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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 9 — May. 6, 2013
  • pp: 11037–11047
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Hybrid photonic-plasmonic molecule based on metal/Si disks

Qing Wang, Hang Zhao, Xu Du, Weichun Zhang, Min Qiu, and Qiang Li  »View Author Affiliations


Optics Express, Vol. 21, Issue 9, pp. 11037-11047 (2013)
http://dx.doi.org/10.1364/OE.21.011037


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Abstract

Optical properties of two identical coupled disks forming a “hybrid photonic-plasmonic molecule” are investigated. Each disk is a metal-dielectric structure supporting hybrid plasmonic-photonic whispering-gallery (WG) modes. The WG modes of a molecule split into two groups of nearly-degenerate modes, i.e., bonding and anti-bonding modes. The oscillation of quality factor (Q) with the inter-disk gap d and significant enhancement at certain inter-disk gaps can be observed. An enhanced Q factor of 1821 for a hybrid photonic-plasmonic molecule composed of two 1.2 μm-diameter disks, compared with that for a single disk, is achieved. The corresponding Purcell factor is 191, making the hybrid photonic-plasmonic molecule an optimal choice for subwavelength-scale device miniaturization and light-matter interactions. Moreover, the far-field emission pattern of the hybrid photonic-plasmonic molecule exhibits an enhanced directional light output by tuning the azimuthal mode number for both bonding and anti-bonding modes.

© 2013 OSA

1. Introduction

Photonic molecules composed of a cluster of mutually-coupled optical microcavities have aroused keen interest in the last decade [1

1. M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, “Optical modes in photonic molecules,” Phys. Rev. Lett. 81(12), 2582–2585 (1998). [CrossRef]

]. Conventional configurations of photonic molecules include two or more optical resonators, such as microdisks, microrings, microspheres and point-defect cavities in photonic crystals, etc [2

2. H. Lin, J. H. Chen, S. S. Chao, M. C. Lo, S. D. Lin, and W. H. Chang, “Strong coupling of different cavity modes in photonic molecules formed by two adjacent microdisk microcavities,” Opt. Express 18(23), 23948–23956 (2010). [CrossRef] [PubMed]

12

12. S. V. Boriskina, T. M. Benson, and P. Sewell, “Photonic molecules made of matched and mismatched microcavities: new functionalities of microlasers and optoelectronic components,” Proc. SPIE 6452, 64520X, 64520X-10 (2007). [CrossRef]

]. By playing with the structures and the compositions of the microcavities, photonic molecules can be optimized to exhibit many unique optical properties including light confinements in the wavelength-scale. Therefore, the photonic molecule is regarded as one of key components for a variety of optical applications, such as low-threshold semiconductor microlasers [3

3. E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, “Threshold reduction in a cyclic photonic molecule laser composed of identical microdisks with whispering-gallery modes,” Opt. Lett. 31(7), 921–923 (2006). [CrossRef] [PubMed]

, 12

12. S. V. Boriskina, T. M. Benson, and P. Sewell, “Photonic molecules made of matched and mismatched microcavities: new functionalities of microlasers and optoelectronic components,” Proc. SPIE 6452, 64520X, 64520X-10 (2007). [CrossRef]

, 13

13. L. Shang, L. Liu, and L. Xu, “Single-frequency coupled asymmetric microcavity laser,” Opt. Lett. 33(10), 1150–1152 (2008). [CrossRef] [PubMed]

], optical filters and switches [7

7. J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photon. Technol. Lett. 12(3), 320–322 (2000). [CrossRef]

, 14

14. F. Xia, M. Rooks, L. Sekaric, and Y. Vlasov, “Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects,” Opt. Express 15(19), 11934–11941 (2007). [CrossRef] [PubMed]

, 15

15. A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, “High-order tunable filters based on a chain of coupled crystalline whispering gallery-mode resonators,” IEEE Photon. Technol. Lett. 17(1), 136–138 (2005). [CrossRef]

], information processing [16

16. M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “Quantum many-body phenomena in coupled cavity arrays,” Laser Photon. Rev. 2(6), 527–556 (2008). [CrossRef]

], biochemical sensing [17

17. T. W. Lu and P. T. Lee, “Ultra-high sensitivity optical stress sensor based on double-layered photonic crystal microcavity,” Opt. Express 17(3), 1518–1526 (2009). [CrossRef] [PubMed]

, 18

18. S. V. Boriskina, “Spectrally engineered photonic molecules as optical sensors with enhanced sensitivity: a proposal and numerical analysis,” J. Opt. Soc. Am. B 23(8), 1565–1573 (2006). [CrossRef]

], et al.

