Abstract

We propose an optomechanical approach for dispersion dynamic tuning and microengineering by taking advantage of the optical force in nano-optomechanical structures. Simulations of a suspended coupled silicon waveguide show that the zero-dispersion wavelength can be tuned by 40 nm by an optical pump power of 3 mW. Our approach exhibits great potential for broad applications in dispersion-sensitive processes, which not only offers a new root toward versatile tunable nonlinear photonics but may also open up a great avenue toward a new regime of nonlinear dynamics coupling between nonlinear optical and optomechanical effects.

© 2013 Optical Society of America

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2012

H. Ryu, J. Kim, Y. M. Jhon, S. Lee, and N. Park, Opt. Express 20, 13189 (2012).
[CrossRef]

U. Moller, S. T. Sorensen, C. Larsen, Peter M. Moselund, C. Jakobsen, J. Johansen, C. L. Thomsen, and O. Bang, Opt. Fiber Technol. 18, 304 (2012).
[CrossRef]

2011

2010

2009

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, Nature Nanotechnol. 4, 510 (2009).

M. Li, W. H. P. Pernice, and H. X. Tang, Nat. Photonics 3, 464 (2009).

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, Nature 459, 550 (2009).
[CrossRef]

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, Phys. Rev. Lett. 103, 103601 (2009).
[CrossRef]

J. Rosenberg, Q. Lin, and O. Painter, Nat. Photonics 3, 478 (2009).

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, Nature 462, 633 (2009).
[CrossRef]

J. Ma and M. L. Povinelli, Opt. Express 17, 17818 (2009).
[CrossRef]

P. T. Rakich, M. A. Popovic, and Z. Wang, Opt. Express 17, 18116 (2009).
[CrossRef]

2008

2007

Q. Lin, O. Painter, and G. P. Agrawal, Opt. Express 15, 16604 (2007), and references therein.
[CrossRef]

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, Nat. Photonics 1, 658 (2007).

2006

2005

Agrawal, G. P.

Aspelmeyer, M.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” arXiv 1303.0733v1 (2013).

Baehr-Jones, T.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 408 (2008).

Baets, R.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, Nature Nanotechnol. 4, 510 (2009).

Bang, O.

U. Moller, S. T. Sorensen, C. Larsen, Peter M. Moselund, C. Jakobsen, J. Johansen, C. L. Thomsen, and O. Bang, Opt. Fiber Technol. 18, 304 (2012).
[CrossRef]

Beausoleil, R. G.

Camacho, R.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, Nature 459, 550 (2009).
[CrossRef]

Capasso, F.

Caraquitena, J.

Chan, J.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, Nature 459, 550 (2009).
[CrossRef]

Chang, D.

Q. Lin, J. Rosenberg, D. Chang, and O. Painter, in Quantum Electronics and Laser Science Conference 2010 (2010), paper QTuA1.

Chen, L.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, Nature 462, 633 (2009).
[CrossRef]

Chen, X.

Choi, D.-Y.

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Dadap, J. I.

De La Rue, R. M.

de Nobriga, C. E.

De Vlaminck, I.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, Nature Nanotechnol. 4, 510 (2009).

Deng, Y. J.

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Eggleton, B. J.

Eichenfield, M.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, Nature 459, 550 (2009).
[CrossRef]

Foster, M. A.

Gaeta, A. L.

Gai, X.

Galan, J. V.

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Gondarenko, A.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, Nature 462, 633 (2009).
[CrossRef]

Gorbach, A. V.

D. V. Skryabin and A. V. Gorbach, Rev. Mod. Phys. 82, 1287 (2010).
[CrossRef]

Green, W. M. J.

Hobbs, G. D.

Hochberg, M.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 408 (2008).

Hsieh, I-W.

Ibanescu, M.

Ippen, E. P.

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, Nat. Photonics 1, 658 (2007).

Jakobsen, C.

U. Moller, S. T. Sorensen, C. Larsen, Peter M. Moselund, C. Jakobsen, J. Johansen, C. L. Thomsen, and O. Bang, Opt. Fiber Technol. 18, 304 (2012).
[CrossRef]

Jhon, Y. M.

Jiang, X.

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, Phys. Rev. Lett. 103, 103601 (2009).
[CrossRef]

Joannopoulos, J. D.

Johansen, J.

U. Moller, S. T. Sorensen, C. Larsen, Peter M. Moselund, C. Jakobsen, J. Johansen, C. L. Thomsen, and O. Bang, Opt. Fiber Technol. 18, 304 (2012).
[CrossRef]

Johnson, S. G.

Kim, J.

Kippenberg, T. J.

T. J. Kippenberg and K. J. Vahala, Science 321, 1172 (2008).
[CrossRef]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” arXiv 1303.0733v1 (2013).

Knight, J. C.

Knox, W. H.

Kuramochi, E.

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, Phys. Rev. B 81, 121101(R) (2010).

Lagae, L.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, Nature Nanotechnol. 4, 510 (2009).

Lamont, M. R. E.

Larsen, C.

U. Moller, S. T. Sorensen, C. Larsen, Peter M. Moselund, C. Jakobsen, J. Johansen, C. L. Thomsen, and O. Bang, Opt. Fiber Technol. 18, 304 (2012).
[CrossRef]

Lee, S.

Levy, J. S.

Li, M.

M. Li, W. H. P. Pernice, and H. X. Tang, Nat. Photonics 3, 464 (2009).

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 408 (2008).

Lin, Q.

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, Phys. Rev. Lett. 103, 103601 (2009).
[CrossRef]

J. Rosenberg, Q. Lin, and O. Painter, Nat. Photonics 3, 478 (2009).

Q. Lin, O. Painter, and G. P. Agrawal, Opt. Express 15, 16604 (2007), and references therein.
[CrossRef]

Q. Lin, J. Rosenberg, D. Chang, and O. Painter, in Quantum Electronics and Laser Science Conference 2010 (2010), paper QTuA1.

Lipson, M.

Liu, X.

Loncar, M.

Lu, F.

Luther-Davies, B.

Ma, J.

Madden, S.

Maes, B.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, Nature Nanotechnol. 4, 510 (2009).

Manolatou, C.

Marquardt, F.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” arXiv 1303.0733v1 (2013).

Marti, J.

Martinelli, M.

Mas, S.

Matsuo, S.

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, Phys. Rev. B 81, 121101(R) (2010).

Melloni, A.

Moller, U.

U. Moller, S. T. Sorensen, C. Larsen, Peter M. Moselund, C. Jakobsen, J. Johansen, C. L. Thomsen, and O. Bang, Opt. Fiber Technol. 18, 304 (2012).
[CrossRef]

Morichetti, F.

Moselund, Peter M.

U. Moller, S. T. Sorensen, C. Larsen, Peter M. Moselund, C. Jakobsen, J. Johansen, C. L. Thomsen, and O. Bang, Opt. Fiber Technol. 18, 304 (2012).
[CrossRef]

Notomi, M.

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, Phys. Rev. B 81, 121101(R) (2010).

Okawachi, Y.

Osgood, R. M.

Painter, O.

J. Rosenberg, Q. Lin, and O. Painter, Nat. Photonics 3, 478 (2009).

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, Phys. Rev. Lett. 103, 103601 (2009).
[CrossRef]

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, Nature 459, 550 (2009).
[CrossRef]

Q. Lin, O. Painter, and G. P. Agrawal, Opt. Express 15, 16604 (2007), and references therein.
[CrossRef]

Q. Lin, J. Rosenberg, D. Chang, and O. Painter, in Quantum Electronics and Laser Science Conference 2010 (2010), paper QTuA1.

Park, N.

Pernice, W. H. P.

M. Li, W. H. P. Pernice, and H. X. Tang, Nat. Photonics 3, 464 (2009).

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 408 (2008).

Popovic, M. A.

P. T. Rakich, M. A. Popovic, and Z. Wang, Opt. Express 17, 18116 (2009).
[CrossRef]

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, Nat. Photonics 1, 658 (2007).

Povinelli, M.

Povinelli, M. L.

Rakich, P. T.

P. T. Rakich, M. A. Popovic, and Z. Wang, Opt. Express 17, 18116 (2009).
[CrossRef]

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, Nat. Photonics 1, 658 (2007).

Roels, J.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, Nature Nanotechnol. 4, 510 (2009).

Roh, Y.-G.

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, Phys. Rev. B 81, 121101(R) (2010).

Rosenberg, J.

J. Rosenberg, Q. Lin, and O. Painter, Nat. Photonics 3, 478 (2009).

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, Phys. Rev. Lett. 103, 103601 (2009).
[CrossRef]

Q. Lin, J. Rosenberg, D. Chang, and O. Painter, in Quantum Electronics and Laser Science Conference 2010 (2010), paper QTuA1.

Russell, P. St. J.

Ryu, H.

Saha, K.

Samarelli, A.

Sanchis, P.

Sato, T.

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, Phys. Rev. B 81, 121101(R) (2010).

Schmidt, B. S.

Sharping, J. E.

Shinya, A.

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, Phys. Rev. B 81, 121101(R) (2010).

Skryabin, D. V.

Smythe, E. J.

Soljacic, M.

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, Nat. Photonics 1, 658 (2007).

Sorel, M.

Sorensen, S. T.

U. Moller, S. T. Sorensen, C. Larsen, Peter M. Moselund, C. Jakobsen, J. Johansen, C. L. Thomsen, and O. Bang, Opt. Fiber Technol. 18, 304 (2012).
[CrossRef]

Tanabe, T.

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, Phys. Rev. B 81, 121101(R) (2010).

Tang, H. X.

M. Li, W. H. P. Pernice, and H. X. Tang, Nat. Photonics 3, 464 (2009).

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 408 (2008).

Taniyama, H.

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, Phys. Rev. B 81, 121101(R) (2010).

Thomsen, C. L.

U. Moller, S. T. Sorensen, C. Larsen, Peter M. Moselund, C. Jakobsen, J. Johansen, C. L. Thomsen, and O. Bang, Opt. Fiber Technol. 18, 304 (2012).
[CrossRef]

Turner, A. C.

Vahala, K. J.

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, Phys. Rev. Lett. 103, 103601 (2009).
[CrossRef]

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, Nature 459, 550 (2009).
[CrossRef]

T. J. Kippenberg and K. J. Vahala, Science 321, 1172 (2008).
[CrossRef]

Van Thourhout, D.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, Nature Nanotechnol. 4, 510 (2009).

Vlasov, Y. A.

Wadsworth, W. J.

Wang, J.

Wang, Z.

Wen, Y. H.

Wiederhecker, G. S.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, Nature 462, 633 (2009).
[CrossRef]

Willner, A. E.

Xiao-Li, Y.

Xiong, C.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 408 (2008).

Yue, Y.

Zhang, L.

J. Lightwave Technol.

J. Opt. Soc. Am. B

Nat. Photonics

P. T. Rakich, M. A. Popovic, M. Soljacic, and E. P. Ippen, Nat. Photonics 1, 658 (2007).

M. Li, W. H. P. Pernice, and H. X. Tang, Nat. Photonics 3, 464 (2009).

J. Rosenberg, Q. Lin, and O. Painter, Nat. Photonics 3, 478 (2009).

Nature

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, Nature 462, 633 (2009).
[CrossRef]

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, Nature 459, 550 (2009).
[CrossRef]

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 408 (2008).

Nature Nanotechnol.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, Nature Nanotechnol. 4, 510 (2009).

Opt. Express

Opt. Fiber Technol.

U. Moller, S. T. Sorensen, C. Larsen, Peter M. Moselund, C. Jakobsen, J. Johansen, C. L. Thomsen, and O. Bang, Opt. Fiber Technol. 18, 304 (2012).
[CrossRef]

Opt. Lett.

Phys. Rev. B

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, Phys. Rev. B 81, 121101(R) (2010).

Phys. Rev. Lett.

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, Phys. Rev. Lett. 103, 103601 (2009).
[CrossRef]

Rev. Mod. Phys.

D. V. Skryabin and A. V. Gorbach, Rev. Mod. Phys. 82, 1287 (2010).
[CrossRef]

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Science

T. J. Kippenberg and K. J. Vahala, Science 321, 1172 (2008).
[CrossRef]

Other

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” arXiv 1303.0733v1 (2013).

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

Q. Lin, J. Rosenberg, D. Chang, and O. Painter, in Quantum Electronics and Laser Science Conference 2010 (2010), paper QTuA1.

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Figures (4)

Fig. 1.
Fig. 1.

Optical forces for the quasi-TE-like bonded (blue) and antibonded (red) modes as a function of waveguide spacing. Each of the coupled silicon waveguides has a width w=770nm and a height h=220nm, with air as the cladding. The optical force per unit length per unit optical power is given by F=(1/c)(neff/x) [29], where neff is the effective modal index, which is simulated by the finite element method (FEM), x is the spacing between the coupled waveguides, and c is the velocity of light in vacuum. The insets show the simulated optical mode profiles.

Fig. 2.
Fig. 2.

Waveguide spacing change induced by the attractive optical force, with an optical power of 3 mW, launched at a wavelength of 1550 nm into the coupled waveguide with a length of 300 μm and an initial spacing of 100 nm, simulated by FEM (for silicon, Young’s modulus E=170GPa and mass density ρ=2330kg/m3). The individual waveguide has the same cross section as Fig. 1. The inset shows the schematic of the induced mechanical deformation of the suspended silicon waveguide structure sitting on a SiO2 substrate.

Fig. 3.
Fig. 3.

GVD for the quasi-TE-like modes as a function of waveguide spacing. Each individual waveguide has the same cross section as in Fig. 1. (a) Bonded mode. The waveguide spacing changes by 20 nm for each curve. The two black dashed curves show the GVD for a single waveguide (WG) with a width of 1540 and 770 nm, respectively, which set the boundaries of the GVD tuning range. (b) Antibonded mode. The red and blue curves show the cases for waveguide spacings of 60 and 180 nm, respectively. In both figures, the insets show the optical mode profiles for the bonded and antibonded mode, respectively.

Fig. 4.
Fig. 4.

Position-dependent dispersion profile of the waveguide corresponding to the mechanical displacement shown in Fig. 2. (a) GVD profile. (b) ZDWL as a function of position along the waveguide, where the dots are simulated by FEM and the solid line is a fitting to the dots.

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