Abstract

As an advantage, random lasers may be elaborated from a large variety of materials and do not require any cavity oscillators that usually necessitate complicated and expensive fabrication techniques. Since the feedback process of those non-conventional laser systems is provided by light interference in a disordered medium, spectral and temporal uncertainties are usually considered as an intrinsic part of their optical proprieties. We investigated random laser action under two photon absorption experiments through an auto-organized InGaN/GaN quantum-disks ensemble. Thanks to our experimental approach, we evidence random lasing based on a gain medium constituted by point-sized structures. In such context, a stabilised and individual emission mode is observed as for conventional semiconductor lasers. By controlling the emission energy of these nanostructures, a tuneable and stable random laser may be built. Moreover, our findings suggest that disordered medium should play an important role in the conception of low cost quantum dot and up conversion laser systems.

© 2011 OSA

1. Introduction

Random lasers [1] are based on the intimate combination between a disordered medium that confines light and a gain medium that amplifies light. Such laser systems have a huge application potential because they can be elaborated from a large variety of materials [26], fabricated on diverse material surfaces, and do not require any cavity oscillators that usually necessitate complicated and expensive fabrication techniques. As their feedback processes are provided by light multi-scattering through a disordered medium, the laser modes are randomly distributed in the structure. Because of mode competition and mode repulsion that occur via the gain medium [7], the emission energy and the temporal dynamic of a random laser are difficult to predict. Therefore, spectral and temporal uncertainties are invariably considered as intrinsic properties of random lasers and are characterised by multimode emission and stochastic frequency behaviour [8, 9]. If these optical properties lead to interesting applications such as all optical fast random numbers generator [10], they also restrain considerably the application field of random lasers, because many optical devices necessitate single mode laser system operating in non-stochastic regime.

In the present work, we investigated random laser action in a disordered InGaN/GaN quantum-disks (Q-disks) ensemble. By using two photon absorption processes, we selectively pumped the point-sized (PS) structures that are included in the InGaN active layer of the Q-disks [11]. In such context, the lasing action arising from the system is produced exclusively by stimulated emission from the PS structures. Hence, one can consider our random laser system as a cavityless quantum dot laser. Y. Chen et al. [12] reported very recently random lasing on colloidal CdSe/ZnS quantum dots system dispersed into a rough micron-scale groove fabricated on glass substrate. Nevertheless, to the best of our knowledge, random laser action based on quantum dots structures fabricated by epitaxy and therefore embedded inside a three dimensional semiconductor matrix has not been reported yet. Indeed, it is technically difficult to isolate such random lasing by conventional experimental approach (one photon absorption experiments) because it would be hidden by the luminescence from the surrounding of the quantum dots system. From now on, quantum dot-like random laser systems can be envisaged based in all-optical-communication semiconductor materials system.

2. Experiment and results

We investigated random laser action in a disordered medium constituted by auto-organized InGaN/GaN semiconductor Q-disks. The sample was grown by molecular-beam epitaxy with a nitrogen-plasma source on a 0001-oriented sapphire substrate [13]. The Q-disks are constituted by an embedded 5 nm InGaN active layer between a 1.45 µm GaN nanocolumn and a 35 nm GaN capping layer. Their lateral size ranges between 80 and 150 nm; their spatial density is about 7×109 cm−2; the estimated filling fraction is about 0.5 ± 0.2 [14]. The sample was cooled at 10 K. In two photon absorption (TPA) experiment, we used the fundamental mode of a pulsed Ti-Sapphire laser emitting at 800 nm. The repetition rate and the duration of the pulses were respectively set at 80 MHz and 10 ps. A 40× optical objective lens was used to excite and also to collect the luminescence. The laser spot size is of 2.5 µm. Thus, as we see in Fig. 1(a) , each laser pulse covers about 300 Q-disks. The luminescence was dispersed by a 50 cm spectrometer mounted by a 600 groves/mm grating and coupled to a nitrogen-cooled charged-couple device (CCD). The experimental setup is depicted in Fig. 1(b).

 

Fig. 1 (a) Scanning electron microscope image from the top of the Q-disks sample; the green circular and dashed line represents laser the spot size under two photon absorption experiments. (b) Simplified schematic of the experimental set up. Micro-photoluminescence spectra acquired at the same location on the quantum disks sample for a laser excitation energy set (c) at 3.1 eV under one photon absorption experiment and (d) at 1.55 eV under two photon absorption. The acquisition time was set at 500 ms and 5 s respectively. In inset of Fig. 1(d) we plotted the power dependency of the integrated intensity of the peaks X and XX.

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The InGaN active layer of the Q-disks contains PS structures formed by local fluctuation of the indium composition that occurred during the growth process [11]. These PS structures confine the photo-created electron-hole (e-h) pairs in all the spatial directions. In the present study we aimed to use these PS nanostructures as the gain medium of our random laser system. To this end, we blocked the recombination of the photo-created e-h pairs out of the PS structures by using TPA as the pump process. Indeed, it has been demonstrated by Jarjour et al. in Ref [15]. that the implication of virtual states in the TPA process [16] drastically increased the capture cross section of PS structures at the expense of the surrounding semiconductor matrix. Hence, by analogy with a random laser made of cold atom, the gain medium and the scattering material of our random laser system are constituted by the same entity (the InGaN/GaN quantum disks) and the stimulated emission is induced by individual “dipoles” (excitons that are confined in the PS structures) [17].

Figure 1(c) shows a micro-photoluminescence spectrum collected from the Q-disks ensemble under one photon absorption experiment. This spectrum exhibits several broad emission peaks centred at 2.2, 2.3, 2.5, and 2.8 eV that arise from the luminescence of a large number of Q-disks. In such conditions, any random laser action engendered by the PS structures is hidden by the luminescence from the entire InGaN layer of the Q-disks. In Fig. 1(d) we show the µPL spectrum collected at the same position than in Fig. 1(c), but obtained by TPA excitation. We remark that only two groups of sharp peaks, centred at 2.55 eV and 2.90 eV subsist in the spectrum. Those sharp emission peaks arise from the spontaneous recombination of excitonic complexes trapped in PS structures [11]. The inset of Fig. 1(b) depicts the integrated intensity of the peaks X and XX with the power excitation density (P). We observe that X and XX depend respectively in P2 and P4. Such power dependencies characterised the emission peak of an exciton (peak X) and a bi-exciton (peak XX) [17] that are both confined in the same PS structures; the negative value of the bi-exciton binding energy of −46 meV confirms that the PS structures confine the exciton in all spatial directions [18]. On over 20 different positions investigated over the entire sample, we reach the same conclusion as Jarjour et al. [15]: TPA preferentially populates PS nanostructures. Thus, those preliminary results legitimatize the use of TPA techniques in the investigation of random laser generated by PS structures.

