Abstract

We theoretically investigate the influence of optical gradient forces on nonlinear frequency conversion in a typical nanoscale optomechanical system, which consists of two parallel, suspended waveguides. The waveguides deform with the input power and the phase-matching wavelength changes along the waveguides. Utilizing the spread of deformations collectively allows phase matching over a wider range of pump wavelengths. The third harmonic phase-matching wavelength shift can be as large as 3.6 nm/mW when the waveguide length is 100 μm and the initial gap is 150 nm. It is analogous to chirping the poling period of quasi-phase-matched devices to extend their bandwidths, and allows broad third harmonic to be generated for uses such as biological spectroscopy. Finally, we discuss the conversion efficiency and the optimal phase-matching wavelength with a single-frequency pump.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  4. J. Ma and M. L. Povinelli, “Mechanical Kerr nonlinearities due to bipolar optical forces between deformable silicon waveguides,” Opt. Express 19(11), 10102–10110 (2011).
    [Crossref] [PubMed]
  5. B. Zheng, W. Luo, F. Xu, and Y. Lu, “Influence of van der Waals forces on the waveguide deformation and power limit of nanoscale waveguide devices,” Phys. Rev. A 89(4), 043810 (2014).
    [Crossref]
  6. J. Ma and M. L. Povinelli, “Large tuning of birefringence in two strip silicon waveguides via optomechanical motion,” Opt. Express 17(20), 17818–17828 (2009).
    [Crossref] [PubMed]
  7. K. Y. Fong, W. H. Pernice, M. Li, and H. X. Tang, “Tunable optical coupler controlled by optical gradient forces,” Opt. Express 19(16), 15098–15108 (2011).
    [Crossref] [PubMed]
  8. Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2(4), 242–246 (2008).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  15. T. Ning, O. Hyvärinen, H. Pietarinen, T. Kaplas, M. Kauranen, and G. Genty, “Third-harmonic UV generation in silicon nitride nanostructures,” Opt. Express 21(2), 2012–2017 (2013).
    [Crossref] [PubMed]
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  20. H. R. Philipp, “Optical properties of silicon nitride,” ECS J. Solid State Sci. Technol. 120, 295–300 (1973).
  21. J. J. Vlassak and W. D. Nix, “A new bulge test technique for the determination of Young’s modulus and Poisson’s ratio of thin films,” J. Mater. Res. 7(12), 3242–3249 (1992).
    [Crossref]
  22. 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]
  23. V. Grubsky and A. Savchenko, “Glass micro-fibers for efficient third harmonic generation,” Opt. Express 13(18), 6798–6806 (2005).
    [Crossref] [PubMed]
  24. G. H. Shao, X. S. Song, F. Xu, and Y. Q. Lu, “Optical parametric amplification of arbitrarily polarized light in periodically poled LiNbO3,” Opt. Express 20(17), 19343–19348 (2012).
    [Crossref] [PubMed]
  25. Z. Y. Yu, F. Xu, X. W. Lin, X. S. Song, X. S. Qian, Q. Wang, and Y. Q. Lu, “Tunable broadband isolator based on electro-optically induced linear gratings in a nonlinear photonic crystal,” Opt. Lett. 35(20), 3327–3329 (2010).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  27. A. Butsch, F. Biancalana, C. Conti, and P. S. J. Russell, “Optomechanical self-channelling of light in freely suspended dual-planar-waveguide structure,” in 2011 Conference on Lasers and Electro-Optics (CLEO) (IEEE, 2011), paper QWE4.

