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Ultra-high-Q photonic double-heterostructure nanocavityBONG-SHIK SONG1, SUSUMU NODA1*, TAKASHI ASANO1 AND YOSHIHIRO AKAHANE1,21Department of Electronic Science and Engineering, Kyoto University, Katsura, Nishikyo-ku, Kyoto 615-8510, Japan2Semiconductor Technologies R&D Laboratories, Sumitomo Electric Industries, Itami, Hyogo 664-0016, Japan*e-mail: snoda@kuee.kyoto-u.ac.jp

Published online: 13 February 2005; doi:10.1038/nmat1320

High-quality factor (Q) photonic nanocavities that strongly confi ne photons in volumes of optical-wavelength dimension are attracting much attention in various fi elds, including photonics15, telecommunications6,7, quantum information8 and cavity quantum electrodynamics9,10, because a strong lightmatter interaction is obtained. An important design rule has been proposed11 in an attempt to realize high-Q nanocavities in two-dimensional photonic-crystal slabs. Th e form of the cavity electric-fi eld distribution should slowly vary, most ideally as described by a gaussian function, in order to suppress out-of-slab photon leakage. However, the exact cavity structure that minimizes photon leakage has not yet been established. Here, we demonstrate the importance of the formation of a photonic double-heterostructure, which has resulted in the realization of nanocavities with extremely high-Q factors of 600,000, more than one order of magnitude higher than any previous reports1114. We have also shown theoretically that Q-factors greater than 20,000,000 may be obtained when optimizing the structure.

The sample design for successful formation of high-Q nanocavities in photonic crystals is as follows11: A two-dimensional (2D) photonic-crystal slab of optical wavelength thickness is used as the base material and an artifi cial point defect is introduced to form a nanocavity in the slab. When the cavity has an internal electric-fi eld distribution that changes abruptly at the cavity edges, there are signifi cant leaky components that do not satisfy the conditions for total internal refl ection at the slabair interface, resulting in a low Q factor. Cavities with less-abrupt electric-fi eld distributions have less leaky components and a corresponding increase in Q factor. It has been found that an electric-fi eld distribution described by a gaussian function is one of the most promising for achievement of ultimately high-Q nanocavities. This was established by analysis of the leaky electric-fi eld components for various functions, including lorentzian, exponential and cosine expressions. The leaky component for a given function can be derived from the Fourier transformation of the electric-fi eld distribution11,15, and the validity and applicability of this method were discussed in detail in refs 16, 17. On the basis of the design rule adopted here, a unique approach of tuning of air-holes has been introduced11 in order to control the electric-fi eld distribution inside the cavity. Using this approach, the Bragg-refl ection condition at the cavity edges can be modifi ed so

that the electric-fi eld distribution inside the cavity is controllable. In addition, this structural tuning may have the effect of improving impedance-wave matching at the cavity edges16,17. In previous work, two air holes at the cavity edges were shifted in position (or tuned) and a high Q-factor of 45,000 was experimentally obtained11. These encouraging results were further extended by tuning the

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Figure 1 The basic photonic-crystal structure and photonic double-heterostructure investigated in this work. a, A 2D photonic-crystal slab of triangular-lattice structure with a line-defect waveguide formed by a missing row of air holes in the J direction. b, The calculated band structure for a. The blue arrow indicates the transmission region where the propagation of photons is allowed through the waveguide, and the red arrow indicates the mode-gap region in which propagation is inhibited. c, Photonic double-heterostructures, constructed by connecting the basic photonic crystals structures I and II. Photonic-crystal I has a triangular-lattice structure with a lattice constant of a1. Photonic crystal II has a deformed triangular-lattice structure with a face-centred rectangular lattice of constant a2 (>a1) in the waveguide direction; it retains the same constant as photonic-crystal I in the orthogonal direction in order to satisfy the lattice-matching conditions. d, Schematic of the band diagram along the waveguide direction. Photons of a specifi c energy can exist only in the waveguide of photonic crystal II.

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positions of not only the nearest-neighbour air holes at the cavity edges, but also the second- and third-nearest-neighbour air holes. However, so far it has only been possible to increase the cavity Q-factor by a factor of two using this method. Although the electric-fi eld distribution can be modifi ed in the region of air-hole tuning, it is clear that uniform and rigorous control of the electric-fi eld distribution throughout the cavity, a necessary requirement in order to form a gaussian function, is diffi cult. This indicates that the air-hole-tuning approach is insuffi cient for the realization of ultimately high-Q nanocavities, and that other approaches should be investigated. Here, we demonstrate that photonic double-heterostructures are an important concept for the realization of ultimately high-Q nanocavities.

