OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 16 — Jul. 30, 2012
  • pp: 17873–17879
« Show journal navigation

Single-mode GaN nanowire lasers

Qiming Li, Jeremy B. Wright, Weng W. Chow, Ting Shan Luk, Igal Brener, Luke F. Lester, and George T. Wang  »View Author Affiliations


Optics Express, Vol. 20, Issue 16, pp. 17873-17879 (2012)
http://dx.doi.org/10.1364/OE.20.017873


View Full Text Article

Acrobat PDF (1789 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We demonstrate stable, single-frequency output from single, as-fabricated GaN nanowire lasers operating far above lasing threshold. Each laser is a linear, double-facet GaN nanowire functioning as gain medium and optical resonator, fabricated by a top-down technique that exploits a tunable dry etch plus anisotropic wet etch for precise control of the nanowire dimensions and high material gain. A single-mode linewidth of ~0.12 nm and >18dB side-mode suppression ratio are measured. Numerical simulations indicate that single-mode lasing arises from strong mode competition and narrow gain bandwidth.

© 2012 OSA

1. Introduction

Advances in nanowire lasers are occurring at a rapid pace, with optically pumped lasers demonstrated in a variety of semiconductor material systems, including Group III-nitrides [1

1. J. C. Johnson, H. J. Choi, K. P. Knutsen, R. D. Schaller, P. D. Yang, and R. J. Saykally, “Single gallium nitride nanowire lasers,” Nat. Mater. 1(2), 106–110 (2002). [CrossRef] [PubMed]

6

6. P. C. Upadhya, Q. M. Li, G. T. Wang, A. J. Fischer, A. J. Taylor, and R. P. Prasankumar, “The influence of defect states on non-equilibrium carrier dynamics in GaN nanowires,” Semicond. Sci. Technol. 25(2), 024017 (2010). [CrossRef]

], Group III-V [7

7. B. Hua, J. Motohisa, Y. Kobayashi, S. Hara, and T. Fukui, “Single GaAs/GaAsP coaxial core-shell nanowire lasers,” Nano Lett. 9(1), 112–116 (2009). [CrossRef] [PubMed]

, 8

8. R. Chen, T. T. D. Tran, K. W. Ng, W. S. Ko, L. C. Chuang, F. G. Sedgwick, and C. Chang-Hasnain, “Nanolasers grown on silicon,” Nat. Photonics 5(3), 170–175 (2011). [CrossRef]

], and Group II-VI [9

9. X. F. Duan, Y. Huang, R. Agarwal, and C. M. Lieber, “Single-nanowire electrically driven lasers,” Nature 421(6920), 241–245 (2003). [CrossRef] [PubMed]

, 10

10. M. A. Zimmler, F. Capasso, S. Muller, and C. Ronning, “Optically pumped nanowire lasers: invited review,” Semicond. Sci. Technol. 25(2), 024001 (2010). [CrossRef]

]. To achieve single-mode lasing, Xiao et al. used a CdSe active medium and a complex resonator comprising of coupled loops of long, flexible nanowires [11

11. Y. Xiao, C. Meng, P. Wang, Y. Ye, H. K. Yu, S. S. Wang, F. X. Gu, L. Dai, and L. M. Tong, “Single-Nanowire Single-Mode Laser,” Nano Lett. 11(3), 1122–1126 (2011). [CrossRef] [PubMed]

]. Recently, Scofield et al. reported single-mode lasing from a defect mode in an InGaAs photonic crystal consisting of a 2-dimensional array of InGaAs nanowires [12

12. A. C. Scofield, S. H. Kim, J. N. Shapiro, A. Lin, B. L. Liang, A. Scherer, and D. L. Huffaker, “Bottom-up Photonic Crystal Lasers,” Nano Lett. 11(12), 5387–5390 (2011). [CrossRef] [PubMed]

]. To circumvent the need for fabrication and manipulation of complicated optical structures, we concentrated our effort towards a simple, linear, Fabry-Perot nanowire laser, where the factors enabling single-mode lasing are short cavity length, small cross section and very high material gain. By reducing the nanowire size, the number of cavity modes within the gain bandwidth is dramatically reduced. This in turn requires high material gain, necessary to compensate for the reduced gain length. Low defect density and high sample uniformity are also necessary to reduce carrier losses and inhomogeneous broadening, in order to achieve high carrier density and increase gain competition, respectively. By satisfying these requirements, we are able to demonstrate single-mode lasing with a linewidth of ~0.12 nm and >18dB side-mode suppression ratio, in a 135 nm wide, 4.7 μm long GaN nanowire, under optical pumping. Single-mode operation is maintained far above lasing threshold. With GaN (or InGaN), the payoff is single-mode laser operation at ultraviolet (or green) wavelengths, which is an important spectral region not covered well by present semiconductor lasers.

2. Experiment

To achieve single mode lasing, precise control over the nanowire geometry is required. This requirement is satisfied by a top-down fabrication technique which produces uniform and vertically aligned GaN nanowire arrays from c-plane GaN epilayers on sapphire with low defect density and smooth sidewalls. We previously demonstrated this technique to fabricate nanowire LED structures with an axial GaN/InGaN multi-quantum structure [13

13. Q. M. Li, K. R. Westlake, M. H. Crawford, S. R. Lee, D. D. Koleske, J. J. Figiel, K. C. Cross, S. Fathololoumi, Z. T. Mi, and G. T. Wang, “Optical performance of top-down fabricated InGaN/GaN nanorod light emitting diode arrays,” Opt. Express 19(25), 25528–25534 (2011). [CrossRef] [PubMed]

]. Figure 1
Fig. 1 Cross sectional SEM images showing GaN posts morphology transiting into GaN nanowires (a) before wet etch, (b) after 2 hours, (c) after 6 hours and (d) after 9 hours from start of wet etch. All images have the same magnification. Scale bars are 2 μm.
shows SEM images of top-down GaN nanowires during the fabrication process. Starting from Si-doped planar GaN epilayers grown on 2” c-plane sapphire wafers in a Veeco D-125 metal organic chemical vapor deposition reactor, a 2-step etching process is used: a lithographic dry etch followed by an anisotropic wet etch. Following a process reported by Reculusa and Ravaine [14

14. S. Reculusa and S. Ravaine, “Synthesis of colloidal crystals of controllable thickness through the Langmuir-Blodgett technique,” Chem. Mater. 15(2), 598–605 (2003). [CrossRef]

], a monolayer of 3 μm diameter silica colloids was self-assembled on the GaN surface in a Langmuir-Blodgett trough prior to etching to serve as a semi-periodic lithographic etch mask. GaN posts are subsequently formed by a plasma (dry) etch. As shown in Fig. 1(a), the resulting posts are tapered with large cross-section areas, and therefore, are unsuitable for single-mode nanowire lasers. Moreover, ion bombardment during the plasma etch damages the nanowire surface, as evidenced by significant increase in yellow luminescence [13

13. Q. M. Li, K. R. Westlake, M. H. Crawford, S. R. Lee, D. D. Koleske, J. J. Figiel, K. C. Cross, S. Fathololoumi, Z. T. Mi, and G. T. Wang, “Optical performance of top-down fabricated InGaN/GaN nanorod light emitting diode arrays,” Opt. Express 19(25), 25528–25534 (2011). [CrossRef] [PubMed]

]. These issues are resolved during the second (wet) etch step [Figs. 1(b)1(d)]. With the anisotropic wet-etch step, non-tapered GaN nanowires are created with damage-free surfaces, hexagonal cross sections with m-plane {10-10} sidewall facets, and a top c-plane (0001) resonator (end) facet. The GaN nanowire length is determined by the original GaN epilayers thickness and its width is determined by the duration of the wet-etch. Similar axial GaN/InGaN nanowire LED structures prepared by this top-down approach were largely dislocation free (~94% of the nanowires) [13

13. Q. M. Li, K. R. Westlake, M. H. Crawford, S. R. Lee, D. D. Koleske, J. J. Figiel, K. C. Cross, S. Fathololoumi, Z. T. Mi, and G. T. Wang, “Optical performance of top-down fabricated InGaN/GaN nanorod light emitting diode arrays,” Opt. Express 19(25), 25528–25534 (2011). [CrossRef] [PubMed]

].

