of Condensed Matter (ICL2014)
Light localization and stimulated emission in InGaN/GaN nanocolumns Y. Inosea,*, H. Uedaa, N. Shimosakoa, K. Emaa,b, Y. Igawaa, and K. Kishinoa,b a Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan Sophia Nanotechnology Research Center, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan
b
Abstract We report the dependence of stimulated emission phenomena on randomness in a collection of regularly arranged InGaN/GaN nanocolumns. By comparing the stimulated emission behavior for two samples with different degrees of randomness, we found that localization effects are inevitable even in the almost perfect sample, and several modes partially overlapping in space will compete with each other. The ultrafast dynamics of stimulated emission under femtosecond pulsed laser excitation were also investigated, and the emission peaks were observed to change with time. ©©2015 Authors. Published by Elsevier B.V. B.V. This is an open access article under the CC BY-NC-ND license 2015The The Authors. Published by Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of The Organizing Committee of the 17th International Conference on Luminescence and Peer-review under responsibility of The Organizing Committee of the 17th International Conference on Luminescence and Optical Optical Spectroscopy of Condensed Matter. Spectroscopy of Condensed Matter Keywords: random lasing; Anderson localization; distributed feedback; photonic crystal; nanostructure; InGaN; indium gallium nitride; nanocolumn; nanorod;
1. Introduction In two-dimensional (2D) random dielectric systems, the combination of multiple-light scattering and opticalinterference effects induces Anderson localization of light [1]. Furthermore, the localized light can form closed loop paths, and lasing action may occur if a gain mechanism is introduced into the system [2]. In previous word with 2D samples composed of a disordered array of self-organized gallium nitride (GaN) nanocolumns [3], multiple strong emission peaks were detected, suggesting that we observed “random lasing” on the GaN nanocolumns [4]. On the other hand, in 2D periodic systems, photonic band structures are formed [5]. Lasing modes over a large periodic 2D area can be controlled using a multi-directional distributed feedback (DFB) mechanism [6]. However, it
1875-3892 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of The Organizing Committee of the 17th International Conference on Luminescence and Optical Spectroscopy of Condensed Matter doi:10.1016/j.phpro.2015.10.012
69
Y. Inose et al. / Physics Procedia 76 (2015) 68 – 72
is difficult in practice to produce perfect photonic crystal samples. In a previous paper the authors reported a clear relationship between the strength of light localization and the occurrence of random laser action through numerical calculations [7]. We report here the dependence of stimulated emission on the randomness in the periodic nanocolumn samples. The samples consisted of parallel nano-sized columnar indium gallium nitride (InGaN) crystals. Since InGaN can emit at wavelengths over the full visible region, this semiconductor shows promise for use in novel light-emitting devices. However, in the case of film samples, internal electric fields and threading dislocation are formed because of the crystal lattice strain, leading to degraded luminescent properties with decreased emission photon energy. On the other hand, it has been found that semiconductor nanocolumns show strong photoluminescence (PL) due to their high crystal quality [8]. In addition, these columns have nano-scale structure as an important feature. We have thus focused on light propagation phenomena in periodic nanocolumn samples. 2. Samples and Experiment Setup Two different samples, labeled as sample-1 and sample-2, were prepared for this study. Figures 1 (a) and (b) show the top views of the scanning electron microscope (SEM) images of the samples. These samples consist of regularly arranged GaN nanocolumns produced using the selective area growth (SAG) method [9], and InGaN/GaN multiple quantum wells (MQWs) were integrated in the upper portions of the samples. The target thickness of the InGaN well layers and the GaN barrier layers in the MQWs were 3 and 12 nm, respectively. The resulting regular configuration is known as a photonic crystal, in which Bragg diffraction is the most dominant effect, producing photonic band structures and photonic lasers. Both samples seem to be neatly aligned, but they are not perfect photonic crystals.
(a)
(b)
1 μm
1 μm H~ k
(c)
100 (d)
10-5
Fig. 1. Top view SEM images for the nanocolumn arrays [(a) sample-1, (b) sample-2], and FT images [(c) sample-1, (d) sample-2].
