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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 18 — Sep. 9, 2013
  • pp: 20900–20910
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Surface phonon-polariton enhanced optical forces in silicon carbide nanostructures

Dongfang Li, Nabil M. Lawandy, and Rashid Zia  »View Author Affiliations


Optics Express, Vol. 21, Issue 18, pp. 20900-20910 (2013)
http://dx.doi.org/10.1364/OE.21.020900


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Abstract

The enhanced optical forces induced by surface phonon-polariton (SPhP) modes are investigated in different silicon carbide (SiC) nanostructures. Specifically, we calculate optical forces using the Maxwell stress tensor for three different geometries: spherical particles, slab waveguides, and rectangular waveguides. We show that SPhP modes in SiC can produce very large forces, more than one order of magnitude larger than the surface plasmon-polariton (SPP) forces in analogous metal nanostructures. The material and geometric basis for these large optical forces are examined in terms of dispersive permittivity, separation distance, and operating wavelength.

© 2013 OSA

1. Introduction

Optomechanical devices [1

1. D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics 4(4), 211–217 (2010). [CrossRef]

, 2

2. J. Ma and M. L. Povinelli, “Applications of optomechanical effects for on-chip manipulation of light signals,” Curr. Opin. Solid State Mater. Sci. 16(2), 82–90 (2012). [CrossRef]

], especially those leveraging the optical forces produced by guide modes in photonic waveguides [3

3. 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]

6

6. 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]

], have attracted great interest. In this context, the surface plasmon-polariton (SPP) enhanced optical forces in metal nanostructures have been thoroughly investigated in both theoretical [7

7. L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79(4), 645–648 (1997). [CrossRef]

21

21. A. Bonakdar, J. Kohoutek, D. Dey, and H. Mohseni, “Optomechanical nanoantenna,” Opt. Lett. 37(15), 3258–3260 (2012). [CrossRef] [PubMed]

] and experimental [22

22. V. Garcés-Chávez, R. Quidant, P. J. Reece, G. Badenes, L. Torner, and K. Dholakia, “Extended organization of colloidal microparticles by surface plasmon polariton excitation,” Phys. Rev. B 73(8), 085417 (2006). [CrossRef]

31

31. K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, “Trapping and rotating nanoparticles using a plasmonic nano-tweezer with an integrated heat sink,” Nat. Commun. 2, 469 (2011). [CrossRef] [PubMed]

] studies. (For a detailed review of surface plasmon forces in the context of optical tweezers, see [29

29. M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011). [CrossRef]

].) Similar to SPP modes supported by metals, polar dielectrics support surface phonon-polariton (SPhP) modes that can be used to guide and concentrate intense electromagnetic energy, creating a strong enhancement of optical forces. The investigation of SPhP enhanced optical forces may allow the extension of optomechanical devices into new material systems and frequency regimes.

For example, silicon carbide (SiC) materials are widely used for their exceptional electronic, mechanical, and thermal properties. SiC is an important semiconductor with a large band gap and high thermal conductivity. Given its high Young's modulus to density ratio [32

32. M. F. Ashby, Materials Selection in Mechanical Design (Butterworth-Heinemann, 2005).

], SiC is an ideal material for high frequency mechanical resonators, and it has been explored for applications in nano-electro-mechanical systems (NEMS) [33

33. Y. T. Yang, K. L. Ekinci, X. M. H. Huang, L. M. Schiavone, M. L. Roukes, C. A. Zorman, and M. Mehregany, “Monocrystalline silicon carbide nanoelectromechanical systems,” Appl. Phys. Lett. 78(2), 162–164 (2001). [CrossRef]

35

35. S. C. Jun, J. H. Cho, W. K. Kim, Y. M. Jung, S. Hwang, S. Shin, J. Y. Kang, J. Shin, I. Song, J. Y. Choi, S. Lee, and J. M. Kim, “Resonance properties of 3C-SiC nanoelectromechanical resonator in room-temperature magnetomotive transduction,” IEEE Electron Device Lett. 30(10), 1042–1044 (2009). [CrossRef]

]. SiC also exhibits unique optical properties that may make it ideally suited for optomechanical devices. As a polar dielectric, SiC supports strong SPhP resonances in the infrared region around 11 μm [36

36. H. Mutschke, A. C. Andersen, D. Clement, T. Henning, and G. Peiter, “Infrared properties of SiC particles,” Astron. Astrophys. 345, 187–202 (1999).

]. These resonances have been the topic of considerable study in the near-field and nano-optics community for applications in high-resolution infrared microscopy [37

37. R. Hillenbrand, T. Taubner, and F. Keilmann, “Phonon-enhanced light matter interaction at the nanometre scale,” Nature 418(6894), 159–162 (2002). [CrossRef] [PubMed]

, 38

38. T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313(5793), 1595–1595 (2006). [CrossRef] [PubMed]

], coherent thermal emission [39

39. J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. P. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416(6876), 61–64 (2002). [CrossRef] [PubMed]

], thermal radiation microscopy [40

40. Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. A. Lemoine, K. Joulain, J. P. Mulet, Y. Chen, and J. J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444(7120), 740–743 (2006). [CrossRef] [PubMed]

], thermal optical antennas [41

41. J. A. Schuller, T. Taubner, and M. L. Brongersma, “Optical antenna thermal emitters,” Nat. Photonics 3(11), 658–661 (2009). [CrossRef]

], and dielectric metamaterials [42

42. J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99(10), 107401 (2007). [CrossRef] [PubMed]

]. Compared to flexible and lossy metals, SiC has a considerably higher Young's modulus and lower optical damping constant. The longer wavelength SPhPs in SiC can also induce stronger coupling and larger optical forces for similarly sized structures.

To highlight the similarities and differences between the optical properties of SiC and metallic materials, the plots in Figs. 1(a)
Fig. 1 Comparison of the (a) real and (b) imaginary parts of the relative permittivity for Au in visible range and 6H-SiC in the direction perpendicular to the principal axis around 11 μm.
and 1(b) show the complex permittivity for SiC and gold (Au). In particular, we plot the frequency-dependent relative permittivity εr(ω) of 6H-SiC in the direction perpendicular to the principal axis [36

36. H. Mutschke, A. C. Andersen, D. Clement, T. Henning, and G. Peiter, “Infrared properties of SiC particles,” Astron. Astrophys. 345, 187–202 (1999).

] around 11 µm, and we compare this to the relative permittivity of Au in the visible range [43

43. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998). [CrossRef] [PubMed]

]. (For simplicity throughout this paper, we model SiC as an isotropic material with the complex permittivity shown here and, therefore, neglect the minor variations in SiC optical properties due to polytype and orientation.) Note that the real parts of the relative permittivity Re{εr(ω)} for Au and SiC are comparable over these two different spectral regimes. However, the imaginary part Im{εr(ω)} of SiC is significantly smaller than that of Au. This suggests that SiC nanostructures can support infrared SPhP modes that are very similar to the visible SPP modes of Au nanostructures, but with substantially lower optical losses.

In this paper, we examine the optical forces arising from SiC SPhP modes and Au SPP modes in three different geometries. First, under the quasistatic approximation, we calculate the optical forces between two spherical particles and investigate the effect of the complex permittivity. Next, the optical forces between two slab waveguides are simulated, from which the effect of the operating wavelength is studied and an approximate analytical explanation is derived. Finally, we calculate the optical forces in a more practical structure consisting of two free standing rectangular waveguides. Our simulation results show that the optical forces in SiC nanostructures are more than one order of magnitude stronger than those in similar Au nanostructures.

2. Simulation methods and results

2.1 Attractive optical forces between two spherical particles

First, we investigate the optical force between two spherical particles with identical radius r0 = 30 nm in an external electric fieldE=E0eiωtz^. As shown in the inset of Fig. 2(a)
Fig. 2 (a) Magnitude of the attractive optical forces versus relative permittivity for a fixed gap width of 100 nm, r0 = 30 nm, and incident power intensity of 1 kW/cm2. The inset shows a sketch of the two spherical particles system. Dashed lines show the relative permittivity of Au (black) and SiC (red). (b) Attractive optical forces calculated for two Au and two SiC spheres.
, the two spheres are placed in free space a distance 2d apart from each other along the z-axis such that there is a small gap width (w = 2d2r0) between them.

We consider the case where the sphere radius is much smaller than the operating wavelength (r0λ0), whereby retardation effects can be neglected and the problem becomes quasistatic. In this scenario, the two spheres will be polarized along the z-axis due to the displacement in opposite directions of positively-charged Si and negatively-charged C sites, inducing an attractive force between the two spheres.

In the quasistatic limit, the Helmholtz wave equation reduces to Laplace’s equation. Following the method used by Aravind et al. [44

44. P. K. Aravind, A. Nitzan, and H. Metiu, “The interaction between electromagnetic resonances and its role in spectroscopic studies of molecules adsorbed on colloidal particles or metal spheres,” Surf. Sci. 110(1), 189–204 (1981). [CrossRef]

], a general solution to Laplace’s equation can be obtained by separation of variables for the two-particle system in bispherical coordinates (µ, η, φ). In this coordinate system, the constant μ0=±sinh1(d2r02/r0) defines spherical shells with radius r0 centered a distance d from the origin along the z-axis. Using the Maxwell stress tensor (MST), the force expression can be written as [9

9. A. J. Hallock, P. L. Redmond, and L. E. Brus, “Optical forces between metallic particles,” Proc. Natl. Acad. Sci. U.S.A. 102(5), 1280–1284 (2005). [CrossRef] [PubMed]

]:
F=TdS=z^ε0π0πsin(η)(cosh(μ0)cos(η)1)4(cosh(μ0)cos(η))2(n=0nmaxXnm=0mmaxXm*)dη.
(1)
Xn=e(n+12)μ0An0[(2n+1)(cos(η)cosh(μ0))sinh(μ0)]+e(n+12)μ0[2cE02π(2n+1)+An0][(2n+1)(cos(η)cosh(μ0))+sinh(μ0)],
(2)
where Tis the MST, Sis the surface of the sphere defined by μ0, An0are the expansion coefficients in the potential expression of the surrounding environment ϕ=E0z+cosh(μ)cos(η)n=0[An0e(n+1/2)μAn0e(n+1/2)μ]Yn0(η,φ), ε0 is the vacuum permittivity, and nmax and mmax are the cutoff numbers for the respective summations. Here, we use nmax = mmax = 40, which is sufficient to confirm convergence of the summations.

In addition to a fixed gap width, we also investigated the optical forces as a function of varying gap width. These calculations were performed at four different infrared wavelengths for SiC and four corresponding wavelengths for Au, in which Re{εr(ω)} are equal but Im{εr(ω)} differs. The inset of Fig. 3
Fig. 3 Optical forces between two identical spherical particles with radius 30 nm versus gap width. Incident power intensity is 1 kW/cm2. The inset shows the optical forces for small gap widths. Dashed lines show the optical forces calculated for Au particles for illumination wavelengths of 476.5 nm (black), 501 nm (green), 543 nm (blue), and 637 nm (red). Solid lines show the optical forces calculated for SiC particles for illumination wavelengths of 10.73 μm (black), 10.88 μm (green), 11.12 μm (blue), and 11.5 μm (red).
shows that at short gap widths (w < 30 nm) for certain values of relative permittivity with small imaginary parts, the optical force doesn’t decrease monotonically as the gap width increases, but rather, exhibits several resonant peaks. This is due to a matching of the relative permittivity and gap width to collective modes [14

14. P. Chu and D. L. Mills, “Laser-induced forces in metallic nanosystems: the role of plasmon resonances,” Phys. Rev. Lett. 99(12), 127401 (2007). [CrossRef] [PubMed]

16

16. P. Chu and D. L. Mills, “Laser-induced forces in metallic nanosystems: the role of plasmon resonances,” Phys. Rev. Lett. 99(12), 127401 (2007). [CrossRef] [PubMed]

, 18

18. J. Ng, R. Tang, and C. T. Chan, “Electrodynamics study of plasmonic bonding and antibonding forces in a bisphere,” Phys. Rev. B 77(19), 195407 (2008). [CrossRef]

]. However, at large gap widths (w > 30 nm), as the gap width is increased, the interaction between two spheres becomes weaker and the optical forces monotonically decrease. As shown in Fig. 3, the optical forces of SiC (red solid line) and Au (red dashed lines) at Re{εr(ω)} = −10 overlap with each other; when Re{εr(ω)} is far from the resonance condition, the Im{εr(ω)} has little effect on optical forces. As Re{εr(ω)} approaches the εr(ω) = −2 resonance condition though, the Im{εr(ω)} has a much larger effect. Compared to the optical forces for Au at Re{εr(ω)} = −2 (black dashed line), those for SiC (black solid line) are over two orders stronger. Notably, this large optical force enhancement is also sustained for a large range of gap widths (30-500 nm).

2.2 Optical forces between two slab waveguides

The second structure we consider is composed of two parallel slab waveguides as shown in Fig. 4(a)
Fig. 4 (a) Sketch of the five-layer, coupled two-slab waveguide system. (b) and (c) show schematic representations of the field profiles for the antisymmetric and symmetric modes. (d) and (e) compare the magnitude of optical forces for SPhPs in SiC and SPPs in Au for the: (d) attractive antisymmetric mode and (e) repulsive symmetric mode. Solid curves are calculated by the iteration method whereas empty circles are the results of FDFD calculation.
, where d defines the thickness of the slabs and w is half of the gap width between them. SPhPs and SPPs in this structure exist as transverse magnetic (TM) modes propagating along the z-axis. Only Hx, Ey and Ez field components are non-zero and the modes are defined according to the symmetry of the electric field component Ez, with respect to x-z plane, as shown in Figs. 4(b) and 4(c). The wave vector is given byki=kziz^ikyiy^, where the subscript i = 1 denotes the slabs (SiC or Au) and i = 2 is the surrounding material (air in our calculations). The time averaged optical force Fy between the two slabs is proportional to Tyy component of the MST, which can be written as:

Tyy=ε0EyEy*12[ε0(EyEy*+EzEz*)+μ0HxHx*]=12[ε0(EyEy*EzEz*)μ0HxHx*].
(3)

Two different methods are applied to obtain field profiles. In the first method, the field profiles are obtained using a vectorial magnetic field finite-difference frequency-domain (FDFD) mode solver [46

46. P. Lusse, P. Stuwe, J. Schule, and H. G. Unger, “Analysis of vectorial mode fields in optical waveguides by a new finite-difference method,” J. Lightwave Technol. 12(3), 487–494 (1994). [CrossRef]

]. In the second method, we use an iteration technique [47

47. R. D. Kekatpure, A. C. Hryciw, E. S. Barnard, and M. L. Brongersma, “Solving dielectric and plasmonic waveguide dispersion relations on a pocket calculator,” Opt. Express 17(26), 24112–24129 (2009). [CrossRef] [PubMed]

] to solve the complex transcendental dispersion equation for TM modes. For the antisymmetric mode in a five layer system, the dispersion equation is [19

19. D. Woolf, M. Loncar, and F. Capasso, “The forces from coupled surface plasmon polaritons in planar waveguides,” Opt. Express 17(22), 19996–20011 (2009). [CrossRef] [PubMed]

]:
ky2ε1ky1ε2tanh(ky2w)=ky1ε1sinh(ky1d)+ky2ε2cosh(ky1d)ky1ε1cosh(ky1d)+ky2ε2sinh(ky1d).
(4)
We selectively choose the following form for the iteration function due to its rapid convergence (Δky2 < 1 m−1 in less than 20 iterations for most data points):
ky2=ky1ε1ε2(1+tanh(ky2w))+[ε1ε2(1+tanh(ky2w))]24(ε1ε2)2tanh2(ky1d)tanh(ky2w)2(ε1ε2)2tanh(ky1d)tanh(ky2w).
(5)
For the symmetric mode, the same procedure is followed with coth(ky2w)being substituted for tanh(ky2w)in Eqs. (4) and (5). The field profiles are then calculated following the formalism in [19

19. D. Woolf, M. Loncar, and F. Capasso, “The forces from coupled surface plasmon polaritons in planar waveguides,” Opt. Express 17(22), 19996–20011 (2009). [CrossRef] [PubMed]

].

Compared to the optical forces for Au at wavelengths of 543 nm and 637 nm, the optical forces for SiC with similar real parts of relative permittivity are around 20 (50) times stronger for the antisymmetric (symmetric) modes at small gap widths (w < δ2). To understand the underlying reason for this enhancement, we analytically investigate the effect of wavelength on the optical forces for both symmetric and antisymmetric modes. In the following analysis, we focus on small gap width structures w < δ2, where largest forces are seen and which are equivalent to ky2w < 1. For long wavelengths, λi2π/|kz| whereλiλ0/|εri|, kzky1ky2 can be obtained. Furthermore, for a sufficiently small thickness d, we can make the assumption that ky1d < 1. Applying the above approximations to Eq. (4) and approximating tanh(x) ≈x, we obtain the following expression for the antisymmetric mode:
ky2(ε1ε2w+d)+(ε1ε2w+d)24(ε1ε2)3wd2(ε1ε2)2wd.
(6)
Similarly, for the symmetric mode under the same assumptions, we obtain:

ky2ε2ε1d+ε2w.
(7)

Due to the assumption |kz| 2π/ λi and the relation Ey = −kzHx/(ωε) derived from Maxwell’s equations, we find thatε0EyEy*/(μ0HxHx*)=|kz|2/k02>>1. Thus, the Hx magnetic field contribution to the optical force can be neglected compared to theEycontribution, which reduces the MST in Eq. (3) toTyyε0(EyEy*EzEz*)/2. Equations (6) and (7) show that the wavevector kis independent of wavelength under the above assumptions. Interestingly though, both EyEy* and EzEz*are directly proportional to the wavelength, as can be seen from the formalism of Woolf et al. in [19

19. D. Woolf, M. Loncar, and F. Capasso, “The forces from coupled surface plasmon polaritons in planar waveguides,” Opt. Express 17(22), 19996–20011 (2009). [CrossRef] [PubMed]

]. (Note that the Ey and Ez terms both contain an explicit λ0 dependence through the frequency ω, as shown in Eqs. (4) and (5) in [19

19. D. Woolf, M. Loncar, and F. Capasso, “The forces from coupled surface plasmon polaritons in planar waveguides,” Opt. Express 17(22), 19996–20011 (2009). [CrossRef] [PubMed]

], but there is an additional 1/λ0 term from the field amplitude coefficients, see Eq. (13) in [19

19. D. Woolf, M. Loncar, and F. Capasso, “The forces from coupled surface plasmon polaritons in planar waveguides,” Opt. Express 17(22), 19996–20011 (2009). [CrossRef] [PubMed]

]. Therefore, EyEy* and EzEz*both scale linearly with λ0.) From these derivations, we clearly see that the optical force is approximately proportional to the operating wavelength under the assumptions that (i) the penetration depth is larger than the structure size (w < δ2 and d < δ2) and (ii) we are operating at long wavelengths (λi2π/|kz|).

In Figs. 5(a)
Fig. 5 Magnitude of the optical forces for the (a) attractive antisymmetric mode and (b) repulsive symmetric mode calculated by the iteration method (solid lines) and analytical approximation (empty circles) for a hypothetical material with relative permittivity εr = −10 + 2i at different operating wavelengths.
and 5(b), we consider a hypothetical material with relative permittivity εr = −10 + 2i for a range of wavelengths and compare the magnitude of optical forces calculated by the iteration method (solid lines) and our analytical approximation (empty circles). For long wavelengths, the analytical approximation accurately predicts the optical forces for both the antisymmetric and symmetric cases, and thus, we find that the optical forces do indeed scale linearly with operating wavelength. For small operating wavelengths, the analytical approximation also accurately predicts the forces calculated for the antisymmetric case, but as the wavelength is no longer large enough compared to 2π/|kz|, the approximation begins to fail and overestimates the forces for the symmetric mode. For completeness, it should also be noted that this approximation fails for both antisymmetric and symmetric modes when the relative permittivity approaches the surface polariton resonance condition (εr = −1); for small magnitudes of the relative permittivity (e.g. εr ≈−2), minor errors in the approximate kvector have a disproportion impact on the predicted forces, and thus the analytical approximation diverges from the iteration result. (Also, for small magnitudes of the relative permittivity, Eq. (6) will no longer be a good approximation for the antisymmetric modes, because ky1d < 1 will not be satisfied.)

With the above calculations, we have shown that the optical forces between SiC slab waveguides are more than one order of magnitude larger than those for Au slab waveguides. Furthermore, we have derived a simple analytical approximation that illustrates how this optical force enhancement can be directly attributed to the increased operating wavelength for SiC. Accordingly, the observed 20-50 fold enhancements shown in Fig. 4 are consistent with the ~20 fold increase in operating wavelength from ~500 nm for Au to ~10 μm for SiC.

2.3 Optical forces between two rectangular waveguides

Similar to the simulation for the slab waveguides, we again calculate the optical forces for a range of operating wavelengths that correspond to the same Re{εr(ω)} for SiC and Au. Figure 6(d) shows the resulting optical forces for the antisymmetric mode. As compared with the SPP optical forces in Au at λ0 = 543 and 637 nm, the SPhP optical forces in SiC at 11.12 and 11.5 μm are enhanced by a factor of 20. Based on the magnitude of this enhancement, it is likely that its origin stems from a wavelength scale enhancement similar to the one derived analytically for the slab case in Section 2.2. Given the additional geometric complexity of the modes in this structure though, we are unable to provide a similar closed form approximation.

Such SPhP waveguides provide both stronger optical forces and lower optical losses than plasmonic waveguides. Similar to recent works on hybrid plasmonic waveguides [20

20. C. G. Huang and L. Zhu, “Enhanced optical forces in 2D hybrid and plasmonic waveguides,” Opt. Lett. 35(10), 1563–1565 (2010). [CrossRef] [PubMed]

, 48

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

, 49

49. H. Li, J. W. Noh, Y. Chen, and M. Li, “Enhanced optical forces in integrated hybrid plasmonic waveguides,” Opt. Express 21(10), 11839–11851 (2013). [CrossRef] [PubMed]

], one could envision creating a hybrid phonon-polariton waveguide by combining a polar solid (e.g. SiC) with a nonpolar dielectric. Note that such hybrid waveguides could combine the advantages of low-loss photonic waveguides with strong confinement polariton waveguides, and thus, could help tailor a tradeoff between losses and force enhancement. Nevertheless, due to the material and wavelength advantages highlighted in this work, SPhPs by themselves already provide significant improvements in terms of both enhanced optical forces and reduced losses. More importantly, SPhPs can help expand optomechanical systems to new materials, such as SiC which present superior mechanical properties to the metals used in plasmonic and hybrid plasmonic waveguides.

3. Conclusions

Acknowledgments

The authors thank S. Cueff, C.M. Dodson, M. Jiang, S. Karaveli, and J. A. Kurvits for fruitful discussions. This work was supported by the Air Force Office of Scientific Research (PECASE award FA-9550-10-1-0026), the National Science Foundation (CAREER award EECS-0846466, MRSEC award DMR-0520651), and a Richard B. Salomon Faculty Research Award from Brown University.

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L. Huang and O. J. F. Martin, “Reversal of the optical force in a plasmonic trap,” Opt. Lett. 33(24), 3001–3003 (2008). [CrossRef] [PubMed]

18.

J. Ng, R. Tang, and C. T. Chan, “Electrodynamics study of plasmonic bonding and antibonding forces in a bisphere,” Phys. Rev. B 77(19), 195407 (2008). [CrossRef]

19.

D. Woolf, M. Loncar, and F. Capasso, “The forces from coupled surface plasmon polaritons in planar waveguides,” Opt. Express 17(22), 19996–20011 (2009). [CrossRef] [PubMed]

20.

C. G. Huang and L. Zhu, “Enhanced optical forces in 2D hybrid and plasmonic waveguides,” Opt. Lett. 35(10), 1563–1565 (2010). [CrossRef] [PubMed]

21.

A. Bonakdar, J. Kohoutek, D. Dey, and H. Mohseni, “Optomechanical nanoantenna,” Opt. Lett. 37(15), 3258–3260 (2012). [CrossRef] [PubMed]

22.

V. Garcés-Chávez, R. Quidant, P. J. Reece, G. Badenes, L. Torner, and K. Dholakia, “Extended organization of colloidal microparticles by surface plasmon polariton excitation,” Phys. Rev. B 73(8), 085417 (2006). [CrossRef]

23.

G. Volpe, R. Quidant, G. Badenes, and D. Petrov, “Surface plasmon radiation forces,” Phys. Rev. Lett. 96(23), 238101 (2006). [CrossRef] [PubMed]

24.

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Phys. 3(7), 477–480 (2007). [CrossRef]

25.

A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photonics 2(6), 365–370 (2008). [CrossRef]

26.

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, “Surface plasmon optical tweezers: tunable Optical Manipulation in the Femtonewton Range,” Phys. Rev. Lett. 100(18), 186804 (2008). [CrossRef] [PubMed]

27.

K. Wang, E. Schonbrun, and K. B. Crozier, “Propulsion of gold nanoparticles with surface plasmon polaritons: evidence of enhanced optical force from near-field coupling between gold particle and gold film,” Nano Lett. 9(7), 2623–2629 (2009). [CrossRef] [PubMed]

28.

K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, “Scannable plasmonic trapping using a gold stripe,” Nano Lett. 10(9), 3506–3511 (2010). [CrossRef] [PubMed]

29.

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011). [CrossRef]

30.

J. Kohoutek, D. Dey, A. Bonakdar, R. Gelfand, A. Sklar, O. G. Memis, and H. Mohseni, “Opto-mechanical force mapping of deep subwavelength plasmonic modes,” Nano Lett. 11(8), 3378–3382 (2011). [CrossRef] [PubMed]

31.

K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, “Trapping and rotating nanoparticles using a plasmonic nano-tweezer with an integrated heat sink,” Nat. Commun. 2, 469 (2011). [CrossRef] [PubMed]

32.

M. F. Ashby, Materials Selection in Mechanical Design (Butterworth-Heinemann, 2005).

33.

Y. T. Yang, K. L. Ekinci, X. M. H. Huang, L. M. Schiavone, M. L. Roukes, C. A. Zorman, and M. Mehregany, “Monocrystalline silicon carbide nanoelectromechanical systems,” Appl. Phys. Lett. 78(2), 162–164 (2001). [CrossRef]

34.

X. M. Henry Huang, C. A. Zorman, M. Mehregany, and M. L. Roukes, “Nanoelectromechanical systems: nanodevice motion at microwave frequencies,” Nature 421(6922), 496–496 (2003). [CrossRef] [PubMed]

35.

S. C. Jun, J. H. Cho, W. K. Kim, Y. M. Jung, S. Hwang, S. Shin, J. Y. Kang, J. Shin, I. Song, J. Y. Choi, S. Lee, and J. M. Kim, “Resonance properties of 3C-SiC nanoelectromechanical resonator in room-temperature magnetomotive transduction,” IEEE Electron Device Lett. 30(10), 1042–1044 (2009). [CrossRef]

36.

H. Mutschke, A. C. Andersen, D. Clement, T. Henning, and G. Peiter, “Infrared properties of SiC particles,” Astron. Astrophys. 345, 187–202 (1999).

37.

R. Hillenbrand, T. Taubner, and F. Keilmann, “Phonon-enhanced light matter interaction at the nanometre scale,” Nature 418(6894), 159–162 (2002). [CrossRef] [PubMed]

38.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313(5793), 1595–1595 (2006). [CrossRef] [PubMed]

39.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. P. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416(6876), 61–64 (2002). [CrossRef] [PubMed]

40.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. A. Lemoine, K. Joulain, J. P. Mulet, Y. Chen, and J. J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444(7120), 740–743 (2006). [CrossRef] [PubMed]

41.

J. A. Schuller, T. Taubner, and M. L. Brongersma, “Optical antenna thermal emitters,” Nat. Photonics 3(11), 658–661 (2009). [CrossRef]

42.

J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99(10), 107401 (2007). [CrossRef] [PubMed]

43.

A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998). [CrossRef] [PubMed]

44.

P. K. Aravind, A. Nitzan, and H. Metiu, “The interaction between electromagnetic resonances and its role in spectroscopic studies of molecules adsorbed on colloidal particles or metal spheres,” Surf. Sci. 110(1), 189–204 (1981). [CrossRef]

45.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006).

46.

P. Lusse, P. Stuwe, J. Schule, and H. G. Unger, “Analysis of vectorial mode fields in optical waveguides by a new finite-difference method,” J. Lightwave Technol. 12(3), 487–494 (1994). [CrossRef]

47.

R. D. Kekatpure, A. C. Hryciw, E. S. Barnard, and M. L. Brongersma, “Solving dielectric and plasmonic waveguide dispersion relations on a pocket calculator,” Opt. Express 17(26), 24112–24129 (2009). [CrossRef] [PubMed]

48.

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

49.

H. Li, J. W. Noh, Y. Chen, and M. Li, “Enhanced optical forces in integrated hybrid plasmonic waveguides,” Opt. Express 21(10), 11839–11851 (2013). [CrossRef] [PubMed]

OCIS Codes
(220.4880) Optical design and fabrication : Optomechanics
(230.7370) Optical devices : Waveguides
(240.5420) Optics at surfaces : Polaritons
(240.6680) Optics at surfaces : Surface plasmons
(240.6690) Optics at surfaces : Surface waves
(350.4855) Other areas of optics : Optical tweezers or optical manipulation

ToC Category:
Optics at Surfaces

History
Original Manuscript: June 26, 2013
Revised Manuscript: August 15, 2013
Manuscript Accepted: August 16, 2013
Published: August 30, 2013

Virtual Issues
Vol. 8, Iss. 10 Virtual Journal for Biomedical Optics

Citation
Dongfang Li, Nabil M. Lawandy, and Rashid Zia, "Surface phonon-polariton enhanced optical forces in silicon carbide nanostructures," Opt. Express 21, 20900-20910 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-18-20900


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  24. M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, “Parallel and selective trapping in a patterned plasmonic landscape,” Nat. Phys.3(7), 477–480 (2007). [CrossRef]
  25. A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photonics2(6), 365–370 (2008). [CrossRef]
  26. M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, “Surface plasmon optical tweezers: tunable Optical Manipulation in the Femtonewton Range,” Phys. Rev. Lett.100(18), 186804 (2008). [CrossRef] [PubMed]
  27. K. Wang, E. Schonbrun, and K. B. Crozier, “Propulsion of gold nanoparticles with surface plasmon polaritons: evidence of enhanced optical force from near-field coupling between gold particle and gold film,” Nano Lett.9(7), 2623–2629 (2009). [CrossRef] [PubMed]
  28. K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, “Scannable plasmonic trapping using a gold stripe,” Nano Lett.10(9), 3506–3511 (2010). [CrossRef] [PubMed]
  29. M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics5(6), 349–356 (2011). [CrossRef]
  30. J. Kohoutek, D. Dey, A. Bonakdar, R. Gelfand, A. Sklar, O. G. Memis, and H. Mohseni, “Opto-mechanical force mapping of deep subwavelength plasmonic modes,” Nano Lett.11(8), 3378–3382 (2011). [CrossRef] [PubMed]
  31. K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, “Trapping and rotating nanoparticles using a plasmonic nano-tweezer with an integrated heat sink,” Nat. Commun.2, 469 (2011). [CrossRef] [PubMed]
  32. M. F. Ashby, Materials Selection in Mechanical Design (Butterworth-Heinemann, 2005).
  33. Y. T. Yang, K. L. Ekinci, X. M. H. Huang, L. M. Schiavone, M. L. Roukes, C. A. Zorman, and M. Mehregany, “Monocrystalline silicon carbide nanoelectromechanical systems,” Appl. Phys. Lett.78(2), 162–164 (2001). [CrossRef]
  34. X. M. Henry Huang, C. A. Zorman, M. Mehregany, and M. L. Roukes, “Nanoelectromechanical systems: nanodevice motion at microwave frequencies,” Nature421(6922), 496–496 (2003). [CrossRef] [PubMed]
  35. S. C. Jun, J. H. Cho, W. K. Kim, Y. M. Jung, S. Hwang, S. Shin, J. Y. Kang, J. Shin, I. Song, J. Y. Choi, S. Lee, and J. M. Kim, “Resonance properties of 3C-SiC nanoelectromechanical resonator in room-temperature magnetomotive transduction,” IEEE Electron Device Lett.30(10), 1042–1044 (2009). [CrossRef]
  36. H. Mutschke, A. C. Andersen, D. Clement, T. Henning, and G. Peiter, “Infrared properties of SiC particles,” Astron. Astrophys.345, 187–202 (1999).
  37. R. Hillenbrand, T. Taubner, and F. Keilmann, “Phonon-enhanced light matter interaction at the nanometre scale,” Nature418(6894), 159–162 (2002). [CrossRef] [PubMed]
  38. T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science313(5793), 1595–1595 (2006). [CrossRef] [PubMed]
  39. J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. P. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature416(6876), 61–64 (2002). [CrossRef] [PubMed]
  40. Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. A. Lemoine, K. Joulain, J. P. Mulet, Y. Chen, and J. J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature444(7120), 740–743 (2006). [CrossRef] [PubMed]
  41. J. A. Schuller, T. Taubner, and M. L. Brongersma, “Optical antenna thermal emitters,” Nat. Photonics3(11), 658–661 (2009). [CrossRef]
  42. J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett.99(10), 107401 (2007). [CrossRef] [PubMed]
  43. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt.37(22), 5271–5283 (1998). [CrossRef] [PubMed]
  44. P. K. Aravind, A. Nitzan, and H. Metiu, “The interaction between electromagnetic resonances and its role in spectroscopic studies of molecules adsorbed on colloidal particles or metal spheres,” Surf. Sci.110(1), 189–204 (1981). [CrossRef]
  45. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006).
  46. P. Lusse, P. Stuwe, J. Schule, and H. G. Unger, “Analysis of vectorial mode fields in optical waveguides by a new finite-difference method,” J. Lightwave Technol.12(3), 487–494 (1994). [CrossRef]
  47. R. D. Kekatpure, A. C. Hryciw, E. S. Barnard, and M. L. Brongersma, “Solving dielectric and plasmonic waveguide dispersion relations on a pocket calculator,” Opt. Express17(26), 24112–24129 (2009). [CrossRef] [PubMed]
  48. X. D. Yang, Y. M. Liu, R. F. Oulton, X. B. Yin, and X. A. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett.11(2), 321–328 (2011). [CrossRef] [PubMed]
  49. H. Li, J. W. Noh, Y. Chen, and M. Li, “Enhanced optical forces in integrated hybrid plasmonic waveguides,” Opt. Express21(10), 11839–11851 (2013). [CrossRef] [PubMed]

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