As expected, aside from spontaneous emission processes generated by TPA, stimulated emission processes are also encounter from some specific position on the sample. For instance, Figs. 2(a) and (b) exhibit two spectra collected in two different locations where the main luminescence process differs from spontaneous emission. Indeed, as it happen for peaks D and E, we remark that by increasing the excitation power density a single peak dominates these spectra. Interestingly, while the peak D’ in Fig. 2(a) exhibit a quadratic dependency with P (inset of Fig. 2(c)), i.e. a spontaneous emission character, the main peak D exhibit a linear dependency above a threshold at 3.5 MW/cm2 (see Fig. 2(c)) accompanied by a narrowing (see Fig. 2(d)) of its full width at half maximum (FWHM). The same behavior is observed in the case of peak E (not plotted here): after a threshold at 1.5 MV/cm2, its integrated intensity increases linearly with P, accompanied by a narrowing of its FWHM. A similar result has been found by numerical calculation on random system in Ref [19]. In this reference, the emission processes below the threshold were attributed to amplified spontaneous emission. As such stimulated emission process is not observed in the spectra from single Q-disk spectroscopy under TPA excitation, we conclude that D and E are issued from a collective effect through the Q-disks ensemble. Moreover, considering the experimental work of Sakai et al. in Ref [14]. and the theoretical calculation of Inose et al. in Ref [20]. realized both on very similar nitride nano-columnar structures, we assert that we exhibit here the occurrence of random laser action in InGaN/GaN Q-disks.

 

Fig. 2 (a) (b) Power dependency spectra obtained under two photon absorption experiment at two different position on the Q-disk sample. (c). Power dependency of the integrated intensity of the peak D plotted in linear scale. In inset of Fig. 2(c), power dependency of the integrated intensity of the peak D’ (see Fig. 2(a)) plotted in log-log scale. (d) Power dependency of the full width at half maximum of the peak D.

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The notable particularity of our system is that the gain medium is constituted by selectively pumped PS structures. As a consequence, our random laser system exhibits a single emission mode (peaks D and E) out of any stochastic behavior as usually observed in random laser systems (for instance in Ref [14] multiple emission modes and chaotic regime are exhibited). Nevertheless, the suppression of the stochastic phenomena occurs also in strongly scattering disordered media. Indeed, in such media, the overlap of the modes that initiate mode competitions is strongly reduced because of the weak spatial extent of the light mode [21]. However, despite the strong scattering character of our disordered medium, Sakai et al. [16] observed stochastic frequency behavior in very similar system to us in which, no InGaN layer is embedded and so, no PS structures exist. Therefore, we conclude that it is the PS structures that we used as gain medium in our system that induce the suppression of the stochastic frequency behavior.

3. Steady states simulation

To evaluate the extent in which random lasing may be generated from the emission of PS structures, we performed simulations using the commercial software “Poynting for Optics” (FUJITSU, Japan). Our FDTD model was built by taking in consideration the real dimension of the Q-disks trough our sample as measured on scanning electron microscope (SEM) images. The quantum disks were modelled by GaN cylinders that have a refractive index of 2.4 [22]. The discretization of the calculation space gives a spatial and a temporal resolution of about 5 nm (in the plan (X, Y)) and 1 attosecond respectively. A perfectly matched layer (PML) [23] has been chosen as boundary condition. To simulate the emission of a single PS structure, we considered a punctual and monochromatic light source S located inside a nanocolumn. This light source emits during the first 10 fs of the calculation. The phase origin is taken at the light source position.

The amplitude distribution of the steady states is plotted in Fig. 3(a) . It appears that the electric field is not uniformly spread and some light paths are formed through the nano-columnar structure. These light paths represent light localization modes that are fed by the punctual source. We observe on Fig. 3(a) a spatial extent of the mode of about 800 nm consistently with the experimental result of Van der Molen et al. [24]. In addition, we plotted in Fig. 3(b), the temporal evolution of the electric field amplitude at a given point M (see Fig. 3(a)). When the light source is set at 700, 500 and 450 nm, we remark that the wave packages in M are weakly delayed and vanish relatively fast. Conversely, when the light source S emits at 400 nm, a strong back and forth effect is observed at M: the spectral distribution of the light localized modes is not uniform in the structure. As a consequence, for a random laser system in a strong localized regime, the laser modes are built on the passive light mode of the disordered medium [25, 26]. In other words, a punctual and monochromatic light source, such as a PS structures, can only feed the preexisting contiguous lasing modes that oscillate in quasi-resonance with its emission energy. This underline the crucial role of the PS structures in the random laser system: thanks to their sharp emission window, the PS structures induce indirectly a drastic reduction of the spectral distribution of the gain. Hence, as the spectral gain distribution is narrowed, modes competition and modes repulsion are suppressed.

 

Fig. 3 (a) Spatial distribution of the amplitude of the electric field steady state through the GaN nanocolumn sample calculated by FDTD simulation. The phase difference with the light source is set at zero. (b) Temporal evolution of the calculated electric field amplitude extracted from the point M (see Fig. 3(a)) considering four different light source emission wavelengths.

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4. Model and discussion

We illustrate in Fig. 4 the mechanism that describes random lasing through the Q-disks ensemble (this mechanism can be generalized to many other random laser systems that include PS structures). Given that the capture time of the PS structures is much faster than the excitonic radiative recombination [11], we describe our laser structure as a three level laser system [27]. As illustrated in Fig. 4(a), an exciton created under TPA at the level “2” in the InGaN layer, relaxes by non-radiative processes into a PS structures state at the energy level 3. Let us now consider a sub-ensemble of Q-disks in which PS structures are selectively populated via TPA processes. The exciton lifetime at the level “3” is much longer than the non radiative transition between levels “2” and “3”, thus above the threshold, the occupation density of the energy level “3” will be more important than for the level “1”; we describe here a classical case of population inversion between levels “1” and “3”. The spatial positions of the Q-disks as well as the energy level of the PS structures from a quantum disk to another are randomly distributed in the structure. Therefore, there is a non-negligible probability to encounter the situation illustrated in Fig. 4(b): a sub-ensemble of PS structures that are emitting in the same narrow spectral range are also located on the light path of a given localized mode. When the resonance frequency of this localized mode matches with the emission energy of this sub-ensemble of PS structures, stimulated emission occurred and gives rise to random laser action as illustrated in Fig. 4(c).

 

Fig. 4 (a) TPA processes at the scale of a single Q-disk: the energy levels 1, 2, and 3 correspond respectively to the ground state of the system, the excited states of the two-dimensional InGaN active layer, and the lowest radiative level of a PS structure state. (b) Sub-ensemble of PS structures selectively excited by TPA and located on the path of a light localized mode. (c) When the emission energy of the sub-ensemble of PS structures matches with the energy resonance of the light localized mode, stimulated emission occurs and gives rise to random laser action.

