Abstract

We have succeeded in fabricating a photonic crystal nanocavity with a photon lifetime of 2.1 ns, which corresponds to a quality factor of 2.5×106. This lifetime is the longest recorded thus far in photonic crystal cavities, and was brought about by improvements in the fabrication process. Comparing our experimental quality factor with the results of calculations shows that we have suppressed variations in the radii and positions of the air holes composing a nanocavity such that their standard deviations are less than 1 nm.

©2007 Optical Society of America

1. Introduction

Nanocavities in two-dimensional (2D) photonic crystal (PC) slabs [15] can strongly confine light within a volume of optical-wavelength dimensions, and are currently attracting much attention in various fields of research. They are expected to allow the realization of single-photon emitters [6], low-threshold nanolasers [79], ultra-small filters [10, 11], and highly-efficient emitters in which the spontaneous emission of light is controlled [5,6,9]. Increasing the quality factor (Q) of the nanocavities while retaining a small modal volume is essential not only for the fabrication of these devices but also for applications in quantum-information processing [5,1214] and compact optical-buffer memories [15].

In 2003, we reported an important design rule for increasing the value of Q in 2D-PC nanocavities [1]: the electric-field distribution should vary slowly along the cavity, ideally being described by a Gaussian function, in order to reduce the leakage of the out-of-slab radiation. Subsequently, in 2005 we proposed a photonic heterostructure [2] that takes advantage of the photonic mode gap (PMG) effect instead of the photonic band gap (PBG) effect to achieve the confinement of light with an electric-field profile that varies smoothly at the cavity edges [16]. Because this type of PC structure has a simple form and high flexibility, we can control the cavity electric-field distribution to a great extent.

Shortly thereafter, we fabricated the nanocavities with a two-step heterostructure and attained an experimental Q factor (Q exp) of approximately 106 [3]. However, the theoretical Q factor (Q ideal) for this nanocavity, calculated using the three-dimensional (3D) finite-difference time-domain (FDTD) method, is 1.5×107. We have demonstrated that this discrepancy between Q exp and Q ideal can be attributed to structural imperfections in the fabricated cavities [17], which give rise to an additional Q factor (Q loss). In other words, the values of Q exp that have recently been achieved for heterostructure nanocavities are determined by Q loss and not by Q ideal. A similar situation has been reported by another group whose cavity design essentially follows that of the high-Q heterostructure nanocavity [4,18]. Thus, in order to increase the value of Q exp, it is essential to minimize imperfections in the structure of the cavity by improving the fabrication process.

In line with the developments in high-Q research described above, we recently reported on the realization of a nanocavity with a Q exp value of 2.0×106 and a photon lifetime of 1.7 ns [5]. In this letter, we detail the features of such high-Q nanocavities, focusing on the latest results. We have performed two different measurements on several samples in order to estimate Q exp with certainty. By improving the entire fabrication process, we have obtained enhanced Q exp value and photon lifetime of 2.5×106 and 2.1 ns, respectively. We show, using 3D-FDTD calculations, that variations in the radii and positions of the air holes have been suppressed, with standard deviations of less than 1 nm.

2. Sample structure

Figure 1(a) shows a scanning electron microscope (SEM) image of the type of nanocavity studied in this work, formed using a two-step heterostructure. The PC consists of a triangular lattice of circular air holes with radii of 115 nm in a 250-nm-thick silicon (Si) slab. The cavity consists of a line defect with the lattice constant in the x-direction increasing every two periods as it approaches the center. The lattice constants of the central (PC2), intermediate (PC2’), and outer regions (PC1) of the cavity are a 2=420 nm, a 2’=415 nm, and a 1=410 nm, respectively. As a result, the transmission and mode-gap band frequencies of the waveguide vary slightly with position, as shown in Fig. 1(b). In this band structure, the resonant mode in the ground state is confined to the PC2 and PC2’ regions, and is represented by the dashed curve. The differences in the PMG between regions are designed such that the envelope of the electric field closely resembles a Gaussian function. Therefore, this acts as the high-Q nanocavity mode for which the calculated values of Q ideal and modal volume are 1.5×107 and 1.4 (λ/n)3, respectively, according to the 3D-FDTD method.

Figure 1(c) shows the extended structure surrounding the cavity. The nanocavity is formed by the lower line defect of 27 missing air holes. The wider upper line defect is the excitation waveguide used to inject light into the cavity through evanescent mode coupling, the strength of which can be approximately controlled by the separation between the two line defects. In this article, we use samples where the nanocavities are separated from their corresponding excitation waveguides by between four and seven rows of air holes.

The samples were fabricated using the same process steps as previously reported [2]. A silicon-on-insulator (SOI) substrate was first prepared, and PC patterns were drawn on the top resist mask by electron-beam (EB) lithography. The developed-mask patterns were transferred to the Si slab by sulfur hexafluoride (SF6)-based dry etching. The silicon dioxide (SiO2) insulator layer underneath the patterned region was then removed by selective wet etching to form an air-bridge structure.

