Abstract

Titanium dioxide is an emerging optical material, with a relatively high refractive index (n ∼ 2), which allows for high confinement of the electromagnetic field. Extensive research has been conducted on the negatively charged nitrogen vacancy centre in diamond due to its robust electronic and optical properties. In particular, its stable room-temperature photoluminescence properties have been considered for quantum optical applications. Nanobeam cavities are a geometry that offer exceptionally large-Q values given their minimal footprint, a must for high density and compact optical architecture. This paper presents an ultrahigh-Q nanobeam cavity within titanium dioxide in a low-refractive index environment operating at the negatively charged nitrogen vacancy centre of diamond. This research opens the possibility of hybrid optical devices utilising titanium dioxide and diamond.

© 2017 Optical Society of America

1. Introduction

Titanium dioxide (TiO2) has recently emerged as a promising optical material in which waveguide and resonator structures have been fabricated [1–13]. It is a wide bandgap semiconductor with a bandgap energy range of 3–3.3 eV which is dependent on the crystalline phase [14]. It has a has a relatively high refractive index for visible wavelengths (n = 2.3 at 550 nm [15]), allowing for strong light confinement, and is also optically transparent. Amorphous and polycrystalline TiO2 thin films can be deposited using conventional methods, such as electron-beam evaporation and ion sputtering [16], allowing for on-chip integration with other materials.

Diamond has garnered interest as a future photonic material [17] and has a similar refractive index to TiO2. Research has focussed on enhancing the emission of the zero-phonon line (ZPL) of the negatively charged nitrogen vacancy (NV) colour centre [18–24]. The ZPL emission has a narrow linewidth which constitutes 3–5% of the total NV photoluminescence and enhancement can be achieved by coupling this emission to a high-Q optical cavity through the Purcell effect. The magnitude of enhancement is quantified by the Purcell factor which is dependent on the ratio between quality factor and modal volume (∼Q/V); the larger this ratio, the greater the enhancement of the spontaneous emission rate.

Diamond substrates for photonic applications can be classified as either: individual micro-and nano-crystalline diamond (ND); polycrystalline diamond films and single-crystal diamond. The last classification is the leading candidate for diamond photonics, however it requires an intensive processing effort to engineer devices into the single crystal morphology. Individual ND have also attracted interest and the intrinsic fluorescence for the NV colour centre has been used for bioimaging applications [25]. Given the similar refractive indices of TiO2 and diamond, it is a natural progression to combine both materials for hybrid applications where the former has already been shown to be an emerging visible photonic material [1,2,7,10–13].

An optical cavity geometry that offers high-Q with minimal footprint is known as the nanobeam cavity; it is a photonic crystal cavity with periodic refractive index change in one-dimension. High-Q designs have been theoretically proposed (on the order of 107) [26–30] and experimentally demonstrated (in the order of 105) [27, 31, 32]. Previous high-Q designs generally considered high refractive index contrast environments ensuring the light was concentrated in the cavity region.

In this article, we present an ultrahigh-Q TiO2 nanobeam cavity design with a quality factor in the order of 107 operating at the ZPL of NV of diamond. 3D FDTD simulations show that an ultrahigh-Q cavity is possible in this low refractive index contrast environment using a relatively simple design recipe.

2. TiO2 nanobeam geometry and model

The design for this optical cavity was based on previous work by Quan et al. [33,34] which has a design philosophy following three main rules: (1) the cavity length should be zero, i.e. no defect is introduced into the periodicity; (2) the periodicity was kept constant; and (3) the requirement for a modulated Bragg mirror (referred in the rest of this letter as the Gaussian mirror). Rule (1) ensures the modal volume (V) is kept to a minimum alongside a high-Q cavity will result in a large Q/V ratio necessary for strong cavity interactions. Rule (2) guarantees a constant phase velocity between the periodic elements, i.e. the airholes. Finally, rule (3) results in a gentle modulation of the electric field between the Bragg mirrors which was achieved by a Gaussian envelope function [35]. The modulation maximises the Q for the nanobeam by minimising the Fourier components that exist above the light line, i.e. radiation loss into free space. It must be mentioned, another loss mechanism within our system was due to the additional mirror section which tapers into a feeding waveguide. If there are not a sufficient number of airholes in this section, leakage of light from the modulated Bragg mirror section can occur. This leakage was minimised by simply adding more airholes within the additional mirror section. Figure 1 shows a cross-sectional view at the cavity centre with a TiO2 trapezium profile resultant of the etching recipe by Bradley et al. [6], and the top-view schematic of the nanobeam showing different sections: additional mirror (A), where the airhole size tapers down and becomes a waveguide; Gaussian mirror (G) and the centre (C).

 

Fig. 1 The geometry of the ultrahigh-Q TiO2 nanobeam. (a) Cross-sectional trapezium profile which results from Bradley et al.’s [6] etching recipe. Here, w and s represent the top and bottom lengths of the TiO2 trapezium, b is the width of the airhole which changes as you move along the nanobeam in the ±z-direction, tTiO2 and tSiO2 are the thicknesses of TiO2 and SiO2 layers. (b) Top-view schematic of the nanobeam with additional mirror (A), Gaussian mirror (G) and the centre (C) shown. Note: the airholes have a tapered profile from the centre of the cavity.

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The nanobeam’s periodicity consisted of airholes perforating the TiO2 layer which sits upon an SiO2 layer. This oxide layer was grown by oxidation of the silicon wafer and we choose to keep this layer as to demonstrate a high-Q cavity is possible in a low refractive index environment. The silicon substrate was not included in the simulations. The resonant wavelength of the nanobeam is chosen to be at the ZPL of the NV centre which is 637 nm.

The original design recipe by Quan et al. [33, 34] assumed vertical side walls only. Angled side walls was an appropriate consideration since we based the design on the etching recipe in Ref. [6]. The thicknesses of the TiO2 and SiO2 were set to tTiO2 = 0.27 μm and tSiO2 = 0.99 μm. Finally, the refractive indices of TiO2 and SiO2 were set to 2.27 and 1.46 respectively.

Three-dimensional FDTD simulations (Lumerical) were performed to determine the Q of the cavity. An electric dipole was placed closed to the centre of the nanobeam cavity at coordinates of (x, y, z) = (0, 0.2, 0)μm. The spatial grid size was 22 nm; the PML thicknesses were different at each boundary: 2.51 μm (top of nanobeam), 2.37 μm (sides of the nanobeam), and 400 nm (longitudinal directions of the nanobeam). Vertical airholes were considered for all the simulations.

3. Results and discussion

Before exploring the significant enhancement achieved from the nanobeam, it is worth examining the electrodynamics for a simple system first. The emission rate of an emitter in a homogenous refractive index environment can be modified via simple encapsulation in a planar interface environment. The NV centre can be approximated as a classical oscillating dipole radiating within a dielectric sphere near an interface [36, 37]. The power radiated by the dipole is inversely proportional to the emitter’s fluorescence lifetime. Three-dimensional FDTD simulations (RSoft) were considered for three unstructured environment scenarios: (1) ND in air, (2) ND in TiO2 and (3) ND on TiO2 in air. The refractive indices were taken to be: nND = 2.4, nair = 1 and nTiO2. The dipole resides at the centre of the spherical ND with a diameter of 60 nm and has an emission wavelength of 637 nm. For scenarios (1) and (2), the dipole is emitting into a homogenous environment. For scenario (3), there is a planar interface between the TiO2 and the surrounding air. This interface acts as the reference point for parallel (‖) and orthogonal (⊥) dipole polarisations. The total radiated power by the dipole (PS) was calculated by summation over the time-averaged Poynting vector of six faces of a cubed power monitor when the simulation had reached a steady state solution. The computational domain size was 1×1×1 μm3, the spatial grid size was 3 nm and PML was 1 μm for all simulations. The enhancement (ζ) was calculated as the ratio between PS and the total power radiated from the ND in air (i.e. scenario (1)) for both parallel and orthogonal dipole orientations. Table 1 summarises these numerical FDTD results.