The basic photonic crystal structure used in the construction of the photonic double-heterostructure is shown in Fig. 1a. This is a 2D photonic-crystal slab with a triangular-lattice structure and a line-defect waveguide formed by a missing row of air holes in the J direction18. The band diagram for the structure is shown in Fig. 1b, illustrating that the waveguide mode forms within the bandgap region. The blue arrow indicates the transmission region, in which photons can propagate through the waveguide, and the red arrow indicates the mode-gap region where propagation is inhibited6,19. Careful attention was paid to the presence of the transmission and mode-gap regions in the waveguide mode, and two photonic crystals (I and II) were joined to form a double-heterostructure (Fig. 1c). Photonic crystal I has a triangular-lattice structure of lattice constant a1. In contrast, photonic crystal II has a deformed triangular-lattice structure in the waveguide direction, equivalent to a face-centred rectangular-lattice structure of lattice constant a2 (a2 > a1); it retains the same lattice constant as photonic crystal I in the orthogonal direction in order to satisfy lattice-matching conditions. As the lattice constants in the waveguide direction of photonic crystals I and II vary, the transmission and mode-gap regions also differ (Fig. 1d). This ensures that photons with a specifi c energy can exist only in the waveguide of photonic crystal II. When the waveguide in

photonic crystal II is short enough, the frequencies that photons can take in this region become quantizedsimilar to the situation for electrons in a semiconductor quantum structureand a photonic nanocavity is formed.

The most important feature of the photonic double-heterostructure nanocavity is that the confi nement of photons in the waveguide direction is not directly due to the photonic bandgap effect resulting from the periodic array of air holes. Instead, it is a consequence of the mode-gap effect6,19 in the waveguide of photonic crystal I, which is due to the lattice-constant difference between photonic crystals I and II. As a result, the evanescent behaviour of the electric fi eld confi ned in photonic crystal II into the waveguide of photonic crystal I, can be uniformly controlled along the

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Figure 2 Calculated results that illustrate the effect of a photonic double-heterostructure. a,b, The electric-fi eld distribution in the photonic double-heterostructure cavity and its profi le along the waveguide direction, respectively. The 3D FDTD method was used for this calculation. The solid-black and broken-red lines in b indicate the calculated results and the ideal gaussian profi le, respectively. c,d, The results for a point-defect cavity with three missing air holes, in which two of the air holes at the cavity edges are shifted by 0.2a. a = 420 nm.

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Figure 3 Experimental results. a, An SEM image of the fabricated photonic double-heterostructure cavity. b, The resonant spectrum of the cavity over a wide range of wavelengths. The insets show the near-fi eld image observed using an infrared camera and the detailed spectrum at the resonance, respectively. Extremely narrow line-widths of 2.8 pm, corresponding to Q-factors approaching 106, were obtained.

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waveguide by changing the lattice-constant difference between the two crystals. Furthermore, using a multistep heterostructure (see later), more fl exible and rigorous control of the electric-fi eld distribution is possible. Figure 2a,b shows the calculated electric-fi eld distribution of the photonic double-heterostructure cavity and its profi le along the waveguide direction, respectively. In Fig. 2b, the solid-black and broken-red lines indicate the calculated electric-fi eld distribution and an ideal gaussian profi le, respectively. For the calculation, we used the 3D fi nite-difference time-domain (FDTD) method, assuming lattice constants for photonic crystals I and II of a1 = 410 nm and a2 = 420 nm, respectively, and a slab thickness of T = 0.6a2. The calculated results for a previously reported point-defect cavity that used air-hole tuning at the cavity edges in order to make the electric-fi eld profi le11 vary more gently, are shown in Fig. 2c and d. Clearly, the electric-fi eld profi le in the modifi ed point-defect cavity deviates from the ideal gaussian curve and the abrupt change remains at the profi le. By contrast, the electric-fi eld profi le of the photonic double-heterostructure cavity is very close to the ideal gaussian curve over a wider area. This is because the fi eld distribution can be uniformly controlled by adjustments to the lattice-constant difference (as described above). The more-ideal gaussian envelope in the photonic double-heterostructure cavity is consistent with the theoretically calculated Q-factors of the two structures. The double-heterostructure cavity was determined to have a Q-factor of the order of one million (106), whereas that of the shifted point-defect cavity was one order of magnitude smaller. The modal volume of the photonic double-heterostructure cavity was as small as ~1.2 (0/n)3 in the theoretical calculation, where 0 is the resonant wavelength in air and n is the refractive index of the slab. Such small cavity mode volume, despite the very small lattice-constant difference between photonic crystals I and II, is a result of the unusual dispersion relation of the photonic-crystal waveguide (see Supplementary Information for details).

