OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 13 — Jun. 22, 2009
  • pp: 10522–10528
« Show journal navigation

Numerical analysis of resonant properties of a waveguide structure within a random medium

Hideki Fujiwara, Yosuke Hamabata, and Keiji Sasaki  »View Author Affiliations


Optics Express, Vol. 17, Issue 13, pp. 10522-10528 (2009)
http://dx.doi.org/10.1364/OE.17.010522


View Full Text Article

Acrobat PDF (250 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We propose a simple structure for manipulating resonant conditions in random structures, which is composed of a waveguide structure as a defect region embedded in a random structure. Using the two-dimensional finite-difference time-domain method, we examine the resonant properties of localized modes bound in the waveguide. From the results, we confirm that long-lived modes are strongly confined in the waveguide only when the resonant frequency matches the frequency windows in the transmitted intensity spectrum of the surrounding random structure.

© 2009 OSA

1. Introduction

Wavelength-scale-disordered structures composed of strong scattering nanoparticles (random structures) have attracted attention as unique microcavity structures because of their potential for photon localization due to the interference of multiply scattered light [1

1. C. Gouedard, D. Husson, C. Sauteret, F. Auzel, and A. Migus, “Generation of spatially incoherent short pulses in laser-pumped neodymium stoichiometric crystals and powders,” J. Opt. Soc. Am. B 10(12), 2358–2363 (1993). [CrossRef]

21

21. S. Gottardo, R. Sapienza, P. D. Garcia, A. Blanco, D. S. Wiersma, and C. Lopez, “Resonance-driven random lasing,” Nat. Photonics 2(7), 429–432 (2008). [CrossRef]

]. Utilizing nanoparticle assembly, self-generated surface roughness, or biological tissues, random structures have suggested a potential for the realization of easily fabricated and low-cost applications, such as low-threshold nonlinear optical devices. Although spectral and spatial overlaps between long-lived modes and materials doped in the random structure are required to achieve highly efficient light-matter interactions within the structures, their resonant frequencies and positions are randomly determined by local conditions of the structure. Therefore, it is difficult to induce intended long-lived modes in random structures. In addition, since such long-lived modes would typically exist deep inside the structure because of leakage loss from the surface, it is also difficult to access these long-lived modes from the outside or collect their output because of multiple scattering. Therefore, technological developments for manipulating intended modes, including their location and frequency as well as input-output characteristics within the structure, would be indispensable.

To address this issue, we have conceived that a waveguide structure can be used as a defect region within a random structure, similar to photonic crystal waveguides, and is expected to improve both the input-output characteristics and the control of resonant conditions of long-lived modes. The results reported by Topolancik et al. suggested useful information regarding such a waveguide structure [28

28. J. Topolancik, F. Vollmer, and B. Llic, “Random high-Q cavities in disordered photonic crystal waveguides,” Appl. Phys. Lett. 91(20), 201102 (2007). [CrossRef]

,29

29. J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99(25), 253901 (2007). [CrossRef]

]. They experimentally demonstrated that the shape disorder of airholes in photonic crystal waveguides played an important role in the realization of strong localization in the waveguide due to the coherent interference of scattered waves from periodic airholes. However, their structure was still a highly ordered structure, unlike that considered here. Another idea for guiding random laser output using a waveguide were also experimentally demonstrated by Watanabe et al. [17

17. H. Watanabe, Y. Oki, M. Maeda, and T. Omatsu, “Waveguide dye laser including a SiO2 nanoparticle-dispersed random scattering active layer,” Appl. Phys. Lett. 86(15), 151123 (2005). [CrossRef]

] and Yuen et al [18

18. C. Yuen, S. F. Yu, E. S. P. Leong, H. Y. Yang, S. P. Lau, N. S. Chen, and H. H. Hng, “Low-loss and directional output ZnO thin-film ridge waveguide random lasers with MgO capped layer,” Appl. Phys. Lett. 86(3), 031112 (2005). [CrossRef]

]. In Ref. 17

17. H. Watanabe, Y. Oki, M. Maeda, and T. Omatsu, “Waveguide dye laser including a SiO2 nanoparticle-dispersed random scattering active layer,” Appl. Phys. Lett. 86(15), 151123 (2005). [CrossRef]

, a dual-layered waveguide dye laser was demonstrated, in which a waveguide layer was over coated on a random active layer, whereas in Ref. 18