 

Fig. 1. (a). SEM image of the nanocavity with a two-step heterostructure. PC1 has a triangular-lattice structure with a lattice constant of a 1. PC2 and PC2’ have a deformed triangular-lattice structure with lattice constants of a 2 and a 2’ in the x-direction; they retain the same lattice constant as PC1 in the y-direction in order to satisfy lattice-matching conditions. (b) Schematic view of the band diagram along the x-direction for the line defect in Fig. 1(a). The ground-state nanocavity mode mainly exists in the waveguide section formed by PC2 and PC2’. (c) SEM image of the region around the nanocavity and schematic picture of the transmission spectroscopy experiment.

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3. Decreasing 1/Qloss

The Q exp of the nanocavity is related to the Q ideal derived from 3D-FDTD calculations and the Q loss due to structural imperfections of the nanocavity by the following equation:

1Qexp=1Qideal+1Qloss.

If Q ideal is much larger than Q loss, then Q exp will largely depend on the value of Q loss. Our high-Q nanocavities currently fall into this category, because the value of Q ideal is high at 1.5×107. Therefore, the key to increasing Q exp is to reduce 1/Q loss.

The main factors that contribute to Q loss can be divided into two categories [17]. The first category consists of imperfections of the air holes, which include surface roughness and tilting of the inner walls of the air holes, and variation in their radii and positions. The second category is losses at the Si surface, most of which arise from adsorptive materials such as metals and organic compounds affixing to the sample. Water on the surface [17] and the surface electronic states [19] have been discussed elsewhere as contributing to Q loss, though they were not addressed in this paper. The highest contribution to Q loss from air-hole imperfections likely originates from the fabrication process up until the dry-etching step. Consequently, we optimized the fabrication conditions up until this step, such as the parameters of EB lithography and of dry-etching, the thickness of the resist mask, the time of development, the temperature of the developer, etc. SEM images showed that, as a result, the tilt of the air holes was reduced to less than 1° and the surface roughness of the inner walls was decreased. Any variation in the radii and positions of the air holes was not measurable. The adsorption of materials on the Si surface, which are difficult to remove, can occur at any time during fabrication. We thus improved each step of the procedure in order to prevent the adherence of foreign materials.

4. Experimental results

We performed two different measurements to estimate Q exp for the nanocavities fabricated by the improved process: microscopic-transmission spectroscopy and time-domain measurement. All of the samples in this report were subjected to both measurements at room temperature. Although the more-conventional microscopic transmission spectroscopy was insufficient for nanocavities with Q exp values greater than 106, here we present evidence that clearly demonstrates an enhancement of Q exp.

4.1 Microscopic transmission spectroscopy

In the microscopic-transmission spectroscopy, the light from a tunable continuous-wave semiconductor laser was focused by a 0.42-numerical-aperture objective lens to form a spot on the facet of the excitation waveguide. The intensity of the transmitted light from the opposite facet and the dropped light emitted from the cavity to free space were measured as a function of wavelength, using a wavelength meter with a differential accuracy of ± 0.15 pm. Because the PBG for 2D-PC slabs is inactive for transverse magnetic (TM) polarization, the incident and transmitted light were both set to transverse electric (TE) using polarizers.

Figure 2(a) plots the drop (filled circles) and transmission (open circles) spectra in the vicinity of the resonant wavelength for the cavity separated by four rows of air holes from the excitation waveguide shown in Fig. 1(c). The drop spectrum could be fitted by a Lorentzian function with a full width at half maximum (Δλ) of between 1.6 pm (dashed line) and 2.0 pm (solid line). The asymmetric shape of the drop peak gives rise to a degree of spread in Δλ for the fitted function. We consider the asymmetry of the drop peak and transmission dip to likely be due to the Fano effect [20]. The effective Q factor (Q load), which includes the load of the excitation waveguide, was calculated using the following relationship:

Qload=λ0Δλ.

Here, λ0 is the resonant wavelength of the cavity. The value of Q load was thus in the range of 0.8×106 to 1.0×106. The intrinsic Q factor (Q exp) of the nanocavity, which is not loaded by the excitation waveguide, can be obtained from the minimum transmittance (T 0) at λ 0 in the transmission spectrum. From coupled mode theory, Q exp can be expressed as follows [21]:

Qexp=QloadT0.

Thus, we obtained a value of Q exp between 1.40×106 and 1.75×106 for this nanocavity, which is higher than for samples fabricated before the analysis of Q loss in ref [17].

 

Fig. 2. Drop (filled circle) and transmission (open circle) spectra for cavities separated by (a) four rows and (b) six rows of air holes from the excitation waveguide. The scale of the horizontal axes in (a) and (b) are the same. Solid and dashed lines represent the fits using Lorentzian functions. Small oscillations in the transmission spectra might originate from the laser source.

