## Coupling slot-waveguide cavities for large-scale quantum optical devices |

Optics Express, Vol. 19, Issue 7, pp. 6354-6365 (2011)

http://dx.doi.org/10.1364/OE.19.006354

Acrobat PDF (1288 KB)

### Abstract

By offering effective modal volumes significantly less than a cubic wavelength, slot-waveguide cavities offer a new in-road into strong atom-photon coupling in the visible regime. Here we explore two-dimensional arrays of coupled slot cavities which underpin designs for novel quantum emulators and polaritonic quantum phase transition devices. Specifically, we investigate the lateral coupling characteristics of diamond-air and GaP-air slot waveguides using numerically-assisted coupled-mode theory, and the longitudinal coupling properties via distributed Bragg reflectors using mode-propagation simulations. We find that slot-waveguide cavities in the Fabry-Perot arrangement can be coupled and effectively treated with a tight-binding description, and are a suitable platform for realizing Jaynes-Cummings-Hubbard physics.

© 2011 OSA

## 1. Introduction

1. R. Feynman, “Simulating physics with computers,” Int. J. Theor. Phys. **21**(6-7), 467–488 (1982). [CrossRef]

2. I. Buluta and F. Nori, “Quantum simulators,” Science **326**(5949), 108–111 (2009). [CrossRef] [PubMed]

*Q*cavities [8

8. S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics **1**(8), 449–458 (2007). [CrossRef]

*e.g.*optical defect centres in diamond [9

9. A. D. Greentree, B. A. Fairchild, F. Hossain, and S. Prawer, “Diamond integrated quantum photonics,” Mater. Today **11**(9), 22–31 (2008). [CrossRef]

10. M. Barth, S. Schietinger, S. Fischer, J. Becker, N. Nüsse, T. Aichele, B. Löchel, C. Sönnichsen, and O. Benson, “Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling,” Nano Lett. **10**(3), 891–895 (2010). [CrossRef] [PubMed]

11. K.-M. C. Fu, C. Santori, C. Stanley, M. C. Holland, and Y. Yamamoto, “Coherent population trapping of electron spins in a high-purity n-type GaAs semiconductor,” Phys. Rev. Lett. **95**(18), 187405 (2005). [CrossRef] [PubMed]

12. 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]

13. M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics **2**(12), 741–747 (2008). [CrossRef]

14. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. **29**(11), 1209–1211 (2004). [CrossRef] [PubMed]

15. Q. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. **29**(14), 1626–1628 (2004). [CrossRef] [PubMed]

*i.e.*slot) defined by two regions (rods) of higher refractive index via large dielectric discontinuities. SWCs are then formed as a micro-ring or in a Fabry-Perot (FP) arrangement by combining a slot waveguide with mirrors, PBG or distributed Bragg reflectors (DBRs) [16

16. C. A. Barrios and M. Lipson, “Electrically driven silicon resonant light emitting device based on slot-waveguide,” Opt. Express **13**(25), 10092–10101 (2005). [CrossRef] [PubMed]

17. J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall mode volumes in dielectric optical microcavities,” Phys. Rev. Lett. **95**(14), 143901 (2005). [CrossRef] [PubMed]

19. M. P. Hiscocks, C.-H. Su, B. C. Gibson, A. D. Greentree, L. C. L. Hollenberg, and F. Ladouceur, “Slot-waveguide cavities for optical quantum information applications,” Opt. Express **17**(9), 7295–7303 (2009). [CrossRef] [PubMed]

*Q*limitations to demonstrate strong atom-photon coupling. As the maximum of the optical field is in the central low dielectric (ideally air) region, they are compatible with high-dipole moment emissive nanoparticles that can infiltrate the slot. In particular, we have explored coupling of the SWC to an optically-active defect centre in diamond [19