18. C. Yuen, S. F. Yu, E. S. P. Leong, H. Y. Yang, S. P. Lau, N. S. Chen, and H. H. Hng, “Low-loss and directional output ZnO thin-film ridge waveguide random lasers with MgO capped layer,” Appl. Phys. Lett. 86(3), 031112 (2005). [CrossRef]

, random laser action was also observed from a ridge waveguide formed on a disordered ZnO thin film. In both cases, they suggested that lasing characteristics were improved by using the waveguide structures. However, these proposed structures are markedly different from our proposed structure. Among several proposals using waveguide structures, Miyazaki et al. also proposed a defect waveguide structure within uniformly distributed scatterers [26

26. H. Miyazaki, M. Hase, H. T. Miyazaki, Y. Kurokawa, and N. Shinya, “Photonic material for designing arbitrarily shaped waveguides in two dimensions,” Phys. Rev. B 67(23), 235109 (2003). [CrossRef]

], which was very similar to the structure we propose in this paper. From the numerical results, they suggested that the electric field could be almost completely confined within the waveguide. However, in their numerical proposal, in order to confine photons within the waveguide, a wavelength-scaled periodic sidewall for the defect waveguide was used. Therefore, for making a wavelength-scaled periodic sidewall along the waveguide region, a nanofabrication technique would be necessary and, therefore, the advantage of the easy fabrication of random structures would be spoiled.

In this paper, to improve the input-output characteristics of long-lived modes within random structures as well as the control of the resonant conditions, we propose a simple structure composed of a slab waveguide surrounded by randomly distributed scatterers as a defect region, instead of using a periodic sidewall. By employing a two-dimensional finite-difference time-domain (2D-FDTD) method [22

22. C. Vanneste and P. Sebbah, “Localized modes in random arrays of cylinders,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(2), 026612 (2005). [CrossRef] [PubMed]

25

25. H. Fujiwara, Y. Hamabata, and K. Sasaki, “Numerical analysis of resonant and lasing properties at a defect region within a random structure,” Opt. Express 17(5), 3970–3977 (2009). [CrossRef] [PubMed]

], we numerically analyze the resonant properties of long-lived modes bound in the waveguide within the random structure. From the analysis, we found that long-lived modes strongly bound in the waveguide could be realized, while waves at off-resonant frequencies were rapidly dissipated from the structure. Thus, we expect that the proposed method would provide a useful technique for accessing or manipulating long-lived modes in the random structure and would also facilitate application of such modes in integrated photonic devices or circuits using random structures.

2. Simulation and analysis

Using a 2D-FDTD method [22

22. C. Vanneste and P. Sebbah, “Localized modes in random arrays of cylinders,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(2), 026612 (2005). [CrossRef] [PubMed]

25

25. H. Fujiwara, Y. Hamabata, and K. Sasaki, “Numerical analysis of resonant and lasing properties at a defect region within a random structure,” Opt. Express 17(5), 3970–3977 (2009). [CrossRef] [PubMed]

], we calculated resonant spectra and intensity distributions of the numerical model. We considered only the electric field parallel to the cylinder’s axis. The time step and cell size were set at 7.0 × 10−17 s and 50 nm, respectively. Each calculation was performed for 106 steps (70 ps), and Mur’s second-order absorbing boundary condition was used. Light sources for exciting a fundamental waveguide mode in the waveguide were set at the left edge of the waveguide and generated light waves were propagated only to the right along the waveguide. For creating intensity distributions, the light sources were excited by cosine waves at a given frequency with optimal phases for exciting a fundamental waveguide mode. To obtain resonant spectra, a short Gaussian pulse (duration time about 3.5 × 10−15 s, center frequency about 280 THz, and spectral width about 370 THz) was launched from the light source, and the electric fields of the reflected light waves were recorded at the left side of the light source during the entire calculation time (70 ps). Then, because we wanted to examine only long-lived modes, only about the last 1.3 × 105 steps of the recorded signals (from 63 to 70 ps) were Fourier-transformed.