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In a more prospective way, let’s consider an InGaN/GaN auto-organized nano-columnar heterostructure ensemble fabricated by hetero-epitaxy, and constituted of multiple InGaN active layers as in Ref [28]. By controlling the growth conditions, the nano-columnar heterostructure may be elaborated such as the typical PS structures energy emission differ from an active layer to another. For instance, let’s take nano-columnar hetero-structures that possess three InGaN active layers in which the PS structures of the first layer emit at the typical energy E1, the second layer at the energy E2.and the third one at the energy E3 (with E1< E2< E3). By TPA experiments, we can resonantly populate the PS structures of one of the three layers at the expense of the two others by choosing the adequate pump energy (equal to half of the typical energy of the PS structures). Therefore, from such multi layered disordered nano-columnar systems, one can obtain random lasing with an energy emission set on demand at E1, E2 or E3, depending on the pump energy. Then, as a direct application of our results, the conjoint use of PS structures gain media with the selective TPA pumping seem to be a interesting approach to achieve tunable random laser system.

5. Conclusion

In conclusion, we obtained a condensed matter based random laser system in which the gain medium is composed of atomic-like nanostructures. In addition of providing single and stabilized laser mode emission, our finding shows that we can tune on demand the emission energy of a random laser just by changing the emission wavelength of the PS structures that are designated as the gain medium. Our results should initiate new research axes concerning the coupling between quantum dots systems and electromagnetic field, particularly for the realization of low cost quantum dot lasers, up-conversion lasers and non-linear optics. We strongly believe that disordered media should constitute a key point for the elaboration of quantum communication systems [29].

Acknowledgments

Part of this study was supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science. One of the authors (K.O.) acknowledges support from JST PRESTO.

References and links

1. V. S. Lettokhov, “Quantum statistics of multi-mode radiation from an ensemble of atoms,” Sov. Phys. JETP 26, 835 (1968).

2. N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994). [CrossRef]  

3. W. L. Sha, C. H. Liu, and R. R. Alfano, “Spectral and temporal measurements of laser action of Rhodamine 640 dye in strongly scattering media,” Opt. Lett. 19(23), 1922–1924 (1994). [CrossRef]   [PubMed]  

4. V. M. Markushev, V. F. Zolin, and Ch. M. Briskina, “A powder laser,” Zh. Prikl. Spektrosk 45, 847 (1986).

5. H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Threshold gain behavior of lasing modes in two-dimensional active random media,” Appl. Phys. Lett. 73, 3656 (1998). [CrossRef]  

6. S. F. Yu, C. Yuen, S. P. Lau, W. I. Park, and G.-C. Yi, “Random laser action in ZnO nanorod arrays embedded in ZnO epilayers,” Appl. Phys. Lett. 84(17), 3241 (2004). [CrossRef]  

7. H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320(5876), 643–646 (2008). [CrossRef]   [PubMed]  

8. H. Cao, “Lasing in random media,” Waves Random Media 13(3), R1–R39 (2003). [CrossRef]  

9. P. Sebbah and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B 66(14), 144202 (2002). [CrossRef]  

10. P. Li, Y. C. Wang, and J. Z. Zhang, “All optical fast random number generation,” Opt. Express 18(19), 20360 (2010). [CrossRef]   [PubMed]  

11. R. Bardoux, A. Kaneta, M. Funato, Y. Kawakami, A. Kikuchi, and K. Kishino, “Positive binding energy of a biexciton confined in a localization center formed in a single InxGa1−xN/GaN quantum disk,” Phys. Rev. B 79(15), 155307 (2009). [CrossRef]  

12. Y. Chen, J. Herrnsdorf, B. Guilhabert, Y. Zhang, I. M. Watson, E. Gu, N. Laurand, and M. D. Dawson, “Colloidal quantum dot random laser,” Opt. Express 19(4), 2996–3003 (2011). [CrossRef]   [PubMed]  

13. M. Yoshizawa, A. Kikuchi, M. Mori, N. Fujita, and K. Kishino, “Growth of Self-Organized GaN Nanostructures on Al2O3(0001) by RF-Radical Source Molecular Beam Epitaxy,” Jpn. J. Appl. Phys. 36(Part 2, No. 4B), L459 (1997). [CrossRef]  

14. M. Sakai, Y. Inose, K. Ema, T. Ohtsuki, H. Sekiguchi, A. Kikuchi, and K. Kishino, “Random laser action in GaN nanocolumns,” Appl. Phys. Lett. 97(15), 151109 (2010). [CrossRef]  

15. A. F. Jarjour, A. M. Green, T. J. Parker, R. A. Taylor, R. A. Oliver, G. A. D. Briggs, M. J. Kappers, C. J. Humphreys, R. W. Martin, and I. M. Watson, “Two-photon absorption from single InGaN/GaN quantum dots,” Phys. E 32(1-2), 119–122 (2006). [CrossRef]  

16. V. Nathan, A. H. Guenther, and S. S. Mitra, “Review of multiphoton absorption in crystalline solids,” J. Opt. Soc. Am. B 2(2), 294 (1985). [CrossRef]  

17. W. Guerin, F. Michaud, and R. Kaiser, “Mechanisms for lasing with cold atoms as the gain medium,” Phys. Rev. Lett. 101(9), 093002 (2008). [CrossRef]   [PubMed]  

18. S. Rodt, R. Heitz, A. Schliwa, R. L. Sellin, F. Guffarth, and D. Bimberg, “Repulsive exciton-exciton interaction in quantum dots,” Phys. Rev. B 68(3), 035331 (2003). [CrossRef]  

19. J. Andreasen and H. Cao, Numerical study of amplified spontaneous emission and lasing in random media,” Phys. Rev. A 82, 063825 (2010). [CrossRef]  

20. Y. Inose, M. Sakai, K. Ema, A. Kikuchi, K. Kishino, and T. Ohtsuki, “Light localization characteristics in a random configuration of dielectric cylindrical columns,” Phys. Rev. B 82(20), 205328 (2010). [CrossRef]  

21. H. Cao, X. Jiang, Y. Ling, J. Y. Xu, and C. M. Soukoulis, “Mode repulsion and mode coupling in random lasers,” Phys. Rev. B 67, 161101(R) (2003 [CrossRef]  

22. E. Ejder, “Refractive index of GaN,” Phys. Status Solidi (a) .6(2), 445–448 (1971). [CrossRef]  

23. J. P. Berenger and J. Comput, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994). [CrossRef]  

24. K. L. van der Molen, R. W. Tjerkstra, A. P. Mosk, and A. Lagendijk, “Spatial extent of random laser modes,” Phys. Rev. Lett. 98(14), 143901 (2007). [CrossRef]   [PubMed]  

25. C. Vanneste, P. Sebbah, and H. Cao, “Lasing with resonant feedback in weakly scattering random systems,” Phys. Rev. Lett. 98(14), 143902 (2007). [CrossRef]   [PubMed]  

26. J. Andreasen, A. A. Asatryan, L. C. Botten, M. A. Byrne, H. Cao, L. Ge, L. Labonté, P. Sebbah, A. D. Stone, H. E. Türeci, and C. Vanneste, “Modes of random lasers,” Adv. Opt. Photon. 3, 88–127 (2011). [CrossRef]  