19. M. P. Hiscocks, C.-H. Su, B. C. Gibson, A. D. Greentree, L. C. L. Hollenberg, and F. Ladouceur, “Slot-waveguide cavities for optical quantum information applications,” Opt. Express **17**(9), 7295–7303 (2009). [CrossRef] [PubMed]

20. C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, “Stable solid-state source of single photons,” Phys. Rev. Lett. **85**(2), 290–293 (2000). [CrossRef] [PubMed]

21. F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. **93**(13), 130501 (2004). [CrossRef] [PubMed]

22. T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. **2**(6), 408–413 (2006). [CrossRef]

23. C.-H. Su, A. D. Greentree, W. J. Munro, K. Nemoto, and L. C. L. Hollenberg, “High-speed quantum gates with cavity quantum electrodynamics,” Phys. Rev. A **78**(6), 062336 (2008). [CrossRef]

24. C.-H. Su, A. D. Greentree, W. J. Munro, K. Nemoto, and L. C. L. Hollenberg, “Pulse shaping by coupled cavities: single photons and qudits,” Phys. Rev. A **80**(3), 033811 (2009). [CrossRef]

25. A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J.-P. Poizat, and P. Grangier, “Single photon quantum cryptography,” Phys. Rev. Lett. **89**(18), 187901 (2002). [CrossRef] [PubMed]

## 2. Slot-waveguide cavity array

26. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. **24**(11), 711–713 (1999). [CrossRef]

27. D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B **27**(2), 985–1009 (1983). [CrossRef]

*n*= 2.4 for diamond and 3.3 for GaP). On these structures, an air-slot and waveguiding patterns can be fabricated using electron beam [15

15. Q. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. **29**(14), 1626–1628 (2004). [CrossRef] [PubMed]

28. K.-M. C. Fu, C. Santori, P. E. Barclay, I. Aharonovich, S. Prawer, N. Meyer, A. M. Holm, and R. G. Beausoleil, “Coupling of nitrogen-vacancy centers in diamond to a GaP waveguide,” Appl. Phys. Lett. **93**(23), 234107 (2008). [CrossRef]

29. M. P. Hiscocks, K. Ganesan, B. C. Gibson, S. T. Huntington, F. Ladouceur, and S. Prawer, “Diamond waveguides fabricated by reactive ion etching,” Opt. Express **16**(24), 19512–19519 (2008). [CrossRef] [PubMed]

*z*-direction (slot direction) to form a slot-waveguide cavity (SWC) is achieved by appending the ends of the waveguide with reflective boundaries such as mirrors, PBG or DBRs. Using narrow slots of

*w*= 20 nm width and an optimal

_{S}*w*×

_{R}*h*= 140 × 110 nm diamond rods, the fundamental quasi-TE modes of the structure occupies a cavity mode volume of 0.1λ

^{3}/

*n*

_{,}where λ is the operating wavelength of 637 nm and the mode is assumed to span over a cavity length of λ/2. The mode volume reduces to 0.02λ

^{3}/

*n*when replaced with 5 nm slot or a 110 × 70 nm GaP rods. Further reduction is possible using angled sidewalls for the slot [30

30. F. Dell’Olio and V. M. N. Passaro, “Optical sensing by optimized silicon slot waveguides,” Opt. Express **15**(8), 4977–4993 (2007). [CrossRef] [PubMed]

31. A. Säynätjoki, T. Alasaarela, A. Khanna, L. Karvonen, P. Stenberg, M. Kuittinen, A. Tervonen, and S. Honkanen, “Angled sidewalls in silicon slot waveguides: conformal filling and mode properties,” Opt. Express **17**(23), 21066–21076 (2009). [CrossRef] [PubMed]

^{−30}Cm and emission wavelength 637 nm, the single-photon Rabi frequency Ω, can in theory reach as high as Ω

**10**

*=*^{11}rad/s [19

19. M. P. Hiscocks, C.-H. Su, B. C. Gibson, A. D. Greentree, L. C. L. Hollenberg, and F. Ladouceur, “Slot-waveguide cavities for optical quantum information applications,” Opt. Express **17**(9), 7295–7303 (2009). [CrossRef] [PubMed]