3. Results and discussion

From the resonant spectrum indicated by curve (a) in Fig. 2, we found sharp resonant peaks randomly appearing in the spectrum. Their resonant frequencies coincided well with the frequency windows in the transmitted intensity of the surrounding random structure [curve (b) in Fig. 2], which shows three sharp dips around 170, 290, and 400 THz. By repeating the calculations for ten different distributions of scatterers with the same filling factor and waveguide structure, a similar tendency was also observed, and the resonant peaks of long-lived modes appeared only within the frequency windows. The circle with error bars in Fig. 2 indicates the average resonant frequency and its deviation (286 ± 6 THz); we confirmed that the resonant peak positions of long-lived modes coincided well with the frequency windows. Indeed, when we Fourier-transformed the recorded electric fields for every 10 ps, we confirmed that spectral peaks at frequencies outside the frequency windows completely disappeared within 10 ps. This result suggested that these peaks were leaky modes, which should be immediately scattered out from the waveguide and also from the random structure. In addition, from the calculation of the reflected intensity spectrum of the waveguide alone [curve (c) in Fig. 2], we clearly found that there was no distinct resonant peak, only weak ripple structures due to interference between waves propagating back and forth in the waveguide. From these results, the observed sharp resonant peaks originated from the surrounding scatterers, not from interference in the waveguide. Therefore, we considered that the surrounding scatterers could work as filters or mirrors with specific frequency bands and give random feedback depending on the frequency windows. Thus, the data suggests that the observed resonant peaks in the frequency windows could be long-lived modes surviving only within the waveguide.

To confirm the intensity distribution of long-lived modes appearing in Fig. 2, we calculated these distributions at on- and off-resonant frequencies. Figure 3
Fig. 3 Intensity distributions at (a) on- and (b) off-resonant frequencies (281 and 325 THz, respectively). The distributions were normalized by individual maximum values and the maximum intensity of the image at the off-resonant frequency was about 103 times smaller than that at the on-resonant frequency.
shows the results at (a) on- and (b) off-resonant frequencies in the spectrum of Fig. 2 (281 and 325 THz, respectively). Each distribution was normalized by each maximum, and the maximum intensity of the image at the off-resonant frequency was about 103 times smaller than that at the on-resonant frequency. At the on-resonant frequency (281 THz), we clearly found that the intensity distribution was strongly bound in the waveguide, and no distinct mode was observed in the surrounding structure. However, when the frequency was set at the off-resonant condition (325 THz), the intensity distribution was spread over the structure, in contrast with the on-resonant case, and immediately dissipated from the structure. As seen in Fig. 3(b), a light wave incident on the waveguide at the off-resonant frequency was strongly dissipated by surrounding scatterers and leaked from the structure, resulting in steep intensity decay along the waveguide. By repeating the calculations at different resonant frequencies, we confirmed that the intensity distributions exhibited different resonant mode distributions from the result shown in Fig. 3, but the individual distributions were strongly bound in the waveguide and showed similar tendencies.

In the above discussion, the existence of the long-lived mode was attributed solely to the surrounding random structure. However, the details of the mechanism for inducing the long-lived modes are still unclear and it might be more complicated. In Fig. 3(a), the intensity pattern in the waveguide suggests that the fundamental mode of the waveguide is coupled to a higher order mode. This situation looks similar to the discussions of a ministop band in a photonic-crystal waveguide, due to the anticrossing between the fundamental and higher order modes of the waveguide caused by the surrounding photonic crystal [30

30. M. Agio and C. M. Soukoulis, “Ministop bands in single-defect photonic crystal waveguides,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5 Pt 2), 055603 (2001). [CrossRef] [PubMed]

]. Therefore, we should note the possibility that the long-lived modes are induced inside the waveguide because of the ministop band as in the photonic crystal waveguide. However, the mechanism of the long-lived modes is still under investigation and remains as our future work.

4. Conclusion

To manipulate long-lived modes in random structures, we proposed a simple structure composed of a waveguide embedded in a random structure. From numerical analysis using a 2D-FDTD method, we found that resonant peaks of long-lived modes in the spectra appeared only when the resonant frequency matched the frequency windows of the surrounding random structure. In addition, the intensity distributions indicated that photons at the resonant frequencies could be strongly confined within the waveguide, while those at off-resonant frequencies rapidly dissipated from the waveguide and the random structure. These results suggest that intended long-lived modes could be realized in a waveguide structure embedded in a random structure, and therefore, we have believed the possibility that the long-lived modes could be easily accessed from outside of the random structure via the waveguide. Although further numerical studies and experimental verifications are necessary, we expect that the potential of the proposed structure to improve the input-output characteristics as well as to manipulate the resonant conditions of long-lived modes within a waveguide can open novel possibilities for technological applications, such as integrated photonic devices or circuits using random structures.

