## 1D photonic band formation and photon localization in finite-size photonic-crystal waveguides

Optics Express, Vol. 18, Issue 1, pp. 117-122 (2010)

http://dx.doi.org/10.1364/OE.18.000117

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### Abstract

A transition from discrete optical modes to 1D photonic bands is experimentally observed and numerically studied in planar photonic-crystal (PhC) L_{N} microcavities of length N. For increasing N the confined modes progressively acquire a well-defined momentum, eventually reconstructing the band dispersion of the corresponding waveguide. Furthermore, photon localization due to disorder is observed experimentally in the membrane PhCs using spatially resolved photoluminescence spectroscopy. Implications on single-photon sources and transfer lines based on quasi-1D PhC structures are discussed.

© 2009 OSA

1. K. J. Vahala, “Optical microcavities,” Nature **424**(6950), 839–846 (2003). [CrossRef] [PubMed]

3. S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics **1**(8), 449–458 (2007). [CrossRef]

4. A. J. Shields, “Semiconductor quantum light sources,” Nat. Photonics **1**(4), 215–223 (2007). [CrossRef]

5. W. H. Chang, W. Y. Chen, H. S. Chang, T. P. Hsieh, J. I. Chyi, and T. M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. **96**(11), 117401 (2006). [CrossRef] [PubMed]

6. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature **432**(7014), 200–203 (2004). [CrossRef] [PubMed]

7. S. Strauf, K. Hennessy, M. T. Rakher, Y. S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. **96**(12), 127404 (2006). [CrossRef] [PubMed]

8. M. Nomura, S. Iwamoto, K. Watanabe, N. Kumagai, Y. Nakata, S. Ishida, and Y. Arakawa, “Room temperature continuous-wave lasing in photonic crystal nanocavity,” Opt. Express **14**(13), 6308–6315 (2006). [CrossRef] [PubMed]

9. N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics **1**(3), 165–171 (2007). [CrossRef]

10. J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, “Quantum State Transfer and Entanglement Distribution among Distant Nodes in a Quantum Network,” Phys. Rev. Lett. **78**(16), 3221–3224 (1997). [CrossRef]

11. C. Monroe, “Quantum information processing with atoms and photons,” Nature **416**(6877), 238–246 (2002). [CrossRef] [PubMed]

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

13. 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] [PubMed]

14. D. Englund, A. Faraon, B. Zhang, Y. Yamamoto, and J. Vucković, “Generation and transfer of single photons on a photonic crystal chip,” Opt. Express **15**(9), 5550–5558 (2007). [CrossRef] [PubMed]

15. D. P. Fussell, S. Hughes, and M. M. Dignam, “Influence of fabrication disorder on the optical properties of coupled-cavity photonic crystal waveguides,” Phys. Rev. B **78**(14), 144201 (2008). [CrossRef]

_{N}cavities, consisting of line defects formed by N missing holes in a 2D PhC hexagonal lattice, have been employed in many important experiments in nano-photonics and quantum physics, in particular on single-photon sources [5

5. W. H. Chang, W. Y. Chen, H. S. Chang, T. P. Hsieh, J. I. Chyi, and T. M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. **96**(11), 117401 (2006). [CrossRef] [PubMed]

14. D. Englund, A. Faraon, B. Zhang, Y. Yamamoto, and J. Vucković, “Generation and transfer of single photons on a photonic crystal chip,” Opt. Express **15**(9), 5550–5558 (2007). [CrossRef] [PubMed]

7. S. Strauf, K. Hennessy, M. T. Rakher, Y. S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. **96**(12), 127404 (2006). [CrossRef] [PubMed]

8. M. Nomura, S. Iwamoto, K. Watanabe, N. Kumagai, Y. Nakata, S. Ishida, and Y. Arakawa, “Room temperature continuous-wave lasing in photonic crystal nanocavity,” Opt. Express **14**(13), 6308–6315 (2006). [CrossRef] [PubMed]

_{N}cavities have been identified as good candidates for producing extremely high spontaneous-emission enhancement factors, realizing “on chip” single-photon guns [2]. A PhC waveguide-based single-photon source has also been demonstrated experimentally [17

17. T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. **101**(11), 113903 (2008). [CrossRef] [PubMed]

_{N}cavities of increasing length (N = 3 to 35). By expressing the L

_{N}cavity modes as a linear combination of the 1D Bloch eigenstates of the corresponding W1 waveguide, we show that in an ideal case the spectra of the confined modes approach the 1D dispersion starting from N~35. However, fabrication-induced disorder limits the extension of the photon wavefunction to shorter lengths. Using finite-difference (FD) computations and spatially resolved micro-photoluminescence (PL) measurements, we directly probe this localization and its dependence on the photon mode index.

_{N}cavities with N=3,6,11,21 and 35 were characterized using GaAs membrane structures incorporating InGaAs/GaAs site-controlled (lateral alignment precision ~40nm) V-groove QWRs serving as an internal light source (ILS) (see [19

19. K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, “Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity,” Appl. Phys. Lett. **90**(15), 153107 (2007). [CrossRef]

_{11}sample is shown in Fig. 1(c). Post-processing by digital etching [20

20. K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atature, J. Dreiser, and A. Imamoglu, “Tuning photonic crystal nanocavity modes by wet chemical digital etching,” Appl. Phys. Lett. **87**(2), 021108 (2005). [CrossRef]

_{3}, M

_{0}state) up to ~7500 (in L

_{21}, L

_{35}). The measured mode wavelengths differ from the calculated ones by ≈ 13nm, mainly due to a difference of ~2 nm in the lattice constant (yielding Δλ~+8 nm) and to fluctuations in the hole diameter along

*z*(reduced diameter at the half-slab level giving Δλ~+5 nm) as compared with the design target. However, since such a small offset does not involve an appreciable spectrum stretching, the experimental spectra and the N-dependence match the computations quite well.

_{N}cavities to those of a W1 waveguide and gain more insight into the formation of 1D photonic bands, it is possible to expand the

*m*-th mode of the L

_{N}cavity,

*V*is the domain volume, and the sum was centered on the minimum of the W1 band,

*k*. Since we are focusing on the odd cavity modes, only Bloch modes belonging to the corresponding odd band of the waveguide [see Fig. 1(b)] were taken into account. For the cavity modes studied in the present work, the

_{x}=π/a*y*-component of

*y*,

*G*=

*n*=0,1,…,∞) is the one-dimensional reciprocal lattice vector, and the

_{N}cavity mode possessing the right parity (

*i.e.*, odd for reflections about the

*xz*plane); only for very small values of N (approximately N<3) the cavity modes become too

*localized*to be expressed in terms of a small number of “extended” photonic crystal states, such as the waveguide eigenmodes. In these cases, the sum in Eq. (1) has to be modified to include a larger number of PhC bands. The

*m*-th mode of the L

_{N}cavity –via the mode’s 1D Fourier transform,

_{N}cavities, as shown in Fig. 3 . Even for the smallest values of N, all cavity modes localize around particular

*k*-values, and with increasing cavity length their distributions converge to discrete values of the W1 band. Hence, the cavity modes shift rapidly in energy down to a certain level [compare also to Figs. 2(b) and 2(d)], which, for the ground state (M

_{x}_{0}) is near the minimum of the dispersion curve. Starting from this point (

*i.e.*, for N~35 in the ideal case), any additional shift of M

_{0}is negligible, and the state practically becomes 1D.

_{35}). In order to get further insight, we performed 2D-FD numerical computations based on a realistic dielectric constant imported directly from SEM images of the fabricated samples [see Fig. 4(a) ]. Notwithstanding a good PhC quality (a preliminary statistical analysis suggests a relative standard deviation smaller than 3

*%*for both the hole position and radius), in the fabricated L

_{35}cavity the computed near-field patterns are clearly localized in different sections [Fig. 4(b)]. Analyzing the field patterns along the lines followed for the ideal cavities, we observe that such spatial localization manifests itself through a broadening of the mode field distributions in

*k*-space, and hence in a blueshift [see Fig. 4(c)] arising from the random-disorder potential. For the localized modes the effective cavity length is thus shorter,

_{x}*e.g*., for the M

_{0}mode of the fabricated L

_{35}the effective cavity length is actually similar to that of an ideal L

_{11}. Since the different modes are localized at different sections of the cavity, it is possible to probe the localization directly using spatially resolved micro-PL spectroscopy of these PhC structures. Figure 5 shows the measured micro-PL spectra of an L

_{35}cavity excited with a ~1.5µm wide laser spot at several positions along its axis. The different modes in each spectrum are identified based on their spectral position withthe aid of the calculated spectra (corresponding to the field distributions shown in Fig. 4). As evidenced by the variation of the integrated micro-PL intensity of the first 6 cavity modes as a function of the position of the laser spot within the cavity –displayed in Fig. 5(a)– the relative mode intensities depend strongly on the excitation position, reflecting the localization of the different modes in different sections of the long cavity as predicted by the model calculations. In particular, the fundamental mode M

_{0}is excited most efficiently when the excitation spot is located at the center of the cavity, whereas modes M

_{1}and M

_{2}are best excited when the laser spot is positioned at either extreme end of the cavity. The observed variation in the excitation efficiency of the different modes with the position of the laser spot is qualitatively consistent with the FD-calculated mode patterns [Fig. 4(b)]. It is important to note that a significant localization [bringing also disorder in the mode spectral positions, see Fig. 2(c)] arises only for the lowest-order modes [

*e.g.*, from M

_{0}to M

_{3}in Fig. 4(c)]. On the other hand, the higher-order ones (starting from ~M

_{4}-M

_{5}for the measured L

_{35}) are less disorder-sensitive. This observation reflects the fact that the high-order cavity modes stem mainly from the

*index-guided*W1 states (linear part of the dispersion band, see Fig. 1(b) and Ref [22

22. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. **87**(25), 253902 (2001). [CrossRef] [PubMed]

*photonic gap-guided*modes (close to the minimum of the W1 dispersion band) “sense” even slight fabrication-induced PhC-lattice periodicity imperfections [22

22. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. **87**(25), 253902 (2001). [CrossRef] [PubMed]

*e.g.*, QD coupling with photonic wires [17

17. T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. **101**(11), 113903 (2008). [CrossRef] [PubMed]

23. G. Dasbach, A. A. Dremin, M. Bayer, V. D. Kulakovskii, N. A. Gippius, and A. Forchel, “Oscillations in the differential transmission of a semiconductor microcavity with reduced symmetry,” Phys. Rev. B **65**(24), 2453161–2453166 (2002). [CrossRef]

14. D. Englund, A. Faraon, B. Zhang, Y. Yamamoto, and J. Vucković, “Generation and transfer of single photons on a photonic crystal chip,” Opt. Express **15**(9), 5550–5558 (2007). [CrossRef] [PubMed]

24. Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, R. Raj, G. Roelkens, and D. V. Thourhout, “Hybrid InP-based photonic crystal lasers on silicon on insulators wires,” Appl. Phys. Lett. **95**, 201119 (2009). [CrossRef]

_{N}cavities of increasing length, both experimentally and in the ideal case. The complete band formation, generally speaking, depends on the spectral width of each cavity mode, which needs to be greater than the spectral mode separation in order to allow for propagation along the axis of the photonic wire. In practice, the observed saturation in the variation of the eigenmode frequencies with increasing N suggests the onset of the formation of a 1D photonic band already for N~35. In addition, we presented direct evidence of disorder-induced photonic mode localization along the cavities, with characteristic localization patterns depending on the mode index. Such weak localization effects limit the formation of fully-extended quasi-1D photon states with predictable mode patterns, and need to be removed in case efficient QD-cavity coupling or photon transfer along the 1D photonic structure is desired,

*e.g.*, for applications in on-chip single-photon generation and transfer.

## References and links

1. | K. J. Vahala, “Optical microcavities,” Nature |

2. | V. S. C. Manga Rao and S. Hughes, “"Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: Proposal for an efficient "on chip" single photon gun,” Phys. Rev. Lett. |

3. | S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics |

4. | A. J. Shields, “Semiconductor quantum light sources,” Nat. Photonics |

5. | W. H. Chang, W. Y. Chen, H. S. Chang, T. P. Hsieh, J. I. Chyi, and T. M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. |

6. | T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature |

7. | S. Strauf, K. Hennessy, M. T. Rakher, Y. S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. |

8. | M. Nomura, S. Iwamoto, K. Watanabe, N. Kumagai, Y. Nakata, S. Ishida, and Y. Arakawa, “Room temperature continuous-wave lasing in photonic crystal nanocavity,” Opt. Express |

9. | N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics |

10. | J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, “Quantum State Transfer and Entanglement Distribution among Distant Nodes in a Quantum Network,” Phys. Rev. Lett. |

11. | C. Monroe, “Quantum information processing with atoms and photons,” Nature |

12. | D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature |

13. | J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. |

14. | D. Englund, A. Faraon, B. Zhang, Y. Yamamoto, and J. Vucković, “Generation and transfer of single photons on a photonic crystal chip,” Opt. Express |

15. | D. P. Fussell, S. Hughes, and M. M. Dignam, “Influence of fabrication disorder on the optical properties of coupled-cavity photonic crystal waveguides,” Phys. Rev. B |

16. | M. Qiu, “Band gap effects in asymmetric photonic crystal slabs,” Phys. Rev. B |

17. | T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. |

18. | Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature |

19. | K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, “Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity,” Appl. Phys. Lett. |

20. | K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atature, J. Dreiser, and A. Imamoglu, “Tuning photonic crystal nanocavity modes by wet chemical digital etching,” Appl. Phys. Lett. |

21. | M. Felici, K. A. Atlasov, and E. Kapon, in preparation. |

22. | M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. |

23. | G. Dasbach, A. A. Dremin, M. Bayer, V. D. Kulakovskii, N. A. Gippius, and A. Forchel, “Oscillations in the differential transmission of a semiconductor microcavity with reduced symmetry,” Phys. Rev. B |

24. | Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, R. Raj, G. Roelkens, and D. V. Thourhout, “Hybrid InP-based photonic crystal lasers on silicon on insulators wires,” Appl. Phys. Lett. |

**OCIS Codes**

(230.5590) Optical devices : Quantum-well, -wire and -dot devices

(230.7370) Optical devices : Waveguides

(230.5298) Optical devices : Photonic crystals

**ToC Category:**

Photonic Crystals

**History**

Original Manuscript: September 29, 2009

Revised Manuscript: November 13, 2009

Manuscript Accepted: December 14, 2009

Published: December 22, 2009

**Citation**

Kirill A. Atlasov, Marco Felici, Karl Fredrik Karlsson, Pascal Gallo, Alok Rudra, Benjamin Dwir, and Eli Kapon, "1D photonic band formation and photon localization in finite-size photonic-crystal waveguides," Opt. Express **18**, 117-122 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-1-117

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### References

- K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003). [CrossRef] [PubMed]
- V. S. C. Manga Rao and S. Hughes, “"Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: Proposal for an efficient "on chip" single photon gun,” Phys. Rev. Lett. 99, 193101 (2007).
- S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007). [CrossRef]
- A. J. Shields, “Semiconductor quantum light sources,” Nat. Photonics 1(4), 215–223 (2007). [CrossRef]
- W. H. Chang, W. Y. Chen, H. S. Chang, T. P. Hsieh, J. I. Chyi, and T. M. Hsu, “Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,” Phys. Rev. Lett. 96(11), 117401 (2006). [CrossRef] [PubMed]
- T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004). [CrossRef] [PubMed]
- S. Strauf, K. Hennessy, M. T. Rakher, Y. S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96(12), 127404 (2006). [CrossRef] [PubMed]
- M. Nomura, S. Iwamoto, K. Watanabe, N. Kumagai, Y. Nakata, S. Ishida, and Y. Arakawa, “Room temperature continuous-wave lasing in photonic crystal nanocavity,” Opt. Express 14(13), 6308–6315 (2006). [CrossRef] [PubMed]
- N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1(3), 165–171 (2007). [CrossRef]
- J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, “Quantum State Transfer and Entanglement Distribution among Distant Nodes in a Quantum Network,” Phys. Rev. Lett. 78(16), 3221–3224 (1997). [CrossRef]
- C. Monroe, “Quantum information processing with atoms and photons,” Nature 416(6877), 238–246 (2002). [CrossRef] [PubMed]
- D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997). [CrossRef]
- 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] [PubMed]
- D. Englund, A. Faraon, B. Zhang, Y. Yamamoto, and J. Vucković, “Generation and transfer of single photons on a photonic crystal chip,” Opt. Express 15(9), 5550–5558 (2007). [CrossRef] [PubMed]
- D. P. Fussell, S. Hughes, and M. M. Dignam, “Influence of fabrication disorder on the optical properties of coupled-cavity photonic crystal waveguides,” Phys. Rev. B 78(14), 144201 (2008). [CrossRef]
- M. Qiu, “Band gap effects in asymmetric photonic crystal slabs,” Phys. Rev. B 66(3), 331031–331034 (2002). [CrossRef]
- T. Lund-Hansen, S. Stobbe, B. Julsgaard, H. Thyrrestrup, T. Sünner, M. Kamp, A. Forchel, and P. Lodahl, “Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide,” Phys. Rev. Lett. 101(11), 113903 (2008). [CrossRef] [PubMed]
- Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003). [CrossRef] [PubMed]
- K. A. Atlasov, K. F. Karlsson, E. Deichsel, A. Rudra, B. Dwir, and E. Kapon, “Site-controlled single quantum wire integrated into a photonic-crystal membrane microcavity,” Appl. Phys. Lett. 90(15), 153107 (2007). [CrossRef]
- K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atature, J. Dreiser, and A. Imamoglu, “Tuning photonic crystal nanocavity modes by wet chemical digital etching,” Appl. Phys. Lett. 87(2), 021108 (2005). [CrossRef]
- M. Felici, K. A. Atlasov, and E. Kapon, in preparation.
- M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001). [CrossRef] [PubMed]
- G. Dasbach, A. A. Dremin, M. Bayer, V. D. Kulakovskii, N. A. Gippius, and A. Forchel, “Oscillations in the differential transmission of a semiconductor microcavity with reduced symmetry,” Phys. Rev. B 65(24), 2453161–2453166 (2002). [CrossRef]
- Y. Halioua, T. J. Karle, F. Raineri, P. Monnier, I. Sagnes, R. Raj, G. Roelkens, and D. V. Thourhout, “Hybrid InP-based photonic crystal lasers on silicon on insulators wires,” Appl. Phys. Lett. 95, 201119 (2009). [CrossRef]

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