## 3. Lateral inter-cavity coupling

*N*identical, parallel slot waveguides separated by a distance

*d*, aligned perpendicular to the long axis of the cavities (

*x*-axis in Fig. 1). Coupled-mode theory (CMT) [32

32. W.-P. Huang, “Coupled-mode theory for optical waveguides: an overview,” J. Opt. Soc. Am. A **11**(3), 963–983 (1994). [CrossRef]

*x*-direction if the waveguides are weakly interacting. By working in the regime where the waveguides are sufficiently far apart and strongly guided in the tight-binding regime, the normal modes or the supermodes of the

*N*-coupled array can then be approximated by an expansion of the magnetic

*H*and electric

_{m}*E*modal fields of the individual waveguides modes in isolation [34

_{m}34. M. L. Cooper and S. Mookherjea, “Numerically-assisted coupled-mode theory for silicon waveguide couplers and arrayed waveguides,” Opt. Express **17**(3), 1583–1599 (2009). [CrossRef] [PubMed]

35. E. Kapon, J. Katz, and A. Yariv, “Supermode analysis of phase-locked arrays of semiconductor lasers,” Opt. Lett. **9**(4), 125–127 (1984). [CrossRef] [PubMed]

*xy*-plane. In particular, when each waveguide supports only one TE-like mode in isolation, the total electric field distribution of a supermode is,where

*χ*is the complex propagation constant of this supermode and

*A*is the modal amplitude. Using Eq. (1) as a trial solution, the wave equation can be recast as an eigen-equation in matrix form [34

_{m}34. M. L. Cooper and S. Mookherjea, “Numerically-assisted coupled-mode theory for silicon waveguide couplers and arrayed waveguides,” Opt. Express **17**(3), 1583–1599 (2009). [CrossRef] [PubMed]

**A**= [

*A*

_{1}

*A*

_{2}…

*A*]

_{N}^{T}, and

**B**is a diagonal matrix

*χ*

^{2}

**I**. The elements of the coupling matrix

**M**arewhere

*β*(

_{m}*m*= 1, 2, …

*N*) is the propagation constant of the

*n*th waveguide in isolation and

*β*=

_{m}*β*for identical guides,

*κ*is the mutual coupling coefficient between

_{mn}*m*th and

*n*th guides (

*κ*is the self-coupling coefficient), and

_{nn}*I*denotes the overlap of the non-orthogonal modes of any two guides. The mutual coupling is determined by the integrals over the entire cross section,where

_{mn}*n*is the refractive index of

_{l}*l*th waveguide in absence of the others, and

*n*is the index of the cladding. Hence

_{cl}**M**provides insights into the orthogonality of the modes and the relative strengths of the inter-guide couplings. Cooper and Mookherjea [34

34. M. L. Cooper and S. Mookherjea, “Numerically-assisted coupled-mode theory for silicon waveguide couplers and arrayed waveguides,” Opt. Express **17**(3), 1583–1599 (2009). [CrossRef] [PubMed]

**M**using the relationwhere

*χ*of the

_{m}*m*th supermodes. The purpose of this approach is to allow one to compare the exact scattering matrix with Eq. (2) to ascertain that the assumption of nearest-neighbour coupling is valid. In Sec. 3.1 and 3.2, we employ their approach to investigate TE supermodes of parallel slot-waveguide arrays. We used FIMMWAVE [36

36. FIMMWAVE, Photon Design, http://www.photond.com.

*J*(coupling energy

*ħJ*). Given that the solution of classical Maxwell’s equations can be reinterpreted as a precise quantum description of a one-photon state, we use the classical results and write down the relation for lateral coupling,where the subscript

*L*is used to distinguish lateral coupling from end-to-end coupling (

*J*) discussed in Sec. 4. The propagating field sees an effective refractive index

_{E}*n*

_{eff}of the combined system that we approximate to that of an individual waveguide in isolation.