Acknowledgments

This work was supported by the PRESTO program of the Japan Science and Technology Agency and partly by a KAKENHI grant in the Priority Area “Strong Photon-Molecule Coupling Fields” from MEXT.

References and links

1.

C. Gouedard, D. Husson, C. Sauteret, F. Auzel, and A. Migus, “Generation of spatially incoherent short pulses in laser-pumped neodymium stoichiometric crystals and powders,” J. Opt. Soc. Am. B 10(12), 2358–2363 (1993). [CrossRef]

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.

M. A. Noginov, N. E. Noginova, H. J. Caulfield, P. Venkateswarlu, T. Thompson, M. Mahdi, and V. Ostroumov, “Short-pulsed stimulated emission in the powders of NdAl3(BO3)4, NdSc3(BO3)4, and Nd:Sr5(PO4)3F laser crystals,” J. Opt. Soc. Am. B 13(9), 2024–2033 (1996). [CrossRef]

4.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997). [CrossRef]

5.

A. Kurita, Y. Kanematsu, M. Watanabe, K. Hirata, and T. Kushida, “Wavelength- and Angle-Selective Optical Memory Effect by Interference of Multiple-Scattered Light,” Phys. Rev. Lett. 83(8), 1582–1585 (1999). [CrossRef]

6.

H. Cao, Y. Ling, J. Y. Xu, C. Q. Cao, and P. Kumar, “Photon statistics of random lasers with resonant feedback,” Phys. Rev. Lett. 86(20), 4524–4527 (2001). [CrossRef] [PubMed]

7.

S. I. Bozhevolnyi, V. S. Volkov, and K. Leosson, “Localization and waveguiding of surface plasmon polaritons in random nanostructures,” Phys. Rev. Lett. 89(18), 186801 (2002). [CrossRef] [PubMed]

8.

R. C. Polson and Z. V. Vardeny, “Random lasing in human tissues,” Appl. Phys. Lett. 85(7), 1289–1291 (2004). [CrossRef]

9.

G. Zacharakis, N. A. Papadogiannis, and T. G. Papazoglou, “Random lasing following two-photon excitation of highly scattering gain media,” Appl. Phys. Lett. 81(14), 2511–2513 (2002). [CrossRef]

10.

H. Fujiwara and K. Sasaki, “Observation of upconversion lasing within a thulium-ion-doped glass powder film containing titanium dioxide particles,” Jpn. J. Appl. Phys. 43(No. 10B), L1337–L1339 (2004). [CrossRef]

11.

H. Fujiwara and K. Sasaki, “Observation of optical bistability in a ZnO powder random medium,” Appl. Phys. Lett. 89(7), 071115 (2006). [CrossRef]

12.

G. van Soest, M. Tomita, and A. Lagendijk, “Amplifying volume in scattering media,” Opt. Lett. 24(5), 306–308 (1999). [CrossRef]

13.

G. van Soest and A. Lagendijk, “β factor in a random laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(44 Pt 2B), 047601 (2002). [CrossRef] [PubMed]

14.

H. Cao, J. Y. Xu, E. W. Seeling, and R. P. H. Chang, “Microlaser made of disordered media,” Appl. Phys. Lett. 76(21), 2997–2999 (2000). [CrossRef]

15.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84(24), 5584–5587 (2000). [CrossRef] [PubMed]

16.

Q. Song, L. Wang, S. Xiao, X. Zhou, L. Liu, and L. Xu, “Random laser emission from a surface-corrugated waveguide,” Phys. Rev. B 72(3), 035424 (2005). [CrossRef]

17.

H. Watanabe, Y. Oki, M. Maeda, and T. Omatsu, “Waveguide dye laser including a SiO2 nanoparticle-dispersed random scattering active layer,” Appl. Phys. Lett. 86(15), 151123 (2005). [CrossRef]

18.

C. Yuen, S. F. Yu, E. S. P. Leong, H. Y. Yang, S. P. Lau, N. S. Chen, and H. H. Hng, “Low-loss and directional output ZnO thin-film ridge waveguide random lasers with MgO capped layer,” Appl. Phys. Lett. 86(3), 031112 (2005). [CrossRef]

19.

S. Furumi, H. Fudouzi, H. T. Miyazaki, and Y. Sakka, “Flexible polymer colloidal-crystal random lasers with a light-emitting planar defect,” Adv. Mater. 19(16), 2067–2072 (2007). [CrossRef]

20.