2014 (1)

B. Zheng, W. Luo, F. Xu, and Y. Lu, “Influence of van der Waals forces on the waveguide deformation and power limit of nanoscale waveguide devices,” Phys. Rev. A 89(4), 043810 (2014).
[Crossref]

2013 (1)

2012 (5)

2011 (4)

2010 (3)

2009 (3)

2008 (2)

F. Riboli, A. Recati, M. Antezza, and I. Carusotto, “Radiation induced force between two planar waveguides,” Eur. Phys. J. D 46(1), 157–164 (2008).
[Crossref]

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2(4), 242–246 (2008).
[Crossref]

2006 (1)

T. Corbitt, D. Ottaway, E. Innerhofer, J. Pelc, and N. Mavalvala, “Measurement of radiation-pressure-induced optomechanical dynamics in a suspended Fabry-Perot cavity,” Phys. Rev. A 74(2), 021802 (2006).
[Crossref]

2005 (2)

2002 (1)

R. P. Schmid, T. Schneider, and J. Reif, “Optical processing on a femtosecond time scale,” Opt. Commun. 207(1-6), 155–160 (2002).
[Crossref]

1997 (1)

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70(8), 922 (1997).
[Crossref]

1992 (1)

J. J. Vlassak and W. D. Nix, “A new bulge test technique for the determination of Young’s modulus and Poisson’s ratio of thin films,” J. Mater. Res. 7(12), 3242–3249 (1992).
[Crossref]

1973 (1)

H. R. Philipp, “Optical properties of silicon nitride,” ECS J. Solid State Sci. Technol. 120, 295–300 (1973).

Aleksandrova, A.

Antezza, M.

F. Riboli, A. Recati, M. Antezza, and I. Carusotto, “Radiation induced force between two planar waveguides,” Eur. Phys. J. D 46(1), 157–164 (2008).
[Crossref]

Barad, Y.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70(8), 922 (1997).
[Crossref]

Biancalana, F.

C. Conti, A. Butsch, F. Biancalana, and P. S. J. Russell, “Dynamics of optomechanical spatial solitons in dual-nanoweb structures,” Phys. Rev. A 86(1), 013830 (2012).
[Crossref]

Brambilla, G.

Broderick, N. G.

Butsch, A.

C. Conti, A. Butsch, F. Biancalana, and P. S. J. Russell, “Dynamics of optomechanical spatial solitons in dual-nanoweb structures,” Phys. Rev. A 86(1), 013830 (2012).
[Crossref]

Capasso, F.

Carusotto, I.

F. Riboli, A. Recati, M. Antezza, and I. Carusotto, “Radiation induced force between two planar waveguides,” Eur. Phys. J. D 46(1), 157–164 (2008).
[Crossref]

Chashnikova, M.

Chen, L.

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

Chen, X. F.

Codemard, C. A.

Conti, C.

C. Conti, A. Butsch, F. Biancalana, and P. S. J. Russell, “Dynamics of optomechanical spatial solitons in dual-nanoweb structures,” Phys. Rev. A 86(1), 013830 (2012).
[Crossref]

Corbitt, T.

T. Corbitt, D. Ottaway, E. Innerhofer, J. Pelc, and N. Mavalvala, “Measurement of radiation-pressure-induced optomechanical dynamics in a suspended Fabry-Perot cavity,” Phys. Rev. A 74(2), 021802 (2006).
[Crossref]

Ding, M.

Eisenberg, H.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70(8), 922 (1997).
[Crossref]

Fainman, Y.

D. T. H. Tan, K. Ikeda, P. C. Sun, and Y. Fainman, “Group velocity dispersion and self phase modulation in silicon nitride waveguides,” Appl. Phys. Lett. 96(6), 061101 (2010).
[Crossref]

Fedosenko, O.

Flores, Y.

Fong, K. Y.

Foster, M. A.

Gaeta, A. L.

Genty, G.

Gondarenko, A.

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

Green, W. M. J.

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2(4), 242–246 (2008).
[Crossref]

Grubsky, V.

Gruska, B.

Halir, R.

Horowitz, M.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70(8), 922 (1997).
[Crossref]

Huang, C.

Hyvärinen, O.

Ibanescu, M.

Ikeda, K.