70
Y. Inose et al. / Physics Procedia 76 (2015) 68 – 72
In order to investigate the degree of randomness of the samples, we first converted the SEM images to spatial images to simply the analysis of the spatial information at the single-bit level. Next, we computed the Fourier transform (FT) of the spatial images, and obtained FT images in wave-number space, as shown in Figs. 1 (c) and (d). It can be seen that the column configuration of sample-1 is somewhat imperfect, while that of sample-2 is almost perfect. We performed optical experiments using a microspectroscopy system because the area of each sample was a square as small as 150 μm on a side. We measured the PL from the samples at liquid nitrogen temperature, namely 77 K. The center photon energy of the incident pulsed laser was 3.1 eV, the pulse width was about 200 fs, and the repetition rate was 10 kHz. The pump pulse was focused onto the samples using a lens with a focal length of 200 mm to excite a wide area for investigating light propagation phenomena. The spot-size at the sample surface was about 60 μm in diameter. In this experiment, the objective lens of the microspectroscopy system was used to identify the precise position of the samples and collect the emission from the samples. 3. Experiment Results and Discussion A previous study found that in periodic InGaN/GaN nanocolumn samples, strong emission peaks were observed under nanosecond-pulsed laser excitation [11]. The single-shot spectrum changed randomly from one pump pulse to another, and it was found that several sharp peaks were localized at different areas. These results are typical behavior for random lasing, suggesting that these sharp emissions were not coming from the photonic effect, but from random lasing. Since our sample does not have a completely perfect lattice, the localization effect is inevitable. In this paper, we report the stimulated emission dynamics observed using a femtosecond pulsed laser, and the dependence of stimulated emission on the randomness of the periodic samples. We have observed excitation-density dependence of the PL spectra from the nanocolumns, as shown in Figs. 2 (a) and (b). In these figures, the horizontal axes are shifted gradually to the right with increasing excitation density to make them more visible. As the pump power was increased, stimulated emission peaks appeared in both samples. We performed numerical calculations based on plane-wave expansion methods [10], and the results indicated that the selectivity of photon energy for light propagation phenomena is derived from the Bragg diffraction effect. Figures 3 (a) and (b) show the spatial distribution of the stimulation emission. The white ellipses show the beam waist of the excitation laser. One can see that the brightness is inhomogeneous in sample-1, while the brightness is almost homogeneous in sample-2. These results are consistent with the FT images in Figs. 1 (c) and (d). Spectra in Fig. 2 seem to indicate perfect photonic laser action from the nanocolumn ensemble. However, we found that a slight fluctuation of the sample configuration has a large effect on the spatial distribution of the stimulated emission. We presume that the stimulated emission occurs in small areas corresponding to each different photon energy in sample1 as discussed in Ref. [11].
Wavelength (nm)
PL Intensity (arb. units)
600
550
Excitation Density 2 (MW/cm ) 20812 6547 2092 1468 659 205 66
2.0
2.2 2.4 2.6 Photon Energy (eV)
Wavelength (nm)
(b)
500
650 600
PL Intensity (arb. units)
(a)
550
500
450
Excitation Density 2 (MW/cm ) 20245 6441 2028 1357 669 202 65
1.8
2.0
2.2 2.4 2.6 2.8 Photon Energy (eV)
3.0
Fig. 2. Spontaneous emission and stimulated emission spectra [(a) sample-1, (b) sample-2].
71
Y. Inose et al. / Physics Procedia 76 (2015) 68 – 72
(a)
(b)
100
524
Wavelength (nm) 522 520
(d)
518
Intensity (arb. units)
Intensity (arb. units)
(c) 80 60 40 20 0
2.36
2.37 2.38 2.39 Photon Energy (eV)
2.40
100
538
Wavelength (nm) 536 534
532
530
80 60 40 20 0
2.30
2.31 2.32 2.33 Photon Energy (eV)
2.34
Fig. 3. Spatial distribution of stimulated emission [(a) sample-1, (b) sample-2], and spatial dependence of stimulated emission spectra over areas with a diameter of 2.5μm [(c) sample-1, (d) sample-2] at 6.5 GW/cm2. In order to test this presumption, we observed the spatial dependence of the stimulated emission spectra for the lowest threshold modes in Fig. 2. Figures 3 (c) and (d) show the stimulated emission spectra at eight different areas, where each spectrum is detected from an area 2.5 μm in diameter on the samples. These spectral shapes from the small areas are quite different from each other in sample-1, while the shapes are nearly identical among the different points in sample-2. These results indicate that sample-1 is apparently random lasing because of the configuration fluctuation. While sample-2 also shows some configuration fluctuation, it is very close to nearly perfect photonic lasing. This experiment verifies that slight fluctuations of the sample configuration have a large effect on the stimulated emission. In the case of nanosecond pulsed laser excitation, the spectral shape changes randomly because only a few modes can survive for the relatively long excitation time. On the other hand, the spectral line width under femtosecond pulsed laser excitation seems large for a single DFB mode. We postulate that the stimulated emission occurs for all the localization modes under the short excitation time, and many modes compete with each other under the femtosecond pulsed laser even in the almost perfect sample-2. Finally, we show time-resolved spectra of the stimulated emission on sample-2 measured using a high-speed streak camera in Fig. 4. This result indicates that the stimulated emission dynamics occur on an ultrafast time scale. We found that the photon energy of each emission peak changed slightly over time, and the amount of the shift was different among the three peaks. In the DFB phenomenon, the spatial pattern of the standing wave differs from one mode to another, thus the non-linear optical effects may vary a great deal depending on the DFB modes. With our high-speed streak camera, we cannot resolve this fast relaxation process because the relaxation time is less than the time resolution. In order to clarify this, we are planning to perform ultrafast time-resolved measurements, using the Kerr-gate method.
