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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 20 — Sep. 24, 2012
  • pp: 22372–22382
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Giant transverse optical forces in nanoscale slot waveguides of hyperbolic metamaterials

Yingran He, Sailing He, Jie Gao, and Xiaodong Yang  »View Author Affiliations


Optics Express, Vol. 20, Issue 20, pp. 22372-22382 (2012)
http://dx.doi.org/10.1364/OE.20.022372


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Abstract

Here we demonstrate that giant transverse optical forces can be generated in nanoscale slot waveguides of hyperbolic metamaterials, with more than two orders of magnitude stronger compared to the force created in conventional silicon slot waveguides, due to the nanoscale optical field enhancement and the extreme optical energy compression within the air slot region. Both numerical simulation and analytical treatment are carried out to study the dependence of the optical forces on the waveguide geometries and the metamaterial permittivity tensors, including the attractive optical forces for the symmetric modes and the repulsive optical forces for the anti-symmetric modes. The significantly enhanced transverse optical forces result from the strong optical mode coupling strength between two metamaterial waveguides, which can be explained with an explicit relation derived from the coupled mode theory. Moreover, the calculation on realistic metal-dielectric multilayer structures indicates that the predicted giant optical forces are achievable in experiments, which will open the door for various optomechanical applications in nanoscale, such as optical nanoelectromechanical systems, optical sensors and actuators.

© 2012 OSA

1. Introduction

Optical forces arising from the gradient of light field have been extensively employed to realize exciting applications for light-matter interactions, such as optical amplification and cooling of mechanical modes [1

1. T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008). [CrossRef] [PubMed]

], actuation of nanophotonic structures [2

2. M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008). [CrossRef] [PubMed]

4

4. M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3(8), 464–468 (2009). [CrossRef]

], optomechanical wavelength and energy conversion [5

5. M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical wavelength and energy conversion in high-Q double-layer cavities of photonic crystal slabs,” Phys. Rev. Lett. 97(2), 023903 (2006). [CrossRef] [PubMed]

], and optical trapping and transport of nanoparticles and biomolecules [6

6. S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10(1), 99–104 (2010). [CrossRef] [PubMed]

, 7

7. A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009). [CrossRef] [PubMed]

]. It has been shown that optical forces can be remarkably enhanced with coupled high-Q optical resonators where the circulating optical power is considerably amplified due to the long photon lifetime [8

8. M. L. Povinelli, S. G. Johnson, M. Lonèar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering-gallery- mode resonators,” Opt. Express 13(20), 8286–8295 (2005). [CrossRef] [PubMed]

, 9

9. G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009). [CrossRef] [PubMed]

]. Besides, such gradient optical forces can also be significantly enhanced through the compression of optical energy into deep subwavelength scale. Recently, strongly enhanced optical forces have been obtained in dielectric slot waveguides [10

10. 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]

, 11

11. M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett. 30(22), 3042–3044 (2005). [CrossRef] [PubMed]

] and hybrid plasmonic waveguides [12

12. X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett. 11(2), 321–328 (2011). [CrossRef] [PubMed]

]. Since the optical field enhancement is proportional to the index-contrast at the slot interfaces, a material with a higher refractive index is desirable to further boost the optical force in slot waveguide structures. Metamaterials can be carefully designed to exhibit ultrahigh refractive indices [13

13. J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005). [CrossRef] [PubMed]

15

15. M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011). [CrossRef] [PubMed]

], which are not available in naturally occurring materials at optical frequencies. Especially, hyperbolic metamaterials constructed with metal-dielectric multilayers supports huge wave vectors and therefore also ultrahigh refractive indices, due to the extreme anisotropy of permittivity tensor [16

16. Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006). [CrossRef] [PubMed]

19

19. Y. He, S. He, J. Gao, and X. Yang, “Nanoscale metamaterial optical waveguides with ultrahigh refractive indices,” J. Opt. Soc. Am. B 29(9), 2559–2566 (2012). [CrossRef]

].