27. W. Koechner, Solid state laser engineering. Springer Series in Optical Sciences (2003).

28. M. Yoshizawa, A. Kikuchi, N. Fujita, K. Kushi, H. Sasamoto, and K. Kishino, “Self-organization of GaN/Al0.18Ga0.82N multi-layer nano-columns on (0 0 0 1) Al2O3 by RF molecular beam epitaxy for fabricating GaN quantum disks,” J. Cryst. Growth 189-190 (1-2), 138–141 (1998). [CrossRef]  

29. S. Diederik, “Wiersma. Random quantum networks,” Sciences (New York) 327(5971), 1333–1334 (2010). [CrossRef]  

References

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  1. V. S. Lettokhov, “Quantum statistics of multi-mode radiation from an ensemble of atoms,” Sov. Phys. JETP 26, 835 (1968).
  2. N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994).
    [CrossRef]
  3. W. L. Sha, C. H. Liu, and R. R. Alfano, “Spectral and temporal measurements of laser action of Rhodamine 640 dye in strongly scattering media,” Opt. Lett. 19(23), 1922–1924 (1994).
    [CrossRef] [PubMed]
  4. V. M. Markushev, V. F. Zolin, and Ch. M. Briskina, “A powder laser,” Zh. Prikl. Spektrosk 45, 847 (1986).
  5. H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Threshold gain behavior of lasing modes in two-dimensional active random media,” Appl. Phys. Lett. 73, 3656 (1998).
    [CrossRef]
  6. S. F. Yu, C. Yuen, S. P. Lau, W. I. Park, and G.-C. Yi, “Random laser action in ZnO nanorod arrays embedded in ZnO epilayers,” Appl. Phys. Lett. 84(17), 3241 (2004).
    [CrossRef]
  7. H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320(5876), 643–646 (2008).
    [CrossRef] [PubMed]
  8. H. Cao, “Lasing in random media,” Waves Random Media 13(3), R1–R39 (2003).
    [CrossRef]
  9. P. Sebbah and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B 66(14), 144202 (2002).
    [CrossRef]
  10. P. Li, Y. C. Wang, and J. Z. Zhang, “All optical fast random number generation,” Opt. Express 18(19), 20360 (2010).
    [CrossRef] [PubMed]
  11. R. Bardoux, A. Kaneta, M. Funato, Y. Kawakami, A. Kikuchi, and K. Kishino, “Positive binding energy of a biexciton confined in a localization center formed in a single InxGa1−xN/GaN quantum disk,” Phys. Rev. B 79(15), 155307 (2009).
    [CrossRef]
  12. Y. Chen, J. Herrnsdorf, B. Guilhabert, Y. Zhang, I. M. Watson, E. Gu, N. Laurand, and M. D. Dawson, “Colloidal quantum dot random laser,” Opt. Express 19(4), 2996–3003 (2011).
    [CrossRef] [PubMed]
  13. M. Yoshizawa, A. Kikuchi, M. Mori, N. Fujita, and K. Kishino, “Growth of Self-Organized GaN Nanostructures on Al2O3(0001) by RF-Radical Source Molecular Beam Epitaxy,” Jpn. J. Appl. Phys. 36(Part 2, No. 4B), L459 (1997).
    [CrossRef]
  14. M. Sakai, Y. Inose, K. Ema, T. Ohtsuki, H. Sekiguchi, A. Kikuchi, and K. Kishino, “Random laser action in GaN nanocolumns,” Appl. Phys. Lett. 97(15), 151109 (2010).
    [CrossRef]
  15. A. F. Jarjour, A. M. Green, T. J. Parker, R. A. Taylor, R. A. Oliver, G. A. D. Briggs, M. J. Kappers, C. J. Humphreys, R. W. Martin, and I. M. Watson, “Two-photon absorption from single InGaN/GaN quantum dots,” Phys. E 32(1-2), 119–122 (2006).
    [CrossRef]
  16. V. Nathan, A. H. Guenther, and S. S. Mitra, “Review of multiphoton absorption in crystalline solids,” J. Opt. Soc. Am. B 2(2), 294 (1985).
    [CrossRef]
  17. W. Guerin, F. Michaud, and R. Kaiser, “Mechanisms for lasing with cold atoms as the gain medium,” Phys. Rev. Lett. 101(9), 093002 (2008).
    [CrossRef] [PubMed]
  18. S. Rodt, R. Heitz, A. Schliwa, R. L. Sellin, F. Guffarth, and D. Bimberg, “Repulsive exciton-exciton interaction in quantum dots,” Phys. Rev. B 68(3), 035331 (2003).
    [CrossRef]
  19. J. Andreasen and H. Cao, Numerical study of amplified spontaneous emission and lasing in random media,” Phys. Rev. A 82, 063825 (2010).
    [CrossRef]
  20. Y. Inose, M. Sakai, K. Ema, A. Kikuchi, K. Kishino, and T. Ohtsuki, “Light localization characteristics in a random configuration of dielectric cylindrical columns,” Phys. Rev. B 82(20), 205328 (2010).
    [CrossRef]
  21. H. Cao, X. Jiang, Y. Ling, J. Y. Xu, and C. M. Soukoulis, “Mode repulsion and mode coupling in random lasers,” Phys. Rev. B 67, 161101(R) (2003
    [CrossRef]
  22. E. Ejder, “Refractive index of GaN,” Phys. Status Solidi (a) .6(2), 445–448 (1971).
    [CrossRef]
  23. J. P. Berenger and J. Comput, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
    [CrossRef]
  24. K. L. van der Molen, R. W. Tjerkstra, A. P. Mosk, and A. Lagendijk, “Spatial extent of random laser modes,” Phys. Rev. Lett. 98(14), 143901 (2007).
    [CrossRef] [PubMed]
  25. C. Vanneste, P. Sebbah, and H. Cao, “Lasing with resonant feedback in weakly scattering random systems,” Phys. Rev. Lett. 98(14), 143902 (2007).
    [CrossRef] [PubMed]
  26. J. Andreasen, A. A. Asatryan, L. C. Botten, M. A. Byrne, H. Cao, L. Ge, L. Labonté, P. Sebbah, A. D. Stone, H. E. Türeci, and C. Vanneste, “Modes of random lasers,” Adv. Opt. Photon. 3, 88–127 (2011).
    [CrossRef]
  27. W. Koechner, Solid state laser engineering. Springer Series in Optical Sciences (2003).
  28. M. Yoshizawa, A. Kikuchi, N. Fujita, K. Kushi, H. Sasamoto, and K. Kishino, “Self-organization of GaN/Al0.18Ga0.82N multi-layer nano-columns on (0 0 0 1) Al2O3 by RF molecular beam epitaxy for fabricating GaN quantum disks,” J. Cryst. Growth 189-190 (1-2), 138–141 (1998).
    [CrossRef]
  29. S. Diederik, “Wiersma. Random quantum networks,” Sciences (New York) 327(5971), 1333–1334 (2010).
    [CrossRef]

2011 (2)

2010 (5)

M. Sakai, Y. Inose, K. Ema, T. Ohtsuki, H. Sekiguchi, A. Kikuchi, and K. Kishino, “Random laser action in GaN nanocolumns,” Appl. Phys. Lett. 97(15), 151109 (2010).
[CrossRef]