72
Y. Inose et al. / Physics Procedia 76 (2015) 68 – 72
Fig. 4. Time-resolved spectra of stimulated emission on sample-2 at 6.5 GW/cm2. 4. Conclusion We have observed the randomness dependence of stimulated emission phenomena in regularly-arranged InGaN/GaN nanocolumns. We estimated the randomness of the sample configurations by computing the Fourier transform of the spatial images of the samples, and compared the stimulated emission behavior for two samples with different degrees of randomness. This work showed that several modes are present in different areas of an imperfect sample, and a distributed feedback effect is prominently visible in the almost perfect sample. However, we found that several modes which partially overlapped in the same space appeared to compete with each other, even in the almost perfect sample. These results indicate that localization effects are inevitable in any sample because there is no such thing as a perfect lattice. We also investigated the ultrafast time response of stimulated emission under femtosecond pulsed laser excitation. We observed that the emission peaks changed with time, and that the shift amounts differed from each other because the several modes present had diverse spatial patterns. Acknowledgements This work was supported by JSPS KAKENHI Grant Numbers 25800180, 24000013. References [1] John, S., 1984. Electromagnetic Absorption in a Disordered Medium near a Photon Mobility Edge. Physical Review Letters 53, 2169. [2] Cao, H., Xu, J. Y., Zhang, D. Z., Chang, S.-H., Ho, S. T., Seelig, E. W., Liu, X., Chang, R. P. H., 2000, Spatial Confinement of Laser Light in Active Random Media. Physical Review Letters 84, 5584. [3] Yoshizawa, M., Kikuchi, A., Mori, M., Fujita, N., Kishino, K., 1997. Growth of Self-Organized GaN Nanostructures on Al2O3(0001) by RFRadical Source Molecular Beam Epitaxy. Japanise Journal of Applied Physics, Part2 36, L459. [4] Sakai, M., Inose, Y., Ema, K., Ohtsuki, T., Sekiguchi, H., Kikuchi, A., Kishino, K., 2010. Random laser action in GaN nanocolumns. Applied Physics Retters 97, 151109. [5] Yablonovitch, E., 1987. Inhibited Spontaneous Emission in Solid-State Physics and Electrons. Physical Review Letters 58, 2059. [6] Imada, M., Chutinan, A., Noda, S., Mochizuki, M., 2002. Multidirectionally distributed feedback photonic crystal lasers. Physical Review B 65, 195306. [7] Inose, Y., Sakai, M., Ema, K., Kikuchi, A., Kishino, K., Ohtsuki, T., 2010. Light localization characteristics in a random configuration of dielectric cylindrical columns. Physical Review B 82, 205328. [8] Kikuchi, A., Yamano, K., Tada, M., Kishino, K., 2004. Stimulated emission from GaN nanocolumns. Physica Status Solidi (b) 241, 2754. [9] Kishino, K., Sekiguchi, H., Kikuchi, A., 2009. Improved Ti-mask selective-area growth (SAG) by rf-plasma-assisted molecular beam epitaxy demonstrating extremely uniform GaN nanocolumn arrays. Journal of Crystal Growth 311, 2063. [10] Plihal, M., Maradudin, A. A., 1991. Photonic band structure of two-dimensional systems: The triangular lattice. Physical Review B 44, 8565. [11] Ishizawa, S., Kishino, K., Araki, R., Kikuchi, A., Sugimoto, S., 2011. Optically Pumped Green (530–560 nm) Stimulated Emissions from InGaN/GaN Multiple-Quantum-Well Triangular-Lattice Nanocolumn Arrays. Applied Physics Express 4, 055001.