In this paper, we will demonstrate that the transverse optical forces in slot waveguides of hyperbolic metamaterials can be over two orders of magnitude stronger than that in conventional dielectric slot waveguides [11

11. M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett. 30(22), 3042–3044 (2005). [CrossRef] [PubMed]

]. The mechanism of such optical force enhancement will be investigated both numerically using Maxwell’s stress tensor integration, and analytically using a 2D approximation of the 3D slot waveguide system. Moreover, the relation between the optical force and the waveguide mode coupling strength is derived based on the coupled mode theory analysis [20

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

]. The comprehensive understanding of the enhanced transverse optical forces in metamaterial slot waveguides will be very useful for nanoscale optomechanical applications, such as optical tweezers [21

21. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970). [CrossRef]

, 22

22. S. Chu, “Laser manipulation of atoms and particles,” Science 253(5022), 861–866 (1991). [CrossRef] [PubMed]

], optomechanical device actuation [23

23. H. Cai, K. J. Xu, A. Q. Liu, Q. Fang, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Nano-opto-mechanical actuator driven by gradient optical force,” Appl. Phys. Lett. 100(1), 013108 (2012). [CrossRef]

] and sensitive mechanical sensors [24

24. G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Riviere, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009). [CrossRef]

].

2. Deep mode confinement and giant optical force

Figure 1(a)
Fig. 1 (a) The schematic of nanoscale slot waveguides of hyperbolic metamaterials. Giant transverse optical forces are expected to occur due to the strong coupling between the two waveguides. (b) The dependence of the effective permittivity tensor on the silver filling ratio fm. (c) The effective refractive indices along the propagation direction neff,z and (d) the propagation length Lm for slot waveguide modes as functions of gap sizes g. In (c) and (d), Ma, Ms and M0 represent the anti-symmetric mode, the symmetric mode and the unperturbed mode of an individual waveguide, respectively.
shows the schematic of the hyperbolic metamaterial slot waveguides. Two identical waveguides with width Lx = 40 nm and height Ly = 30 nm are separated with a nanoscale air gap g along the y direction. In each waveguide, the metamaterial is constructed with alternative thin layers of silver (Ag) and germanium (Ge). The multilayer metamaterial can be regarded as a homogeneous effective medium and the principle components of the permittivity tensor can be determined from the effective medium theory (EMT) [25

25. J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89(26), 261102 (2006). [CrossRef]

]
εx=εz=fmεm+(1fm)εd,εy=εmεdfmεd+(1fm)εm
(1)
where fm is the volume filling ratio of silver, εd and εm are the permittivity of germanium and silver, respectively. εd = 16, and εm(ω) = ε-ωp2/(ω2 + iωγ) from the Drude model, with a background dielectric constant ε = 5, plasma frequency ωp = 1.38 × 1016 rad/s and collision frequency γ = 5.07 × 1013 rad/s. Figure 1(b) shows the dependence of the permittivity tensor on the silver filling ratio fm at the telecom wavelength λ0 = 1.55 μm. All the components of the permittivity tensor will grow in magnitude as the filling ratio increases. For instance, the permittivity tensors of hyperbolic metamaterial are εy = 29.2 + 0.12i, εx = εz = −39.8 + 2.1i for fm = 0.4, and εy = 76.3 + 1.4i, εx = εz = −81.7 + 3.6i for fm = 0.7, respectively. It should be noted that the wavelength λ0 = 1.55 μm is merely used as an example throughout the paper, and this design can actually work in a broadband frequency range due to the non-resonant nature of hyperbolic metamaterials [26

26. Y. Liu, G. Bartal, and X. Zhang, “All-angle negative refraction and imaging in a bulk medium made of metallic nanowires in the visible region,” Opt. Express 16(20), 15439–15448 (2008). [CrossRef] [PubMed]

].

The strong mode coupling between the two closely spaced waveguides will generate mode splitting of the individual waveguide mode and result in two eigenmodes; one is the symmetric mode (denoted by Ms) and the other is the anti-symmetric mode (denoted by Ma). Both of the two modes are TM-like (in which Hx, Ey and Ez components are dominant), so an incident light with Ey polarization is necessary to efficiently excite these two modes. The effective indices neff,zkz/k0 and the propagation length Lm ≡ 1/2Im(kz) corresponding to the two eigenmodes are obtained by finite-element method (FEM) with the software package COMSOL (where k0 is the wave vector in free space and kz is the wave vector along the propagation direction z). Figure 1(c) and (d) show that the dependences of neff,z and Lm on the gap sizes are distinct for the two eigenmodes. As the gap size g shrinks, neff,z grows dramatically for mode Ms but decreases slightly for mode Ma. In fact, the magnitude of the effective index variation is equivalent to the mode coupling strength between two identical waveguides [12