Tables Icon

Table 1. The enhancement of parallel and orthogonal dipole polarisations for 637 nm emission in various refractive index distributions. The polarisations are measured with respect to the TiO2–air interface (scenario 3).

The simulation results show that preferential enhancement in the parallel orientation of the dipole. It shows that if a ND is any high refractive index environment there will be an enhancement of the emission rate without any structured environment such as an optical cavity.

To obtain a sufficiently high-Q cavity, it was found that the Gaussian mirror section should contain fifty airholes (see Figure 1(b), G sections). In addition, to best reflect an experimental situation where the nanobeam can be characterised, an additional mirror (A, see Figure 1(b)) section was also included in the simulations which was tapered down to a feeding waveguide [33]. The additional mirror section consisted of ten airholes. The total length of the nanobeam was then determined to be 20.26 μm, measured from the outer edges of the tenth airholes of the additional mirror sections.

Figure 2 shows the variation in the calculated Q values and their associated resonance wavelengths for vertical sidewalls for the TiO2 nanobeam cavity.

 

Fig. 2 Q values with their respective resonance wavelengths for the TiO2 nanobeam as a function of the number of airholes that constitute both Gaussian mirrors (G). The results shown in this figure were for vertical sidewalls with a width of w = 0.44 μm and a periodicity for the airholes of 0.17 μm.

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The trend shows that by increasing the number of airholes in the Gaussian mirror, the Q value increases with a blue shifting resonant wavelength. This means that the value chosen for G is arbitrary, any value greater than 40 was sufficient in obtaining a high-Q value. With more airholes this will impart more partial reflections on the light and results in stronger enhancement without sacrificing a large shift in a resonance wavelength. A value of G = 50 was chosen as an appropriate starting point in accomplishing an ultrahigh-Q cavity. The resonance wavelength for G = 50 mirror was found to be 635.15 nm, approximately a 2 nm difference with respect to the ZPL NV wavelength. This can be shifted to 637 nm by either: changing the starting or ending filling fractions of the Gaussian mirror (equivalent to changing the radii of the airholes) or adjusting the width of the nanobeam. The latter can drastically shift the resonance wavelength as more modes fall below the substrate light line.

As mentioned in the previous subsection, to best reflect an experimental situation when the TiO2 is etched, a sidewall angle was considered for the waveguide; this results in the resonance wavelength of the vertical sidewall nanobeam shifting from 635.15 nm. A parameter search of the top and bottom widths of the TiO2 was conducted to target the 637 nm wavelength with the trapezium profile of the nanobeam. At widths of w = 0.38 μm and s = 0.52 μm, the L0 TiO2 nanobeam cavity yielded a Q = 1.04×107 with a resonance wavelength of 637.37 nm and V = 3.7(λ/n)3. This results in a Purcell factor of F = (3/4π2)(λ/n)3(Q/V) ≈ 2.14×105, a considerably large value.

This represents a substantially large Q for an optical cavity in a low refractive index contrast environment compared to previous work in polymeric nanobeam cavities [38]. However, the modal volume is large due to the presence of the SiO2 substrate which results low refractive index contrast between (nTiO2/nSiO2 = 2.27/1.46 = 1.55). The refractive index difference between TiO2 and the SiO2 substrate is smaller than with TiO2–air and therefore the mode penetrates into the SiO2 rather than being reflected back for a high refractive index difference which would be the case for a free-standing nanobeam, i.e. an all air environment.

Figure 3 cross-sectional and top-view power distributions that were calculated for the L0 TiO2 nanobeam cavity with w = 0.38 μm and s = 0.52 μm.

 

Fig. 3 The power distribution of the TiO2 nanobeam. (a) Cross-sectional and (b) top-view profiles. The dashed white lines represent the sidewalls of the nanobeam. Note: by default, Lumerical measures the Poynting vector in their power monitors.

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The power profiles reveal that the majority within the cavity centre at (x, z) = (0, 0) in Figure 3. The results show that this nanobeam design has the potential to significantly enhance the ZPL emission from the NV centre for an embedded ND. In the vertical direction (y), the peak power distribution is slightly below the centre of the cavity and therefore this would need to be a consideration when embedding the ND into the growth process of the TiO2 layer. This is only for the case that an appropriate ND size can be supported between the Gaussian mirrors at the cavity centre.

The results show that an ultrahigh-Q TiO2 nanobeam cavity can be realised to operate at the ZPL of the NV centre for diamond. The Q can be made arbitrarily high by simply increasing the number of airholes that constitute the Gaussian mirrors. This will inherently shift the resonance wavelength slightly, but a parameter search can be conducted on any physical aspect of the nanobeam to re-adjust the resonance wavelength. The only drawback for this short wavelength operation is the critical dimensions of the design become increasingly small which makes it more difficult to fabricate and is limited to current lithographic resolution.

In addition, incidental losses, those not included in the design, will impact the fabricated device. Unintentional refractive index changes can form scattering sites such as grain and mask inhomogeneities. Figure 4 shows a scanning electron micrograph of a the surface of a TiO2 substrate created via electron-beam deposition that would be considered for the fabrication of the device.

 

Fig. 4 A scanning electron micrograph of the TiO2 substrate with embedded NDs.

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If a TiO2 nanobeam was to be fabricated using this particular substrate, the optical loss would be significant, and therefore a reduced Q value, due to scattering of the light because the grain boundaries are significantly smaller compared to the total length of the nanobeam (20.26 μm).

Another point of discussion is the absence of a ND encapsulating the electric dipole, i.e. a ND-TiO2 interface, within our simulations and incorporating this would be a much more realistic estimation of the physical system. Since the refractive indices of TiO2 (nTiO2 = 2.27) and diamond (nND = 2.4) are comparable, therefore at the interface there will be minimal scattering of the light. McCutcheon et al. [39] showed that Q values for silicon nitride (n = 2.0) nanobeams reduced by approximately 10–20% from a bare cavity when compared to an embedded 20 nm cubic ND in the cavity centre. In addition, van der Sar et al. [40] also explored the positional effects of a ND on the optical properties of gallium phosphide (GaP) S1 and L3 cavities. In this system, the refractive index contrast is much larger because GaP has a refractive index of 3.4. When a ND of 50 nm diameter is placed at the maximum mode intensity of the S1 cavity the original Q value decreases by <10%. When a 60 nm ND is placed at various depths within the GaP substrate, the Q value is greatest near the centre (5% of the original) and decreases near the edges because light is scattered by the ND at the surface is lost from the cavity. Therefore, previous work indicates that ND embedded within a substrate does not significantly change the Q value, only when it’s near the surface with a larger refractive index contrast will there be increased losses due to the scattering.

4. Conclusions

It has been shown that TiO2 can be a viable material for creating an ultrahigh-Q nanobeam cavity at the ZPL of the NV centre. Using the design recipe by Quan et al. [33, 34], a Q of 1.04 × 107 at 637.37 nm can be achieved. The Q value can be arbitrarily increased by additional airholes within the Gaussian mirror. This paves the way for TiO2 to become a future visible photonic material.