Most optical microcavities designed so far are based on dielectric materials. Hence a further size reduction is hindered by the diffraction [19

19. S. V. Boriskina, “Theoretical prediction of a dramatic Q-factor enhancement and degeneracy removal of whispering gallery modes in symmetrical photonic molecules,” Opt. Lett. 31(3), 338–340 (2006). [CrossRef] [PubMed]

21

21. S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Effect of a layered environment on the complex natural frequencies of two-dimensional WGM dielectric-ring resonators,” J. Lightwave Technol. 20(8), 1563–1572 (2002). [CrossRef]

]. Moreover, as the size of a disk cavity decreases, the total internal reflection of the microcavity becomes weak, resulting into an increase in the mode radiation loss and an exponential decrease in the quality factor (Q) [20

20. S. V. Boriskina, “Photonic molecules and spectral engineering,” in Photonic microresonator research and applications, I. Chremmos, O. Schwelb, and N. Uzonoglu, eds. (Springer, New York, 2010).

]. Thus the desire for a high Q and that for device miniaturization seem contradictory. Recently the plasmonic cavities, which are capable of further reducing the mode volume to subwavelength scale while maintaining a relatively high Q due to the effect of surface plasmon polaritons (SPPs), are proposed as an alternative [22

22. J. Yang, C. Sauvan, A. Jouanin, S. Collin, J. L. Pelouard, and P. Lalanne, “Ultrasmall metal-insulator-metal nanoresonators: impact of slow-wave effects on the quality factor,” Opt. Express 20(15), 16880–16891 (2012). [CrossRef]

27

27. Y. Song, J. Wang, M. Yan, and M. Qiu, “Subwavelength hybrid plasmonic nanodisk with high Q factor and Purcell factor,” J. Opt. 13(7), 075001 (2011). [CrossRef]

].

2. The structure of the hybrid photonic-plasmonic molecule

The hybrid photonic-plasmonic molecule consists of two identical 1.2 μm-diameter disks on a silica substrate. As shown in Fig. 1
Fig. 1 Schematic diagram of the hybrid photonic- plasmonic molecule consisting of two disks.
, the disk is a sandwich-like geometry, which is composed of the top silver layer, the middle alumina and the bottom silicon. Numerical simulation based on our home-made three-dimensional finite-difference time-domain (FDTD) code is conducted to model the hybrid photonic-plasmonic molecule [35

35. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966). [CrossRef]

, 36

36. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994). [CrossRef]

]. The total computation domain is 4.4 μm × 4 μm × 1.2 μm along the x, y and z directions. The spatial resolution is 15 nm in the x and y direction and 10 nm in the z direction. The absorbing boundary condition used in the simulation is perfectly matched layers (PMLs). The permittivities of the silica substrate and the silicon layer are εSiO2 = 2.1 and εSi = 11.9, respectively. The lower index layer is alumina with a permittivity of εAl2O3 = 3. The dispersive permittivity of silver is modeled according to the Drude model which is fitted with experimental data [37

37. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

]. The heights of each layer are hSi = 250 nm, hAg = 100 nm and hAl2O3 = 50 nm, respectively. For a practical device, a layer of silica is usually deposited atop to prevent it from oxidizing.

3. Mode splitting in the hybrid photonic-plasmonic molecule

Similar to the photonic molecules, when two hybrid photonic-plasmonic atoms (disks) are brought into proximity, their WG modes will couple and split into two double-degenerate WG modes, i.e., bonding (even) and anti-bonding (odd) modes, depending on symmetry of the mode with respect to the y-axis. If we consider the mode symmetry with respect to the x- axis further, the bonding (even) mode includes x-even/y-even (EE) mode and x-odd/y-even (OE) mode. While for the anti-bonding (odd) mode, it includes x-even/y-odd (EO) mode and x-odd/y-odd (OO) mode. Figure 2
Fig. 2 Mode splitting in a hybrid photonic-plasmonic molecule with an inter-disk gap d = 120 nm. (a) The profiles of the electric field Ez in the x-y plane of bonding (OE, EE) and anti-bonding (OO, EO) modes for m = 8. (b) The profile of the electric field Ez in the x-z plane for EE mode.
illustrates the mode-splitting behavior in a hybrid photonic-plasmonic molecule composed of two 1.2 μm diameter disks. For a single disk, there is a resonant mode with the azimuthal number m = 8 at the wavelength λ = 1025 nm. When the two disks are brought together with an inter-disk gap of d = 120 nm, the single-disk mode splits into red-shifted bonding modes (resonant wavelength λ = 1028 nm (OE) and λ = 1026 nm (EE)) and blue-shifted anti-bonding modes (resonant wavelength λ = 1023 nm (OO) and λ = 1022 nm (EO)). The profile of the dominant electric field component Ez over the x-y plane in the center of the alumina layer is shown in Fig. 2(a). Figure 2(b) shows the profile of the electric field Ez in the x-z plane for EE mode. Most of the electric field is confined within the disk edge of the middle layer, yielding a rather small mode volume.