12. X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett. 11(2), 321–328 (2011). [CrossRef] [PubMed]

], and therefore the distinguished variations of effective indices for two eigenmodes imply a strong coupling strength for mode Ms and a weak coupling strength for mode Ma. Furthermore, the opposite effective index variations for two eigenmodes indicate an attractive force for mode Ms and a repulsive force for mode Ma. The propagation length Lm decreases for mode Ms and increases for mode Ma as the gap size gets narrower, due to the tradeoff between the optical mode confinement and the propagation loss. The effective index and the propagation length for the unperturbed mode of the individual waveguide are shown in Fig. 1(c) and (d) for comparison (denoted by M0).

The optical mode profiles of field components Ey, Hx and Sz for slot waveguides with g = 10 nm are shown in Fig. 2
Fig. 2 The 2D optical mode profiles of (a) Ey, (b) Hx and (c) Sz for metamaterial slot waveguide with g = 10 nm. The crossing line plots along x = 0 are also shown for clarity. In each panel, the optical mode profiles for the symmetric mode Ms are plotted at the top and the profiles for the anti-symmetric mode Ma are plotted at the bottom.
. As can be seen from Fig. 2(a), distinct behaviors in electric field Ey are obtained for modes Ms and Ma, where a strong (weak) electric field is localized in the gap region for Ms (Ma) mode. It has been proposed that the optical field could be tightly confined and greatly enhanced in the nanoscale slot region due to the large discontinuity of normal electric fields (Ey in our case) at the high-index-contrast interface [10

10. 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]

]. Here we demonstrate that strong optical field confinement is achievable in the slot region for the symmetric modes, due to the constructively interfered electric field. While for the anti-symmetric modes, weak optical field confinement is obtained in the slot region. Figure 2(b) shows that the magnetic fields are always tightly confined within the hyperbolic metamaterials for both eigenmodes due to the absence of magnetic response for the metamaterials at an optical frequency. Accordingly, a large amount of energy flow is guided in the slot region for the symmetric mode, while a negligible amount of energy is confined in the slot region for the anti-symmetric mode [see Fig. 2(c)].

Figure 3
Fig. 3 The calculated effective refractive indices neff,z and optical forces fopt in metamaterial slot waveguides with different gap sizes g, (a) and (b) for the symmetric modes, and (c) and (d) for the anti-symmetric modes. Results from FEM simulations (FEM) are plotted in solid lines, and results from 2D coupled slab waveguide approximation (Slab Appr.) are plotted in the dashed lines. Two waveguide heights Ly = 30 nm and Ly = 80 nm are shown for comparison.
shows the effective indices neff,z and the optical forces through the integration of Maxwell’s stress tensor for both the symmetric mode and the anti-symmetric mode. neff,z for the symmetric mode increases noticeably as the gap size shrinks [see Fig. 3(a)], implying a strong mode coupling strength between the two waveguides. Accordingly, the attractive optical force for the symmetric mode grows dramatically with the decreased gap sizes, resulting in optical forces up to 8 nNμm−1mW−1 for Ly = 30 nm and 4 nNμm−1mW−1 for Ly = 80 nm [see Fig. 3(b)], over two orders of magnitude larger than that in a dielectric slot waveguide [11

11. M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett. 30(22), 3042–3044 (2005). [CrossRef] [PubMed]

]. On the contrary, neff,z for the anti-symmetric modes show negligible variation with gap sizes [see Fig. 3(c)], so that the repulsive optical forces for the anti-symmetric modes just increase slightly when the gap size shrinks [see Fig. 3(d)]. As a result, optical forces for the anti-symmetric mode are much weaker than that of symmetric modes, in sharp contrast to the case in dielectric slot waveguides, where the optical forces for the symmetric mode and the anti-symmetric mode are comparable in magnitude [4

4. M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3(8), 464–468 (2009). [CrossRef]

, 11

11. M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett. 30(22), 3042–3044 (2005). [CrossRef] [PubMed]

, 28

28. W. H. P. Pernice, M. Li, K. Y. Fong, and H. X. Tang, “Modeling of the optical force between propagating lightwaves in parallel 3D waveguides,” Opt. Express 17(18), 16032–16037 (2009). [CrossRef] [PubMed]

]. It is the strong interaction between the two waveguides that leads to the distinct mode coupling strengths and the distinguished optical forces obtained from the two eigenmodes. Furthermore, stronger optical forces are achieved in slot waveguides with a smaller cross section, for both the symmetric modes and the anti-symmetric modes, due to larger effective indices and thus stronger mode coupling strength.

3. Mode coupling analysis

After substituting the optical fields into the Maxwell’s stress tensor and taking into account that neff,z = kz/k0 >> 1, we obtain the following analytical expression for the optical forces in the slot waveguides of hyperbolic metamaterials:
fopt12cLyneff,z1εy+|εz|sinh2(γg2),symmetricmodefopt12cLyneff,z|εz|cosh2(γg2),anti-symmetricmode
(4)
where c is the speed of light in vacuum. Figure 3 also plots the analytically derived effective indices neff,z and optical forces fopt, which match the numerical FEM simulation results quite well. The critical dependence of the optical forces on the gap size g can be explained using Eq. (4). The constructive (destructive) interference of exponentially decayed evanescent optical fields in the slot region gives rise to hyperbolic-sine-function (hyperbolic-cosine-function) dependence on gap sizes, resulting in strong (weak) transverse optical forces for the symmetric (anti-symmetric) modes as the gap size gets small. When the gap sizes becomes larger (g > 20 nm), the two waveguides can only couple weakly with each other through the tails of the evanescent optical fields, so that fopt becomes quite weak for both eigenmodes. According to Eq. (4), the waveguide height Ly, the mode indices neff,z and the permittivity εy and εz also affect the magnitude of optical forces.

4. Broadband operation

In contrast to the metamaterials based on electric or magnetic resonances, the hyperbolic metamaterial based on metal-dielectric multilayer structure is intrinsically non-resonant and thus can support giant optical transverse force in a broad wavelength range. As shown in Fig. 6(a)
Fig. 6 The variation of optical forces fopt as the operating wavelength λ0 changes, where (a) and (b) correspond to the cases of the symmetric modes and the anti-symmetric modes, respectively.
, giant optical forces are obtained for the symmetric modes with operating wavelength λ0 from 1 μm to 2 μm, which verify the broadband nature of our design. The optical forces for the anti-symmetric modes are relatively weak and drop very fast as the operating wavelength increases [Fig. 6(b)].

5. Realistic multilayer structures

Finally, a realistic hyperbolic metamaterial slot waveguide is constructed using alternative silver and germanium layers with a period of 10 nm and a silver filling ratio of fm = 0.4. The comparison between the multilayer structures and the ideal effective medium is shown in Fig. 7
Fig. 7 The calculated effective refractive indices neff,z and optical forces fopt on the realistic metal-dielectric multilayer structures (in diamonds) with the layer pitch of 10 nm and the filling ratio of 0.4 at different gap sizes, (a) and (b) for the symmetric modes and (c) and (d) for the anti-symmetric modes. Results from ideal effective medium theory (EMT) are plotted in solid lines for comparison.
. With the height of Ly = 80 nm, the slot waveguides of multilayer structures can reproduce the results of the effective indices neff,z and the optical forces fopt calculated based on the waveguides of ideal effective media, for both the symmetric modes and the anti-symmetric modes. While with Ly = 30 nm, both neff,z and fopt become smaller than the results of the effective media calculation, which is due to that the large wave vector along the y direction becomes close to the Brillouin zone of periodic multilayer structures, so that the waveguide mode profiles begin to deviate from those predicted from the effective medium theory.

Considering that a realistic hyperbolic metamaterial from metal-dielectric multilayer structure is always lossy due to the energy dissipation in metal, the optical force will gradually decrease along the propagation direction for a certain incident optical power. Specifically, the optical force can be expressed as fopt(z) = fopt(z = 0)∙exp[-2Im(neff,z)k0z], where the optical force is normalized to the incident optical power at z = 0 [12

12. X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett. 11(2), 321–328 (2011). [CrossRef] [PubMed]

]. However, the optical force is still considerably strong even if the energy dissipation is taken into account.

6. Conclusions

In conclusion, we have demonstrated giant transverse optical forces up to 8 nNμm−1mW−1 in nanoscale slot waveguides of hyperbolic metamaterials, due to the strong optical field confinement and extreme optical energy compression within the air slot region. The influences of the waveguide geometries and the metal filling ratios of the hyperbolic metamaterials on both the symmetric modes and the anti-symmetric modes are studied numerically using the Maxwell stress tensor integration method, together with an analytical approach using a 2D approximation of the 3D coupled waveguides. Furthermore, the relation between the transverse optical forces and the waveguide mode coupling strength is derived from the coupled mode theory, revealing the mechanism of optical force enhancement in slot waveguide system. Finally, it is shown that the predicted giant optical force is achievable in realistic metal-dielectric multilayer structures. The strongly enhanced optical forces in slot waveguides of hyperbolic metamaterial will open a new realm in many exciting nanoscale optomechanical applications.

Acknowledgments

This work was partially supported by the Department of Mechanical and Aerospace Engineering, the Materials Research Center, the Intelligent Systems Center, and the Energy Research and Development Center at Missouri S&T, the University of Missouri Research Board, the Ralph E. Powe Junior Faculty Enhancement Award, and the National Natural Science Foundation of China (61178062 and 60990322).

References and links

1.

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008). [CrossRef] [PubMed]

2.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008). [CrossRef] [PubMed]

3.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009). [CrossRef] [PubMed]

4.

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3(8), 464–468 (2009). [CrossRef]

5.

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical wavelength and energy conversion in high-Q double-layer cavities of photonic crystal slabs,” Phys. Rev. Lett. 97(2), 023903 (2006). [CrossRef] [PubMed]

6.

S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett. 10(1), 99–104 (2010). [CrossRef] [PubMed]

7.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009). [CrossRef] [PubMed]

8.

M. L. Povinelli, S. G. Johnson, M. Lonèar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering-gallery- mode resonators,” Opt. Express 13(20), 8286–8295 (2005). [CrossRef] [PubMed]

9.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009). [CrossRef] [PubMed]

10.

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]

11.

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett. 30(22), 3042–3044 (2005). [CrossRef] [PubMed]

12.

X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett. 11(2), 321–328 (2011). [CrossRef] [PubMed]

13.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005). [CrossRef] [PubMed]

14.

J. Shin, J.-T. Shen, and S. Fan, “Three-dimensional metamaterials with an ultrahigh effective refractive index over a broad bandwidth,” Phys. Rev. Lett. 102(9), 093903 (2009). [CrossRef] [PubMed]

15.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011). [CrossRef] [PubMed]

16.

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006). [CrossRef] [PubMed]

17.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007). [CrossRef] [PubMed]

18.

J. Yao, X. Yang, X. Yin, G. Bartal, and X. Zhang, “Three-dimensional nanometer-scale optical cavities of indefinite medium,” Proc. Natl. Acad. Sci. U.S.A. 108(28), 11327–11331 (2011). [CrossRef] [PubMed]

19.

Y. He, S. He, J. Gao, and X. Yang, “Nanoscale metamaterial optical waveguides with ultrahigh refractive indices,” J. Opt. Soc. Am. B 29(9), 2559–2566 (2012). [CrossRef]

20.

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

21.

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970). [CrossRef]

22.

S. Chu, “Laser manipulation of atoms and particles,” Science 253(5022), 861–866 (1991). [CrossRef] [PubMed]

23.

H. Cai, K. J. Xu, A. Q. Liu, Q. Fang, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Nano-opto-mechanical actuator driven by gradient optical force,” Appl. Phys. Lett. 100(1), 013108 (2012). [CrossRef]

24.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Riviere, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009). [CrossRef]

25.

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89(26), 261102 (2006). [CrossRef]

26.

Y. Liu, G. Bartal, and X. Zhang, “All-angle negative refraction and imaging in a bulk medium made of metallic nanowires in the visible region,” Opt. Express 16(20), 15439–15448 (2008). [CrossRef] [PubMed]

27.

J. D. Jackson, Classical electrodynamics (Wiley, New York, 1999).

28.

W. H. P. Pernice, M. Li, K. Y. Fong, and H. X. Tang, “Modeling of the optical force between propagating lightwaves in parallel 3D waveguides,” Opt. Express 17(18), 16032–16037 (2009). [CrossRef] [PubMed]

29.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008). [CrossRef]

OCIS Codes
(230.7370) Optical devices : Waveguides
(160.3918) Materials : Metamaterials
(250.5403) Optoelectronics : Plasmonics
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Metamaterials

History
Original Manuscript: June 15, 2012
Revised Manuscript: August 29, 2012
Manuscript Accepted: August 30, 2012
Published: September 14, 2012

Citation
Yingran He, Sailing He, Jie Gao, and Xiaodong Yang, "Giant transverse optical forces in nanoscale slot waveguides of hyperbolic metamaterials," Opt. Express 20, 22372-22382 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-20-22372


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References

  1. T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science321(5893), 1172–1176 (2008). [CrossRef] [PubMed]
  2. M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature456(7221), 480–484 (2008). [CrossRef] [PubMed]
  3. M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature459(7246), 550–555 (2009). [CrossRef] [PubMed]
  4. M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics3(8), 464–468 (2009). [CrossRef]
  5. M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical wavelength and energy conversion in high-Q double-layer cavities of photonic crystal slabs,” Phys. Rev. Lett.97(2), 023903 (2006). [CrossRef] [PubMed]
  6. S. Mandal, X. Serey, and D. Erickson, “Nanomanipulation using silicon photonic crystal resonators,” Nano Lett.10(1), 99–104 (2010). [CrossRef] [PubMed]
  7. A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature457(7225), 71–75 (2009). [CrossRef] [PubMed]
  8. M. L. Povinelli, S. G. Johnson, M. Lonèar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering-gallery- mode resonators,” Opt. Express13(20), 8286–8295 (2005). [CrossRef] [PubMed]
  9. G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature462(7273), 633–636 (2009). [CrossRef] [PubMed]
  10. 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]
  11. M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett.30(22), 3042–3044 (2005). [CrossRef] [PubMed]
  12. X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett.11(2), 321–328 (2011). [CrossRef] [PubMed]
  13. J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett.94(19), 197401 (2005). [CrossRef] [PubMed]
  14. J. Shin, J.-T. Shen, and S. Fan, “Three-dimensional metamaterials with an ultrahigh effective refractive index over a broad bandwidth,” Phys. Rev. Lett.102(9), 093903 (2009). [CrossRef] [PubMed]
  15. M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature470(7334), 369–373 (2011). [CrossRef] [PubMed]
  16. Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express14(18), 8247–8256 (2006). [CrossRef] [PubMed]
  17. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science315(5819), 1686 (2007). [CrossRef] [PubMed]
  18. J. Yao, X. Yang, X. Yin, G. Bartal, and X. Zhang, “Three-dimensional nanometer-scale optical cavities of indefinite medium,” Proc. Natl. Acad. Sci. U.S.A.108(28), 11327–11331 (2011). [CrossRef] [PubMed]
  19. Y. He, S. He, J. Gao, and X. Yang, “Nanoscale metamaterial optical waveguides with ultrahigh refractive indices,” J. Opt. Soc. Am. B29(9), 2559–2566 (2012). [CrossRef]
  20. W.-P. Huang, “Coupled-mode theory for optical waveguides: an overview,” J. Opt. Soc. Am. A11(3), 963–983 (1994). [CrossRef]
  21. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett.24(4), 156–159 (1970). [CrossRef]
  22. S. Chu, “Laser manipulation of atoms and particles,” Science253(5022), 861–866 (1991). [CrossRef] [PubMed]
  23. H. Cai, K. J. Xu, A. Q. Liu, Q. Fang, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Nano-opto-mechanical actuator driven by gradient optical force,” Appl. Phys. Lett.100(1), 013108 (2012). [CrossRef]
  24. G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Riviere, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys.5(12), 909–914 (2009). [CrossRef]
  25. J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett.89(26), 261102 (2006). [CrossRef]
  26. Y. Liu, G. Bartal, and X. Zhang, “All-angle negative refraction and imaging in a bulk medium made of metallic nanowires in the visible region,” Opt. Express16(20), 15439–15448 (2008). [CrossRef] [PubMed]
  27. J. D. Jackson, Classical electrodynamics (Wiley, New York, 1999).
  28. W. H. P. Pernice, M. Li, K. Y. Fong, and H. X. Tang, “Modeling of the optical force between propagating lightwaves in parallel 3D waveguides,” Opt. Express17(18), 16032–16037 (2009). [CrossRef] [PubMed]
  29. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008). [CrossRef]

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