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The value of Q exp determined above is for a nanocavity with a large load from the excitation waveguide, and contains a degree of uncertainty because our transmission measurement tends to overestimate the value of T 0 in Eq. (3). This is due to the background light that arises mainly at the waveguide facets, which have no sophisticated structure to reduce the scattering and rotation of polarization. Accordingly, it is necessary to measure samples with smaller loads; nanocavities separated by five to seven rows of air holes from the excitation waveguide were thus fabricated on the same chip, close to the device measured in Fig. 2(a). Figure 2(b) shows the corresponding spectra for a cavity with six rows of separation. The fitted value of Δλ was estimated to be only 0.4–0.7 pm, which is equivalent to a Q load value of between 2.3×106 and 4.0×106. The large uncertainty is due to factors such as the limited resolution of the wavelength meter and temperature fluctuations. Therefore, we also performed time-resolved measurements for the cavities with five to seven rows of separation in order to estimate Q exp more accurately.

4.2 Time-domain measurements

The value of Q load is proportional to the lifetime of the photons (τ) in a nanocavity; the relationship is expressed as Q load=ωτ. When Q load of the nanocavity is greater than 106, the value of τ enters the nanosecond range, which is sufficiently longer than the resolution limits of the time-resolved measurements. Furthermore, τ is stable with respect to the surroundings of the nanocavity, so time-resolved measurements are a more reliable way to estimate Q load. As the separation between the two line defects increases, the value of Q load approaches that of Q exp, as explained above. Our transmission measurements confirmed that Q load was close to Q exp for the cavities with six or seven rows of separation, because the value of T 0 in Eq. (3) was almost 1.0, as is apparent in Fig. 2(b). Therefore, measuring the value of τ for the nanocavities with six and seven rows of separation is the most accurate way to estimate Q exp.

For this measurement, the samples were placed in an isolation chamber to stabilize the cavity temperature, because temperature fluctuations lead to a deterioration of the signal-to-noise (S/N) ratio. The light from the continuous-wave laser was modulated by an external electro-optical modulator, and rectangular pulses with widths of approximately 4 ns were produced. The center wavelength of the pulses was set to the resonant wavelength λ0, and they were coupled to the excitation waveguide via a lens fiber. The dropped light was collimated using a 0.26-numerical-aperture objective lens, and coupled using another lens to an optical fiber with a core diameter of 80 µm. This configuration allowed the elimination of stray light that did not resonate with the nanocavity. Finally, the time-domain evolution of emission from the nanocavities was measured using a photomultiplier tube by applying the time-correlated single-photon counting method.

 

Fig. 3. (a). Time-resolved signal of input pulse. (b)–(d) Time-resolved signals for nanocavities with six, five, and seven rows of separation from the excitation waveguide, respectively.

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Figure 3 presents the time-resolved signals, with photon counts on a logarithmic scale. Figure 3(a) shows the scattered light signal at the transmission facet, which allowed us to confirm the shape of the input pulse, with a width of 4 ns and an acceptable S/N ratio. The decay time τ in the fitted exponential curve exp(-t/τ) is 140 ps for the rectangular pulse edge, so this is the measurement resolution. Figures 3(b)–3(d) show the signals for nanocavities with six, five, and seven rows of separation, giving τ values of 2.13, 1.01, and 1.78 ns, respectively. The corresponding values of λ0 are 1593.5 nm, 1593.4 nm, and 1592.2 nm, respectively. The longest photon lifetime of 2.13 ns implies a Q exp value of 2.52×106. In Fig. 3(c), the value of Q load is only 1.20×106 due to the relatively large load from the excitation waveguide, and it is apparent that the initial rise of the cavity response is rapid compared with that in Fig. 3(b). This is an expected characteristic of lower-Q cavities, because the light injected into the cavity and the light released from the cavity reach equilibrium in a shorter time, due to the shorter τ. The photon lifetime for the cavity with seven rows of separation (1.78 ns) is shorter than that for the cavity with six rows of separation. This apparent discrepancy suggests that structural imperfections were randomly introduced into the cavity during fabrication. Despite being next to one another on the chip, the value of λ0 for the different nanocavities varied, which also supports this assumption.

High-Q nanocavities with ultra-small V can exhibit strong nonlinearity induced by two-photon absorption, which shortens the values of τ experimentally determined [18]. We thus investigated the time evolution of the emission for different pulse widths. Figure 4(a) shows the results of simulations for a nanocavity with a 2-ns photon lifetime, using coupled-mode theory in the absence of nonlinear effects. The value of τ is constant for pulse widths of 4 ns, 6 ns, and 8 ns. In the presence of nonlinear effects, τ would decrease for longer pulses due to the higher total energy stored in the cavity. Figure 4(b) shows the experimental results for a nanocavity with seven rows of separation, which was fabricated in a different process run to that of the samples measured in Figs. 2 and 3. The experimental and simulated results are in good agreement. The evolution of stored light at the initial rise is smooth for all three pulse widths, and the values of τ for pulse widths of 4 ns, 6 ns, and 8 ns are 2.04 ns, 2.04 ns, and 2.02 ns, respectively. These results indicate that there are no nonlinear effects in our measurements because the input pulse power is low.

 

Fig. 4. Evolution of emission from a nanocavity using pulse widths of 4 ns, 6 ns, and 8 ns. (a) Calculated results for a nanocavity with τ=2 ns using coupled-mode theory in the absence of nonlinear effects. (b) Experimental results for a nanocavity with seven rows of separation.