The nanowires were characterized by scanning electron microscopy (SEM), x-ray diffraction (XRD) and transmission electron microscopy (TEM). For the optical pumping measurements, the nanowires were removed from their sapphire growth substrate and transferred to clean Si3N4 surfaces on TEM grids. Each nanowire was optically pumped at room temperature with a 10 kHz, 100 ps pulsed quadrupled YAG laser emitting at 267 nm. The intensity incident on the nanowire was varied using neutral density filters. A 50 × ultraviolet objective lens is used to image the pump laser output to an approximately 5 µm diameter spot on the GaN nanowire. Optical emission from the nanowire was collected with the same objective lens. The collected light was analyzed by a cooled CCD detector and a 300 mm spectrometer with a 2400 groove/mm holographic grating. The schematic of the optical pumping measurement set up is given in Fig. 2
Fig. 2 Schematic of the GaN nanowire optical pumping and measurement setup.
.

3. Theory

The set of coupled mode intensity equations (numbering roughly 300) is solved numerically for the steady-state solution for a given excitation level, α11. Plotting the steady-state In versus the passive cavity-mode frequency Ωn gives the emission spectrum.

4. Results and discussion

The optical properties of the GaN nanowires were characterized by optical pumping using a micro-photoluminescence setup as sketched in Fig. 2(a). For comparison, two nanowires of similar diameters but different lengths were fabricated and characterized. A 135 nm diameter, 4.7 μm long nanowire and a 145 nm diameter, 7.2 μm long nanowire were positioned on SiN substrates. Figures 3(a)
Fig. 3 CCD images of a GaN nanowire pumped below (a) and above (b) lasing threshold, respectively. The nanowire laser emits a highly divergent beam from the facets, some of which is collected by the objective lens. The objective lens also collects radiation emitted from the facets that is scattered by the SiN substrate surface, as well as spontaneous emission exiting perpendicular to the nanowire axis. Scale bars are 2 µm.
and 3(b) show CCD images of optical emission from the shorter GaN nanowire at two pump intensities. At low pump intensity, the CCD image shows roughly uniform optical emission from the entire nanowire length, indicating that unguided (out-of-plane) and guided (on-axis) emission intensities are basically equal [see Fig. 3(a)]. The inference is that the optical emission is entirely from spontaneous emission. At a higher pump intensity, a distinctly different emission pattern emerges. The on-axis emission grows significantly, appearing as two bright spots at the ends of the nanowire indicative of Fabry-Perot lasing, as shown in Fig. 3(b). The light collected by the objective lens is directly from the highly diverging output beam and indirectly from scattering of the output beam by the SiN surface. The large divergence angle of output beam is because of diffraction from a sub-wavelength nanowire aperture. At the same time, there is a clamping of the unguided spontaneous emission, which appears as a darkening (relative to the bright ends and with filters in place) of the entire length of the nanowire, also shown in Fig. 3(b). Also present in the CCD image are concentric rings of optical interference fringes, which is an indication of the spectral coherence of the emitted light.

Summarizing the experimental results at this point, Figs. 3 and 4 together provide strong evidence of single-mode lasing. Figure 3(b) shows the clamping of spontaneous emission and interference fringes indicating coherence in optical emission [19

19. L. K. van Vugt, S. Rühle, and D. Vanmaekelbergh, “Phase-correlated nondirectional laser emission from the end facets of a ZnO nanowire,” Nano Lett. 6(12), 2707–2711 (2006). [CrossRef] [PubMed]

]. There is the presence of a lasing threshold [Fig. 4 (left column, top)] and spectral narrowing to single frequency [Fig. 4 (right column, top)].

The value of the above modeling exercise is three-fold. First is a better understanding of the mechanisms giving rise to single-mode lasing. According to the multimode laser model, single-mode lasing depends on two factors: (1) suppression of modes (e.g. transverse modes) close to the single lasing mode via mode competition, and (2) absence of net gain in the further lying modes because of large longitudinal mode spacing and finite gain bandwidth. The second purpose of the model is to determine the laser parameters necessary for using the multimode laser model to design future lasers. Most important is the determination of the mode-coupling parameter [11

11. Y. Xiao, C. Meng, P. Wang, Y. Ye, H. K. Yu, S. S. Wang, F. X. Gu, L. Dai, and L. M. Tong, “Single-Nanowire Single-Mode Laser,” Nano Lett. 11(3), 1122–1126 (2011). [CrossRef] [PubMed]