4. Q factor enhancement of hybrid photonic-plasmonic molecule modes

Veff=ε(x,y,z)|E(x,y,z)|2dxdydzmax{ε(x,y,z)|E(x,y,z)|2}.
(2)

As shown in Fig. 4, the highest Q factor of the hybrid photonic-plasmonic molecule is Q = 1821 at d = 540 nm. Correspondingly, a large Purcell factor FP = 191 can be realized for the hybrid photonic-plasmonic molecule at 1025 nm resonant wavelength. Those properties offered by the hybrid photonic-plasmonic molecule demonstrate a way of reducing the microcavity size to the order of subwavelength scale while maintaining a relatively high Q factor.

5. The far-field pattern from hybrid photonic-plasmonic molecule

High directional radiation and selective mode enhancement are desirable for the applications of microcavities [39

39. S. V. Boriskina, T. M. Benson, P. D. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors in 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175–1182 (2006). [CrossRef]

42

42. S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Q factor and emission pattern control of the WG modes in notched microdisk resonators,” IEEE J. Sel. Top. Quantum Electron. 12(1), 52–58 (2006). [CrossRef]

]. For a single microcavity, the disadvantage of multi-beam emission pattern hinders its further optical applications. When two identical disks are brought into proximity, the far-field emission properties of the hybrid photonic-plasmonic molecule are modified by near-field coupling. The exact emission patterns of the hybrid photonic-plasmonic molecule can be quite different among different WG modes. Appropriate control of the mutual coupling between individual cavities forming the hybrid photonic-plasmonic molecule enables enhancement of the directional emission.

In our FDTD calculation, the whole structure is first enclosed in a cube to collect near-field electromagnetic components at resonant wavelengths. Then the far-field patterns are calculated from the Fourier transformed near-field electromagnetic components based on the Green’s theorem [43

43. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, inc., Norwood, MA, 1995).

]. The observed near-field distributions of the hybrid photonic-plasmonic molecule are analogous to those of multi-dipoles (m = 7 and 8) arranged along the edge of circle disks. Their far-field emission patterns results from the multi-dipoles (m = 7 and 8) of individual disk and the interactions between coupled disks. The radiations from multi-dipoles of individual disk for m = 7 and m = 8 are different. The interactions between coupled disks further complicate the radiation patterns, leading to a substantial difference between the patterns for m = 7 and m = 8.

Figure 6
Fig. 6 The far-field emission patterns of H-plane (a) for the individual disk of WG modes of m = 7, (b), (d) the bonding modes (OE and EE) and (c), (e) the anti-bonding modes (OO and EO) for hybrid photonic-plasmonic molecule.
shows the normalized H-plane emission patterns of the WG modes of m = 7 for individual atom and a hybrid photonic-plasmonic molecule. As for a single disk, there exists multi-beam emission (Fig. 6(a)), while the number of main emission beams decreases in the hybrid photonic-plasmonic molecule. There are main emission beams in the direction of ϕ = 90° and 270° for OE and EE modes, while these beams disappear for OO and EO modes. Meanwhile, there are negligible emission beams in the direction of ϕ = 0° and 180° for OE and OO modes. The far-field emission patterns of the hybrid photonic-plasmonic molecule for m = 8 are shown in Fig. 7
Fig. 7 The far-field emission patterns of H-plane (a) for the individual disk of WG modes of m = 8, (b), (d) the bonding modes (OE and EE) and (c), (e) the anti-bonding modes (OO and EO) for hybrid photonic-plasmonic molecule.
. The emission pattern for a single disk is similar to that of m = 7. In contrast to the case of bonding modes (OE and EE), the anti-bonding modes (OO and EO) have a better directional emission with four main beams of emission shown in Fig. 7(c) and 7(e).

Figure 8
Fig. 8 The far-field emission patterns of E-plane (a) for the individual disk of WG modes of m = 7, (b), (d) the bonding modes (OE and EE) and (c), (e) the anti-bonding modes (OO and EO) for hybrid photonic-plasmonic molecule.
shows the normalized E-plane emission patterns of the WG modes of m = 7 for individual hybrid photonic-plasmonic atom and a hybrid photonic-plasmonic molecule. From Fig. 8, the E-plane emission concentrates mainly in the direction of ϕ = 0° and 180° for the individual disk, OE and EE modes, whereas the electric field emit downward for OO and EO modes. The E-plane emission patterns of m = 8 are shown in Fig. 9
Fig. 9 The far-field emission patterns of E-plane (a) for the individual disk of WG modes of m = 8, (b), (d) the bonding modes (OE and EE) and (c), (e) the anti-bonding modes (OO and EO) for hybrid photonic-plasmonic molecule.
, which shows that the directions of main emission beam slope are unique for the four modes. However, there is no emission energy in the direction of ϕ = 90° and 270° for both a single disk and a hybrid photonic-plasmonic molecule owing to the top silver layer.

The far-field emission patterns of the hybrid photonic-plasmonic molecule can be efficiently manipulated by varying the azimuthal mode number. Furthermore, the emission pattern of OE mode m = 7 shows enhanced directivity in the H-plane.

6. Conclusions

A new type of coupled resonator named “hybrid photonic-plasmonic molecule” comprising of two identical disks is studied. For the molecule, each azimuthal mode can split into two groups of nearly-degenerate modes, i.e., the bonding (OE, EE) and anti-bonding (EO, OO) modes. The coupling strength and shifted resonant wavelength of the two modes decrease with the inter-disk distance. Compared with the photonic molecule, the hybrid photonic-plasmonic molecule can acquire a high Purcell factor 191 accompanied by a Q factor of 1821. Moreover, the far-field emission patterns of the coupling WG modes are investigated. The emission patterns of the hybrid photonic-plasmonic molecule show an enhanced directivity in the H-plane with fewer main beams of emission for both bonding and anti-bonding coupling modes by varying the azimuthal mode number. Compared with photonic molecule geometries, the hybrid photonic-plasmonic molecule cannot only further reduce the cavity size to the subwavelength dimension but also lower the threshold of WG modes lasers, while a high Q factor and a small mode volume are maintained. These capabilities drive its potential applications in a single photon source, laser, optical memory, etc [20

20. S. V. Boriskina, “Photonic molecules and spectral engineering,” in Photonic microresonator research and applications, I. Chremmos, O. Schwelb, and N. Uzonoglu, eds. (Springer, New York, 2010).

, 44

44. M. T. Hill, H. J. Dorren, T. De Vries, X. J. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004). [CrossRef] [PubMed]

]. For example, when a quantum dot is embedded in the hybrid photonic-plasmonic molecule, the optical cavities with increased local density of optical states can enhance the emission rate, which is beneficial for single photon sources [45

45. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vucković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95(1), 013904 (2005). [CrossRef] [PubMed]

].

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant Nos. 61205030, 61275030 and 61235007), the Opened Fund of State Key Laboratory of Advanced Optical Communication Systems and Networks, the Opened Fund of State Key Laboratory on Integrated Optoelectronics, the Fundamental Research Funds for the Central Universities (2012QNA5003), Doctoral Fund of Ministry of Education of China (Grant No 20120101120128), the Swedish Foundation for Strategic Research (SSF) and the Swedish Research Council (VR).

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42.

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Q factor and emission pattern control of the WG modes in notched microdisk resonators,” IEEE J. Sel. Top. Quantum Electron. 12(1), 52–58 (2006). [CrossRef]

43.

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, inc., Norwood, MA, 1995).

44.

M. T. Hill, H. J. Dorren, T. De Vries, X. J. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004). [CrossRef] [PubMed]

45.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vucković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95(1), 013904 (2005). [CrossRef] [PubMed]

OCIS Codes
(230.4555) Optical devices : Coupled resonators
(250.5403) Optoelectronics : Plasmonics
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Integrated Optics

History
Original Manuscript: March 12, 2013
Revised Manuscript: April 23, 2013
Manuscript Accepted: April 24, 2013
Published: April 29, 2013

Citation
Qing Wang, Hang Zhao, Xu Du, Weichun Zhang, Min Qiu, and Qiang Li, "Hybrid photonic-plasmonic molecule based on metal/Si disks," Opt. Express 21, 11037-11047 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-9-11037


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