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It is clear from Figs. 3 and 4 that we have succeeded in fabricating high-Q nanocavities with photon lifetimes of up to 2.1 ns, the longest recorded thus far, which corresponds to a Q exp value of 2.5×106. We emphasize that this was achieved by the improvements in the fabrication process described in section 3 and not by altering the design of the cavity.

Finally, we estimate the remaining variation in the radii and positions of the air holes that comprise our current high-Q nanocavities. Because 2D-PCs operate on the basis of the periodic refractive index variation, these imperfections can have significant effect. According to our previous estimations [17], the contribution to Q loss was relatively large in both cases. However, any variation in the radii and positions of the air holes for the fabricated sample was smaller than the resolution of our direct observation methods (SEM, optical microscopy, etc.), and so we investigated their influence on Q exp numerically using the 3D-FDTD method. In calculation, we approximated that these two types of imperfections are the dominant factors contributing to Q loss. For the 2D-PC structure used in the 3D-FDTD, we independently varied the radii and positions of each air hole at random, such that the distribution of each variation took the form of the Gaussian function exp{-(x-x0)2/2σ2}. We will report the detail of calculation procedures in another paper. The curves in Fig. 5 show Q exp as a function of standard deviation (σ) for 10 different fluctuation patterns. The calculated values of Q exp for a given σ are dependent on the fluctuation pattern, which is in agreement with the experimental results in Figs. 3(b) and 3(d). Averaging the results of the calculations, we estimate that σ for the current fabrication techniques is in the range of 0.6 to 1.0 nm, compared with between 1.0 and 1.4 nm for previous techniques. Taking into account the small contribution of other factors to Q loss and, hence, to Q exp, these findings strongly suggest that we have suppressed the σ of variations in the air hole radii and positions to less than 1 nm.

 

Fig. 5. Q factors calculated using the 3D-FDTD method by introducing variations in the radii and positions of the air holes according to a Gaussian distribution. The horizontal axis represents the σ for each type of variation. The curves show the results of calculations for 10 different fluctuation patterns. The value of Q exp at σ=0 nm corresponds to a Q ideal of 1.5×107.

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5. Summary

We have improved the fabrication process of high-Q nanocavities with a two-step heterostructure and modal volume of 1.4 (λ/n)3. We have performed time-domain measurements for several cavities to accurately estimate Q exp. The improvement in fabrication procedure yielded the longest observed photon lifetime of 2.1 ns, which corresponds to a Q exp value of 2.5×106, the highest reported thus far in photonic crystal cavities. Numerical simulations showed that we have suppressed the variation in the radii and positions of the air holes such that their standard deviations are less than 1 nm.

In order to further increase Q exp, it will be necessary to improve the fabrication process and to use nanocavities with higher values of Q ideal. We have already designed a nanocavity with a Q ideal value of 109, which will be reported elsewhere. Another effective approach might be to design a nanocavity that is resistant to variations in the radii and positions of air holes. To this end, there is merit to studying modified types of hetero cavities designed by either continuous change of waveguide width [4], refractive index [22], or air hole radii within the cavity region. By developing these ideas and methods, we hope to realize nanocavities with Q exp values of 107 within the next few years.

Acknowledgments

This work was partly supported by Kyoto Nanotechnology Cluster, by CREST of the Japan Science and Technology Agency, by G-COE, by Special Coordination Funds for Promoting Science and Technology and Research Grants, and by a Grant-in-Aid from the MEXT, Japan.

References and links

1. Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003). [CrossRef]   [PubMed]  

2. B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-High-Q photonic double-heterostructure nanocavity,” Nature Mater. 4, 207–210 (2005). [CrossRef]  

3. T. Asano, B. S. Song, Y. Akahane, and S. Noda, “Ultrahigh-Q nanocavities in two-dimensional photonic crystal slabs,” IEEE J. Select. Top. Quantum Electron. 12, 1123–1134 (2006). [CrossRef]  

4. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006). [CrossRef]  

5. S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nature Photon. 1, 449–458 (2007). [CrossRef]  

6. 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]  

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, 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, 6308–6315 (2006). [CrossRef]   [PubMed]  

9. S. Noda, “Seeking the ultimate nanolaser,” Science 314, 260–261 (2006). [CrossRef]   [PubMed]  

10. B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science 300, 1537 (2003). [CrossRef]   [PubMed]  

11. H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly efficient multi-channel drop filter in a twodimensional hetero photonic crystal,” Opt. Express 14, 3491–3496 (2006). [CrossRef]   [PubMed]  

12. 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, 200–203 (2004). [CrossRef]   [PubMed]  

13. G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nature Phys. 2, 81–90 (2006). [CrossRef]  

14. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007). [CrossRef]   [PubMed]  

15. Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, “Dynamic control of the Q factors in a photonic crystal nanocavity,” Nature Mater. 6, 862–865 (2007). [CrossRef]  

16. In fact there are three guidance mechanisms in the photonic heterostructures: the total internal reflection at the slab-air interface, the photonic band gap effect across the waveguide, and the photonic mode gap effect along the waveguide.

17. T. Asano, B. S. Song, and S. Noda, “Analysis of the experimental Q factors (~1 million) of photonic crystal nanocavities,” Opt. Express 14, 1996–2002 (2006). [CrossRef]   [PubMed]  

18. T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nature Photon. 1, 49–52 (2007). [CrossRef]  

19. M. Borselli, T. J. Johnson, and O. Painter, “Measuring the role of surface chemistry in silicon microphotonics,” Appl. Phys. Lett. 88, 131114 (2006). [CrossRef]  

20. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961). [CrossRef]  

21. A. Chutinan, M. Mochizuki, M. Imada, and S. Noda, “Surface-emitting channel drop filters using single defects in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 79, 2690–2692 (2001). [CrossRef]  

22. S. Tomljenovic-Hanic, M. J. Steel, C.M. Sterke, and D. J. Moss, “High-Q cavities in photosensitive photonic crystals,” Optics Lett. 32, 542–544 (2007). [CrossRef]  

References

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  1. Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
    [Crossref] [PubMed]
  2. B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-High-Q photonic double-heterostructure nanocavity,” Nature Mater. 4, 207–210 (2005).
    [Crossref]
  3. T. Asano, B. S. Song, Y. Akahane, and S. Noda, “Ultrahigh-Q nanocavities in two-dimensional photonic crystal slabs,” IEEE J. Select. Top. Quantum Electron. 12, 1123–1134 (2006).
    [Crossref]
  4. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
    [Crossref]
  5. S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nature Photon. 1, 449–458 (2007).
    [Crossref]
  6. 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]
  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, 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, 6308–6315 (2006).
    [Crossref] [PubMed]
  9. S. Noda, “Seeking the ultimate nanolaser,” Science 314, 260–261 (2006).
    [Crossref] [PubMed]
  10. B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science 300, 1537 (2003).
    [Crossref] [PubMed]
  11. H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly efficient multi-channel drop filter in a twodimensional hetero photonic crystal,” Opt. Express 14, 3491–3496 (2006).
    [Crossref] [PubMed]
  12. 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, 200–203 (2004).
    [Crossref] [PubMed]
  13. G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nature Phys. 2, 81–90 (2006).
    [Crossref]
  14. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
    [Crossref] [PubMed]
  15. Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, “Dynamic control of the Q factors in a photonic crystal nanocavity,” Nature Mater. 6, 862–865 (2007).
    [Crossref]
  16. In fact there are three guidance mechanisms in the photonic heterostructures: the total internal reflection at the slab-air interface, the photonic band gap effect across the waveguide, and the photonic mode gap effect along the waveguide.
  17. T. Asano, B. S. Song, and S. Noda, “Analysis of the experimental Q factors (~1 million) of photonic crystal nanocavities,” Opt. Express 14, 1996–2002 (2006).
    [Crossref] [PubMed]
  18. T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nature Photon. 1, 49–52 (2007).
    [Crossref]
  19. M. Borselli, T. J. Johnson, and O. Painter, “Measuring the role of surface chemistry in silicon microphotonics,” Appl. Phys. Lett. 88, 131114 (2006).
    [Crossref]
  20. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
    [Crossref]
  21. A. Chutinan, M. Mochizuki, M. Imada, and S. Noda, “Surface-emitting channel drop filters using single defects in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 79, 2690–2692 (2001).
    [Crossref]
  22. S. Tomljenovic-Hanic, M. J. Steel, C.M. Sterke, and D. J. Moss, “High-Q cavities in photosensitive photonic crystals,” Optics Lett. 32, 542–544 (2007).
    [Crossref]

2007 (5)

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nature Photon. 1, 449–458 (2007).
[Crossref]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, “Dynamic control of the Q factors in a photonic crystal nanocavity,” Nature Mater. 6, 862–865 (2007).
[Crossref]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nature Photon. 1, 49–52 (2007).
[Crossref]

S. Tomljenovic-Hanic, M. J. Steel, C.M. Sterke, and D. J. Moss, “High-Q cavities in photosensitive photonic crystals,” Optics Lett. 32, 542–544 (2007).
[Crossref]

2006 (9)

G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nature Phys. 2, 81–90 (2006).
[Crossref]

M. Borselli, T. J. Johnson, and O. Painter, “Measuring the role of surface chemistry in silicon microphotonics,” Appl. Phys. Lett. 88, 131114 (2006).
[Crossref]

T. Asano, B. S. Song, and S. Noda, “Analysis of the experimental Q factors (~1 million) of photonic crystal nanocavities,” Opt. Express 14, 1996–2002 (2006).
[Crossref] [PubMed]

H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly efficient multi-channel drop filter in a twodimensional hetero photonic crystal,” Opt. Express 14, 3491–3496 (2006).
[Crossref] [PubMed]

T. Asano, B. S. Song, Y. Akahane, and S. Noda, “Ultrahigh-Q nanocavities in two-dimensional photonic crystal slabs,” IEEE J. Select. Top. Quantum Electron. 12, 1123–1134 (2006).
[Crossref]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[Crossref]

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, 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, 6308–6315 (2006).
[Crossref] [PubMed]

S. Noda, “Seeking the ultimate nanolaser,” Science 314, 260–261 (2006).
[Crossref] [PubMed]

2005 (2)

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-High-Q photonic double-heterostructure nanocavity,” Nature Mater. 4, 207–210 (2005).
[Crossref]

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]

2004 (1)

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, 200–203 (2004).
[Crossref] [PubMed]

2003 (2)

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science 300, 1537 (2003).
[Crossref] [PubMed]

2001 (1)

A. Chutinan, M. Mochizuki, M. Imada, and S. Noda, “Surface-emitting channel drop filters using single defects in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 79, 2690–2692 (2001).
[Crossref]

1961 (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[Crossref]

Akahane, Y.

T. Asano, B. S. Song, Y. Akahane, and S. Noda, “Ultrahigh-Q nanocavities in two-dimensional photonic crystal slabs,” IEEE J. Select. Top. Quantum Electron. 12, 1123–1134 (2006).
[Crossref]

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-High-Q photonic double-heterostructure nanocavity,” Nature Mater. 4, 207–210 (2005).
[Crossref]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

Andreani, L. C.

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, 127404 (2006).
[Crossref] [PubMed]

Arakawa, Y

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]

Arakawa, Y.

Asano, T.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nature Photon. 1, 449–458 (2007).
[Crossref]

Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, “Dynamic control of the Q factors in a photonic crystal nanocavity,” Nature Mater. 6, 862–865 (2007).
[Crossref]

T. Asano, B. S. Song, and S. Noda, “Analysis of the experimental Q factors (~1 million) of photonic crystal nanocavities,” Opt. Express 14, 1996–2002 (2006).
[Crossref] [PubMed]

T. Asano, B. S. Song, Y. Akahane, and S. Noda, “Ultrahigh-Q nanocavities in two-dimensional photonic crystal slabs,” IEEE J. Select. Top. Quantum Electron. 12, 1123–1134 (2006).
[Crossref]

H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly efficient multi-channel drop filter in a twodimensional hetero photonic crystal,” Opt. Express 14, 3491–3496 (2006).
[Crossref] [PubMed]

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-High-Q photonic double-heterostructure nanocavity,” Nature Mater. 4, 207–210 (2005).
[Crossref]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science 300, 1537 (2003).
[Crossref] [PubMed]

Atature, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

Badolato, A.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[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, 127404 (2006).
[Crossref] [PubMed]

Borselli, M.

M. Borselli, T. J. Johnson, and O. Painter, “Measuring the role of surface chemistry in silicon microphotonics,” Appl. Phys. Lett. 88, 131114 (2006).
[Crossref]

Bouwmeester, D.

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, 127404 (2006).
[Crossref] [PubMed]

Choi, Y.-S.

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, 127404 (2006).
[Crossref] [PubMed]

Chutinan, A.

A. Chutinan, M. Mochizuki, M. Imada, and S. Noda, “Surface-emitting channel drop filters using single defects in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 79, 2690–2692 (2001).
[Crossref]

Deppe, D. G.

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, 200–203 (2004).
[Crossref] [PubMed]

Ell, C.

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, 200–203 (2004).
[Crossref] [PubMed]

Englund, D.

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]

Falt, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

Fano, U.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[Crossref]

Fattal, D.

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]

Fujita, M.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nature Photon. 1, 449–458 (2007).
[Crossref]

Gerace, D.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

Gibbs, H. M.

G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nature Phys. 2, 81–90 (2006).
[Crossref]

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, 200–203 (2004).
[Crossref] [PubMed]

Gulde, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

Hendrickson, J.

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, 200–203 (2004).
[Crossref] [PubMed]

Hennessy, K.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[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, 127404 (2006).
[Crossref] [PubMed]

Hu, E. L.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[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, 127404 (2006).
[Crossref] [PubMed]

Imada, M.

A. Chutinan, M. Mochizuki, M. Imada, and S. Noda, “Surface-emitting channel drop filters using single defects in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 79, 2690–2692 (2001).
[Crossref]

Imamoglu, A.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

Ishida, S.

Iwamoto, S.

Johnson, T. J.

M. Borselli, T. J. Johnson, and O. Painter, “Measuring the role of surface chemistry in silicon microphotonics,” Appl. Phys. Lett. 88, 131114 (2006).
[Crossref]

Khitrova, G.

G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nature Phys. 2, 81–90 (2006).
[Crossref]

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, 200–203 (2004).
[Crossref] [PubMed]

Kira, M.

G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nature Phys. 2, 81–90 (2006).
[Crossref]

Koch, S. W.

G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nature Phys. 2, 81–90 (2006).
[Crossref]

Kumagai, N.

Kuramochi, E.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nature Photon. 1, 49–52 (2007).
[Crossref]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[Crossref]

Mitsugi, S.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[Crossref]

Mochizuki, M.

A. Chutinan, M. Mochizuki, M. Imada, and S. Noda, “Surface-emitting channel drop filters using single defects in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 79, 2690–2692 (2001).
[Crossref]

Moss, D. J.