], C≡θnmθmn/(βnβm), which is extremely difficult to obtain from first-principles because of complicated many-body correlation effects. Theory/experiment comparisons with different length nanowire lasers gives 0.7 < C < 1.0, putting the GaN active medium in the upper end of the weak-coupling regime. Consequently, suppression of side modes comes entirely from the effective net gain αnnmαmm<0 [8

8. R. Chen, T. T. D. Tran, K. W. Ng, W. S. Ko, L. C. Chuang, F. G. Sedgwick, and C. Chang-Hasnain, “Nanolasers grown on silicon,” Nat. Photonics 5(3), 170–175 (2011). [CrossRef]

] which gives rise to the condition of longitudinal mode space > 10 meV and ΓT/ ΓL < 0.9 for single-mode lasing, where ΓT and ΓL are transverse and longitudinal mode confinement factors, respectively. Further study is necessary to confirm these conditions. The third value of the modeling is to provide information on the laser gain and carrier density achieved in our experiments. We estimated material gain and carrier density created under optical pumping to be ≈5.8 × 103 cm−1 and 1.4 × 1019 cm−3, respectively, which are appreciably higher than found in conventional lasers and is evidence for high material quality.

5. Conclusion

We have demonstrated stable, single-frequency output from single, as fabricated nanowire lasers operating far above lasing threshold. Each laser consists of a linear, double-facet GaN nanowire functioning as gain medium and optical resonator. A single-mode linewidth of ~0.12 nm and >18dB side-mode suppression ratio are measured. Crucial to achieving single-mode lasing is reducing the number of cavity modes within the gain bandwidth. This requires significant reduction and precise control of nanowire dimensions, as well as high material gain necessary to compensate for the reduced gain length. These challenges are met using a top-down technique that exploits a tunable dry etch plus anisotropic wet etch. Numerical simulations based on a multimode laser theory indicate that single-mode lasing arises from strong mode competition and narrow gain bandwidth.

Acknowledgments

This work was funded by Sandia’s Solid-State-Lighting Science Energy Frontier Research Center, funded by the U. S. Department of Energy, Office of Science, and Office of Basic Energy Sciences. This work was performed, in part, at the Center for Integrated Nanotechnologies, a U.S. Department of Energy, Office of Basic Energy Sciences user facility at Los Alamos National Laboratory (Contract DE-AC52-06NA25396) and Sandia National Laboratories (Contract DE-AC04-94AL85000). We thank Daniel Koleske for assistance with the GaN film growth. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

References and links

1.

J. C. Johnson, H. J. Choi, K. P. Knutsen, R. D. Schaller, P. D. Yang, and R. J. Saykally, “Single gallium nitride nanowire lasers,” Nat. Mater. 1(2), 106–110 (2002). [CrossRef] [PubMed]

2.

S. Gradecak, F. Qian, Y. Li, H. G. Park, and C. M. Lieber, “GaN nanowire lasers with low lasing thresholds,” Appl. Phys. Lett. 87(17), 173111 (2005). [CrossRef]

3.

F. Qian, Y. Li, S. Gradecak, H.-G. Park, Y. Dong, Y. Ding, Z. L. Wang, and C. M. Lieber, “Multi-quantum-well nanowire heterostructures for wavelength-controlled lasers,” Nat. Mater. 7(9), 701–706 (2008). [CrossRef] [PubMed]

4.

J. Heo, W. Guo, and P. Bhattacharya, “Monolithic single GaN nanowire laser with photonic crystal microcavity on silicon,” Appl. Phys. Lett. 98(2), 021110 (2011). [CrossRef]

5.

J. B. Schlager, N. A. Sanford, K. A. Bertness, and A. Roshko, “Injection-level-dependent internal quantum efficiency and lasing in low-defect GaN nanowires,” J. Appl. Phys. 109(4), 044312 (2011). [CrossRef]

6.

P. C. Upadhya, Q. M. Li, G. T. Wang, A. J. Fischer, A. J. Taylor, and R. P. Prasankumar, “The influence of defect states on non-equilibrium carrier dynamics in GaN nanowires,” Semicond. Sci. Technol. 25(2), 024017 (2010). [CrossRef]

7.

B. Hua, J. Motohisa, Y. Kobayashi, S. Hara, and T. Fukui, “Single GaAs/GaAsP coaxial core-shell nanowire lasers,” Nano Lett. 9(1), 112–116 (2009). [CrossRef] [PubMed]

8.