S. Diederik, “Wiersma. Random quantum networks,” Sciences (New York) 327(5971), 1333–1334 (2010).
[CrossRef]

P. Li, Y. C. Wang, and J. Z. Zhang, “All optical fast random number generation,” Opt. Express 18(19), 20360 (2010).
[CrossRef] [PubMed]

J. Andreasen and H. Cao, Numerical study of amplified spontaneous emission and lasing in random media,” Phys. Rev. A 82, 063825 (2010).
[CrossRef]

Y. Inose, M. Sakai, K. Ema, A. Kikuchi, K. Kishino, and T. Ohtsuki, “Light localization characteristics in a random configuration of dielectric cylindrical columns,” Phys. Rev. B 82(20), 205328 (2010).
[CrossRef]

2009 (1)

R. Bardoux, A. Kaneta, M. Funato, Y. Kawakami, A. Kikuchi, and K. Kishino, “Positive binding energy of a biexciton confined in a localization center formed in a single InxGa1−xN/GaN quantum disk,” Phys. Rev. B 79(15), 155307 (2009).
[CrossRef]

2008 (2)

W. Guerin, F. Michaud, and R. Kaiser, “Mechanisms for lasing with cold atoms as the gain medium,” Phys. Rev. Lett. 101(9), 093002 (2008).
[CrossRef] [PubMed]

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320(5876), 643–646 (2008).
[CrossRef] [PubMed]

2007 (2)

K. L. van der Molen, R. W. Tjerkstra, A. P. Mosk, and A. Lagendijk, “Spatial extent of random laser modes,” Phys. Rev. Lett. 98(14), 143901 (2007).
[CrossRef] [PubMed]

C. Vanneste, P. Sebbah, and H. Cao, “Lasing with resonant feedback in weakly scattering random systems,” Phys. Rev. Lett. 98(14), 143902 (2007).
[CrossRef] [PubMed]

2006 (1)

A. F. Jarjour, A. M. Green, T. J. Parker, R. A. Taylor, R. A. Oliver, G. A. D. Briggs, M. J. Kappers, C. J. Humphreys, R. W. Martin, and I. M. Watson, “Two-photon absorption from single InGaN/GaN quantum dots,” Phys. E 32(1-2), 119–122 (2006).
[CrossRef]

2004 (1)

S. F. Yu, C. Yuen, S. P. Lau, W. I. Park, and G.-C. Yi, “Random laser action in ZnO nanorod arrays embedded in ZnO epilayers,” Appl. Phys. Lett. 84(17), 3241 (2004).
[CrossRef]

2003 (3)

H. Cao, “Lasing in random media,” Waves Random Media 13(3), R1–R39 (2003).
[CrossRef]

S. Rodt, R. Heitz, A. Schliwa, R. L. Sellin, F. Guffarth, and D. Bimberg, “Repulsive exciton-exciton interaction in quantum dots,” Phys. Rev. B 68(3), 035331 (2003).
[CrossRef]

H. Cao, X. Jiang, Y. Ling, J. Y. Xu, and C. M. Soukoulis, “Mode repulsion and mode coupling in random lasers,” Phys. Rev. B 67, 161101(R) (2003
[CrossRef]

2002 (1)

P. Sebbah and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B 66(14), 144202 (2002).
[CrossRef]

1998 (2)

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Threshold gain behavior of lasing modes in two-dimensional active random media,” Appl. Phys. Lett. 73, 3656 (1998).
[CrossRef]

M. Yoshizawa, A. Kikuchi, N. Fujita, K. Kushi, H. Sasamoto, and K. Kishino, “Self-organization of GaN/Al0.18Ga0.82N multi-layer nano-columns on (0 0 0 1) Al2O3 by RF molecular beam epitaxy for fabricating GaN quantum disks,” J. Cryst. Growth 189-190 (1-2), 138–141 (1998).
[CrossRef]

1997 (1)

M. Yoshizawa, A. Kikuchi, M. Mori, N. Fujita, and K. Kishino, “Growth of Self-Organized GaN Nanostructures on Al2O3(0001) by RF-Radical Source Molecular Beam Epitaxy,” Jpn. J. Appl. Phys. 36(Part 2, No. 4B), L459 (1997).
[CrossRef]

1994 (3)

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994).
[CrossRef]

J. P. Berenger and J. Comput, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

W. L. Sha, C. H. Liu, and R. R. Alfano, “Spectral and temporal measurements of laser action of Rhodamine 640 dye in strongly scattering media,” Opt. Lett. 19(23), 1922–1924 (1994).
[CrossRef] [PubMed]

1986 (1)

V. M. Markushev, V. F. Zolin, and Ch. M. Briskina, “A powder laser,” Zh. Prikl. Spektrosk 45, 847 (1986).

1985 (1)

1971 (1)

E. Ejder, “Refractive index of GaN,” Phys. Status Solidi (a) .6(2), 445–448 (1971).
[CrossRef]

1968 (1)

V. S. Lettokhov, “Quantum statistics of multi-mode radiation from an ensemble of atoms,” Sov. Phys. JETP 26, 835 (1968).

Alfano, R. R.

Andreasen, J.

Asatryan, A. A.

Balachandran, R. M.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994).
[CrossRef]

Bardoux, R.

R. Bardoux, A. Kaneta, M. Funato, Y. Kawakami, A. Kikuchi, and K. Kishino, “Positive binding energy of a biexciton confined in a localization center formed in a single InxGa1−xN/GaN quantum disk,” Phys. Rev. B 79(15), 155307 (2009).
[CrossRef]

Berenger, J. P.

J. P. Berenger and J. Comput, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

Bimberg, D.

S. Rodt, R. Heitz, A. Schliwa, R. L. Sellin, F. Guffarth, and D. Bimberg, “Repulsive exciton-exciton interaction in quantum dots,” Phys. Rev. B 68(3), 035331 (2003).
[CrossRef]

Botten, L. C.

Briggs, G. A. D.

A. F. Jarjour, A. M. Green, T. J. Parker, R. A. Taylor, R. A. Oliver, G. A. D. Briggs, M. J. Kappers, C. J. Humphreys, R. W. Martin, and I. M. Watson, “Two-photon absorption from single InGaN/GaN quantum dots,” Phys. E 32(1-2), 119–122 (2006).
[CrossRef]

Briskina, Ch. M.

V. M. Markushev, V. F. Zolin, and Ch. M. Briskina, “A powder laser,” Zh. Prikl. Spektrosk 45, 847 (1986).

Byrne, M. A.

Cao, H.

J. Andreasen, A. A. Asatryan, L. C. Botten, M. A. Byrne, H. Cao, L. Ge, L. Labonté, P. Sebbah, A. D. Stone, H. E. Türeci, and C. Vanneste, “Modes of random lasers,” Adv. Opt. Photon. 3, 88–127 (2011).
[CrossRef]

J. Andreasen and H. Cao, Numerical study of amplified spontaneous emission and lasing in random media,” Phys. Rev. A 82, 063825 (2010).
[CrossRef]

C. Vanneste, P. Sebbah, and H. Cao, “Lasing with resonant feedback in weakly scattering random systems,” Phys. Rev. Lett. 98(14), 143902 (2007).
[CrossRef] [PubMed]

H. Cao, “Lasing in random media,” Waves Random Media 13(3), R1–R39 (2003).
[CrossRef]

H. Cao, X. Jiang, Y. Ling, J. Y. Xu, and C. M. Soukoulis, “Mode repulsion and mode coupling in random lasers,” Phys. Rev. B 67, 161101(R) (2003
[CrossRef]

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Threshold gain behavior of lasing modes in two-dimensional active random media,” Appl. Phys. Lett. 73, 3656 (1998).
[CrossRef]

Chang, R. P. H.

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Threshold gain behavior of lasing modes in two-dimensional active random media,” Appl. Phys. Lett. 73, 3656 (1998).
[CrossRef]

Chen, Y.

Comput, J.

J. P. Berenger and J. Comput, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

Dai, J. Y.

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Threshold gain behavior of lasing modes in two-dimensional active random media,” Appl. Phys. Lett. 73, 3656 (1998).
[CrossRef]

Dawson, M. D.

Diederik, S.

S. Diederik, “Wiersma. Random quantum networks,” Sciences (New York) 327(5971), 1333–1334 (2010).
[CrossRef]

Ejder, E.

E. Ejder, “Refractive index of GaN,” Phys. Status Solidi (a) .6(2), 445–448 (1971).
[CrossRef]

Ema, K.

M. Sakai, Y. Inose, K. Ema, T. Ohtsuki, H. Sekiguchi, A. Kikuchi, and K. Kishino, “Random laser action in GaN nanocolumns,” Appl. Phys. Lett. 97(15), 151109 (2010).
[CrossRef]

Y. Inose, M. Sakai, K. Ema, A. Kikuchi, K. Kishino, and T. Ohtsuki, “Light localization characteristics in a random configuration of dielectric cylindrical columns,” Phys. Rev. B 82(20), 205328 (2010).
[CrossRef]

Fujita, N.

M. Yoshizawa, A. Kikuchi, N. Fujita, K. Kushi, H. Sasamoto, and K. Kishino, “Self-organization of GaN/Al0.18Ga0.82N multi-layer nano-columns on (0 0 0 1) Al2O3 by RF molecular beam epitaxy for fabricating GaN quantum disks,” J. Cryst. Growth 189-190 (1-2), 138–141 (1998).
[CrossRef]

M. Yoshizawa, A. Kikuchi, M. Mori, N. Fujita, and K. Kishino, “Growth of Self-Organized GaN Nanostructures on Al2O3(0001) by RF-Radical Source Molecular Beam Epitaxy,” Jpn. J. Appl. Phys. 36(Part 2, No. 4B), L459 (1997).
[CrossRef]

Funato, M.

R. Bardoux, A. Kaneta, M. Funato, Y. Kawakami, A. Kikuchi, and K. Kishino, “Positive binding energy of a biexciton confined in a localization center formed in a single InxGa1−xN/GaN quantum disk,” Phys. Rev. B 79(15), 155307 (2009).
[CrossRef]

Ge, L.

Gomes, A. S. L.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994).
[CrossRef]

Green, A. M.

A. F. Jarjour, A. M. Green, T. J. Parker, R. A. Taylor, R. A. Oliver, G. A. D. Briggs, M. J. Kappers, C. J. Humphreys, R. W. Martin, and I. M. Watson, “Two-photon absorption from single InGaN/GaN quantum dots,” Phys. E 32(1-2), 119–122 (2006).
[CrossRef]

Gu, E.

Guenther, A. H.

Guerin, W.

W. Guerin, F. Michaud, and R. Kaiser, “Mechanisms for lasing with cold atoms as the gain medium,” Phys. Rev. Lett. 101(9), 093002 (2008).
[CrossRef] [PubMed]

Guffarth, F.

S. Rodt, R. Heitz, A. Schliwa, R. L. Sellin, F. Guffarth, and D. Bimberg, “Repulsive exciton-exciton interaction in quantum dots,” Phys. Rev. B 68(3), 035331 (2003).
[CrossRef]

Guilhabert, B.

Heitz, R.

S. Rodt, R. Heitz, A. Schliwa, R. L. Sellin, F. Guffarth, and D. Bimberg, “Repulsive exciton-exciton interaction in quantum dots,” Phys. Rev. B 68(3), 035331 (2003).
[CrossRef]

Herrnsdorf, J.

Ho, S. T.

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Threshold gain behavior of lasing modes in two-dimensional active random media,” Appl. Phys. Lett. 73, 3656 (1998).
[CrossRef]

Humphreys, C. J.

A. F. Jarjour, A. M. Green, T. J. Parker, R. A. Taylor, R. A. Oliver, G. A. D. Briggs, M. J. Kappers, C. J. Humphreys, R. W. Martin, and I. M. Watson, “Two-photon absorption from single InGaN/GaN quantum dots,” Phys. E 32(1-2), 119–122 (2006).
[CrossRef]

Inose, Y.

Y. Inose, M. Sakai, K. Ema, A. Kikuchi, K. Kishino, and T. Ohtsuki, “Light localization characteristics in a random configuration of dielectric cylindrical columns,” Phys. Rev. B 82(20), 205328 (2010).
[CrossRef]

M. Sakai, Y. Inose, K. Ema, T. Ohtsuki, H. Sekiguchi, A. Kikuchi, and K. Kishino, “Random laser action in GaN nanocolumns,” Appl. Phys. Lett. 97(15), 151109 (2010).
[CrossRef]

Jarjour, A. F.

A. F. Jarjour, A. M. Green, T. J. Parker, R. A. Taylor, R. A. Oliver, G. A. D. Briggs, M. J. Kappers, C. J. Humphreys, R. W. Martin, and I. M. Watson, “Two-photon absorption from single InGaN/GaN quantum dots,” Phys. E 32(1-2), 119–122 (2006).
[CrossRef]

Jiang, X.

H. Cao, X. Jiang, Y. Ling, J. Y. Xu, and C. M. Soukoulis, “Mode repulsion and mode coupling in random lasers,” Phys. Rev. B 67, 161101(R) (2003
[CrossRef]

Kaiser, R.

W. Guerin, F. Michaud, and R. Kaiser, “Mechanisms for lasing with cold atoms as the gain medium,” Phys. Rev. Lett. 101(9), 093002 (2008).
[CrossRef] [PubMed]

Kaneta, A.

R. Bardoux, A. Kaneta, M. Funato, Y. Kawakami, A. Kikuchi, and K. Kishino, “Positive binding energy of a biexciton confined in a localization center formed in a single InxGa1−xN/GaN quantum disk,” Phys. Rev. B 79(15), 155307 (2009).
[CrossRef]

Kappers, M. J.

A. F. Jarjour, A. M. Green, T. J. Parker, R. A. Taylor, R. A. Oliver, G. A. D. Briggs, M. J. Kappers, C. J. Humphreys, R. W. Martin, and I. M. Watson, “Two-photon absorption from single InGaN/GaN quantum dots,” Phys. E 32(1-2), 119–122 (2006).
[CrossRef]

Kawakami, Y.

R. Bardoux, A. Kaneta, M. Funato, Y. Kawakami, A. Kikuchi, and K. Kishino, “Positive binding energy of a biexciton confined in a localization center formed in a single InxGa1−xN/GaN quantum disk,” Phys. Rev. B 79(15), 155307 (2009).
[CrossRef]

Kikuchi, A.

M. Sakai, Y. Inose, K. Ema, T. Ohtsuki, H. Sekiguchi, A. Kikuchi, and K. Kishino, “Random laser action in GaN nanocolumns,” Appl. Phys. Lett. 97(15), 151109 (2010).
[CrossRef]

Y. Inose, M. Sakai, K. Ema, A. Kikuchi, K. Kishino, and T. Ohtsuki, “Light localization characteristics in a random configuration of dielectric cylindrical columns,” Phys. Rev. B 82(20), 205328 (2010).
[CrossRef]

R. Bardoux, A. Kaneta, M. Funato, Y. Kawakami, A. Kikuchi, and K. Kishino, “Positive binding energy of a biexciton confined in a localization center formed in a single InxGa1−xN/GaN quantum disk,” Phys. Rev. B 79(15), 155307 (2009).
[CrossRef]

M. Yoshizawa, A. Kikuchi, N. Fujita, K. Kushi, H. Sasamoto, and K. Kishino, “Self-organization of GaN/Al0.18Ga0.82N multi-layer nano-columns on (0 0 0 1) Al2O3 by RF molecular beam epitaxy for fabricating GaN quantum disks,” J. Cryst. Growth 189-190 (1-2), 138–141 (1998).
[CrossRef]

M. Yoshizawa, A. Kikuchi, M. Mori, N. Fujita, and K. Kishino, “Growth of Self-Organized GaN Nanostructures on Al2O3(0001) by RF-Radical Source Molecular Beam Epitaxy,” Jpn. J. Appl. Phys. 36(Part 2, No. 4B), L459 (1997).
[CrossRef]

Kishino, K.

Y. Inose, M. Sakai, K. Ema, A. Kikuchi, K. Kishino, and T. Ohtsuki, “Light localization characteristics in a random configuration of dielectric cylindrical columns,” Phys. Rev. B 82(20), 205328 (2010).
[CrossRef]

M. Sakai, Y. Inose, K. Ema, T. Ohtsuki, H. Sekiguchi, A. Kikuchi, and K. Kishino, “Random laser action in GaN nanocolumns,” Appl. Phys. Lett. 97(15), 151109 (2010).
[CrossRef]

R. Bardoux, A. Kaneta, M. Funato, Y. Kawakami, A. Kikuchi, and K. Kishino, “Positive binding energy of a biexciton confined in a localization center formed in a single InxGa1−xN/GaN quantum disk,” Phys. Rev. B 79(15), 155307 (2009).
[CrossRef]

M. Yoshizawa, A. Kikuchi, N. Fujita, K. Kushi, H. Sasamoto, and K. Kishino, “Self-organization of GaN/Al0.18Ga0.82N multi-layer nano-columns on (0 0 0 1) Al2O3 by RF molecular beam epitaxy for fabricating GaN quantum disks,” J. Cryst. Growth 189-190 (1-2), 138–141 (1998).
[CrossRef]

M. Yoshizawa, A. Kikuchi, M. Mori, N. Fujita, and K. Kishino, “Growth of Self-Organized GaN Nanostructures on Al2O3(0001) by RF-Radical Source Molecular Beam Epitaxy,” Jpn. J. Appl. Phys. 36(Part 2, No. 4B), L459 (1997).
[CrossRef]

Kushi, K.

M. Yoshizawa, A. Kikuchi, N. Fujita, K. Kushi, H. Sasamoto, and K. Kishino, “Self-organization of GaN/Al0.18Ga0.82N multi-layer nano-columns on (0 0 0 1) Al2O3 by RF molecular beam epitaxy for fabricating GaN quantum disks,” J. Cryst. Growth 189-190 (1-2), 138–141 (1998).
[CrossRef]

Labonté, L.

Lagendijk, A.

K. L. van der Molen, R. W. Tjerkstra, A. P. Mosk, and A. Lagendijk, “Spatial extent of random laser modes,” Phys. Rev. Lett. 98(14), 143901 (2007).
[CrossRef] [PubMed]

Lau, S. P.

S. F. Yu, C. Yuen, S. P. Lau, W. I. Park, and G.-C. Yi, “Random laser action in ZnO nanorod arrays embedded in ZnO epilayers,” Appl. Phys. Lett. 84(17), 3241 (2004).
[CrossRef]

Laurand, N.

Lawandy, N. M.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994).
[CrossRef]

Lettokhov, V. S.

V. S. Lettokhov, “Quantum statistics of multi-mode radiation from an ensemble of atoms,” Sov. Phys. JETP 26, 835 (1968).

Li, P.

Ling, Y.

H. Cao, X. Jiang, Y. Ling, J. Y. Xu, and C. M. Soukoulis, “Mode repulsion and mode coupling in random lasers,” Phys. Rev. B 67, 161101(R) (2003
[CrossRef]

Liu, C. H.

Markushev, V. M.

V. M. Markushev, V. F. Zolin, and Ch. M. Briskina, “A powder laser,” Zh. Prikl. Spektrosk 45, 847 (1986).

Martin, R. W.

A. F. Jarjour, A. M. Green, T. J. Parker, R. A. Taylor, R. A. Oliver, G. A. D. Briggs, M. J. Kappers, C. J. Humphreys, R. W. Martin, and I. M. Watson, “Two-photon absorption from single InGaN/GaN quantum dots,” Phys. E 32(1-2), 119–122 (2006).
[CrossRef]

Michaud, F.

W. Guerin, F. Michaud, and R. Kaiser, “Mechanisms for lasing with cold atoms as the gain medium,” Phys. Rev. Lett. 101(9), 093002 (2008).
[CrossRef] [PubMed]

Mitra, S. S.

Mori, M.

M. Yoshizawa, A. Kikuchi, M. Mori, N. Fujita, and K. Kishino, “Growth of Self-Organized GaN Nanostructures on Al2O3(0001) by RF-Radical Source Molecular Beam Epitaxy,” Jpn. J. Appl. Phys. 36(Part 2, No. 4B), L459 (1997).
[CrossRef]

Mosk, A. P.

K. L. van der Molen, R. W. Tjerkstra, A. P. Mosk, and A. Lagendijk, “Spatial extent of random laser modes,” Phys. Rev. Lett. 98(14), 143901 (2007).
[CrossRef] [PubMed]

Nathan, V.

Ohtsuki, T.

M. Sakai, Y. Inose, K. Ema, T. Ohtsuki, H. Sekiguchi, A. Kikuchi, and K. Kishino, “Random laser action in GaN nanocolumns,” Appl. Phys. Lett. 97(15), 151109 (2010).
[CrossRef]

Y. Inose, M. Sakai, K. Ema, A. Kikuchi, K. Kishino, and T. Ohtsuki, “Light localization characteristics in a random configuration of dielectric cylindrical columns,” Phys. Rev. B 82(20), 205328 (2010).
[CrossRef]

Oliver, R. A.

A. F. Jarjour, A. M. Green, T. J. Parker, R. A. Taylor, R. A. Oliver, G. A. D. Briggs, M. J. Kappers, C. J. Humphreys, R. W. Martin, and I. M. Watson, “Two-photon absorption from single InGaN/GaN quantum dots,” Phys. E 32(1-2), 119–122 (2006).
[CrossRef]

Ong, H. C.

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Threshold gain behavior of lasing modes in two-dimensional active random media,” Appl. Phys. Lett. 73, 3656 (1998).
[CrossRef]

Park, W. I.

S. F. Yu, C. Yuen, S. P. Lau, W. I. Park, and G.-C. Yi, “Random laser action in ZnO nanorod arrays embedded in ZnO epilayers,” Appl. Phys. Lett. 84(17), 3241 (2004).
[CrossRef]

Parker, T. J.

A. F. Jarjour, A. M. Green, T. J. Parker, R. A. Taylor, R. A. Oliver, G. A. D. Briggs, M. J. Kappers, C. J. Humphreys, R. W. Martin, and I. M. Watson, “Two-photon absorption from single InGaN/GaN quantum dots,” Phys. E 32(1-2), 119–122 (2006).
[CrossRef]

Rodt, S.

S. Rodt, R. Heitz, A. Schliwa, R. L. Sellin, F. Guffarth, and D. Bimberg, “Repulsive exciton-exciton interaction in quantum dots,” Phys. Rev. B 68(3), 035331 (2003).
[CrossRef]

Rotter, S.

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320(5876), 643–646 (2008).
[CrossRef] [PubMed]

Sakai, M.

Y. Inose, M. Sakai, K. Ema, A. Kikuchi, K. Kishino, and T. Ohtsuki, “Light localization characteristics in a random configuration of dielectric cylindrical columns,” Phys. Rev. B 82(20), 205328 (2010).
[CrossRef]

M. Sakai, Y. Inose, K. Ema, T. Ohtsuki, H. Sekiguchi, A. Kikuchi, and K. Kishino, “Random laser action in GaN nanocolumns,” Appl. Phys. Lett. 97(15), 151109 (2010).
[CrossRef]

Sasamoto, H.

M. Yoshizawa, A. Kikuchi, N. Fujita, K. Kushi, H. Sasamoto, and K. Kishino, “Self-organization of GaN/Al0.18Ga0.82N multi-layer nano-columns on (0 0 0 1) Al2O3 by RF molecular beam epitaxy for fabricating GaN quantum disks,” J. Cryst. Growth 189-190 (1-2), 138–141 (1998).
[CrossRef]

Sauvain, E.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994).
[CrossRef]

Schliwa, A.

S. Rodt, R. Heitz, A. Schliwa, R. L. Sellin, F. Guffarth, and D. Bimberg, “Repulsive exciton-exciton interaction in quantum dots,” Phys. Rev. B 68(3), 035331 (2003).
[CrossRef]

Sebbah, P.

J. Andreasen, A. A. Asatryan, L. C. Botten, M. A. Byrne, H. Cao, L. Ge, L. Labonté, P. Sebbah, A. D. Stone, H. E. Türeci, and C. Vanneste, “Modes of random lasers,” Adv. Opt. Photon. 3, 88–127 (2011).
[CrossRef]

C. Vanneste, P. Sebbah, and H. Cao, “Lasing with resonant feedback in weakly scattering random systems,” Phys. Rev. Lett. 98(14), 143902 (2007).
[CrossRef] [PubMed]

P. Sebbah and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B 66(14), 144202 (2002).
[CrossRef]

Sekiguchi, H.

M. Sakai, Y. Inose, K. Ema, T. Ohtsuki, H. Sekiguchi, A. Kikuchi, and K. Kishino, “Random laser action in GaN nanocolumns,” Appl. Phys. Lett. 97(15), 151109 (2010).
[CrossRef]

Sellin, R. L.

S. Rodt, R. Heitz, A. Schliwa, R. L. Sellin, F. Guffarth, and D. Bimberg, “Repulsive exciton-exciton interaction in quantum dots,” Phys. Rev. B 68(3), 035331 (2003).
[CrossRef]

Sha, W. L.

Soukoulis, C. M.

H. Cao, X. Jiang, Y. Ling, J. Y. Xu, and C. M. Soukoulis, “Mode repulsion and mode coupling in random lasers,” Phys. Rev. B 67, 161101(R) (2003
[CrossRef]

Stone, A. D.

Taylor, R. A.

A. F. Jarjour, A. M. Green, T. J. Parker, R. A. Taylor, R. A. Oliver, G. A. D. Briggs, M. J. Kappers, C. J. Humphreys, R. W. Martin, and I. M. Watson, “Two-photon absorption from single InGaN/GaN quantum dots,” Phys. E 32(1-2), 119–122 (2006).
[CrossRef]

Tjerkstra, R. W.

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Figures (4)

Fig. 1
Fig. 1

(a) Scanning electron microscope image from the top of the Q-disks sample; the green circular and dashed line represents laser the spot size under two photon absorption experiments. (b) Simplified schematic of the experimental set up. Micro-photoluminescence spectra acquired at the same location on the quantum disks sample for a laser excitation energy set (c) at 3.1 eV under one photon absorption experiment and (d) at 1.55 eV under two photon absorption. The acquisition time was set at 500 ms and 5 s respectively. In inset of Fig. 1(d) we plotted the power dependency of the integrated intensity of the peaks X and XX.

Fig. 2
Fig. 2

(a) (b) Power dependency spectra obtained under two photon absorption experiment at two different position on the Q-disk sample. (c). Power dependency of the integrated intensity of the peak D plotted in linear scale. In inset of Fig. 2(c), power dependency of the integrated intensity of the peak D’ (see Fig. 2(a)) plotted in log-log scale. (d) Power dependency of the full width at half maximum of the peak D.

Fig. 3
Fig. 3

(a) Spatial distribution of the amplitude of the electric field steady state through the GaN nanocolumn sample calculated by FDTD simulation. The phase difference with the light source is set at zero. (b) Temporal evolution of the calculated electric field amplitude extracted from the point M (see Fig. 3(a)) considering four different light source emission wavelengths.

Fig. 4
Fig. 4

(a) TPA processes at the scale of a single Q-disk: the energy levels 1, 2, and 3 correspond respectively to the ground state of the system, the excited states of the two-dimensional InGaN active layer, and the lowest radiative level of a PS structure state. (b) Sub-ensemble of PS structures selectively excited by TPA and located on the path of a light localized mode. (c) When the emission energy of the sub-ensemble of PS structures matches with the energy resonance of the light localized mode, stimulated emission occurs and gives rise to random laser action.

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