Funding

ARC Australian Research Fellowship (DP1096288)

Acknowledgments

K.C. would like to acknowledge an Overseas Research Experience Scholarship provided by The University of Melbourne to visit Prof. Lončar’s group. K.C. would also like to thank Jennifer T. Choy, Parag B. Deotare, Qimin Quan, Young-Ik Sohn and Orad Reshef for helpful discussion. The authors would also like to acknowledge Y.H. Leung and A.B. Djurišić for providing the titanium dioxide sample. S.T-H. would like to acknowledge computational resources provided by the Australian Government through NCI under the National Computational Merit Allocation Scheme.

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References

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  1. G. Subramania, Y.-J. Lee, I. Brener, T. S. Luk, and P. G. Clem, “Nano-lithographically fabricated titanium dioxide based visible frequency three dimensional gap photonic crystal,” Opt. Express 15, 13049–13057 (2007).
    [Crossref] [PubMed]
  2. G. Subramania, Y.-J. Lee, A. J. Fischer, and D. D. Koleske, “Log-pile TiO2 photonic crystal for light control at near-UV and visible wavelengths,” Adv. Mater. 22, 487–491 (2010).
    [Crossref] [PubMed]
  3. M. Furuhashi, M. Fujiwara, T. Ohshiro, M. Tsutsui, K. Matsubara, M. Taniguchi, S. Takeuchi, and T. Kawai, “Development of microfabricated TiO2 channel waveguides,” AIP Adv. 1, 032102 (2011).
    [Crossref]
  4. M. Furuhashi, M. Fujiwara, T. Ohshiro, K. Matsubara, M. Tsutsui, M. Taniguchi, S. Takeuchi, and T. Kawai, “Embedded TiO2 waveguides for sensing nanofluorophores in a microfluidic channel,” Appl. Phys. Lett. 101, 153115 (2012).
    [Crossref]
  5. Z.-F. Bi, L. Wang, X.-H. Liu, S.-M. Zhang, M.-M. Dong, Q.-Z. Zhao, X.-L. Wu, and K.-M. Wang, “Optical waveguides in TiO2 formed by He ion implantation,” Opt. Express 20, 6712–6719 (2012).
    [Crossref] [PubMed]
  6. J. D. B. Bradley, C. C. Evans, J. T. Choy, O. Reshef, P. B. Deotare, F. Parsy, K. C. Phillips, M. Lončar, and E. Mazur, “Submicrometer-wide amorphous and polycrystalline anatase TiO2 waveguides for microphotonic devices,” Opt. Express 20, 23821–31 (2012).
    [Crossref] [PubMed]
  7. J. T. Choy, J. D. B. Bradley, P. B. Deotare, I. B. Burgess, C. C. Evans, E. Mazur, and M. Lončar, “Integrated TiO2 resonators for visible photonics,” Opt. Lett. 37, 539–541 (2012).
    [Crossref] [PubMed]
  8. F. Qiu, A. M. Spring, F. Yu, I. Aoki, A. Otomo, and S. Yokoyama, “Thin TiO2 core and electro-optic polymer cladding waveguide modulators,” Appl. Phys. Lett. 102, 233504 (2013).
    [Crossref]
  9. M. Häyrinen, M. Roussey, V. Gandhi, P. Stenberg, A. Säynätjoki, L. Karvonen, M. Kuittinen, and S. Honkanen, “Low-loss titanium dioxide strip waveguides fabricated by atomic layer deposition,” J. Light. Technol. 32, 208–212 (2014).
    [Crossref]
  10. J. Park, S. K. Ozdemir, F. Monifi, T. Chadha, S. H. Huang, P. Biswas, and L. Yang, “Titanium Dioxide Whispering Gallery Microcavities,” Adv. Opt. Mater. 2, 711–717 (2014).
    [Crossref]
  11. O. Reshef, K. Shtyrkova, M. G. Moebius, S. Griesse-Nascimento, S. Spector, C. C. Evans, E. Ippen, and E. Mazur, “Polycrystalline anatase titanium dioxide microring resonators with negative thermo-optic coefficient,” J. Opt. Soc. Am. B 32, 2288 (2015).
    [Crossref]
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  34. Q. Quan and M. Lončar, “Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities,” Opt. Express 19, 18529–18542 (2011).
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  35. 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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  36. W. Lukosz and R. Kunz, “Fluorescence lifetime of magnetic and electric dipoles near a dielectric interface,” Opt. Commun. 20, 195–199 (1977).
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2015 (4)

O. Reshef, K. Shtyrkova, M. G. Moebius, S. Griesse-Nascimento, S. Spector, C. C. Evans, E. Ippen, and E. Mazur, “Polycrystalline anatase titanium dioxide microring resonators with negative thermo-optic coefficient,” J. Opt. Soc. Am. B 32, 2288 (2015).
[Crossref]

A. Paunoiu, R. S. Moirangthem, and A. Erbe, “Whispering gallery modes in intrinsic TiO2 microspheres coupling to the defect-related photoluminescence after visible excitation,” Phys. Status Solidi RRL 9, 241–244 (2015).
[Crossref]

C. C. Evans, C. Liu, and J. Suntivich, “Low-loss titanium dioxide waveguides and resonators using a dielectric lift-off fabrication process,” Opt. Express 23, 11160–11169 (2015).
[Crossref] [PubMed]

D. Yang, P. Zhang, H. Tian, Y. Ji, and Q. Quan, “Ultrahigh-Q and low-mode-volume parabolic radius-modulated single photonic crystal slot nanobeam cavity for high-sensitivity refractive index sensing,” IEEE Photonics J. 7, 4501408 (2015).
[Crossref]

2014 (3)

C.-S. Deng, Y.-S. Gao, X.-Z. Wu, M.-J. Li, and J.-X. Zhong, “Ultrahigh-Q TE/TM dual-polarized photonic crystal holey fishbone-like nanobeam cavities,” Europhys. Lett. 108, 54006 (2014).
[Crossref]

M. Häyrinen, M. Roussey, V. Gandhi, P. Stenberg, A. Säynätjoki, L. Karvonen, M. Kuittinen, and S. Honkanen, “Low-loss titanium dioxide strip waveguides fabricated by atomic layer deposition,” J. Light. Technol. 32, 208–212 (2014).
[Crossref]

J. Park, S. K. Ozdemir, F. Monifi, T. Chadha, S. H. Huang, P. Biswas, and L. Yang, “Titanium Dioxide Whispering Gallery Microcavities,” Adv. Opt. Mater. 2, 711–717 (2014).
[Crossref]

2013 (3)

F. Qiu, A. M. Spring, F. Yu, I. Aoki, A. Otomo, and S. Yokoyama, “Thin TiO2 core and electro-optic polymer cladding waveguide modulators,” Appl. Phys. Lett. 102, 233504 (2013).
[Crossref]

T.-W. Lu and P.-T. Lee, “Photonic crystal nanofishbone nanocavity,” Opt. Lett. 38, 3129–3132 (2013).
[Crossref] [PubMed]

B. J. M. Hausmann, B. J. Shields, Q. Quan, Y. Chu, N. P. De Leon, R. Evans, M. J. Burek, A. S. Zibrov, M. Markham, D. J. Twitchen, H. Park, M. D. Lukin, and M. Lončar, “Coupling of NV centers to photonic crystal nanobeams in diamond,” Nano Lett. 13, 5791–5796 (2013).
[Crossref] [PubMed]

2012 (6)

A. Faraon, C. Santori, Z. Huang, V. M. Acosta, and R. G. Beausoleil, “Coupling of nitrogen-vacancy centers to photonic crystal cavities in monocrystalline diamond,” Phys. Rev. Lett. 109, 033604 (2012).
[Crossref] [PubMed]

M. Furuhashi, M. Fujiwara, T. Ohshiro, K. Matsubara, M. Tsutsui, M. Taniguchi, S. Takeuchi, and T. Kawai, “Embedded TiO2 waveguides for sensing nanofluorophores in a microfluidic channel,” Appl. Phys. Lett. 101, 153115 (2012).
[Crossref]

Z.-F. Bi, L. Wang, X.-H. Liu, S.-M. Zhang, M.-M. Dong, Q.-Z. Zhao, X.-L. Wu, and K.-M. Wang, “Optical waveguides in TiO2 formed by He ion implantation,” Opt. Express 20, 6712–6719 (2012).
[Crossref] [PubMed]

J. D. B. Bradley, C. C. Evans, J. T. Choy, O. Reshef, P. B. Deotare, F. Parsy, K. C. Phillips, M. Lončar, and E. Mazur, “Submicrometer-wide amorphous and polycrystalline anatase TiO2 waveguides for microphotonic devices,” Opt. Express 20, 23821–31 (2012).
[Crossref] [PubMed]

J. T. Choy, J. D. B. Bradley, P. B. Deotare, I. B. Burgess, C. C. Evans, E. Mazur, and M. Lončar, “Integrated TiO2 resonators for visible photonics,” Opt. Lett. 37, 539–541 (2012).
[Crossref] [PubMed]

T. van der Sar, J. Hagemeier, W. Pfaff, E. Heeres, S. Thon, H. Kim, P. Petroff, O. Tjerk, D. Bouwmeester, and R. Hanson, “Effect of a nanoparticle on the optical properties of a photonic crystal cavity: theory and experiment,” J. Opt. Soc. Am. B 32(4), 698–703 (2012).
[Crossref]

2011 (4)

Q. Quan, I. B. Burgess, S. K. Y. Tang, D. L. Floyd, and M. Lončar, “High-Q, low index-contrast polymeric photonic crystal nanobeam cavities,” Opt. Express 19, 22191 (2011).
[Crossref] [PubMed]

M. Furuhashi, M. Fujiwara, T. Ohshiro, M. Tsutsui, K. Matsubara, M. Taniguchi, S. Takeuchi, and T. Kawai, “Development of microfabricated TiO2 channel waveguides,” AIP Adv. 1, 032102 (2011).
[Crossref]

A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity,” Nat. Photonics 5, 301–305 (2011).
[Crossref]

Q. Quan and M. Lončar, “Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities,” Opt. Express 19, 18529–18542 (2011).
[Crossref] [PubMed]

2010 (3)

Q. Quan, P. B. Deotare, and M. Lončar, “Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide,” Appl. Phys. Lett. 96, 203102 (2010).
[Crossref]

J. Wolters, A. W. Schell, G. Kewes, N. Nüsse, M. Schoengen, H. Döscher, T. Hannappel, B. Löchel, M. Barth, and O. Benson, “Enhancement of the zero phonon line emission from a single nitrogen vacancy center in a nanodiamond via coupling to a photonic crystal cavity,” Appl. Phys. Lett. 97, 141108 (2010).
[Crossref]

G. Subramania, Y.-J. Lee, A. J. Fischer, and D. D. Koleske, “Log-pile TiO2 photonic crystal for light control at near-UV and visible wavelengths,” Adv. Mater. 22, 487–491 (2010).
[Crossref] [PubMed]

2009 (3)

P. E. Barclay, K.-M. C. Fu, C. Santori, and R. G. Beausoleil, “Chip-based microcavities coupled to nitrogen-vacancy centers in single crystal diamond,” Appl. Phys. Lett. 95, 191115 (2009).
[Crossref]

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 12–15 (2009).
[Crossref]

T. L. Wee, Y. W. Mau, C. Y. Fang, H. L. Hsu, C. C. Han, and H. C. Chang, “Preparation and characterization of green fluorescent nanodiamonds for biological applications,” Diam. Relat. Mater. 18, 567–573 (2009).
[Crossref]

2008 (5)

2007 (3)

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, “Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond,” Appl. Phys. Lett. 91, 201112 (2007).
[Crossref]

G. Subramania, Y.-J. Lee, I. Brener, T. S. Luk, and P. G. Clem, “Nano-lithographically fabricated titanium dioxide based visible frequency three dimensional gap photonic crystal,” Opt. Express 15, 13049–13057 (2007).
[Crossref] [PubMed]

S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AIAs/GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett. 90, 251109 (2007).
[Crossref]

2004 (1)

O. Carp, C. L. Huisman, and A. Reller, “Photoinduced reactivity of titanium dioxide,” Prog. Solid State Chem. 32, 33–177 (2004).
[Crossref]

2003 (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]

2002 (1)

Z. Wang, U. Helmersson, and P.-O. Käll, “Optical properties of anatase TiO2 thin films prepared by aqueous sol–gel process at low temperature,” Thin Solid Films 405, 50–54 (2002).
[Crossref]

1989 (1)

1988 (1)

H. Chew, “Radiation and lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38, 3410–3416 (1988).
[Crossref]

1977 (1)

W. Lukosz and R. Kunz, “Fluorescence lifetime of magnetic and electric dipoles near a dielectric interface,” Opt. Commun. 20, 195–199 (1977).
[Crossref]

Acosta, V. M.

A. Faraon, C. Santori, Z. Huang, V. M. Acosta, and R. G. Beausoleil, “Coupling of nitrogen-vacancy centers to photonic crystal cavities in monocrystalline diamond,” Phys. Rev. Lett. 109, 033604 (2012).
[Crossref] [PubMed]

Akahane, Y.

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]

Albrand, G.

Allen, T. H.

Aoki, I.

F. Qiu, A. M. Spring, F. Yu, I. Aoki, A. Otomo, and S. Yokoyama, “Thin TiO2 core and electro-optic polymer cladding waveguide modulators,” Appl. Phys. Lett. 102, 233504 (2013).
[Crossref]

Asano, T.

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]

Awschalom, D. D.

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, “Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond,” Appl. Phys. Lett. 91, 201112 (2007).
[Crossref]

Barclay, P. E.

A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity,” Nat. Photonics 5, 301–305 (2011).
[Crossref]

P. E. Barclay, K.-M. C. Fu, C. Santori, and R. G. Beausoleil, “Chip-based microcavities coupled to nitrogen-vacancy centers in single crystal diamond,” Appl. Phys. Lett. 95, 191115 (2009).
[Crossref]

Barth, M.

J. Wolters, A. W. Schell, G. Kewes, N. Nüsse, M. Schoengen, H. Döscher, T. Hannappel, B. Löchel, M. Barth, and O. Benson, “Enhancement of the zero phonon line emission from a single nitrogen vacancy center in a nanodiamond via coupling to a photonic crystal cavity,” Appl. Phys. Lett. 97, 141108 (2010).
[Crossref]

Beausoleil, R. G.

A. Faraon, C. Santori, Z. Huang, V. M. Acosta, and R. G. Beausoleil, “Coupling of nitrogen-vacancy centers to photonic crystal cavities in monocrystalline diamond,” Phys. Rev. Lett. 109, 033604 (2012).
[Crossref] [PubMed]

A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity,” Nat. Photonics 5, 301–305 (2011).
[Crossref]

P. E. Barclay, K.-M. C. Fu, C. Santori, and R. G. Beausoleil, “Chip-based microcavities coupled to nitrogen-vacancy centers in single crystal diamond,” Appl. Phys. Lett. 95, 191115 (2009).
[Crossref]

Bennett, J. M.

Benson, O.

J. Wolters, A. W. Schell, G. Kewes, N. Nüsse, M. Schoengen, H. Döscher, T. Hannappel, B. Löchel, M. Barth, and O. Benson, “Enhancement of the zero phonon line emission from a single nitrogen vacancy center in a nanodiamond via coupling to a photonic crystal cavity,” Appl. Phys. Lett. 97, 141108 (2010).
[Crossref]

S. Schietinger, T. Schröder, and O. Benson, “One-by-one coupling of single defect centers in nanodiamonds to high-Q modes of an optical microresonator,” Nano Lett. 8, 3911–3915 (2008).
[Crossref] [PubMed]

Bi, Z.-F.

Biswas, P.

J. Park, S. K. Ozdemir, F. Monifi, T. Chadha, S. H. Huang, P. Biswas, and L. Yang, “Titanium Dioxide Whispering Gallery Microcavities,” Adv. Opt. Mater. 2, 711–717 (2014).
[Crossref]

Borgogno, J. P.

Bouwmeester, D.

T. van der Sar, J. Hagemeier, W. Pfaff, E. Heeres, S. Thon, H. Kim, P. Petroff, O. Tjerk, D. Bouwmeester, and R. Hanson, “Effect of a nanoparticle on the optical properties of a photonic crystal cavity: theory and experiment,” J. Opt. Soc. Am. B 32(4), 698–703 (2012).
[Crossref]

Bradley, J. D. B.

Brener, I.

Burek, M. J.

B. J. M. Hausmann, B. J. Shields, Q. Quan, Y. Chu, N. P. De Leon, R. Evans, M. J. Burek, A. S. Zibrov, M. Markham, D. J. Twitchen, H. Park, M. D. Lukin, and M. Lončar, “Coupling of NV centers to photonic crystal nanobeams in diamond,” Nano Lett. 13, 5791–5796 (2013).
[Crossref] [PubMed]

Burgess, I. B.

Butler, J. E.

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, “Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond,” Appl. Phys. Lett. 91, 201112 (2007).
[Crossref]

Carniglia, C. K.

Carp, O.

O. Carp, C. L. Huisman, and A. Reller, “Photoinduced reactivity of titanium dioxide,” Prog. Solid State Chem. 32, 33–177 (2004).
[Crossref]

Chadha, T.

J. Park, S. K. Ozdemir, F. Monifi, T. Chadha, S. H. Huang, P. Biswas, and L. Yang, “Titanium Dioxide Whispering Gallery Microcavities,” Adv. Opt. Mater. 2, 711–717 (2014).
[Crossref]

Chang, H. C.

T. L. Wee, Y. W. Mau, C. Y. Fang, H. L. Hsu, C. C. Han, and H. C. Chang, “Preparation and characterization of green fluorescent nanodiamonds for biological applications,” Diam. Relat. Mater. 18, 567–573 (2009).
[Crossref]

Chew, H.

H. Chew, “Radiation and lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38, 3410–3416 (1988).
[Crossref]

Choy, J. T.

Chu, Y.

B. J. M. Hausmann, B. J. Shields, Q. Quan, Y. Chu, N. P. De Leon, R. Evans, M. J. Burek, A. S. Zibrov, M. Markham, D. J. Twitchen, H. Park, M. D. Lukin, and M. Lončar, “Coupling of NV centers to photonic crystal nanobeams in diamond,” Nano Lett. 13, 5791–5796 (2013).
[Crossref] [PubMed]

Clem, P. G.

De La Rue, R. M.

De Leon, N. P.

B. J. M. Hausmann, B. J. Shields, Q. Quan, Y. Chu, N. P. De Leon, R. Evans, M. J. Burek, A. S. Zibrov, M. Markham, D. J. Twitchen, H. Park, M. D. Lukin, and M. Lončar, “Coupling of NV centers to photonic crystal nanobeams in diamond,” Nano Lett. 13, 5791–5796 (2013).
[Crossref] [PubMed]

Deng, C.-S.

C.-S. Deng, Y.-S. Gao, X.-Z. Wu, M.-J. Li, and J.-X. Zhong, “Ultrahigh-Q TE/TM dual-polarized photonic crystal holey fishbone-like nanobeam cavities,” Europhys. Lett. 108, 54006 (2014).
[Crossref]

Deotare, P. B.

Dong, M.-M.

Döscher, H.

J. Wolters, A. W. Schell, G. Kewes, N. Nüsse, M. Schoengen, H. Döscher, T. Hannappel, B. Löchel, M. Barth, and O. Benson, “Enhancement of the zero phonon line emission from a single nitrogen vacancy center in a nanodiamond via coupling to a photonic crystal cavity,” Appl. Phys. Lett. 97, 141108 (2010).
[Crossref]

Erbe, A.

A. Paunoiu, R. S. Moirangthem, and A. Erbe, “Whispering gallery modes in intrinsic TiO2 microspheres coupling to the defect-related photoluminescence after visible excitation,” Phys. Status Solidi RRL 9, 241–244 (2015).
[Crossref]

Evans, C. C.

Evans, R.

B. J. M. Hausmann, B. J. Shields, Q. Quan, Y. Chu, N. P. De Leon, R. Evans, M. J. Burek, A. S. Zibrov, M. Markham, D. J. Twitchen, H. Park, M. D. Lukin, and M. Lončar, “Coupling of NV centers to photonic crystal nanobeams in diamond,” Nano Lett. 13, 5791–5796 (2013).
[Crossref] [PubMed]

Fairchild, B. A.

A. D. Greentree, B. A. Fairchild, F. M. Hossain, and S. Prawer, “Diamond integrated quantum photonics,” Mater. Today 11, 22–31 (2008).
[Crossref]

Fang, C. Y.

T. L. Wee, Y. W. Mau, C. Y. Fang, H. L. Hsu, C. C. Han, and H. C. Chang, “Preparation and characterization of green fluorescent nanodiamonds for biological applications,” Diam. Relat. Mater. 18, 567–573 (2009).
[Crossref]

Faraon, A.

A. Faraon, C. Santori, Z. Huang, V. M. Acosta, and R. G. Beausoleil, “Coupling of nitrogen-vacancy centers to photonic crystal cavities in monocrystalline diamond,” Phys. Rev. Lett. 109, 033604 (2012).
[Crossref] [PubMed]

A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity,” Nat. Photonics 5, 301–305 (2011).
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Feygelson, T.

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[Crossref]

Reller, A.

O. Carp, C. L. Huisman, and A. Reller, “Photoinduced reactivity of titanium dioxide,” Prog. Solid State Chem. 32, 33–177 (2004).
[Crossref]

Reshef, O.

Roussey, M.

M. Häyrinen, M. Roussey, V. Gandhi, P. Stenberg, A. Säynätjoki, L. Karvonen, M. Kuittinen, and S. Honkanen, “Low-loss titanium dioxide strip waveguides fabricated by atomic layer deposition,” J. Light. Technol. 32, 208–212 (2014).
[Crossref]

Santori, C.

A. Faraon, C. Santori, Z. Huang, V. M. Acosta, and R. G. Beausoleil, “Coupling of nitrogen-vacancy centers to photonic crystal cavities in monocrystalline diamond,” Phys. Rev. Lett. 109, 033604 (2012).
[Crossref] [PubMed]

A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity,” Nat. Photonics 5, 301–305 (2011).
[Crossref]

P. E. Barclay, K.-M. C. Fu, C. Santori, and R. G. Beausoleil, “Chip-based microcavities coupled to nitrogen-vacancy centers in single crystal diamond,” Appl. Phys. Lett. 95, 191115 (2009).
[Crossref]

Saxer, A.

Säynätjoki, A.

M. Häyrinen, M. Roussey, V. Gandhi, P. Stenberg, A. Säynätjoki, L. Karvonen, M. Kuittinen, and S. Honkanen, “Low-loss titanium dioxide strip waveguides fabricated by atomic layer deposition,” J. Light. Technol. 32, 208–212 (2014).
[Crossref]

Schell, A. W.

J. Wolters, A. W. Schell, G. Kewes, N. Nüsse, M. Schoengen, H. Döscher, T. Hannappel, B. Löchel, M. Barth, and O. Benson, “Enhancement of the zero phonon line emission from a single nitrogen vacancy center in a nanodiamond via coupling to a photonic crystal cavity,” Appl. Phys. Lett. 97, 141108 (2010).
[Crossref]

Schietinger, S.

S. Schietinger, T. Schröder, and O. Benson, “One-by-one coupling of single defect centers in nanodiamonds to high-Q modes of an optical microresonator,” Nano Lett. 8, 3911–3915 (2008).
[Crossref] [PubMed]

Schmell, R. A.

Schneider, C.

S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AIAs/GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett. 90, 251109 (2007).
[Crossref]

Schoengen, M.

J. Wolters, A. W. Schell, G. Kewes, N. Nüsse, M. Schoengen, H. Döscher, T. Hannappel, B. Löchel, M. Barth, and O. Benson, “Enhancement of the zero phonon line emission from a single nitrogen vacancy center in a nanodiamond via coupling to a photonic crystal cavity,” Appl. Phys. Lett. 97, 141108 (2010).
[Crossref]

Schröder, T.

S. Schietinger, T. Schröder, and O. Benson, “One-by-one coupling of single defect centers in nanodiamonds to high-Q modes of an optical microresonator,” Nano Lett. 8, 3911–3915 (2008).
[Crossref] [PubMed]

Shields, B. J.

B. J. M. Hausmann, B. J. Shields, Q. Quan, Y. Chu, N. P. De Leon, R. Evans, M. J. Burek, A. S. Zibrov, M. Markham, D. J. Twitchen, H. Park, M. D. Lukin, and M. Lončar, “Coupling of NV centers to photonic crystal nanobeams in diamond,” Nano Lett. 13, 5791–5796 (2013).
[Crossref] [PubMed]

Shtyrkova, K.

Song, B.-S.

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]

Sorel, M.

Spector, S.

Spring, A. M.

F. Qiu, A. M. Spring, F. Yu, I. Aoki, A. Otomo, and S. Yokoyama, “Thin TiO2 core and electro-optic polymer cladding waveguide modulators,” Appl. Phys. Lett. 102, 233504 (2013).
[Crossref]

Stenberg, P.

M. Häyrinen, M. Roussey, V. Gandhi, P. Stenberg, A. Säynätjoki, L. Karvonen, M. Kuittinen, and S. Honkanen, “Low-loss titanium dioxide strip waveguides fabricated by atomic layer deposition,” J. Light. Technol. 32, 208–212 (2014).
[Crossref]

Strauß, M.

S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AIAs/GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett. 90, 251109 (2007).
[Crossref]

Subramania, G.

G. Subramania, Y.-J. Lee, A. J. Fischer, and D. D. Koleske, “Log-pile TiO2 photonic crystal for light control at near-UV and visible wavelengths,” Adv. Mater. 22, 487–491 (2010).
[Crossref] [PubMed]

G. Subramania, Y.-J. Lee, I. Brener, T. S. Luk, and P. G. Clem, “Nano-lithographically fabricated titanium dioxide based visible frequency three dimensional gap photonic crystal,” Opt. Express 15, 13049–13057 (2007).
[Crossref] [PubMed]

Suntivich, J.

Takeuchi, S.

M. Furuhashi, M. Fujiwara, T. Ohshiro, K. Matsubara, M. Tsutsui, M. Taniguchi, S. Takeuchi, and T. Kawai, “Embedded TiO2 waveguides for sensing nanofluorophores in a microfluidic channel,” Appl. Phys. Lett. 101, 153115 (2012).
[Crossref]

M. Furuhashi, M. Fujiwara, T. Ohshiro, M. Tsutsui, K. Matsubara, M. Taniguchi, S. Takeuchi, and T. Kawai, “Development of microfabricated TiO2 channel waveguides,” AIP Adv. 1, 032102 (2011).
[Crossref]

Tang, S. K. Y.

Taniguchi, M.

M. Furuhashi, M. Fujiwara, T. Ohshiro, K. Matsubara, M. Tsutsui, M. Taniguchi, S. Takeuchi, and T. Kawai, “Embedded TiO2 waveguides for sensing nanofluorophores in a microfluidic channel,” Appl. Phys. Lett. 101, 153115 (2012).
[Crossref]

M. Furuhashi, M. Fujiwara, T. Ohshiro, M. Tsutsui, K. Matsubara, M. Taniguchi, S. Takeuchi, and T. Kawai, “Development of microfabricated TiO2 channel waveguides,” AIP Adv. 1, 032102 (2011).
[Crossref]

Thon, S.

T. van der Sar, J. Hagemeier, W. Pfaff, E. Heeres, S. Thon, H. Kim, P. Petroff, O. Tjerk, D. Bouwmeester, and R. Hanson, “Effect of a nanoparticle on the optical properties of a photonic crystal cavity: theory and experiment,” J. Opt. Soc. Am. B 32(4), 698–703 (2012).
[Crossref]

Tian, H.

D. Yang, P. Zhang, H. Tian, Y. Ji, and Q. Quan, “Ultrahigh-Q and low-mode-volume parabolic radius-modulated single photonic crystal slot nanobeam cavity for high-sensitivity refractive index sensing,” IEEE Photonics J. 7, 4501408 (2015).
[Crossref]

Tjerk, O.

T. van der Sar, J. Hagemeier, W. Pfaff, E. Heeres, S. Thon, H. Kim, P. Petroff, O. Tjerk, D. Bouwmeester, and R. Hanson, “Effect of a nanoparticle on the optical properties of a photonic crystal cavity: theory and experiment,” J. Opt. Soc. Am. B 32(4), 698–703 (2012).
[Crossref]

Tsutsui, M.

M. Furuhashi, M. Fujiwara, T. Ohshiro, K. Matsubara, M. Tsutsui, M. Taniguchi, S. Takeuchi, and T. Kawai, “Embedded TiO2 waveguides for sensing nanofluorophores in a microfluidic channel,” Appl. Phys. Lett. 101, 153115 (2012).
[Crossref]

M. Furuhashi, M. Fujiwara, T. Ohshiro, M. Tsutsui, K. Matsubara, M. Taniguchi, S. Takeuchi, and T. Kawai, “Development of microfabricated TiO2 channel waveguides,” AIP Adv. 1, 032102 (2011).
[Crossref]

Tuttle-Hart, T.

Twitchen, D. J.

B. J. M. Hausmann, B. J. Shields, Q. Quan, Y. Chu, N. P. De Leon, R. Evans, M. J. Burek, A. S. Zibrov, M. Markham, D. J. Twitchen, H. Park, M. D. Lukin, and M. Lončar, “Coupling of NV centers to photonic crystal nanobeams in diamond,” Nano Lett. 13, 5791–5796 (2013).
[Crossref] [PubMed]

van der Sar, T.

T. van der Sar, J. Hagemeier, W. Pfaff, E. Heeres, S. Thon, H. Kim, P. Petroff, O. Tjerk, D. Bouwmeester, and R. Hanson, “Effect of a nanoparticle on the optical properties of a photonic crystal cavity: theory and experiment,” J. Opt. Soc. Am. B 32(4), 698–703 (2012).
[Crossref]

Wang, C. F.

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, “Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond,” Appl. Phys. Lett. 91, 201112 (2007).
[Crossref]

Wang, K.-M.

Wang, L.

Wang, Z.

Z. Wang, U. Helmersson, and P.-O. Käll, “Optical properties of anatase TiO2 thin films prepared by aqueous sol–gel process at low temperature,” Thin Solid Films 405, 50–54 (2002).
[Crossref]

Wee, T. L.

T. L. Wee, Y. W. Mau, C. Y. Fang, H. L. Hsu, C. C. Han, and H. C. Chang, “Preparation and characterization of green fluorescent nanodiamonds for biological applications,” Diam. Relat. Mater. 18, 567–573 (2009).
[Crossref]

Wolters, J.

J. Wolters, A. W. Schell, G. Kewes, N. Nüsse, M. Schoengen, H. Döscher, T. Hannappel, B. Löchel, M. Barth, and O. Benson, “Enhancement of the zero phonon line emission from a single nitrogen vacancy center in a nanodiamond via coupling to a photonic crystal cavity,” Appl. Phys. Lett. 97, 141108 (2010).
[Crossref]

Wu, X.-L.

Wu, X.-Z.

C.-S. Deng, Y.-S. Gao, X.-Z. Wu, M.-J. Li, and J.-X. Zhong, “Ultrahigh-Q TE/TM dual-polarized photonic crystal holey fishbone-like nanobeam cavities,” Europhys. Lett. 108, 54006 (2014).
[Crossref]

Yang, D.

D. Yang, P. Zhang, H. Tian, Y. Ji, and Q. Quan, “Ultrahigh-Q and low-mode-volume parabolic radius-modulated single photonic crystal slot nanobeam cavity for high-sensitivity refractive index sensing,” IEEE Photonics J. 7, 4501408 (2015).
[Crossref]

Yang, J.

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, “Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond,” Appl. Phys. Lett. 91, 201112 (2007).
[Crossref]

Yang, L.

J. Park, S. K. Ozdemir, F. Monifi, T. Chadha, S. H. Huang, P. Biswas, and L. Yang, “Titanium Dioxide Whispering Gallery Microcavities,” Adv. Opt. Mater. 2, 711–717 (2014).
[Crossref]

Yokoyama, S.

F. Qiu, A. M. Spring, F. Yu, I. Aoki, A. Otomo, and S. Yokoyama, “Thin TiO2 core and electro-optic polymer cladding waveguide modulators,” Appl. Phys. Lett. 102, 233504 (2013).
[Crossref]

Yu, F.

F. Qiu, A. M. Spring, F. Yu, I. Aoki, A. Otomo, and S. Yokoyama, “Thin TiO2 core and electro-optic polymer cladding waveguide modulators,” Appl. Phys. Lett. 102, 233504 (2013).
[Crossref]

Zhang, P.

D. Yang, P. Zhang, H. Tian, Y. Ji, and Q. Quan, “Ultrahigh-Q and low-mode-volume parabolic radius-modulated single photonic crystal slot nanobeam cavity for high-sensitivity refractive index sensing,” IEEE Photonics J. 7, 4501408 (2015).
[Crossref]

Zhang, S.-M.

Zhang, Y.

Zhao, Q.-Z.

Zhong, J.-X.

C.-S. Deng, Y.-S. Gao, X.-Z. Wu, M.-J. Li, and J.-X. Zhong, “Ultrahigh-Q TE/TM dual-polarized photonic crystal holey fishbone-like nanobeam cavities,” Europhys. Lett. 108, 54006 (2014).
[Crossref]

Zibrov, A. S.

B. J. M. Hausmann, B. J. Shields, Q. Quan, Y. Chu, N. P. De Leon, R. Evans, M. J. Burek, A. S. Zibrov, M. Markham, D. J. Twitchen, H. Park, M. D. Lukin, and M. Lončar, “Coupling of NV centers to photonic crystal nanobeams in diamond,” Nano Lett. 13, 5791–5796 (2013).
[Crossref] [PubMed]

Adv. Mater. (1)

G. Subramania, Y.-J. Lee, A. J. Fischer, and D. D. Koleske, “Log-pile TiO2 photonic crystal for light control at near-UV and visible wavelengths,” Adv. Mater. 22, 487–491 (2010).
[Crossref] [PubMed]

Adv. Opt. Mater. (1)

J. Park, S. K. Ozdemir, F. Monifi, T. Chadha, S. H. Huang, P. Biswas, and L. Yang, “Titanium Dioxide Whispering Gallery Microcavities,” Adv. Opt. Mater. 2, 711–717 (2014).
[Crossref]

AIP Adv. (1)

M. Furuhashi, M. Fujiwara, T. Ohshiro, M. Tsutsui, K. Matsubara, M. Taniguchi, S. Takeuchi, and T. Kawai, “Development of microfabricated TiO2 channel waveguides,” AIP Adv. 1, 032102 (2011).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (8)

P. E. Barclay, K.-M. C. Fu, C. Santori, and R. G. Beausoleil, “Chip-based microcavities coupled to nitrogen-vacancy centers in single crystal diamond,” Appl. Phys. Lett. 95, 191115 (2009).
[Crossref]

J. Wolters, A. W. Schell, G. Kewes, N. Nüsse, M. Schoengen, H. Döscher, T. Hannappel, B. Löchel, M. Barth, and O. Benson, “Enhancement of the zero phonon line emission from a single nitrogen vacancy center in a nanodiamond via coupling to a photonic crystal cavity,” Appl. Phys. Lett. 97, 141108 (2010).
[Crossref]

M. Furuhashi, M. Fujiwara, T. Ohshiro, K. Matsubara, M. Tsutsui, M. Taniguchi, S. Takeuchi, and T. Kawai, “Embedded TiO2 waveguides for sensing nanofluorophores in a microfluidic channel,” Appl. Phys. Lett. 101, 153115 (2012).
[Crossref]

F. Qiu, A. M. Spring, F. Yu, I. Aoki, A. Otomo, and S. Yokoyama, “Thin TiO2 core and electro-optic polymer cladding waveguide modulators,” Appl. Phys. Lett. 102, 233504 (2013).
[Crossref]

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, “Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond,” Appl. Phys. Lett. 91, 201112 (2007).
[Crossref]

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 12–15 (2009).
[Crossref]

S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AIAs/GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett. 90, 251109 (2007).
[Crossref]

Q. Quan, P. B. Deotare, and M. Lončar, “Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide,” Appl. Phys. Lett. 96, 203102 (2010).
[Crossref]

Diam. Relat. Mater. (1)

T. L. Wee, Y. W. Mau, C. Y. Fang, H. L. Hsu, C. C. Han, and H. C. Chang, “Preparation and characterization of green fluorescent nanodiamonds for biological applications,” Diam. Relat. Mater. 18, 567–573 (2009).
[Crossref]

Europhys. Lett. (1)

C.-S. Deng, Y.-S. Gao, X.-Z. Wu, M.-J. Li, and J.-X. Zhong, “Ultrahigh-Q TE/TM dual-polarized photonic crystal holey fishbone-like nanobeam cavities,” Europhys. Lett. 108, 54006 (2014).
[Crossref]

IEEE Photonics J. (1)

D. Yang, P. Zhang, H. Tian, Y. Ji, and Q. Quan, “Ultrahigh-Q and low-mode-volume parabolic radius-modulated single photonic crystal slot nanobeam cavity for high-sensitivity refractive index sensing,” IEEE Photonics J. 7, 4501408 (2015).
[Crossref]

J. Light. Technol. (1)

M. Häyrinen, M. Roussey, V. Gandhi, P. Stenberg, A. Säynätjoki, L. Karvonen, M. Kuittinen, and S. Honkanen, “Low-loss titanium dioxide strip waveguides fabricated by atomic layer deposition,” J. Light. Technol. 32, 208–212 (2014).
[Crossref]

J. Opt. Soc. Am. B (2)

O. Reshef, K. Shtyrkova, M. G. Moebius, S. Griesse-Nascimento, S. Spector, C. C. Evans, E. Ippen, and E. Mazur, “Polycrystalline anatase titanium dioxide microring resonators with negative thermo-optic coefficient,” J. Opt. Soc. Am. B 32, 2288 (2015).
[Crossref]

T. van der Sar, J. Hagemeier, W. Pfaff, E. Heeres, S. Thon, H. Kim, P. Petroff, O. Tjerk, D. Bouwmeester, and R. Hanson, “Effect of a nanoparticle on the optical properties of a photonic crystal cavity: theory and experiment,” J. Opt. Soc. Am. B 32(4), 698–703 (2012).
[Crossref]

Mater. Today (1)

A. D. Greentree, B. A. Fairchild, F. M. Hossain, and S. Prawer, “Diamond integrated quantum photonics,” Mater. Today 11, 22–31 (2008).
[Crossref]

Nano Lett. (2)

S. Schietinger, T. Schröder, and O. Benson, “One-by-one coupling of single defect centers in nanodiamonds to high-Q modes of an optical microresonator,” Nano Lett. 8, 3911–3915 (2008).
[Crossref] [PubMed]

B. J. M. Hausmann, B. J. Shields, Q. Quan, Y. Chu, N. P. De Leon, R. Evans, M. J. Burek, A. S. Zibrov, M. Markham, D. J. Twitchen, H. Park, M. D. Lukin, and M. Lončar, “Coupling of NV centers to photonic crystal nanobeams in diamond,” Nano Lett. 13, 5791–5796 (2013).
[Crossref] [PubMed]

Nat. Photonics (1)

A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity,” Nat. Photonics 5, 301–305 (2011).
[Crossref]

Nature (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).
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Opt. Commun. (1)

W. Lukosz and R. Kunz, “Fluorescence lifetime of magnetic and electric dipoles near a dielectric interface,” Opt. Commun. 20, 195–199 (1977).
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Opt. Express (9)

Q. Quan and M. Lončar, “Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities,” Opt. Express 19, 18529–18542 (2011).
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A. R. Md Zain, N. P. Johnson, M. Sorel, and R. M. De La Rue, “Ultra high quality factor one dimensional photonic crystal/photonic wire micro-cavities in silicon-on-insulator (SOI),” Opt. Express 16, 12084–12089 (2008).
[Crossref]

G. Subramania, Y.-J. Lee, I. Brener, T. S. Luk, and P. G. Clem, “Nano-lithographically fabricated titanium dioxide based visible frequency three dimensional gap photonic crystal,” Opt. Express 15, 13049–13057 (2007).
[Crossref] [PubMed]

Y. Zhang and M. Lončar, “Ultra-high quality factor optical resonators based on semiconductor nanowires,” Opt. Express 16, 17400–17409 (2008).
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C. C. Evans, C. Liu, and J. Suntivich, “Low-loss titanium dioxide waveguides and resonators using a dielectric lift-off fabrication process,” Opt. Express 23, 11160–11169 (2015).
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Z.-F. Bi, L. Wang, X.-H. Liu, S.-M. Zhang, M.-M. Dong, Q.-Z. Zhao, X.-L. Wu, and K.-M. Wang, “Optical waveguides in TiO2 formed by He ion implantation,” Opt. Express 20, 6712–6719 (2012).
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J. D. B. Bradley, C. C. Evans, J. T. Choy, O. Reshef, P. B. Deotare, F. Parsy, K. C. Phillips, M. Lončar, and E. Mazur, “Submicrometer-wide amorphous and polycrystalline anatase TiO2 waveguides for microphotonic devices,” Opt. Express 20, 23821–31 (2012).
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Q. Quan, I. B. Burgess, S. K. Y. Tang, D. L. Floyd, and M. Lončar, “High-Q, low index-contrast polymeric photonic crystal nanobeam cavities,” Opt. Express 19, 22191 (2011).
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M. W. McCutcheon and M. Lončar, “Design of a silicon nitride photonic crystal nano cavity with a Quality factor of one million for coupling to a diamond nanocrystal,” Opt. Express 16, 19136 (2008).
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Opt. Lett. (2)

Phys. Rev. A (1)

H. Chew, “Radiation and lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38, 3410–3416 (1988).
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Phys. Rev. Lett. (1)

A. Faraon, C. Santori, Z. Huang, V. M. Acosta, and R. G. Beausoleil, “Coupling of nitrogen-vacancy centers to photonic crystal cavities in monocrystalline diamond,” Phys. Rev. Lett. 109, 033604 (2012).
[Crossref] [PubMed]

Phys. Status Solidi RRL (1)

A. Paunoiu, R. S. Moirangthem, and A. Erbe, “Whispering gallery modes in intrinsic TiO2 microspheres coupling to the defect-related photoluminescence after visible excitation,” Phys. Status Solidi RRL 9, 241–244 (2015).
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Prog. Solid State Chem. (1)

O. Carp, C. L. Huisman, and A. Reller, “Photoinduced reactivity of titanium dioxide,” Prog. Solid State Chem. 32, 33–177 (2004).
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Thin Solid Films (1)

Z. Wang, U. Helmersson, and P.-O. Käll, “Optical properties of anatase TiO2 thin films prepared by aqueous sol–gel process at low temperature,” Thin Solid Films 405, 50–54 (2002).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 The geometry of the ultrahigh-Q TiO2 nanobeam. (a) Cross-sectional trapezium profile which results from Bradley et al.’s [6] etching recipe. Here, w and s represent the top and bottom lengths of the TiO2 trapezium, b is the width of the airhole which changes as you move along the nanobeam in the ±z-direction, tTiO2 and tSiO2 are the thicknesses of TiO2 and SiO2 layers. (b) Top-view schematic of the nanobeam with additional mirror (A), Gaussian mirror (G) and the centre (C) shown. Note: the airholes have a tapered profile from the centre of the cavity.
Fig. 2
Fig. 2 Q values with their respective resonance wavelengths for the TiO2 nanobeam as a function of the number of airholes that constitute both Gaussian mirrors (G). The results shown in this figure were for vertical sidewalls with a width of w = 0.44 μm and a periodicity for the airholes of 0.17 μm.
Fig. 3
Fig. 3 The power distribution of the TiO2 nanobeam. (a) Cross-sectional and (b) top-view profiles. The dashed white lines represent the sidewalls of the nanobeam. Note: by default, Lumerical measures the Poynting vector in their power monitors.
Fig. 4
Fig. 4 A scanning electron micrograph of the TiO2 substrate with embedded NDs.

Tables (1)

Tables Icon

Table 1 The enhancement of parallel and orthogonal dipole polarisations for 637 nm emission in various refractive index distributions. The polarisations are measured with respect to the TiO2–air interface (scenario 3).

Metrics