R. Chen, T. T. D. Tran, K. W. Ng, W. S. Ko, L. C. Chuang, F. G. Sedgwick, and C. Chang-Hasnain, “Nanolasers grown on silicon,” Nat. Photonics 5(3), 170–175 (2011). [CrossRef]

9.

X. F. Duan, Y. Huang, R. Agarwal, and C. M. Lieber, “Single-nanowire electrically driven lasers,” Nature 421(6920), 241–245 (2003). [CrossRef] [PubMed]

10.

M. A. Zimmler, F. Capasso, S. Muller, and C. Ronning, “Optically pumped nanowire lasers: invited review,” Semicond. Sci. Technol. 25(2), 024001 (2010). [CrossRef]

11.

Y. Xiao, C. Meng, P. Wang, Y. Ye, H. K. Yu, S. S. Wang, F. X. Gu, L. Dai, and L. M. Tong, “Single-Nanowire Single-Mode Laser,” Nano Lett. 11(3), 1122–1126 (2011). [CrossRef] [PubMed]

12.

A. C. Scofield, S. H. Kim, J. N. Shapiro, A. Lin, B. L. Liang, A. Scherer, and D. L. Huffaker, “Bottom-up Photonic Crystal Lasers,” Nano Lett. 11(12), 5387–5390 (2011). [CrossRef] [PubMed]

13.

Q. M. Li, K. R. Westlake, M. H. Crawford, S. R. Lee, D. D. Koleske, J. J. Figiel, K. C. Cross, S. Fathololoumi, Z. T. Mi, and G. T. Wang, “Optical performance of top-down fabricated InGaN/GaN nanorod light emitting diode arrays,” Opt. Express 19(25), 25528–25534 (2011). [CrossRef] [PubMed]

14.

S. Reculusa and S. Ravaine, “Synthesis of colloidal crystals of controllable thickness through the Langmuir-Blodgett technique,” Chem. Mater. 15(2), 598–605 (2003). [CrossRef]

15.

M. Sargent, W. E. Lamb, and R. L. Fork, “Theory of a Zeeman Laser. I,” Phys. Rev. 164(2), 436–449 (1967). [CrossRef]

16.

A. J. Lotka, “Contribution to the theory of periodic reactions,” J. Phys. Chem. 14(3), 271–274 (1910). [CrossRef]

17.

W. W. Chow, “Theory of emission from an active photonic lattice,” Phys. Rev. A 73(1), 013821 (2006). [CrossRef]

18.

W. W. Chow, A. Knorr, and S. W. Koch, “Theory of Laser Gain in Group-III Nitrides,” Appl. Phys. Lett. 67(6), 754–756 (1995). [CrossRef]

19.

L. K. van Vugt, S. Rühle, and D. Vanmaekelbergh, “Phase-correlated nondirectional laser emission from the end facets of a ZnO nanowire,” Nano Lett. 6(12), 2707–2711 (2006). [CrossRef] [PubMed]

OCIS Codes
(250.5230) Optoelectronics : Photoluminescence
(160.4236) Materials : Nanomaterials
(220.4241) Optical design and fabrication : Nanostructure fabrication
(250.5960) Optoelectronics : Semiconductor lasers
(250.5590) Optoelectronics : Quantum-well, -wire and -dot devices

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: May 30, 2012
Revised Manuscript: July 13, 2012
Manuscript Accepted: July 17, 2012
Published: July 20, 2012

Citation
Qiming Li, Jeremy B. Wright, Weng W. Chow, Ting Shan Luk, Igal Brener, Luke F. Lester, and George T. Wang, "Single-mode GaN nanowire lasers," Opt. Express 20, 17873-17879 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-16-17873