Owing to these theoretical calculations, a photonic double-heterostructure cavity was fabricated using the silicon-on-insulator (SiO2) material system. A 2D photonic crystal with a double-heterostructure cavity was formed on the top silicon layer using electron-beam lithography (Elionix, ELS7700) and high-density plasma-etching (Samco, RIE-101iPH) techniques. Special care was paid when the electron-beam resist was removed, where a chemical treatment process (immersion of the sample into sulphuric acid for 10 minutes) was used instead of oxygen plasma ashing in order to avoid the formation of an oxide layer and/or additional plasma damage. The SiO2 under-layer was removed to form a slab structure of 250 nm thickness. The lattice constant of the central photonic crystal II region was set to a2 = 420 nm and that of the surrounding photonic crystal (I) was set to a1 = 410 nm. The length of photonic crystal II was 2a2 and the air-hole radius was set to 0.29a2 for both crystals. A plan-view scanning electron microscope (SEM; Hitachi, S-4800) image of the fabricated sample is shown in Fig. 3a, in which the lattice constant difference is too small to be distinguished visually. Another (input) waveguide was formed parallel to that of the double-heterostructure in order to inject photons into the cavity, as shown in Fig. 3a. The input waveguide was 0.1a1 wider20 than that of the double-heterostructure waveguide for this purpose.

The cavity Q-factor was estimated using a tunable continuous-wave laser as the light source. The inset in Fig. 3b shows the near-fi eld image observed using an infrared camera, when photons were trapped by the cavity. The trapped light spectrum is shown in Fig. 3b. An extremely narrow line-width of 2.8 pm was obtained, which was close to the resolution limit of the measurement system. The intrinsic Q-factor was estimated to be 600,000, taking into account the effect of coupling between the cavity and the input waveguide6. This was approximately the same order of magnitude as the theoretically calculated value of 106 and was more than one

order of magnitude larger than the Q-factors reported thus far for photonic-crystal nanocavities1114.

It is important to investigate theoretically the feasibility of further increases in Q-factor. For this purpose, we modifi ed the double-heterostructure by inserting an additional photonic crystal (II) between photonic crystals I and II, in order to construct a multistep double-heterostructure (Fig. 4a). The use of such a confi guration should allow for more fl exible and rigorous control of the envelope function. The cavity Q-factor was calculated using the 3D FDTD method over a range of lengths (d) for photonic crystal II and for a range of air-hole radii r. The other parameters used in the calculation were as follows: a1 = 410 nm, a2 = 420 nm, a2 = (a1 + a2)/2 and T = 0.6a2. The results are plotted in Fig. 4b, showing that a marked increase in Q-factor can be obtained through slight modifi cation to the structure. The maximum theoretical Q-factor exceeded 24,000,000 when d = 2a2 and r = 0.26a2. The modal volume was calculated separately and the increase resulting from this modifi cation was as little as 10% of the value for the original structure.

The results obtained in this work indicate that, even in the case of nanocavities of optical-wavelength dimension, the Q-factors can be increased to become comparable to those obtained for cavities of much larger modal volumes21,22. Therefore, extremely strong lightmatter interactions can be realized in such photonic crystal nanocavities. We believe that these results will accelerate developments in various areas, including single-photon emitters for quantum communication and computing, zero-threshold

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Figure 4 A nanocavity with a multistep photonic heterostructure. a, Schematic of the cavity, in which photonic crystal II, having an averaged lattice constant a2 = (a1 + a2)/2 is inserted between photonic crystals I and II. b, The Q-factor calculated using the 3D FDTD method as a function of the length (d ) of photonic crystal II and the radius (r ) of individual air holes. The additional parameters used in the calculation were as follows: a1 = 410 nm; a2 = 420 nm; T = 0.6a2.

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nanolasers, ultra-small photonic chips, atom trapping, biosensing and accurate environmental monitors. Furthermore, integrating high-Q nanocavities in photonic chips may make it possible to realize the stopping of light23. These fi ndings will stimulate further developments in the area of photonic-crystal heterostructures, as various structural modifi cations could be made in order to extend the scope of devices for photon control and manipulation.

Received 20 September 2004; accepted 2 December 2004; published 13 February 2005.

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AcknowledgementsThis work was supported by Core Research for Evolution Science and Technology, Japan Science and

Technology Agency, a Grant-in-Aid for Scientifi c Research and an IT program of the Ministry of

Education, Culture, Sports, Science and Technology of Japan.

Correspondence and requests for materials should be addressed to S.N.

Supplementary Information accompanies the paper on www.nature.com/naturematerials.

Competing fi nancial interestsThe authors declare that they have no competing fi nancial interests.

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