S. Tomljenovic-Hanic, M. J. Steel, C.M. Sterke, and D. J. Moss, “High-Q cavities in photosensitive photonic crystals,” Optics Lett. 32, 542–544 (2007).
[Crossref]

Nagashima, T.

Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, “Dynamic control of the Q factors in a photonic crystal nanocavity,” Nature Mater. 6, 862–865 (2007).
[Crossref]

Nakaoka, T.

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]

Nakata, Y.

Noda, S.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nature Photon. 1, 449–458 (2007).
[Crossref]

Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, “Dynamic control of the Q factors in a photonic crystal nanocavity,” Nature Mater. 6, 862–865 (2007).
[Crossref]

T. Asano, B. S. Song, and S. Noda, “Analysis of the experimental Q factors (~1 million) of photonic crystal nanocavities,” Opt. Express 14, 1996–2002 (2006).
[Crossref] [PubMed]

T. Asano, B. S. Song, Y. Akahane, and S. Noda, “Ultrahigh-Q nanocavities in two-dimensional photonic crystal slabs,” IEEE J. Select. Top. Quantum Electron. 12, 1123–1134 (2006).
[Crossref]

S. Noda, “Seeking the ultimate nanolaser,” Science 314, 260–261 (2006).
[Crossref] [PubMed]

H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly efficient multi-channel drop filter in a twodimensional hetero photonic crystal,” Opt. Express 14, 3491–3496 (2006).
[Crossref] [PubMed]

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-High-Q photonic double-heterostructure nanocavity,” Nature Mater. 4, 207–210 (2005).
[Crossref]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science 300, 1537 (2003).
[Crossref] [PubMed]

A. Chutinan, M. Mochizuki, M. Imada, and S. Noda, “Surface-emitting channel drop filters using single defects in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 79, 2690–2692 (2001).
[Crossref]

Nomura, M.

Notomi, M.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nature Photon. 1, 49–52 (2007).
[Crossref]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[Crossref]

Painter, O.

M. Borselli, T. J. Johnson, and O. Painter, “Measuring the role of surface chemistry in silicon microphotonics,” Appl. Phys. Lett. 88, 131114 (2006).
[Crossref]

Petroff, P. M.

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, 127404 (2006).
[Crossref] [PubMed]

Rakher, M. T.

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, 127404 (2006).
[Crossref] [PubMed]

Rupper, G.

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, 200–203 (2004).
[Crossref] [PubMed]

Scherer, A.

G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nature Phys. 2, 81–90 (2006).
[Crossref]

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, 200–203 (2004).
[Crossref] [PubMed]

Shchekin, O. B.

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, 200–203 (2004).
[Crossref] [PubMed]

Shinya, A.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nature Photon. 1, 49–52 (2007).
[Crossref]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[Crossref]

Solomon, G.

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]

Song, B. S.

T. Asano, B. S. Song, Y. Akahane, and S. Noda, “Ultrahigh-Q nanocavities in two-dimensional photonic crystal slabs,” IEEE J. Select. Top. Quantum Electron. 12, 1123–1134 (2006).
[Crossref]

H. Takano, B. S. Song, T. Asano, and S. Noda, “Highly efficient multi-channel drop filter in a twodimensional hetero photonic crystal,” Opt. Express 14, 3491–3496 (2006).
[Crossref] [PubMed]

T. Asano, B. S. Song, and S. Noda, “Analysis of the experimental Q factors (~1 million) of photonic crystal nanocavities,” Opt. Express 14, 1996–2002 (2006).
[Crossref] [PubMed]

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-High-Q photonic double-heterostructure nanocavity,” Nature Mater. 4, 207–210 (2005).
[Crossref]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science 300, 1537 (2003).
[Crossref] [PubMed]

Steel, M. J.

S. Tomljenovic-Hanic, M. J. Steel, C.M. Sterke, and D. J. Moss, “High-Q cavities in photosensitive photonic crystals,” Optics Lett. 32, 542–544 (2007).
[Crossref]

Sterke, C.M.

S. Tomljenovic-Hanic, M. J. Steel, C.M. Sterke, and D. J. Moss, “High-Q cavities in photosensitive photonic crystals,” Optics Lett. 32, 542–544 (2007).
[Crossref]

Strauf, S.

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, 127404 (2006).
[Crossref] [PubMed]

Sugiya, T.

Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, “Dynamic control of the Q factors in a photonic crystal nanocavity,” Nature Mater. 6, 862–865 (2007).
[Crossref]

Takano, H.

Tanabe, T.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nature Photon. 1, 49–52 (2007).
[Crossref]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[Crossref]

Tanaka, Y.

Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, “Dynamic control of the Q factors in a photonic crystal nanocavity,” Nature Mater. 6, 862–865 (2007).
[Crossref]

Taniyama, H.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nature Photon. 1, 49–52 (2007).
[Crossref]

Tomljenovic-Hanic, S.

S. Tomljenovic-Hanic, M. J. Steel, C.M. Sterke, and D. J. Moss, “High-Q cavities in photosensitive photonic crystals,” Optics Lett. 32, 542–544 (2007).
[Crossref]

Upham, J.

Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, “Dynamic control of the Q factors in a photonic crystal nanocavity,” Nature Mater. 6, 862–865 (2007).
[Crossref]

Vuckovic, J.

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]

Waks, E.

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]

Watanabe, K.

Watanabe, T.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[Crossref]

Winger, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

Yamamoto, Y.

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]

Yoshie, T.

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, 200–203 (2004).
[Crossref] [PubMed]

Zhang, B.

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]

Appl. Phys. Lett. (3)

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[Crossref]

M. Borselli, T. J. Johnson, and O. Painter, “Measuring the role of surface chemistry in silicon microphotonics,” Appl. Phys. Lett. 88, 131114 (2006).
[Crossref]

A. Chutinan, M. Mochizuki, M. Imada, and S. Noda, “Surface-emitting channel drop filters using single defects in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 79, 2690–2692 (2001).
[Crossref]

IEEE J. Select. Top. Quantum Electron. (1)

T. Asano, B. S. Song, Y. Akahane, and S. Noda, “Ultrahigh-Q nanocavities in two-dimensional photonic crystal slabs,” IEEE J. Select. Top. Quantum Electron. 12, 1123–1134 (2006).
[Crossref]

Nature (3)

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, 200–203 (2004).
[Crossref] [PubMed]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atature, S. Gulde, S. Falt, E. L. Hu, and A. Imamoglu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445, 896–899 (2007).
[Crossref] [PubMed]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
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Nature Mater. (2)

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-High-Q photonic double-heterostructure nanocavity,” Nature Mater. 4, 207–210 (2005).
[Crossref]

Y. Tanaka, J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, “Dynamic control of the Q factors in a photonic crystal nanocavity,” Nature Mater. 6, 862–865 (2007).
[Crossref]

Nature Photon. (2)

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nature Photon. 1, 49–52 (2007).
[Crossref]

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nature Photon. 1, 449–458 (2007).
[Crossref]

Nature Phys. (1)

G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nature Phys. 2, 81–90 (2006).
[Crossref]

Opt. Express (3)

Optics Lett. (1)

S. Tomljenovic-Hanic, M. J. Steel, C.M. Sterke, and D. J. Moss, “High-Q cavities in photosensitive photonic crystals,” Optics Lett. 32, 542–544 (2007).
[Crossref]

Phys. Rev. (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[Crossref]

Phys. Rev. Lett. (2)

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]

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, 127404 (2006).
[Crossref] [PubMed]

Science (2)

S. Noda, “Seeking the ultimate nanolaser,” Science 314, 260–261 (2006).
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B. S. Song, S. Noda, and T. Asano, “Photonic devices based on in-plane hetero photonic crystals,” Science 300, 1537 (2003).
[Crossref] [PubMed]

Other (1)

In fact there are three guidance mechanisms in the photonic heterostructures: the total internal reflection at the slab-air interface, the photonic band gap effect across the waveguide, and the photonic mode gap effect along the waveguide.

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Figures (5)

Fig. 1.
Fig. 1. (a). SEM image of the nanocavity with a two-step heterostructure. PC1 has a triangular-lattice structure with a lattice constant of a 1. PC2 and PC2’ have a deformed triangular-lattice structure with lattice constants of a 2 and a 2’ in the x-direction; they retain the same lattice constant as PC1 in the y-direction in order to satisfy lattice-matching conditions. (b) Schematic view of the band diagram along the x-direction for the line defect in Fig. 1(a). The ground-state nanocavity mode mainly exists in the waveguide section formed by PC2 and PC2’. (c) SEM image of the region around the nanocavity and schematic picture of the transmission spectroscopy experiment.
Fig. 2.
Fig. 2. Drop (filled circle) and transmission (open circle) spectra for cavities separated by (a) four rows and (b) six rows of air holes from the excitation waveguide. The scale of the horizontal axes in (a) and (b) are the same. Solid and dashed lines represent the fits using Lorentzian functions. Small oscillations in the transmission spectra might originate from the laser source.
Fig. 3.
Fig. 3. (a). Time-resolved signal of input pulse. (b)–(d) Time-resolved signals for nanocavities with six, five, and seven rows of separation from the excitation waveguide, respectively.
Fig. 4.
Fig. 4. Evolution of emission from a nanocavity using pulse widths of 4 ns, 6 ns, and 8 ns. (a) Calculated results for a nanocavity with τ=2 ns using coupled-mode theory in the absence of nonlinear effects. (b) Experimental results for a nanocavity with seven rows of separation.
Fig. 5.
Fig. 5. Q factors calculated using the 3D-FDTD method by introducing variations in the radii and positions of the air holes according to a Gaussian distribution. The horizontal axis represents the σ for each type of variation. The curves show the results of calculations for 10 different fluctuation patterns. The value of Q exp at σ=0 nm corresponds to a Q ideal of 1.5×107.

Equations (3)

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1 Q exp = 1 Q ideal + 1 Q loss .
Q load = λ 0 Δ λ .
Q exp = Q load T 0 .

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