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. C. Johnson, H. J. Choi, K. P. Knutsen, R. D. Schaller, P. D. Yang, and R. J. Saykally, “Single gallium nitride nanowire lasers,” Nat. Mater.1(2), 106–110 (2002). [CrossRef] [PubMed]
  2. S. Gradecak, F. Qian, Y. Li, H. G. Park, and C. M. Lieber, “GaN nanowire lasers with low lasing thresholds,” Appl. Phys. Lett.87(17), 173111 (2005). [CrossRef]
  3. F. Qian, Y. Li, S. Gradecak, H.-G. Park, Y. Dong, Y. Ding, Z. L. Wang, and C. M. Lieber, “Multi-quantum-well nanowire heterostructures for wavelength-controlled lasers,” Nat. Mater.7(9), 701–706 (2008). [CrossRef] [PubMed]
  4. J. Heo, W. Guo, and P. Bhattacharya, “Monolithic single GaN nanowire laser with photonic crystal microcavity on silicon,” Appl. Phys. Lett.98(2), 021110 (2011). [CrossRef]
  5. J. B. Schlager, N. A. Sanford, K. A. Bertness, and A. Roshko, “Injection-level-dependent internal quantum efficiency and lasing in low-defect GaN nanowires,” J. Appl. Phys.109(4), 044312 (2011). [CrossRef]
  6. P. C. Upadhya, Q. M. Li, G. T. Wang, A. J. Fischer, A. J. Taylor, and R. P. Prasankumar, “The influence of defect states on non-equilibrium carrier dynamics in GaN nanowires,” Semicond. Sci. Technol.25(2), 024017 (2010). [CrossRef]
  7. B. Hua, J. Motohisa, Y. Kobayashi, S. Hara, and T. Fukui, “Single GaAs/GaAsP coaxial core-shell nanowire lasers,” Nano Lett.9(1), 112–116 (2009). [CrossRef] [PubMed]
  8. R. Chen, T. T. D. Tran, K. W. Ng, W. S. Ko, L. C. Chuang, F. G. Sedgwick, and C. Chang-Hasnain, “Nanolasers grown on silicon,” Nat. Photonics5(3), 170–175 (2011). [CrossRef]
  9. X. F. Duan, Y. Huang, R. Agarwal, and C. M. Lieber, “Single-nanowire electrically driven lasers,” Nature421(6920), 241–245 (2003). [CrossRef] [PubMed]
  10. M. A. Zimmler, F. Capasso, S. Muller, and C. Ronning, “Optically pumped nanowire lasers: invited review,” Semicond. Sci. Technol.25(2), 024001 (2010). [CrossRef]
  11. Y. Xiao, C. Meng, P. Wang, Y. Ye, H. K. Yu, S. S. Wang, F. X. Gu, L. Dai, and L. M. Tong, “Single-Nanowire Single-Mode Laser,” Nano Lett.11(3), 1122–1126 (2011). [CrossRef] [PubMed]
  12. A. C. Scofield, S. H. Kim, J. N. Shapiro, A. Lin, B. L. Liang, A. Scherer, and D. L. Huffaker, “Bottom-up Photonic Crystal Lasers,” Nano Lett.11(12), 5387–5390 (2011). [CrossRef] [PubMed]
  13. Q. M. Li, K. R. Westlake, M. H. Crawford, S. R. Lee, D. D. Koleske, J. J. Figiel, K. C. Cross, S. Fathololoumi, Z. T. Mi, and G. T. Wang, “Optical performance of top-down fabricated InGaN/GaN nanorod light emitting diode arrays,” Opt. Express19(25), 25528–25534 (2011). [CrossRef] [PubMed]
  14. S. Reculusa and S. Ravaine, “Synthesis of colloidal crystals of controllable thickness through the Langmuir-Blodgett technique,” Chem. Mater.15(2), 598–605 (2003). [CrossRef]
  15. M. Sargent, W. E. Lamb, and R. L. Fork, “Theory of a Zeeman Laser. I,” Phys. Rev.164(2), 436–449 (1967). [CrossRef]
  16. A. J. Lotka, “Contribution to the theory of periodic reactions,” J. Phys. Chem.14(3), 271–274 (1910). [CrossRef]
  17. W. W. Chow, “Theory of emission from an active photonic lattice,” Phys. Rev. A73(1), 013821 (2006). [CrossRef]
  18. W. W. Chow, A. Knorr, and S. W. Koch, “Theory of Laser Gain in Group-III Nitrides,” Appl. Phys. Lett.67(6), 754–756 (1995). [CrossRef]
  19. L. K. van Vugt, S. Rühle, and D. Vanmaekelbergh, “Phase-correlated nondirectional laser emission from the end facets of a ZnO nanowire,” Nano Lett.6(12), 2707–2711 (2006). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited