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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 13 — Jun. 18, 2012
  • pp: 14130–14136
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Photonic crystal waveguides intersection for resonant quantum dot optical spectroscopy detection

Xiaohong Song, Stefan Declair, Torsten Meier, Artur Zrenner, and Jens Förstner  »View Author Affiliations


Optics Express, Vol. 20, Issue 13, pp. 14130-14136 (2012)
http://dx.doi.org/10.1364/OE.20.014130


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Abstract

Using a finite-difference time-domain method, we theoretically investigate the optical spectra of crossing perpendicular photonic crystal waveguides with quantum dots embedded in the central rod. The waveguides are designed so that the light mainly propagates along one direction and the cross talk is greatly reduced in the transverse direction. It is shown that when a quantum dot (QD) is resonant with the cavity, strong coupling can be observed via both the transmission and crosstalk spectrum. If the cavity is far off-resonant from the QD, both the cavity mode and the QD signal can be detected in the transverse direction since the laser field is greatly suppressed in this direction. This structure could have strong implications for resonant excitation and in-plane detection of QD optical spectroscopy.

© 2012 OSA

1. Introduction

Cavity quantum electrodynamics (cavity QED) studies the interaction between a quantum emitter and light confined in a resonant cavity [1

1. P. R. Berman, ed., Cavity Quantum Electrodynamics (Academic, 1994).

, 2

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

]. It gives rise to novel regimes of light-matter interaction and has important applications for quantum information processing [3

3. J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73(3), 565–582 (2001). [CrossRef]

] and highly efficiency light sources [4

4. B. Darquié, M. P. A. Jones, J. Dingjan, J. Beugnon, S. Bergamini, Y. Sortais, G. Messin, A. Browaeys, and P. Grangier, “Controlled single-photon emission from a single trapped two-level atom,” Science 309(5733), 454–456 (2005). [CrossRef] [PubMed]

7

7. P. Yao, V. S. C. Manga Rao, and S. Hughes, “On-chip single photon sources using planar photonic crystals and single quantum dots,” Laser Photon. Rev. 4(4), 499–516 (2010). [CrossRef]

]. In particular, semiconductor quantum dots (QDs) offer an attractive material system for studying cavity QED due to their large exciton dipole moment, fixed in position and stable [7

7. P. Yao, V. S. C. Manga Rao, and S. Hughes, “On-chip single photon sources using planar photonic crystals and single quantum dots,” Laser Photon. Rev. 4(4), 499–516 (2010). [CrossRef]

]. Both weak [8

8. W. H. Chang, W. Y. Chen, H. S. Chang, T. P. Hsieh, J. I. Chyi, and T. M. Hsu, “Efficient Single-Photon Sources Based on Low-Density Quantum Dots in Photonic-Crystal Nanocavities,” Phys. Rev. Lett. 96(11), 117401 (2006). [CrossRef] [PubMed]

] and strong coupling [9

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

11

11. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007). [CrossRef] [PubMed]

] between a single QD and a small volume crystal nanocavity has been observed in photoluminescence, which provides potential for solid-state single-photon sources. However, for QDs, one of main problems is that the scattering laser light is strong, hence it is difficult to differentiate the QD emission from the scattering laser with nearly the same frequency [12

12. A. Muller, E. B. Flagg, P. Bianucci, X. Y. Wang, D. G. Deppe, W. Ma, J. Zhang, G. J. Salamo, M. Xiao, and C. K. Shih, “Resonance fluorescence from a coherently driven semiconductor quantum dot in a cavity,” Phys. Rev. Lett. 99(18), 187402 (2007). [CrossRef] [PubMed]

14

14. S. Ates, S. M. Ulrich, A. Ulhaq, S. Reitzenstein, A. Löffler, S. Höfling, A. Forchel, and P. Michler, “Non-resonant dot-cavity coupling and its potential for resonant single-quantum-dot spectroscopy,” Nat. Photonics 3(12), 724–728 (2009). [CrossRef]

]. Currently, incoherent non-resonant excitation and photoluminescence detection are widely used to detect the emission of QDs [9

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

11

11. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007). [CrossRef] [PubMed]

]. Using a filter, the quantum dot emission can be discriminated from the scattered laser background easily. However, this method does not allow direct coherent manipulation of the quantum states.

To solve this problem, several methods have been proposed, and resonant quantum dots spectroscopy became a hot topic in recent years [7

7. P. Yao, V. S. C. Manga Rao, and S. Hughes, “On-chip single photon sources using planar photonic crystals and single quantum dots,” Laser Photon. Rev. 4(4), 499–516 (2010). [CrossRef]

, 12

12. A. Muller, E. B. Flagg, P. Bianucci, X. Y. Wang, D. G. Deppe, W. Ma, J. Zhang, G. J. Salamo, M. Xiao, and C. K. Shih, “Resonance fluorescence from a coherently driven semiconductor quantum dot in a cavity,” Phys. Rev. Lett. 99(18), 187402 (2007). [CrossRef] [PubMed]

16

16. M. Winger, T. Volz, G. Tarel, S. Portolan, A. Badolato, K. J. Hennessy, E. L. Hu, A. Beveratos, J. Finley, V. Savona, and A. Imamoğlu, “Explanation of photon correlations in the far-off-resonance optical emission from a quantum-dot-cavity system,” Phys. Rev. Lett. 103(20), 207403 (2009). [CrossRef] [PubMed]

]. For example, A. Muller et al. have proposed using a planar optical microcavity to suppress laser scattering [12

12. A. Muller, E. B. Flagg, P. Bianucci, X. Y. Wang, D. G. Deppe, W. Ma, J. Zhang, G. J. Salamo, M. Xiao, and C. K. Shih, “Resonance fluorescence from a coherently driven semiconductor quantum dot in a cavity,” Phys. Rev. Lett. 99(18), 187402 (2007). [CrossRef] [PubMed]

]. This method enabled, for the first time, the resonant excitation of a single QD in a cavity [12

12. A. Muller, E. B. Flagg, P. Bianucci, X. Y. Wang, D. G. Deppe, W. Ma, J. Zhang, G. J. Salamo, M. Xiao, and C. K. Shih, “Resonance fluorescence from a coherently driven semiconductor quantum dot in a cavity,” Phys. Rev. Lett. 99(18), 187402 (2007). [CrossRef] [PubMed]

] and measurement of Mollow-triplet emission spectrum [13

13. E. B. Flagg, A. Muller, J. W. Robertson, S. Founta, D. G. Deppe, M. Xiao, W. Ma, G. J. Salamo, and C. K. Shih, “Resonantly driven coherent oscillations in a solid-state quantum emitter,” Nat. Phys. 5(3), 203–207 (2009). [CrossRef]

] in a semiconductor system. Another method is using non-resonant dot-cavity coupling to detect resonant quantum dots emission properties. This method comes from an intriguing phenomenon which has been observed repeatedly in many semiconductor quantum dot-cavity coupling experiments showing that there is a significant cavity mode emission in photoluminescence even when the quantum dot has a large detuning from the cavity [9

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

, 11

11. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007). [CrossRef] [PubMed]

, 14

14. S. Ates, S. M. Ulrich, A. Ulhaq, S. Reitzenstein, A. Löffler, S. Höfling, A. Forchel, and P. Michler, “Non-resonant dot-cavity coupling and its potential for resonant single-quantum-dot spectroscopy,” Nat. Photonics 3(12), 724–728 (2009). [CrossRef]

, 15

15. D. Englund, A. Majumdar, A. Faraon, M. Toishi, N. Stoltz, P. Petroff, and J. Vucković, “Resonant excitation of a quantum dot strongly coupled to a photonic crystal nanocavity,” Phys. Rev. Lett. 104(7), 073904 (2010). [CrossRef] [PubMed]

]. Though the underlying mechanism of this so called “non-resonantly coupled emission” is still not yet totally understood and aroused a heated discussion recently [16

16. M. Winger, T. Volz, G. Tarel, S. Portolan, A. Badolato, K. J. Hennessy, E. L. Hu, A. Beveratos, J. Finley, V. Savona, and A. Imamoğlu, “Explanation of photon correlations in the far-off-resonance optical emission from a quantum-dot-cavity system,” Phys. Rev. Lett. 103(20), 207403 (2009). [CrossRef] [PubMed]

19

19. K. Koshino, “Theory of resonance fluorescence from a solid-state cavity QED system: effects of pure dephasing,” Phys. Rev. B 84, 033824 (2011).

], it already shows the great potential of using the detuned cavity signal to readout the resonantly excited quantum dot spectroscopy [14

14. S. Ates, S. M. Ulrich, A. Ulhaq, S. Reitzenstein, A. Löffler, S. Höfling, A. Forchel, and P. Michler, “Non-resonant dot-cavity coupling and its potential for resonant single-quantum-dot spectroscopy,” Nat. Photonics 3(12), 724–728 (2009). [CrossRef]

, 15

15. D. Englund, A. Majumdar, A. Faraon, M. Toishi, N. Stoltz, P. Petroff, and J. Vucković, “Resonant excitation of a quantum dot strongly coupled to a photonic crystal nanocavity,” Phys. Rev. Lett. 104(7), 073904 (2010). [CrossRef] [PubMed]

, 20

20. A. Majumdar, A. Papageorge, E. D. Kim, M. Bajcsy, H. Kim, P. Petroff, and J. Vučković, “Probing of single quantum dot dressed states via an off-resonant cavity,” Phys. Rev. B 84(8), 085310 (2011). [CrossRef]

].

In this paper, we introduce a new method based on two crossing perpendicular waveguides to achieve the in-plane resonant excitation and detection of QD. We show that not only the vacuum Rabi splitting but also the pure quantum dots signal can be detected directly through the photonic channel. The structure we employed was first designed by Johnson et al. to eliminate cross talk in waveguide intersections for constructing integrated optical circuits [25

25. S. G. Johnson, C. Manolatou, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Elimination of cross talk in waveguide intersections,” Opt. Lett. 23(23), 1855–1857 (1998). [CrossRef] [PubMed]

]. The main idea is using symmetry mismatch to prevent the resonant excited mode from the input port decaying into the transverse ports. Here we show, for the first time to our knowledge, that this structure can be used as a powerful tool for detecting the resonant optical signal of an embedded QD. The QD is placed in the center rod of the intersection of the two waveguides which form a cavity (see Fig. 1
Fig. 1 (a) Schematic view of the computational cell containing the structure. The red area is a PC-based convolutional perfectly matched layer (CPML) used in the FDTD approach; EI/T/C are the incident/transmitted/crosstalk electric field signals. The blue lines denote the positions where we detect the electric field signals. (b) Zoomed in image of the intersection part. (c) Electric field pattern polarized along z axis. (d) The position of the QD with respect to the cavity mode.
). Since the crosstalk is reduced by the symmetry, the laser background is very weak in the transverse port, so that optical signals of the QD can be detected at this port. This method overcomes the difficulty of differentiating the QD signal from the input laser at nearly the same frequency, and achieves the in-plane optical detection at the same time.

2. Theoretical methods

We consider a two-dimensional crystal of dielectric rods in air on a square array with lattice constant a = 400nm. The radius of the rods r = 0.2a, and the dielectric constant ε = 11.56. The radius of the single rod in the center is increased to 0.33a and surrounded by the photonic crystal layers to create a resonant cavity (see Fig. 1(b)) [25

25. S. G. Johnson, C. Manolatou, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Elimination of cross talk in waveguide intersections,” Opt. Lett. 23(23), 1855–1857 (1998). [CrossRef] [PubMed]

]. A finite-difference time-domain method with enhancements to archive subpixel accuracy was used to analyze the propagation properties of light in this structure [26

26. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, 2005), 3rd edition.

]. To decrease the propagation losses [27

27. V. S. Rao and S. Hughes, “Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: proposal for an efficient “on chip” single photon gun,” Phys. Rev. Lett. 99(19), 193901 (2007). [CrossRef] [PubMed]

] and calculation time, we use a finite-size structure; the computational cell is 40 × 20 lattice constants. The spatial discretization corresponds to Δx = Δy = a/25. To truncate the computation domain, appropriate absorbing boundary conditions must be used. For traditional dielectric waveguides, it has been demonstrated that the perfectly matched layer (PML) boundary condition is robust and efficient for terminating the FDTD lattices [26

26. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, 2005), 3rd edition.

]. But for photonic crystal waveguide, even if the waveguide is terminated with PML, there still exists substantial reflection from the boundary due to the dispersion relation mismatch (on the order of 20% to 30%) [27

27. V. S. Rao and S. Hughes, “Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: proposal for an efficient “on chip” single photon gun,” Phys. Rev. Lett. 99(19), 193901 (2007). [CrossRef] [PubMed]

, 29

29. A. Mekis, S. Fang, and J. D. Joannopoulos, “Absorbing boundary conditions for FDTD simulations of photonic crystal waveguides,” IEEE Microw. Guided W. 9(12), 502–504 (1999). [CrossRef]

, 30

30. M. Koshiba, Y. Tsuji, and S. Sasaki, “High-performance absorbing boundary conditions for photonic crystal waveguide simulations,” IEEE Microw. Wirel. Co. 11(4), 152–154 (2001). [CrossRef]

]. To remove this unphysical reflection from the boundary, Koshiba et al. suggested that the original photonic structure should be continued and exist also in the PML [30

30. M. Koshiba, Y. Tsuji, and S. Sasaki, “High-performance absorbing boundary conditions for photonic crystal waveguide simulations,” IEEE Microw. Wirel. Co. 11(4), 152–154 (2001). [CrossRef]

]. This so-called PC-based PML greatly reduces the reflection amplitude from the photonic crystal waveguide ends. In our setup the reflection is less than −50dB across a wide range of frequencies [30

30. M. Koshiba, Y. Tsuji, and S. Sasaki, “High-performance absorbing boundary conditions for photonic crystal waveguide simulations,” IEEE Microw. Wirel. Co. 11(4), 152–154 (2001). [CrossRef]

]. Here we used a photonic crystal based convolutional perfectly matched layer (PC-based CPML) boundary condition (see the red area in Fig. 1(a)). Compared with PML, the CPML offers a number of advantages, such as independence of the host medium and added capability of effectively absorbing evanescent waves [31

31. J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): An Efficient FDTD Implementation of the CFS-PML for Arbitrary Media,” Microw. Opt. Technol. Lett. 27(5), 334–339 (2000). [CrossRef]

]. The thickness of the PC-based CPML was chosen as d = 10a. The pulse used for excitation is sent to the input port (PI), and then the electric fields are detected at different positions getting the throughput (PT) and the crosstalk spectra (PC) (see Fig. 1(a)).

The QD is embedded in the single central rod. In experiments it has been demonstrated recently using the atomic force microscopy metrology, that cavities can be precisely positioned around a single preselected QD [11

11. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007). [CrossRef] [PubMed]

]. We consider the case that the dipole orientation of the QD is along the z axis which is parallel to the polarization direction of electric field. The interaction of a single QD with the resonant electric field is described by two-level optical Bloch Eq [12

12. A. Muller, E. B. Flagg, P. Bianucci, X. Y. Wang, D. G. Deppe, W. Ma, J. Zhang, G. J. Salamo, M. Xiao, and C. K. Shih, “Resonance fluorescence from a coherently driven semiconductor quantum dot in a cavity,” Phys. Rev. Lett. 99(18), 187402 (2007). [CrossRef] [PubMed]

], which are numerically solved by the Runge-Kutta method, and coupled with the Maxwell Eq. by the macroscopic polarization in a self-consistent approach [32

32. C. Dineen, J. Förstner, A. R. Zakharian, J. V. Moloney, and S. W. Koch, “Electromagnetic field structure and normal mode coupling in photonic crystal nanocavities,” Opt. Express 13(13), 4980–4985 (2005). [CrossRef] [PubMed]

, 33

33. S. Declair, T. Meier, and J. Förstner, “Numerical Investigation of the Coupling Between Microdisk Modes and Quantum Dots,” Phys. Status Solidi 8(4c), 1254–1257 (2011). [CrossRef]

].

3. Results and discussions

First, we investigate the case without embedded QD. We send a 50fs broad-spectrum TM (in-plane magnetic field) Gaussian pulse to the input port (the spectrum is shown in Fig. 2(a)
Fig. 2 Calculated spectra for structure without QD. (a) Spectra profile of the input pulse (EI), (b) transmission spectrum (ET), and (c) the crosstalk spectrum (EC).
) so that we can achieve the propagation information within a wide spectrum regime by only one-time simulation run. The simulated propagating electric field polarized along z direction is shown in Fig. 1(c). The detected throughput (ET) and crosstalk pulses (EC) are Fourier transformed to obtain the throughput and crosstalk spectra which are shown in Fig. 2(b) and 2(c), respectively. It can be seen that, due to large cavity’s quality factor (Q ≈3.5 × 104), the bandwidth of the throughput is very narrow and centered on the resonance frequency of the cavity. As desired for the crosstalk, the intensity is quite low (about 10−11 compared with the input spectrum) (see Fig. 2(a) and 2(c)). Since we consider a finite size photonic crystal, the detection position of the crosstalk is near to the cavity, so there is an obvious signal of the cavity at the resonant frequency of the cavity. The physical mechanism of low-crosstalk was analyzed in detail in Ref [25

25. S. G. Johnson, C. Manolatou, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Elimination of cross talk in waveguide intersections,” Opt. Lett. 23(23), 1855–1857 (1998). [CrossRef] [PubMed]

]: two resonant modes exist in the cavity, each of which is even with respect to one waveguides’ mirror plane and odd with respect to the other. Each resonant state only couples to modes in just one waveguide and is orthogonal to modes in the other waveguide. As a result, the resonant modes that are excited from the input port can be prevented by symmetry from decaying into the transverse port. When increasing the Q of the resonance, the crosstalk can be decreased further.

Next, we focus on the case when the cavity mode is far off-resonance from the QD transition frequency (λq-λc = 6nm). Figure 4(a)
Fig. 4 Throughput spectra when the cavity mode is far off-resonance from the QD transition frequency (λq-λc = 6nm). (a): the dipole moment of the QD μ = 60D; (b): μ = 90D.
and 4(b) show the throughput spectra when the dipole moment of the QD equals to 60D and 90D, respectively. It can be seen that only the cavity mode can be observed. Nearly no difference can be seen between the cases with and without QD (see Fig. 4(a), 4(b) and Fig. 2(b)). This is because, in x direction, the function of the photonic crystal structure we used is similar to a filter, hence nearly 100% throughput can be obtained at the cavity mode frequency [25

25. S. G. Johnson, C. Manolatou, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Elimination of cross talk in waveguide intersections,” Opt. Lett. 23(23), 1855–1857 (1998). [CrossRef] [PubMed]

]. In our case, since the calculation time is not long enough, the calculated throughput intensity at the cavity mode frequency is lower than the input pulse intensity. However, even in this case, the cavity mode is still strong enough to overwhelm the weak signal of QD. As a result, in x direction, it is difficult to detect the signal of QD through optical channel when the QD is largely detuned from the cavity mode.

We obtain the cross-talk spectra by Fourier transformation of the detected electric field (EC) (IC=|FFT(EC)|2). The detected cross-talk electric field EC is composed of two parts: the background (Eb) and the emission of the QD and cavity (EQ/Cavity). The special shape in cross-talk spectra (See in Figs. 2(c) and 5(a)-5(c)) is induced by the coherent superposition of these two part electric fields. The relative phase between them induces the increase and decrease of the superposed spectra respect to the background.

To verify this point, we first calculate the crosstalk field without a QD giving the background field Eb and subtract it from the crosstalk field with QD (EC) in order to obtain the pure emission field of the QD/Cavity (EQ/Cavity): EQ/Cavity = EC- Eb. The generated spectra of QD/Cavity (IQ/Cavity=|FFT(EQ/Cavity)|2) are shown in Fig. 5(d)-5(e) which shows a typical Lorentzian shape. Moreover, as can be seen in Fig. 5, when the dephasing rate is large (Fig. 5(a), 5(b), 5(d), 5(e)), the intensity of the cavity mode is larger than that of the QD signal. With increasing dipole moment of the QD, the cavity mode also increases accordingly. As a result, detecting the cavity mode in the crosstalk spectrum provides a potential route to detect the resonant properties of the QD. When the dephasing rate is lower, the resonant signal of the QD itself can be easily obtained directly from the crosstalk spectra.

In experimental implementations of this scheme, the system may suffer from disorder and manufacturing imperfections, which will reduce the Q factor of the resonant cavity and increase the crosstalk. To overcome the effects of the manufacturing imperfections, one might further increase the cavity size or slightly shift and optimize the dielectric rods to increase the Q factor of the cavity and decrease the crosstalk.

4. Conclusion

In conclusion, we have demonstrated that the photonic crystal waveguide intersection might be used as a powerful tool which allows both the detection of resonant quantum dot optical spectroscopy through non-resonant dot-cavity coupling, and vacuum Rabi splitting under resonant dot-cavity coupling through optical channel. In particular, in-plane excitation and detection will benefit constructing integrated photonic system coupled with solid state emitters.

Acknowledgments

This work is supported by the Deutsche Forschungsgemeinschaft DFG via the Research Training Group (GRK 1464), the Emmy-Noether Group “Computational Nanophotonics”, and the BMBF (01BQ1040).

References and links

1.

P. R. Berman, ed., Cavity Quantum Electrodynamics (Academic, 1994).

2.

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

3.

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73(3), 565–582 (2001). [CrossRef]

4.

B. Darquié, M. P. A. Jones, J. Dingjan, J. Beugnon, S. Bergamini, Y. Sortais, G. Messin, A. Browaeys, and P. Grangier, “Controlled single-photon emission from a single trapped two-level atom,” Science 309(5733), 454–456 (2005). [CrossRef] [PubMed]

5.

M. Keller, B. Lange, K. Hayasaka, W. Lange, and H. Walther, “Continuous generation of single photons with controlled waveform in an ion-trap cavity system,” Nature 431(7012), 1075–1078 (2004). [CrossRef] [PubMed]

6.

J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, and H. J. Kimble, “Deterministic Generation of Single Photons from One Atom Trapped in a Cavity,” Science 303(5666), 1992–1994 (2004). [CrossRef] [PubMed]

7.

P. Yao, V. S. C. Manga Rao, and S. Hughes, “On-chip single photon sources using planar photonic crystals and single quantum dots,” Laser Photon. Rev. 4(4), 499–516 (2010). [CrossRef]

8.

W. H. Chang, W. Y. Chen, H. S. Chang, T. P. Hsieh, J. I. Chyi, and T. M. Hsu, “Efficient Single-Photon Sources Based on Low-Density Quantum Dots in Photonic-Crystal Nanocavities,” Phys. Rev. Lett. 96(11), 117401 (2006). [CrossRef] [PubMed]

9.

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

10.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004). [CrossRef] [PubMed]

11.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007). [CrossRef] [PubMed]

12.

A. Muller, E. B. Flagg, P. Bianucci, X. Y. Wang, D. G. Deppe, W. Ma, J. Zhang, G. J. Salamo, M. Xiao, and C. K. Shih, “Resonance fluorescence from a coherently driven semiconductor quantum dot in a cavity,” Phys. Rev. Lett. 99(18), 187402 (2007). [CrossRef] [PubMed]

13.

E. B. Flagg, A. Muller, J. W. Robertson, S. Founta, D. G. Deppe, M. Xiao, W. Ma, G. J. Salamo, and C. K. Shih, “Resonantly driven coherent oscillations in a solid-state quantum emitter,” Nat. Phys. 5(3), 203–207 (2009). [CrossRef]

14.

S. Ates, S. M. Ulrich, A. Ulhaq, S. Reitzenstein, A. Löffler, S. Höfling, A. Forchel, and P. Michler, “Non-resonant dot-cavity coupling and its potential for resonant single-quantum-dot spectroscopy,” Nat. Photonics 3(12), 724–728 (2009). [CrossRef]

15.

D. Englund, A. Majumdar, A. Faraon, M. Toishi, N. Stoltz, P. Petroff, and J. Vucković, “Resonant excitation of a quantum dot strongly coupled to a photonic crystal nanocavity,” Phys. Rev. Lett. 104(7), 073904 (2010). [CrossRef] [PubMed]

16.

M. Winger, T. Volz, G. Tarel, S. Portolan, A. Badolato, K. J. Hennessy, E. L. Hu, A. Beveratos, J. Finley, V. Savona, and A. Imamoğlu, “Explanation of photon correlations in the far-off-resonance optical emission from a quantum-dot-cavity system,” Phys. Rev. Lett. 103(20), 207403 (2009). [CrossRef] [PubMed]

17.

M. Calic, P. Gallo, M. Felici, K. A. Atlasov, B. Dwir, A. Rudra, G. Biasiol, L. Sorba, G. Tarel, V. Savona, and E. Kapon, “Phonon-mediated coupling of InGaAs/GaAs quantum-dot excitons to photonic crystal cavities,” Phys. Rev. Lett. 106(22), 227402 (2011). [CrossRef] [PubMed]

18.

A. Naesby, T. Suhr, P. T. Kristensen, and J. Mørk, “Influence of pure dephasing on emission spectra from single photon sources,” Phys. Rev. A 78(4), 045802 (2008). [CrossRef]

19.

K. Koshino, “Theory of resonance fluorescence from a solid-state cavity QED system: effects of pure dephasing,” Phys. Rev. B 84, 033824 (2011).

20.

A. Majumdar, A. Papageorge, E. D. Kim, M. Bajcsy, H. Kim, P. Petroff, and J. Vučković, “Probing of single quantum dot dressed states via an off-resonant cavity,” Phys. Rev. B 84(8), 085310 (2011). [CrossRef]

21.

P. Yao and S. Hughes, “Controlled cavity QED and single-photon emission using a photonic-crystal waveguide cavity system,” Phys. Rev. B 80(16), 165128 (2009). [CrossRef]

22.

K. Srinivasan and O. Painter, “Linear and nonlinear optical spectroscopy of a strongly coupled microdisk-quantum dot system,” Nature 450(7171), 862–865 (2007). [CrossRef] [PubMed]

23.

P. Yao and S. Hughes, “Controlled cavity QED and single-photon emission using a photonic-crystal waveguide cavity system,” Phys. Rev. B 80(16), 165128 (2009). [CrossRef]

24.

F. S. F. Brossard, X. L. Xu, D. A. Williams, M. Hadjipanayi, M. Hugues, M. Hopkinson, X. Wang, and R. A. Taylor, “Strongly coupled single quantum dot in a photonic crystal waveguide cavity,” Appl. Phys. Lett. 97(11), 111101 (2010). [CrossRef]

25.

S. G. Johnson, C. Manolatou, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Elimination of cross talk in waveguide intersections,” Opt. Lett. 23(23), 1855–1857 (1998). [CrossRef] [PubMed]

26.

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, 2005), 3rd edition.

27.

V. S. Rao and S. Hughes, “Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: proposal for an efficient “on chip” single photon gun,” Phys. Rev. Lett. 99(19), 193901 (2007). [CrossRef] [PubMed]

28.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High Transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77(18), 3787–3790 (1996). [CrossRef] [PubMed]

29.

A. Mekis, S. Fang, and J. D. Joannopoulos, “Absorbing boundary conditions for FDTD simulations of photonic crystal waveguides,” IEEE Microw. Guided W. 9(12), 502–504 (1999). [CrossRef]

30.

M. Koshiba, Y. Tsuji, and S. Sasaki, “High-performance absorbing boundary conditions for photonic crystal waveguide simulations,” IEEE Microw. Wirel. Co. 11(4), 152–154 (2001). [CrossRef]

31.

J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): An Efficient FDTD Implementation of the CFS-PML for Arbitrary Media,” Microw. Opt. Technol. Lett. 27(5), 334–339 (2000). [CrossRef]

32.

C. Dineen, J. Förstner, A. R. Zakharian, J. V. Moloney, and S. W. Koch, “Electromagnetic field structure and normal mode coupling in photonic crystal nanocavities,” Opt. Express 13(13), 4980–4985 (2005). [CrossRef] [PubMed]

33.

S. Declair, T. Meier, and J. Förstner, “Numerical Investigation of the Coupling Between Microdisk Modes and Quantum Dots,” Phys. Status Solidi 8(4c), 1254–1257 (2011). [CrossRef]

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(230.5590) Optical devices : Quantum-well, -wire and -dot devices

ToC Category:
Photonic Crystals

History
Original Manuscript: March 14, 2012
Revised Manuscript: April 8, 2012
Manuscript Accepted: May 3, 2012
Published: June 11, 2012

Citation
Xiaohong Song, Stefan Declair, Torsten Meier, Artur Zrenner, and Jens Förstner, "Photonic crystal waveguides intersection for resonant quantum dot optical spectroscopy detection," Opt. Express 20, 14130-14136 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-13-14130


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References

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  15. D. Englund, A. Majumdar, A. Faraon, M. Toishi, N. Stoltz, P. Petroff, and J. Vucković, “Resonant excitation of a quantum dot strongly coupled to a photonic crystal nanocavity,” Phys. Rev. Lett.104(7), 073904 (2010). [CrossRef] [PubMed]
  16. M. Winger, T. Volz, G. Tarel, S. Portolan, A. Badolato, K. J. Hennessy, E. L. Hu, A. Beveratos, J. Finley, V. Savona, and A. Imamoğlu, “Explanation of photon correlations in the far-off-resonance optical emission from a quantum-dot-cavity system,” Phys. Rev. Lett.103(20), 207403 (2009). [CrossRef] [PubMed]
  17. M. Calic, P. Gallo, M. Felici, K. A. Atlasov, B. Dwir, A. Rudra, G. Biasiol, L. Sorba, G. Tarel, V. Savona, and E. Kapon, “Phonon-mediated coupling of InGaAs/GaAs quantum-dot excitons to photonic crystal cavities,” Phys. Rev. Lett.106(22), 227402 (2011). [CrossRef] [PubMed]
  18. A. Naesby, T. Suhr, P. T. Kristensen, and J. Mørk, “Influence of pure dephasing on emission spectra from single photon sources,” Phys. Rev. A78(4), 045802 (2008). [CrossRef]
  19. K. Koshino, “Theory of resonance fluorescence from a solid-state cavity QED system: effects of pure dephasing,” Phys. Rev. B84, 033824 (2011).
  20. A. Majumdar, A. Papageorge, E. D. Kim, M. Bajcsy, H. Kim, P. Petroff, and J. Vučković, “Probing of single quantum dot dressed states via an off-resonant cavity,” Phys. Rev. B84(8), 085310 (2011). [CrossRef]
  21. P. Yao and S. Hughes, “Controlled cavity QED and single-photon emission using a photonic-crystal waveguide cavity system,” Phys. Rev. B80(16), 165128 (2009). [CrossRef]
  22. K. Srinivasan and O. Painter, “Linear and nonlinear optical spectroscopy of a strongly coupled microdisk-quantum dot system,” Nature450(7171), 862–865 (2007). [CrossRef] [PubMed]
  23. P. Yao and S. Hughes, “Controlled cavity QED and single-photon emission using a photonic-crystal waveguide cavity system,” Phys. Rev. B80(16), 165128 (2009). [CrossRef]
  24. F. S. F. Brossard, X. L. Xu, D. A. Williams, M. Hadjipanayi, M. Hugues, M. Hopkinson, X. Wang, and R. A. Taylor, “Strongly coupled single quantum dot in a photonic crystal waveguide cavity,” Appl. Phys. Lett.97(11), 111101 (2010). [CrossRef]
  25. S. G. Johnson, C. Manolatou, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Elimination of cross talk in waveguide intersections,” Opt. Lett.23(23), 1855–1857 (1998). [CrossRef] [PubMed]
  26. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, 2005), 3rd edition.
  27. V. S. Rao and S. Hughes, “Single quantum dot spontaneous emission in a finite-size photonic crystal waveguide: proposal for an efficient “on chip” single photon gun,” Phys. Rev. Lett.99(19), 193901 (2007). [CrossRef] [PubMed]
  28. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High Transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett.77(18), 3787–3790 (1996). [CrossRef] [PubMed]
  29. A. Mekis, S. Fang, and J. D. Joannopoulos, “Absorbing boundary conditions for FDTD simulations of photonic crystal waveguides,” IEEE Microw. Guided W.9(12), 502–504 (1999). [CrossRef]
  30. M. Koshiba, Y. Tsuji, and S. Sasaki, “High-performance absorbing boundary conditions for photonic crystal waveguide simulations,” IEEE Microw. Wirel. Co.11(4), 152–154 (2001). [CrossRef]
  31. J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): An Efficient FDTD Implementation of the CFS-PML for Arbitrary Media,” Microw. Opt. Technol. Lett.27(5), 334–339 (2000). [CrossRef]
  32. C. Dineen, J. Förstner, A. R. Zakharian, J. V. Moloney, and S. W. Koch, “Electromagnetic field structure and normal mode coupling in photonic crystal nanocavities,” Opt. Express13(13), 4980–4985 (2005). [CrossRef] [PubMed]
  33. S. Declair, T. Meier, and J. Förstner, “Numerical Investigation of the Coupling Between Microdisk Modes and Quantum Dots,” Phys. Status Solidi8(4c), 1254–1257 (2011). [CrossRef]

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