D. S. Wiersma and S. Cavalieri, “Light emission: A temperature-tunable random laser,” Nature 414(6865), 708–709 (2001). [CrossRef] [PubMed]

21.

S. Gottardo, R. Sapienza, P. D. Garcia, A. Blanco, D. S. Wiersma, and C. Lopez, “Resonance-driven random lasing,” Nat. Photonics 2(7), 429–432 (2008). [CrossRef]

22.

C. Vanneste and P. Sebbah, “Localized modes in random arrays of cylinders,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(2), 026612 (2005). [CrossRef] [PubMed]

23.

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

24.

J. Liu and H. Liu, “Theoretical investigation on the threshold properties of localized modes in two-dimensional random media,” J. Mod. Opt. 53(10), 1429–1439 (2006). [CrossRef]

25.

H. Fujiwara, Y. Hamabata, and K. Sasaki, “Numerical analysis of resonant and lasing properties at a defect region within a random structure,” Opt. Express 17(5), 3970–3977 (2009). [CrossRef] [PubMed]

26.

H. Miyazaki, M. Hase, H. T. Miyazaki, Y. Kurokawa, and N. Shinya, “Photonic material for designing arbitrarily shaped waveguides in two dimensions,” Phys. Rev. B 67(23), 235109 (2003). [CrossRef]

27.

C. Rockstuhl, U. Peschel, and F. Lederer, “Correlation between single-cylinder properties and bandgap formation in photonic structures,” Opt. Lett. 31(11), 1741–1743 (2006). [CrossRef] [PubMed]

28.

J. Topolancik, F. Vollmer, and B. Llic, “Random high-Q cavities in disordered photonic crystal waveguides,” Appl. Phys. Lett. 91(20), 201102 (2007). [CrossRef]

29.

J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99(25), 253901 (2007). [CrossRef]

30.

M. Agio and C. M. Soukoulis, “Ministop bands in single-defect photonic crystal waveguides,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5 Pt 2), 055603 (2001). [CrossRef] [PubMed]

OCIS Codes
(140.0140) Lasers and laser optics : Lasers and laser optics
(290.4210) Scattering : Multiple scattering
(140.3945) Lasers and laser optics : Microcavities

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: April 21, 2009
Revised Manuscript: June 1, 2009
Manuscript Accepted: June 4, 2009
Published: June 8, 2009

Citation
Hideki Fujiwara, Yosuke Hamabata, and Keiji Sasaki, "Numerical analysis of resonant properties of a waveguide structure within a random medium," Opt. Express 17, 10522-10528 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-13-10522