D. T. H. Tan, K. Ikeda, P. C. Sun, and Y. Fainman, “Group velocity dispersion and self phase modulation in silicon nitride waveguides,” Appl. Phys. Lett. 96(6), 061101 (2010).
[Crossref]

Innerhofer, E.

T. Corbitt, D. Ottaway, E. Innerhofer, J. Pelc, and N. Mavalvala, “Measurement of radiation-pressure-induced optomechanical dynamics in a suspended Fabry-Perot cavity,” Phys. Rev. A 74(2), 021802 (2006).
[Crossref]

Joannopoulos, J. D.

Johnson, S. G.

Jung, Y.

Kaplas, T.

Kauranen, M.

Kischkat, J.

Klinkmüller, M.

Kou, J. L.

Lee, T.

Leng, F.

Levy, J. S.

Li, M.

Lin, X. W.

Lipson, M.

Loncar, M.

Lu, Y.

B. Zheng, W. Luo, F. Xu, and Y. Lu, “Influence of van der Waals forces on the waveguide deformation and power limit of nanoscale waveguide devices,” Phys. Rev. A 89(4), 043810 (2014).
[Crossref]

Lu, Y. Q.

Luo, W.

B. Zheng, W. Luo, F. Xu, and Y. Lu, “Influence of van der Waals forces on the waveguide deformation and power limit of nanoscale waveguide devices,” Phys. Rev. A 89(4), 043810 (2014).
[Crossref]

Ma, J.

Machulik, S.

Mavalvala, N.

T. Corbitt, D. Ottaway, E. Innerhofer, J. Pelc, and N. Mavalvala, “Measurement of radiation-pressure-induced optomechanical dynamics in a suspended Fabry-Perot cavity,” Phys. Rev. A 74(2), 021802 (2006).
[Crossref]

Monastyrskyi, G.

Ning, T.

Nix, W. D.

J. J. Vlassak and W. D. Nix, “A new bulge test technique for the determination of Young’s modulus and Poisson’s ratio of thin films,” J. Mater. Res. 7(12), 3242–3249 (1992).
[Crossref]

Okawachi, Y.

Ottaway, D.

T. Corbitt, D. Ottaway, E. Innerhofer, J. Pelc, and N. Mavalvala, “Measurement of radiation-pressure-induced optomechanical dynamics in a suspended Fabry-Perot cavity,” Phys. Rev. A 74(2), 021802 (2006).
[Crossref]

Pelc, J.

T. Corbitt, D. Ottaway, E. Innerhofer, J. Pelc, and N. Mavalvala, “Measurement of radiation-pressure-induced optomechanical dynamics in a suspended Fabry-Perot cavity,” Phys. Rev. A 74(2), 021802 (2006).
[Crossref]

Pernice, W. H.

Peters, S.

Philipp, H. R.

H. R. Philipp, “Optical properties of silicon nitride,” ECS J. Solid State Sci. Technol. 120, 295–300 (1973).

Pietarinen, H.

Povinelli, M. L.

Qian, X. S.

Recati, A.

F. Riboli, A. Recati, M. Antezza, and I. Carusotto, “Radiation induced force between two planar waveguides,” Eur. Phys. J. D 46(1), 157–164 (2008).
[Crossref]

Reif, J.

R. P. Schmid, T. Schneider, and J. Reif, “Optical processing on a femtosecond time scale,” Opt. Commun. 207(1-6), 155–160 (2002).
[Crossref]

Riboli, F.

F. Riboli, A. Recati, M. Antezza, and I. Carusotto, “Radiation induced force between two planar waveguides,” Eur. Phys. J. D 46(1), 157–164 (2008).
[Crossref]

Russell, P. S. J.

C. Conti, A. Butsch, F. Biancalana, and P. S. J. Russell, “Dynamics of optomechanical spatial solitons in dual-nanoweb structures,” Phys. Rev. A 86(1), 013830 (2012).
[Crossref]

Savchenko, A.

Schmid, R. P.

R. P. Schmid, T. Schneider, and J. Reif, “Optical processing on a femtosecond time scale,” Opt. Commun. 207(1-6), 155–160 (2002).
[Crossref]

Schneider, T.

R. P. Schmid, T. Schneider, and J. Reif, “Optical processing on a femtosecond time scale,” Opt. Commun. 207(1-6), 155–160 (2002).
[Crossref]

Semtsiv, M.

Shao, G. H.

Silberberg, Y.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70(8), 922 (1997).
[Crossref]

Smythe, E. J.

Song, X. S.

Sun, P. C.

D. T. H. Tan, K. Ikeda, P. C. Sun, and Y. Fainman, “Group velocity dispersion and self phase modulation in silicon nitride waveguides,” Appl. Phys. Lett. 96(6), 061101 (2010).
[Crossref]

Tan, D. T. H.

D. T. H. Tan, K. Ikeda, P. C. Sun, and Y. Fainman, “Group velocity dispersion and self phase modulation in silicon nitride waveguides,” Appl. Phys. Lett. 96(6), 061101 (2010).
[Crossref]

Tang, H. X.

Ted Masselink, W.

Vlasov, Y.

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2(4), 242–246 (2008).
[Crossref]

Vlassak, J. J.

J. J. Vlassak and W. D. Nix, “A new bulge test technique for the determination of Young’s modulus and Poisson’s ratio of thin films,” J. Mater. Res. 7(12), 3242–3249 (1992).
[Crossref]

Wang, Q.

Wiederhecker, G. S.

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

Xia, F.

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2(4), 242–246 (2008).
[Crossref]

Xu, F.

Yu, Z. Y.

Zheng, B.

B. Zheng, W. Luo, F. Xu, and Y. Lu, “Influence of van der Waals forces on the waveguide deformation and power limit of nanoscale waveguide devices,” Phys. Rev. A 89(4), 043810 (2014).
[Crossref]

Zhu, L.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70(8), 922 (1997).
[Crossref]

D. T. H. Tan, K. Ikeda, P. C. Sun, and Y. Fainman, “Group velocity dispersion and self phase modulation in silicon nitride waveguides,” Appl. Phys. Lett. 96(6), 061101 (2010).
[Crossref]

ECS J. Solid State Sci. Technol. (1)

H. R. Philipp, “Optical properties of silicon nitride,” ECS J. Solid State Sci. Technol. 120, 295–300 (1973).

Eur. Phys. J. D (1)

F. Riboli, A. Recati, M. Antezza, and I. Carusotto, “Radiation induced force between two planar waveguides,” Eur. Phys. J. D 46(1), 157–164 (2008).
[Crossref]

J. Mater. Res. (1)

J. J. Vlassak and W. D. Nix, “A new bulge test technique for the determination of Young’s modulus and Poisson’s ratio of thin films,” J. Mater. Res. 7(12), 3242–3249 (1992).
[Crossref]

Nat. Photonics (1)

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2(4), 242–246 (2008).
[Crossref]

Nature (1)

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

Opt. Commun. (1)

R. P. Schmid, T. Schneider, and J. Reif, “Optical processing on a femtosecond time scale,” Opt. Commun. 207(1-6), 155–160 (2002).
[Crossref]

Opt. Express (9)

V. Grubsky and A. Savchenko, “Glass micro-fibers for efficient third harmonic generation,” Opt. Express 13(18), 6798–6806 (2005).
[Crossref] [PubMed]

G. H. Shao, X. S. Song, F. Xu, and Y. Q. Lu, “Optical parametric amplification of arbitrarily polarized light in periodically poled LiNbO3,” Opt. Express 20(17), 19343–19348 (2012).
[Crossref] [PubMed]

Z. Y. Yu, F. Xu, F. Leng, X. S. Qian, X. F. Chen, and Y. Q. Lu, “Acousto-optic tunable second harmonic generation in periodically poled LiNbO3,” Opt. Express 17(14), 11965–11971 (2009).
[Crossref] [PubMed]

J. Ma and M. L. Povinelli, “Mechanical Kerr nonlinearities due to bipolar optical forces between deformable silicon waveguides,” Opt. Express 19(11), 10102–10110 (2011).
[Crossref] [PubMed]

J. Ma and M. L. Povinelli, “Large tuning of birefringence in two strip silicon waveguides via optomechanical motion,” Opt. Express 17(20), 17818–17828 (2009).
[Crossref] [PubMed]

K. Y. Fong, W. H. Pernice, M. Li, and H. X. Tang, “Tunable optical coupler controlled by optical gradient forces,” Opt. Express 19(16), 15098–15108 (2011).
[Crossref] [PubMed]

J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express 19(12), 11415–11421 (2011).
[Crossref] [PubMed]

T. Ning, O. Hyvärinen, H. Pietarinen, T. Kaplas, M. Kauranen, and G. Genty, “Third-harmonic UV generation in silicon nitride nanostructures,” Opt. Express 21(2), 2012–2017 (2013).
[Crossref] [PubMed]

T. Lee, Y. Jung, C. A. Codemard, M. Ding, N. G. Broderick, and G. Brambilla, “Broadband third harmonic generation in tapered silica fibres,” Opt. Express 20(8), 8503–8511 (2012).
[Crossref] [PubMed]

Opt. Lett. (5)

Phys. Rev. A (3)

B. Zheng, W. Luo, F. Xu, and Y. Lu, “Influence of van der Waals forces on the waveguide deformation and power limit of nanoscale waveguide devices,” Phys. Rev. A 89(4), 043810 (2014).
[Crossref]

T. Corbitt, D. Ottaway, E. Innerhofer, J. Pelc, and N. Mavalvala, “Measurement of radiation-pressure-induced optomechanical dynamics in a suspended Fabry-Perot cavity,” Phys. Rev. A 74(2), 021802 (2006).
[Crossref]

C. Conti, A. Butsch, F. Biancalana, and P. S. J. Russell, “Dynamics of optomechanical spatial solitons in dual-nanoweb structures,” Phys. Rev. A 86(1), 013830 (2012).
[Crossref]

Other (1)

A. Butsch, F. Biancalana, C. Conti, and P. S. J. Russell, “Optomechanical self-channelling of light in freely suspended dual-planar-waveguide structure,” in 2011 Conference on Lasers and Electro-Optics (CLEO) (IEEE, 2011), paper QWE4.

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Figures (5)

Fig. 1
Fig. 1 Schematic of two parallel, suspended silicon nitride waveguides with fixed edges and its cross section, where a = 400 nm, b = 700 nm, g = 150 nm, L = 100 μm.
Fig. 2
Fig. 2 Tuning the phase-matching wavelength shift at the position with maximum deformation by adjusting input power. The figure also shows the relationship between gap and input power. Δλ is the tuning range of phase-matching wavelength.
Fig. 3
Fig. 3 The relationship between Δλ and input power P for coupled waveguides with different length parameters.
Fig. 4
Fig. 4 The phase mismatch and gap along the waveguides with a single-frequency pump (1632 nm) at 10 mW.
Fig. 5
Fig. 5 (a) 3D graph of η p with different input wavelength and input power. δλ is the difference between the input wavelength and the initial phase-matching wavelength λ i. (b) The relationship between the maximum ηp and δλ. We choose the maximum value of ηp at certain input wavelength as the maximum ηp with the input power ranging from 0 mW to 60 mW.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

F = ( T n ^ ) d A = L { ε 2 Re [ ( E n ^ ) E ] ε 4 ( E E ) n ^ + μ 2 Re [ ( H n ^ ) H ] μ 4 ( H H ) n ^ } d l ,
E I d 4 u ( z ) d z 4 = q ( z ) ,
η = P o u t P i n η p = ( 0 L e i Δ β z d z ) 2 P i n 2 .

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