### 3.1. Cladding-separated configuration

*d*, we focus on the diamond-air case of

*d*= 500 nm. The cross-sectional mode distributions of its supermodes are shown in Fig. 4 and the associated coupling matrix is,

*Μ*and

_{nn}*Μ*

_{n,n}_{± 1}terms agree with the values of the nearest-neighbour coupling and self-coupling in the two-waveguide system. The near symmetry of the matrix suggests that the fields inside the individual waveguides remain centered within the slots (Fig. 4) such that it is still accurate to apply CMT and read off the peak amplitudes of the supermodes as the eigenvectors

**A**[34

**17**(3), 1583–1599 (2009). [CrossRef] [PubMed]

*κ*/

_{nn}*κ*

_{n,n}_{± 1},

*κ*

_{n,n}_{+2}/

*κ*

_{n,n}_{+1}decrease rapidly with the separation distance. As a comparison we find that at

*d*= 600 nm matrix asymmetry reduces, the effective indices of the supermodes converge,

*κ*/

_{22}*κ*

_{n,n}_{± 1}≈2

*κ*/

_{11}*κ*

_{n,n}_{± 1}≈0.04, and

*κ*

_{n,n}_{+2}/

*κ*

_{n,n}_{± 1}= 0.03. Thus, accurate implementations of 1D tight-binding models with dominant nearest-neighbour interactions and negligible non-nearest neighbour coupling can be achieved by setting up slot-waveguide arrays in this arrangement with modest guide separations.

### 3.2. Shared-rod configuration

*w*≤ 240 nm and 140 ≤

_{R}*w*≤ 240 nm for diamond-air and GaP-air slots, respectively. As a representative example, we write down the coupling matrix for the case of

_{R}*d*= 220 nm, with its supermodes shown in Figs. 5(b)–5(f),

*κ*does not diminish with increasing separation. Given the fact that there is a pronounced matrix asymmetry, it is no longer accurate to use its modal peak amplitudes as the eigenvectors and the CMT approach. These undesirable features of coupling characteristics, field skewing inside the cavities, and limited operating range, suggest that this setup is not suitable for implementing practical tight-binding systems.

_{nm}## 4. Longitudinal end-to-end coupling

38. FIMMPROP, Photon Design, http://www.photond.com.

*e.g.*, an increase in rod width

*w*of 10 nm as in Ref. [39

_{R}39. J. Mu, H. Zhang, and W.-P. Huang, “A theoretical investigation of slot waveguide Bragg gratings,” IEEE J. Quantum Electron. **44**(7), 622–627 (2008). [CrossRef]

40. M. W. Pruessner, T. H. Stievater, and W. S. Rabinovich, “Integrated waveguide Fabry-Perot microcavities with silicon/air Bragg mirrors,” Opt. Lett. **32**(5), 533–535 (2007). [CrossRef] [PubMed]

*T*+

*R*= 1 to plot the renormalized reflection spectra for different number of grating periods

*N*in Fig. 7(a) . The maximum reflection occurs at the grating period

_{P}*P*of 220 nm that satisfies the relation that

*P*= λ/2

*n*

_{DBR}where we estimate

*n*

_{DBR}= 1.45 using the weighted average of the diamond-air slot (with an effective refractive index of 1.31) and diamond core (index 1.6).

*R*= 10

^{−2}and an effective grating length of

*L*

_{eff}= 560 nm. By increasing the number of periods to 19.5, the reflectivity improves to 1 –

*R*= 10

^{−3}while

*L*

_{eff}hardly changes (570 nm). It is therefore worthwhile to point out that the effective length remains relatively constant around 0.6 μm because the denominator of Eq. (8) increases very slowly with increasing

*R*. Consequently, since the minimum value of the cavity length

*L*is limited only by the size of the atomic system inside the cavity, we can set the overall index

_{c}*N*

_{eff}≈

*n*

_{DBR}and

^{9}–10

^{11}rad/s is possible with structures with 24.5 <

*N*< 39.5 and 200 <

_{P}*P*< 240 nm. Moreover, following Eq. (9), we can expect that a dielectric-based grating design would only increase the cavity mode volume of a λ/2-long SWC reported in Ref. [19

**17**(9), 7295–7303 (2009). [CrossRef] [PubMed]

*L*

_{eff})/(λ/2) = 3.7. The resultant cavity mode volumes are therefore still well below the dimensions of the wavelength of light.

## 5. Conclusions

^{14}rad/s to arbitrarily small values by introducing cladding separation of 500 nm or more. Similarly, the coupling rate in the longitudinal direction can be reduced from 5 × 10

^{14}rad/s by introducing 5 or more Bragg periods. Specifically, there is exponential scaling of coupling strength against these setup parameters. Our DBR analysis furthermore extends and validates the work of Ref. [19

**17**(9), 7295–7303 (2009). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | R. Feynman, “Simulating physics with computers,” Int. J. Theor. Phys. |

2. | I. Buluta and F. Nori, “Quantum simulators,” Science |

3. | M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. |

4. | A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. |

5. | D. G. Angelakis, M. F. Santos, and S. Bose, “Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays,” Phys. Rev. A |

6. | J. Koch, A. A. Houck, K. L. Hur, and S. M. Girvin, “Time-reversal-symmetry breaking in circuit-QED based photon lattices,” Phys. Rev. A |

7. | J. Q. Quach, C.-H. Su, A. M. Martin, A. D. Greentree, and L. C. L. Hollenberg, “A new class of dynamic quantum metamaterials,” http://arxiv.org/abs/1009.4867 (2010). |

8. | S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics |

9. | A. D. Greentree, B. A. Fairchild, F. Hossain, and S. Prawer, “Diamond integrated quantum photonics,” Mater. Today |

10. | M. Barth, S. Schietinger, S. Fischer, J. Becker, N. Nüsse, T. Aichele, B. Löchel, C. Sönnichsen, and O. Benson, “Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling,” Nano Lett. |

11. | K.-M. C. Fu, C. Santori, C. Stanley, M. C. Holland, and Y. Yamamoto, “Coherent population trapping of electron spins in a high-purity n-type GaAs semiconductor,” Phys. Rev. Lett. |

12. | 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 |

13. | M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics |

14. | V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. |

15. | Q. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. |

16. | C. A. Barrios and M. Lipson, “Electrically driven silicon resonant light emitting device based on slot-waveguide,” Opt. Express |

17. | J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall mode volumes in dielectric optical microcavities,” Phys. Rev. Lett. |

18. | A. Gondarenko and M. Lipson, “Low modal volume dipole-like dielectric slab resonator,” Opt. Express |

19. | M. P. Hiscocks, C.-H. Su, B. C. Gibson, A. D. Greentree, L. C. L. Hollenberg, and F. Ladouceur, “Slot-waveguide cavities for optical quantum information applications,” Opt. Express |

20. | C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, “Stable solid-state source of single photons,” Phys. Rev. Lett. |

21. | F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. |

22. | T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. |

23. | C.-H. Su, A. D. Greentree, W. J. Munro, K. Nemoto, and L. C. L. Hollenberg, “High-speed quantum gates with cavity quantum electrodynamics,” Phys. Rev. A |

24. | C.-H. Su, A. D. Greentree, W. J. Munro, K. Nemoto, and L. C. L. Hollenberg, “Pulse shaping by coupled cavities: single photons and qudits,” Phys. Rev. A |

25. | A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J.-P. Poizat, and P. Grangier, “Single photon quantum cryptography,” Phys. Rev. Lett. |

26. | A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. |

27. | D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B |

28. | K.-M. C. Fu, C. Santori, P. E. Barclay, I. Aharonovich, S. Prawer, N. Meyer, A. M. Holm, and R. G. Beausoleil, “Coupling of nitrogen-vacancy centers in diamond to a GaP waveguide,” Appl. Phys. Lett. |

29. | M. P. Hiscocks, K. Ganesan, B. C. Gibson, S. T. Huntington, F. Ladouceur, and S. Prawer, “Diamond waveguides fabricated by reactive ion etching,” Opt. Express |

30. | F. Dell’Olio and V. M. N. Passaro, “Optical sensing by optimized silicon slot waveguides,” Opt. Express |

31. | A. Säynätjoki, T. Alasaarela, A. Khanna, L. Karvonen, P. Stenberg, M. Kuittinen, A. Tervonen, and S. Honkanen, “Angled sidewalls in silicon slot waveguides: conformal filling and mode properties,” Opt. Express |

32. | W.-P. Huang, “Coupled-mode theory for optical waveguides: an overview,” J. Opt. Soc. Am. A |

33. | A. W. Synder and J. D. Love, |

34. | M. L. Cooper and S. Mookherjea, “Numerically-assisted coupled-mode theory for silicon waveguide couplers and arrayed waveguides,” Opt. Express |

35. | E. Kapon, J. Katz, and A. Yariv, “Supermode analysis of phase-locked arrays of semiconductor lasers,” Opt. Lett. |

36. | FIMMWAVE, Photon Design, http://www.photond.com. |

37. | Y. O. Barmenkov, D. Zalvidea, S. Torres-Peiró, J. L. Cruz, and M. V. Andrés, “Effective length of short Fabry-Perot cavity formed by uniform fiber Bragg gratings,” Opt. Express |

38. | FIMMPROP, Photon Design, http://www.photond.com. |

39. | J. Mu, H. Zhang, and W.-P. Huang, “A theoretical investigation of slot waveguide Bragg gratings,” IEEE J. Quantum Electron. |

40. | M. W. Pruessner, T. H. Stievater, and W. S. Rabinovich, “Integrated waveguide Fabry-Perot microcavities with silicon/air Bragg mirrors,” Opt. Lett. |

**OCIS Codes**

(130.2790) Integrated optics : Guided waves

(230.5750) Optical devices : Resonators

(230.7380) Optical devices : Waveguides, channeled

(230.4555) Optical devices : Coupled resonators

(270.5585) Quantum optics : Quantum information and processing

**ToC Category:**

Integrated Optics

**History**

Original Manuscript: November 29, 2010

Manuscript Accepted: February 17, 2011

Published: March 21, 2011

**Citation**

Chun-Hsu Su, Mark P. Hiscocks, Brant C. Gibson, Andrew D. Greentree, Lloyd C. L. Hollenberg, and François Ladouceur, "Coupling slot-waveguide cavities for large-scale quantum optical devices," Opt. Express **19**, 6354-6365 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-7-6354

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### References

- R. Feynman, “Simulating physics with computers,” Int. J. Theor. Phys. 21(6-7), 467–488 (1982). [CrossRef]
- I. Buluta and F. Nori, “Quantum simulators,” Science 326(5949), 108–111 (2009). [CrossRef] [PubMed]
- M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2(12), 849–855 (2006). [CrossRef]
- A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. 2(12), 856–861 (2006). [CrossRef]
- D. G. Angelakis, M. F. Santos, and S. Bose, “Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays,” Phys. Rev. A 76(3), 031805 (2007). [CrossRef]
- J. Koch, A. A. Houck, K. L. Hur, and S. M. Girvin, “Time-reversal-symmetry breaking in circuit-QED based photon lattices,” Phys. Rev. A 82(4), 043811 (2010). [CrossRef]
- J. Q. Quach, C.-H. Su, A. M. Martin, A. D. Greentree, and L. C. L. Hollenberg, “A new class of dynamic quantum metamaterials,” http://arxiv.org/abs/1009.4867 (2010).
- S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007). [CrossRef]
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