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. C. Gouedard, D. Husson, C. Sauteret, F. Auzel, and A. Migus, “Generation of spatially incoherent short pulses in laser-pumped neodymium stoichiometric crystals and powders,” J. Opt. Soc. Am. B 10(12), 2358–2363 (1993). [CrossRef]
  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. M. A. Noginov, N. E. Noginova, H. J. Caulfield, P. Venkateswarlu, T. Thompson, M. Mahdi, and V. Ostroumov, “Short-pulsed stimulated emission in the powders of NdAl3(BO3)4, NdSc3(BO3)4, and Nd:Sr5(PO4)3F laser crystals,” J. Opt. Soc. Am. B 13(9), 2024–2033 (1996). [CrossRef]
  4. D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997). [CrossRef]
  5. A. Kurita, Y. Kanematsu, M. Watanabe, K. Hirata, and T. Kushida, “Wavelength- and Angle-Selective Optical Memory Effect by Interference of Multiple-Scattered Light,” Phys. Rev. Lett. 83(8), 1582–1585 (1999). [CrossRef]
  6. H. Cao, Y. Ling, J. Y. Xu, C. Q. Cao, and P. Kumar, “Photon statistics of random lasers with resonant feedback,” Phys. Rev. Lett. 86(20), 4524–4527 (2001). [CrossRef] [PubMed]
  7. S. I. Bozhevolnyi, V. S. Volkov, and K. Leosson, “Localization and waveguiding of surface plasmon polaritons in random nanostructures,” Phys. Rev. Lett. 89(18), 186801 (2002). [CrossRef] [PubMed]
  8. R. C. Polson and Z. V. Vardeny, “Random lasing in human tissues,” Appl. Phys. Lett. 85(7), 1289–1291 (2004). [CrossRef]
  9. G. Zacharakis, N. A. Papadogiannis, and T. G. Papazoglou, “Random lasing following two-photon excitation of highly scattering gain media,” Appl. Phys. Lett. 81(14), 2511–2513 (2002). [CrossRef]
  10. H. Fujiwara and K. Sasaki, “Observation of upconversion lasing within a thulium-ion-doped glass powder film containing titanium dioxide particles,” Jpn. J. Appl. Phys. 43(No. 10B), L1337–L1339 (2004). [CrossRef]
  11. H. Fujiwara and K. Sasaki, “Observation of optical bistability in a ZnO powder random medium,” Appl. Phys. Lett. 89(7), 071115 (2006). [CrossRef]
  12. G. van Soest, M. Tomita, and A. Lagendijk, “Amplifying volume in scattering media,” Opt. Lett. 24(5), 306–308 (1999). [CrossRef]
  13. G. van Soest and A. Lagendijk, “β factor in a random laser,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(44 Pt 2B), 047601 (2002). [CrossRef] [PubMed]
  14. H. Cao, J. Y. Xu, E. W. Seeling, and R. P. H. Chang, “Microlaser made of disordered media,” Appl. Phys. Lett. 76(21), 2997–2999 (2000). [CrossRef]
  15. H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84(24), 5584–5587 (2000). [CrossRef] [PubMed]
  16. Q. Song, L. Wang, S. Xiao, X. Zhou, L. Liu, and L. Xu, “Random laser emission from a surface-corrugated waveguide,” Phys. Rev. B 72(3), 035424 (2005). [CrossRef]
  17. H. Watanabe, Y. Oki, M. Maeda, and T. Omatsu, “Waveguide dye laser including a SiO2 nanoparticle-dispersed random scattering active layer,” Appl. Phys. Lett. 86(15), 151123 (2005). [CrossRef]
  18. C. Yuen, S. F. Yu, E. S. P. Leong, H. Y. Yang, S. P. Lau, N. S. Chen, and H. H. Hng, “Low-loss and directional output ZnO thin-film ridge waveguide random lasers with MgO capped layer,” Appl. Phys. Lett. 86(3), 031112 (2005). [CrossRef]
  19. S. Furumi, H. Fudouzi, H. T. Miyazaki, and Y. Sakka, “Flexible polymer colloidal-crystal random lasers with a light-emitting planar defect,” Adv. Mater. 19(16), 2067–2072 (2007). [CrossRef]
  20. D. S. Wiersma and S. Cavalieri, “Light emission: A temperature-tunable random laser,” Nature 414(6865), 708–709 (2001). [CrossRef] [PubMed]
  21. S. Gottardo, R. Sapienza, P. D. Garcia, A. Blanco, D. S. Wiersma, and C. Lopez, “Resonance-driven random lasing,” Nat. Photonics 2(7), 429–432 (2008). [CrossRef]
  22. C. Vanneste and P. Sebbah, “Localized modes in random arrays of cylinders,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(2), 026612 (2005). [CrossRef] [PubMed]
  23. P. Sebbah and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B 66(14), 144202 (2002). [CrossRef]
  24. J. Liu and H. Liu, “Theoretical investigation on the threshold properties of localized modes in two-dimensional random media,” J. Mod. Opt. 53(10), 1429–1439 (2006). [CrossRef]
  25. H. Fujiwara, Y. Hamabata, and K. Sasaki, “Numerical analysis of resonant and lasing properties at a defect region within a random structure,” Opt. Express 17(5), 3970–3977 (2009). [CrossRef] [PubMed]
  26. H. Miyazaki, M. Hase, H. T. Miyazaki, Y. Kurokawa, and N. Shinya, “Photonic material for designing arbitrarily shaped waveguides in two dimensions,” Phys. Rev. B 67(23), 235109 (2003). [CrossRef]
  27. C. Rockstuhl, U. Peschel, and F. Lederer, “Correlation between single-cylinder properties and bandgap formation in photonic structures,” Opt. Lett. 31(11), 1741–1743 (2006). [CrossRef] [PubMed]
  28. J. Topolancik, F. Vollmer, and B. Llic, “Random high-Q cavities in disordered photonic crystal waveguides,” Appl. Phys. Lett. 91(20), 201102 (2007). [CrossRef]
  29. J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99(25), 253901 (2007). [CrossRef]
  30. M. Agio and C. M. Soukoulis, “Ministop bands in single-defect photonic crystal waveguides,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5 Pt 2), 055603 (2001). [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
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited