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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 8 — Apr. 13, 2009
  • pp: 6074–6081
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Polarized vertical beaming of an engineered hexapole mode laser

Ju-Hyung Kang, Min-Kyo Seo, Sun-Kyung Kim, Se-Heon Kim, Myung-Ki Kim, Hong-Gyu Park, Ki-Soo Kim, and Yong-Hee Lee  »View Author Affiliations


Optics Express, Vol. 17, Issue 8, pp. 6074-6081 (2009)
http://dx.doi.org/10.1364/OE.17.006074


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Abstract

We demonstrate vertical beaming of linearly-polarized light from the hexapole mode of an engineered single-cell photonic crystal cavity by employing the solid angle scanning system. The vertical emission that is forbidden by the inner symmetry of the hexapole mode is made possible by perturbing its symmetry. Experimentally 56% of photons are funneled within a divergence angle of ±30°. Measured polarization-resolved far-field profiles of the engineered hexapole mode agree well with those of the predictions of finite difference time domain methods.

© 2009 Optical Society of America

1. Introduction

A single-cell photonic-crystal (PhC) cavity [1–4

1. O. Painter, R. Lee, A. Scherer, A. Yariv, J. O’Brien, P. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819–1821 (1999). [CrossRef] [PubMed]

] with high quality (Q) factor and small mode volume can realize various high-performance photonic applications and quantum optical phenomena such as low-threshold lasers [5

5. K. Nozaki, S. Kita, and T. Baba, “Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser,” Opt. Express 15, 7506–7514 (2007). [CrossRef] [PubMed]

], cavity quantum electrodynamics (CQED) experiments [6

6. A. Badolato, K. Hennessy, M. Atature, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoglu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308, 1158–1161 (2005). [CrossRef] [PubMed]

], single photon sources [7

7. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuckovic, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005). [CrossRef] [PubMed]

] and high-speed modulation [3

3. T. Baba, D. Sano, K. Nozaki, K. Inoshita, Y. Kuroki, and F. Koyama, “Observation of fast spontaneous emission decay in GaInAsP photonic crystal point defect nanocavity at room temperature,” Appl. Phys. Lett. 85, 3989–3991 (2004). [CrossRef]

, 8

8. H. Altug, D. Englund, and J. Vuckovic, “Ultra-fast photonic crystal nanolasers,” Nat. Phys. 2, 484–488 (2006). [CrossRef]

]. This cavity can also be used for the sensitive biochemical detection by utilizing its high electromagnetic field localization [9–11

9. M. Loncar, A. Scherer, and Y. Qiu, “Photonic crystal laser sources for chemical detection,” Appl. Phys. Lett. 82, 648–650 (2003). [CrossRef]

]. In general, the photons coming out of such a wavelength-scale cavity are highly diverging due to the strong diffractive tendency [12

12. K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10, 670–684 (2002). [PubMed]

], but the vertical emission and efficient collection of light are crucial for practical applications. While dipole-type modes exhibit vertical emission naturally [13

13. O. Painter and K. Srinivasan, “Polarization properties of dipolelike defect modes in photonic crystal nanocavities,” Opt. Lett. 27, 339–341 (2002). [CrossRef]

, 14

14. C. Grillet, C. Monat, C. L. Smith, B. J. Eggleton, D. J. Moss, S. Frédérick, D. Dalacu, P. J. Poole, J. Lapointe, G. Aers, and R. L. Williams, “Nanowire coupling to photonic crystal nanocavities for single photon sources,” Opt. Express 15, 1267–1276 (2007). [CrossRef] [PubMed]

], both the relatively-low Q factor and degeneracy of the dipole mode limit its quantum optical applicability. Furthermore, for the electrical pumping, Q factor of the dipole mode decreases greatly because the electric field maximum at the center of dipole mode is strongly disturbed due to the central dielectric post which is underneath the PhC slab for current injection [15

15. H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004). [CrossRef] [PubMed]

, 16

16. M. -K. Seo, K. -Y. Jeong, J.-K. Yang, Y.-H. Lee, H.-G. Park, and S.-B. Kim, “Low threshold current single-cell hexapole mode photonic crystal laser,” Appl. Phys. Lett. 90, 171122 (2007). [CrossRef]

]. Alternatively, the nondegenerate hexapole mode, one of the whispering-gallery-type modes, is more attractive thanks to the high Q factor of ~106 and the small mode volume [4

4. H.-Y. Ryu, M. Notomi, and Y.-H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett. 83, 4294–4296 (2003). [CrossRef]

, 17

17. H.-G. Park, J.-K. Hwang, J. Huh, H.-Y. Ryu, S.-H. Kim, J.-S. Kim, and Y.-H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002). [CrossRef]

]. The hexapole mode has an electric field node at the center and thus can be used for the electrically-pumped PhC laser [16

16. M. -K. Seo, K. -Y. Jeong, J.-K. Yang, Y.-H. Lee, H.-G. Park, and S.-B. Kim, “Low threshold current single-cell hexapole mode photonic crystal laser,” Appl. Phys. Lett. 90, 171122 (2007). [CrossRef]

]. However, the typical hexapole mode has a null vertical emission and it is hard to funnel photons into a conventional optical system. Recently, it has been theoretically proposed that linearly-polarized vertical beaming from the hexapole mode can be obtained by simple modification of the single-cell PhC cavity, so that highly efficient coupling into a single mode fiber is achievable [18

18. S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B 73, 235117 (2006). [CrossRef]

]. In this study, we experimentally demonstrate linearly-polarized efficient vertical emission from the hexapole mode of a modified single-cell PhC resonator.

2. Engineered hexapole mode for linearly-polarized vertical beaming

Figure 1(a) shows the schematics of a single-cell PhC cavity based on InGaAsP PhC slab and InP substrate. As suggested by Kim et al, hexapole mode photons could be engineered to go out vertically by destroying the balance of the electric field distribution [18

18. S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B 73, 235117 (2006). [CrossRef]

]. We enlarge two nearest neighbor holes around the cavity along the x-direction as shown in Fig. 1(b). Then the vector summation of Ex fields that have even symmetry becomes non-zero and x-polarized photons are allowed to scatter out along the vertical direction. In comparison, the summation of Ey fields that have odd symmetry remain very close to zero, because each positive Ey component is always cancelled by a partner Ey component of an opposite sign (Fig. 1(c)). The net effect, therefore, shows up as highly x-polarized vertical emission. This loss engineering reduces the theoretical Q factor of hexapole mode to 20,000 [18

18. S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B 73, 235117 (2006). [CrossRef]

], still larger than that of a conventional dipole mode [19

19. J. Vŭcković, M. Lončar, A. Mabuchi, and A. Scherer, “Optimization of Q factor in microcavities based on freestanding membranes,” IEEE J. Quantum Electron. 38, 850–856 (2002). [CrossRef]

]. Furthermore, we can achieve even smaller divergent angle of emission by choosing the air gap size (Fig. 1(a)) encouraging the constructive interference [20

20. S.-H. Kim, M.-K. Seo, J.-Y. Kim, and Y.-H. Lee, “Effects of a bottom substrate on emission properties of a photonic crystal nanolaser,” IPRM 07, IEEE 19th International Conference on, 480–483 (2007).

]. In this study, we measure the far-field emission patterns of the hexapole mode in this “engineered” single-cell PhC cavity of Fig. 1(b) and demonstrate directional and linearly-polarized emission properties.

Fig. 1. (a) Schematics of a single-cell PhC cavity built on InGaAsP slab and InP substrate. (b) Scanning electron microscope image of an engineered single-cell PhC cavity. The radii of two nearest neighbor air holes on the x-axis (r1) are increased up to 0.29a. (c) The calculated Hz, Ex and Ey field profiles of the engineered hexapole mode. (d) Measured lasing spectrum and polarization characteristics of the engineered hexapole mode.

3. Polarization-resolved far-field measurement

3.1. Solid scanning system for far-field measurement

We measure the far-field emission patterns of the lasing modes using the experimental setup of Fig. 2 [21

21. D.-J. Shin, S.-H. Kim, J.-K. Hwang, H.-Y. Ryu, H.-G. Park, D.-S. Song, and Y.-H. Lee, “Far- and near-field investigations on the lasing modes in two dimensional photonic crystal slab lasers,” IEEE J. Quantum Electron 38, 857–866 (2002). [CrossRef]

]. In order to fully characterize the laser emission over the whole upper hemisphere, we rotate both of the sample and the photodetector. The photodetector scans from -90° to 90° in the polar (θ-) direction and from 0° to 180° in the azimuthal (ϕ-) direction, respectively. Because a size of detector cell and a distance between the sample and the detector are 1 mm2 and 30 cm, the angular resolution limit of our measurements can be reduced to 0.2°. In these experiments, however, scanning steps of the angles in θ- and ϕ- directions are roughly set to 10° and 9°, respectively, to decrease total measuring time. The polynomial-interpolation is used to draw smooth far-field emission patterns [22

22. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numeric Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University Press, Cambridge, England, 1992), p.108.

]. To optically excite resonant modes, a 980-nm pumping laser beam is positioned on the backside of the transparent InP substrate. A polarizer is placed in front of the photodetector to measure polarization-resolved far-field emission patterns. The raw data obtained from the measurements over the curved surface of the upper hemisphere are projected onto a two dimensional (2-D) flat surface using a mapping defined by x = θcosϕ and y = θsinϕ to clearly understand the complicated three dimensional (3-D) emission patterns (the inset of Fig. 2).

Fig. 2. Schematics of far-field measurement setup (left) and projection of the curved surface onto a 2-D flat surface (right).

3.2. Far-fields of the engineered hexapole mode laser

Figure 3(a) shows the measured far-field emission patterns of the hexapole mode in the engineered PhC cavity. Note that the vertical beaming is successfully demonstrated from the engineered PhC cavity as expected (Fig. 3(a)). Thus, a large fraction of light is emitted into the vertical direction: 56% of the photons are emitted within a divergence angle of ±30°. We also investigate the cross-sectional intensity distribution of this far-field emission pattern. As shown in Fig. 3(b), the measured cross sectional views along the x- and y-axes (black lines) agree well with the results (red dotted lines) obtained by 3-D finite-difference time-domain (FDTD) method. It is interesting that the Gaussian-like far-field emission pattern is obtained through the simple modification of the cavity. In the cross section along the y-axis, there are two additional weak lobes at an angle near θ = ±65°. This will be discussed in Sec. 4. In addition, we measure the polarization-resolved far-field emission patterns (Figs. 3(c) and 3(d)). θ- and ϕ-components of the hexapole mode each have two intensity lobes, for which these pairs of lobes are perpendicular to each other and have singularities at the central point (θ = 0°). This implies that the emission is linearly-polarized along the x-direction. Consequently, the measured intensity distribution and polarization property strongly support that the engineered hexapole mode has the linearly-polarized Gaussian-like far-field emission pattern and thus can be well overlapped with the fundamental mode (LP01) of an optical fiber. We expect that the efficient light coupling of the PhC cavity to the fiber can be successfully achieved.

Fig. 3. (a) Measured far-field emission patterns in the engineered hexapole mode. (b) Cross sectional scan of the total intensity along x- (left) and y-axes (right). The measurements (black lines) agree well with the 3-D FDTD simulation results (red dotted lines). (c)-(d) Measured polarization-resolved far-field emission patterns. θ- and ϕ-polarization components are measured in (c) and (d), respectively.

3.3. Far-fields of the reference hexapole mode laser

Fig. 4. (a) Measured far-field emission pattern in the reference hexapole mode. (b) SEM image of a reference single-cell PhC cavity. (c)-(d) The polarization-resolved far-field emission patterns. θ- and ϕ-polarization components are measured in (c) and (d), respectively.

4. 3-D FDTD simulations of polarization-resolved far-field emission patterns

To better understand the experimental results, 3-D FDTD simulations are performed to analyze the characteristics of the far-field emission patterns in both engineered and reference hexapole modes (Figs. 5 and 6). We compute the far-field emission patterns transformed from the near-field distribution using fast Fourier transform (FFT) algorithm [18

18. S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B 73, 235117 (2006). [CrossRef]

, 23

23. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain method, 2nd ed. (Artech House, Norwood, MA, 2000).

]. This method has been also used for Q-factor optimization [12

12. K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10, 670–684 (2002). [PubMed]

, 19

19. J. Vŭcković, M. Lončar, A. Mabuchi, and A. Scherer, “Optimization of Q factor in microcavities based on freestanding membranes,” IEEE J. Quantum Electron. 38, 850–856 (2002). [CrossRef]

, 24

24. Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express 13, 1202–1214 (2005). [CrossRef] [PubMed]

, 25

25. D. Englund, I. Fushman, and J. Vŭcković, “General Recipe for Designing Photonic Crystal Cavities,” Opt. Express 12, 5961–5975 (2005). [CrossRef]

]. As shown in Fig. 5, one can easily see that Gaussian-like vertical beaming profile and linear polarization agree with those of the fabricated sample (Fig. 3). Although the structural perturbations degrade the quality factor noticeably, vertical beaming characteristics did not change as sensitively. However, when the relative air-hole size deviates more than ±5%, the output tends to diverge significantly [20

20. S.-H. Kim, M.-K. Seo, J.-Y. Kim, and Y.-H. Lee, “Effects of a bottom substrate on emission properties of a photonic crystal nanolaser,” IPRM 07, IEEE 19th International Conference on, 480–483 (2007).

]. The fraction of photons emitted within ±30° of the engineered hexapole mode is calculated as 67%. In comparison, that of dipole-type mode is reported as 30% [13

13. O. Painter and K. Srinivasan, “Polarization properties of dipolelike defect modes in photonic crystal nanocavities,” Opt. Lett. 27, 339–341 (2002). [CrossRef]

]. The calculated θ- and ϕ-polarization resolved far-field patterns (Figs. 5(b) and 5(c)) agree well with measured data (Figs. 3(c) and 3(d)). One can also confirm in Figs. 5(d) and 5(e) that the vertical output is strongly x-polarized.

Fig. 5. 3-D FDTD simulation results of the far-field emission patterns in the engineered hexapole mode. (a) Total intensity, (b) θ-, (c) ϕ-, (d) x- and (e) y-polarization components of far field patterns are computed.
Fig. 6. 3-D FDTD simulation results of the far-field emission patterns in the reference hexapole mode. (a) Total intensity, (b) θ-, and (c) ϕ-polarization components of far-field patterns are computed.

In these simulations, we apply the InP bottom substrate under the PhC slab as shown in Fig. 1(a). Since the reflectance between the air and the simple InP bottom substrate is around 30%, the reflection from the bottom substrate can increase the vertical out-coupling of total radiated power [20

20. S.-H. Kim, M.-K. Seo, J.-Y. Kim, and Y.-H. Lee, “Effects of a bottom substrate on emission properties of a photonic crystal nanolaser,” IPRM 07, IEEE 19th International Conference on, 480–483 (2007).

]. In our fabricated structure, the ratio of the vertical emitting power to total power is calculated 64%. In addition, the far-field emission pattern can be optimized by controlling the distance between the PhC slab and the bottom substrate and reflectance of the bottom substrate [18

18. S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B 73, 235117 (2006). [CrossRef]

, 20

20. S.-H. Kim, M.-K. Seo, J.-Y. Kim, and Y.-H. Lee, “Effects of a bottom substrate on emission properties of a photonic crystal nanolaser,” IPRM 07, IEEE 19th International Conference on, 480–483 (2007).

]. Near the constructive interference condition for vertical reflection, 2d = 1λ, 2λ, 3λ…, vertical beaming is achievable. We choose air gap size near 0.5λ because smaller air gap size is preferred for making current flowing dielectric post [15

15. H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004). [CrossRef] [PubMed]

, 16

16. M. -K. Seo, K. -Y. Jeong, J.-K. Yang, Y.-H. Lee, H.-G. Park, and S.-B. Kim, “Low threshold current single-cell hexapole mode photonic crystal laser,” Appl. Phys. Lett. 90, 171122 (2007). [CrossRef]

]. We can also see that the additional two weak lobes are along the y-axis at θ = 65° in Fig. 5. Because the air gap distance d between the PhC slab and the bottom substrate is 860 nm, destructive interference makes the intensity node at θ = 42°, which can be obtained by the formula, 2d/cosθ = 1.5λ. This value agrees well with the experimental result (Fig. 3).

We expect that, based on the effect of vertical coupling, this engineered hexapole mode can be employed for micro-photodetector [26

26. J.-K. Yang, M.-K. Seo, I.-K. Hwang, S.-B. Kim, and Y.-H. Lee, “Polarization-selective resonant photonic crystal photodetector,” Appl. Phys. Lett. 93, 211103 (2008). [CrossRef]

] and vertical add-drop devices for photonic integrated circuits [27

27. S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000). [CrossRef] [PubMed]

].

5. Summary

We successfully demonstrate vertical funneling from the engineered hexapole mode of a single-cell PhC cavity using the far-field measurement system. 56% of linearly-polarized light of the resonant mode are measured within a divergence angle of ±30°. With this vertical beaming scheme, the efficient coupling of light from a wavelength-scale cavity with a fundamental mode (LP01) of an optical fiber is expected.

Acknowledgments

This work was supported by the Korea Science and Engineering Foundation (KOSEF) (No.ROA-2006-000-10236-0), the Korea Foundation for International Cooperation of Science and Technology (KICOS) (No. M60605000007-06A0500-00710) through grants provided by the Korean Ministry of Science and Technology (MOST) and the Star-Faculty Project (Grant No. KRF-2007-C00018). H.G. P. acknowledges support by the Korea Research Foundation Grant funed by the Korean Government (KRF-2008-331-C00118) and the Seoul R&BD Program.

References and links

1.

O. Painter, R. Lee, A. Scherer, A. Yariv, J. O’Brien, P. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819–1821 (1999). [CrossRef] [PubMed]

2.

H. -Y. Ryu, S. -H. Kim, H. -G. Park, J. -K. Hwang, Y. -H. Lee, and J. -S. Kim, “Square-lattice photonic band-gap single-cell laser operating in the lowest-order whispering gallery mode,” Appl. Phys. Lett. 80, 3883–3885 (2002). [CrossRef]

3.

T. Baba, D. Sano, K. Nozaki, K. Inoshita, Y. Kuroki, and F. Koyama, “Observation of fast spontaneous emission decay in GaInAsP photonic crystal point defect nanocavity at room temperature,” Appl. Phys. Lett. 85, 3989–3991 (2004). [CrossRef]

4.

H.-Y. Ryu, M. Notomi, and Y.-H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett. 83, 4294–4296 (2003). [CrossRef]

5.

K. Nozaki, S. Kita, and T. Baba, “Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser,” Opt. Express 15, 7506–7514 (2007). [CrossRef] [PubMed]

6.

A. Badolato, K. Hennessy, M. Atature, J. Dreiser, E. Hu, P. M. Petroff, and A. Imamoglu, “Deterministic coupling of single quantum dots to single nanocavity modes,” Science 308, 1158–1161 (2005). [CrossRef] [PubMed]

7.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuckovic, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005). [CrossRef] [PubMed]

8.

H. Altug, D. Englund, and J. Vuckovic, “Ultra-fast photonic crystal nanolasers,” Nat. Phys. 2, 484–488 (2006). [CrossRef]

9.

M. Loncar, A. Scherer, and Y. Qiu, “Photonic crystal laser sources for chemical detection,” Appl. Phys. Lett. 82, 648–650 (2003). [CrossRef]

10.

S.-H. Kim, J.-H. Choi, S.-K. Lee, S.-H. Kim, S.-M. Yang, Y.-H. Lee, C. Seassal, P. Regrency, and P. Viktorovitch, “Optofluidic integration of a photonic crystal nanolaser,” Opt. Express 16, 6515–6527 (2008). [CrossRef] [PubMed]

11.

S. Kita, K. Nozaki, and T. Baba, “Refractive index sensing utilizing a cw photonic crystal nanolaser and its array configuration,” Opt. Express 16, 8174–8180 (2008). [CrossRef] [PubMed]

12.

K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10, 670–684 (2002). [PubMed]

13.

O. Painter and K. Srinivasan, “Polarization properties of dipolelike defect modes in photonic crystal nanocavities,” Opt. Lett. 27, 339–341 (2002). [CrossRef]

14.

C. Grillet, C. Monat, C. L. Smith, B. J. Eggleton, D. J. Moss, S. Frédérick, D. Dalacu, P. J. Poole, J. Lapointe, G. Aers, and R. L. Williams, “Nanowire coupling to photonic crystal nanocavities for single photon sources,” Opt. Express 15, 1267–1276 (2007). [CrossRef] [PubMed]

15.

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004). [CrossRef] [PubMed]

16.

M. -K. Seo, K. -Y. Jeong, J.-K. Yang, Y.-H. Lee, H.-G. Park, and S.-B. Kim, “Low threshold current single-cell hexapole mode photonic crystal laser,” Appl. Phys. Lett. 90, 171122 (2007). [CrossRef]

17.

H.-G. Park, J.-K. Hwang, J. Huh, H.-Y. Ryu, S.-H. Kim, J.-S. Kim, and Y.-H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002). [CrossRef]

18.

S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B 73, 235117 (2006). [CrossRef]

19.

J. Vŭcković, M. Lončar, A. Mabuchi, and A. Scherer, “Optimization of Q factor in microcavities based on freestanding membranes,” IEEE J. Quantum Electron. 38, 850–856 (2002). [CrossRef]

20.

S.-H. Kim, M.-K. Seo, J.-Y. Kim, and Y.-H. Lee, “Effects of a bottom substrate on emission properties of a photonic crystal nanolaser,” IPRM 07, IEEE 19th International Conference on, 480–483 (2007).

21.

D.-J. Shin, S.-H. Kim, J.-K. Hwang, H.-Y. Ryu, H.-G. Park, D.-S. Song, and Y.-H. Lee, “Far- and near-field investigations on the lasing modes in two dimensional photonic crystal slab lasers,” IEEE J. Quantum Electron 38, 857–866 (2002). [CrossRef]

22.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numeric Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University Press, Cambridge, England, 1992), p.108.

23.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain method, 2nd ed. (Artech House, Norwood, MA, 2000).

24.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express 13, 1202–1214 (2005). [CrossRef] [PubMed]

25.

D. Englund, I. Fushman, and J. Vŭcković, “General Recipe for Designing Photonic Crystal Cavities,” Opt. Express 12, 5961–5975 (2005). [CrossRef]

26.

J.-K. Yang, M.-K. Seo, I.-K. Hwang, S.-B. Kim, and Y.-H. Lee, “Polarization-selective resonant photonic crystal photodetector,” Appl. Phys. Lett. 93, 211103 (2008). [CrossRef]

27.

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000). [CrossRef] [PubMed]

OCIS Codes
(140.3945) Lasers and laser optics : Microcavities
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(220.4241) Optical design and fabrication : Nanostructure fabrication
(230.5298) Optical devices : Photonic crystals

ToC Category:
Photonic Crystals

History
Original Manuscript: February 24, 2009
Revised Manuscript: March 28, 2009
Manuscript Accepted: March 28, 2009
Published: March 31, 2009

Citation
Ju-Hyung Kang, Min-Kyo Seo, Sun-Kyung Kim, Se-Heon Kim, Myung-Ki Kim, Hong-Gyu Park, Ki-Soo Kim, and Yong-Hee Lee, "Polarized vertical beaming of an engineered hexapole mode laser," Opt. Express 17, 6074-6081 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-8-6074


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References

  1. O. Painter, R. Lee, A. Scherer, A. Yariv, J. O’Brien, P. Dapkus, and I. Kim, "Two-Dimensional Photonic Band-Gap Defect Mode Laser," Science 284, 1819-1821 (1999). [CrossRef] [PubMed]
  2. H. -Y. Ryu, S. -H. Kim, H. -G. Park, J. -K. Hwang, Y. -H. Lee, and J. -S. Kim, "Square-lattice photonic band-gap single-cell laser operating in the lowest-order whispering gallery mode," Appl. Phys. Lett. 80, 3883-3885 (2002). [CrossRef]
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