Abstract

We study theoretically the optical forces acting on glass nanoplates introduced into hollow waveguides, and show that, depending on the sign of the laser detuning relative to the nanoplate resonance, optomechanical back-action between nanoplate and hollow waveguide can create both traps and anti-traps at intensity nodes and anti-nodes in the supermode field profile, behaving similarly to those experienced by cold atoms when the laser frequency is red or blue detuned of an atomic resonance. This arises from dramatic distortions to the mode profile in the hollow waveguide when the nanoplate is off-resonant, producing gradient forces that vary strongly with nanoplate position. In a planar system, we show that when the nanoplate is constrained by an imaginary mechanical spring, its position exhibits strong bistability as the base position is varied. We then treat a two-dimensional system consisting of an anti-resonant nanoplate in the hollow core of a photonic crystal fiber, and predict the stable dark trapping of nanoplate at core center against both translational and rotational motion. The results show that spatial and angular position of nano-scale objects in hollow waveguides can be optically controlled by launching beams with appropriately synthesized transverse field profiles.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
    [Crossref]
  2. J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452(7183), 72–75 (2008).
    [Crossref] [PubMed]
  3. A. Butsch, C. Conti, F. Biancalana, and P. St. J. Russell, “Optomechanical self-channeling of light in a suspended planar dual-nanoweb waveguide,” Phys. Rev. Lett. 108(9), 093903 (2012).
    [Crossref] [PubMed]
  4. J. R. Koehler, R. E. Noskov, A. A. Sukhorukov, A. Butsch, D. Novoa, and P. St. J. Russell, “Resolving the mystery of milliwatt-threshold opto-mechanical self-oscillation in dual-nanoweb fiber,” APL Photonics 1(5), 056101 (2016).
    [Crossref]
  5. S. Xie, R. Pennetta, and P. St. J. Russell, “Self-alignment of glass fiber nanospike by optomechanical back-action in hollow-core photonic crystal fiber,” Optica 3(3), 277–282 (2016).
    [Crossref]
  6. L. Neumeier, R. Quidant, and D. E. Chang, “Self-induced back-action optical trapping in nanophotonic systems,” New J. Phys. 17(12), 123008 (2015).
    [Crossref]
  7. M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys. 5(12), 915–919 (2009).
    [Crossref]
  8. P. St. J. Russell, T. A. Birks, and F. D. Lloyd-Lucas, “Photonic Bloch Waves and Photonic Band Gaps,” Confined Electrons and Photons, E. Burstein and C. Weisbuch, eds., NATO ASI Series (Plenum Press), Vol. 340, 585–633 (1995).
  9. J. L. Archambault, R. J. Black, S. Lacroix, and J. Bures, “Loss calculations for antiresonant wave-guides,” J. Lightwave Technol. 11(3), 416–423 (1993).
    [Crossref]
  10. A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992).
    [Crossref] [PubMed]
  11. S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, “Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure,” Phys. Rev. Lett. 55(1), 48–51 (1985).
    [Crossref] [PubMed]
  12. P. Uebel, M. C. Günendi, M. H. Frosz, G. Ahmed, N. N. Edavalath, J.-M. Ménard, and P. St. J. Russell, “Broadband robustly single-mode hollow-core PCF by resonant filtering of higher-order modes,” Opt. Lett. 41(9), 1961–1964 (2016).
    [Crossref] [PubMed]
  13. P. Roth, Y. Chen, M. C. Günendi, R. Beravat, N. N. Edavalath, M. H. Frosz, G. Ahmed, G. K. L. Wong, and P. St. J. Russell, “Strong circular dichroism for the HE11 mode in twisted single-ring hollow-core photonic crystal fiber,” Optica 5(10), 1315–1321 (2018).
    [Crossref]
  14. B. Debord, A. Amsanpally, M. Chafer, A. Baz, M. Maurel, J. M. Blondy, E. Hugonnot, F. Scol, L. Vincetti, F. Gerome, and F. Benabid, “Ultralow transmission loss in inhibited-coupling guiding hollow fibers,” Optica 4(2), 209–217 (2017).
    [Crossref]

2018 (1)

2017 (1)

2016 (3)

2015 (1)

L. Neumeier, R. Quidant, and D. E. Chang, “Self-induced back-action optical trapping in nanophotonic systems,” New J. Phys. 17(12), 123008 (2015).
[Crossref]

2014 (1)

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

2012 (1)

A. Butsch, C. Conti, F. Biancalana, and P. St. J. Russell, “Optomechanical self-channeling of light in a suspended planar dual-nanoweb waveguide,” Phys. Rev. Lett. 108(9), 093903 (2012).
[Crossref] [PubMed]

2009 (1)

M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys. 5(12), 915–919 (2009).
[Crossref]

2008 (1)

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452(7183), 72–75 (2008).
[Crossref] [PubMed]

1993 (1)

J. L. Archambault, R. J. Black, S. Lacroix, and J. Bures, “Loss calculations for antiresonant wave-guides,” J. Lightwave Technol. 11(3), 416–423 (1993).
[Crossref]

1992 (1)

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992).
[Crossref] [PubMed]

1985 (1)

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, “Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure,” Phys. Rev. Lett. 55(1), 48–51 (1985).
[Crossref] [PubMed]

Ahmed, G.

Amsanpally, A.

Archambault, J. L.

J. L. Archambault, R. J. Black, S. Lacroix, and J. Bures, “Loss calculations for antiresonant wave-guides,” J. Lightwave Technol. 11(3), 416–423 (1993).
[Crossref]

Ashkin, A.

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992).
[Crossref] [PubMed]

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, “Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure,” Phys. Rev. Lett. 55(1), 48–51 (1985).
[Crossref] [PubMed]

Aspelmeyer, M.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

Baz, A.

Benabid, F.

Beravat, R.

Biancalana, F.

A. Butsch, C. Conti, F. Biancalana, and P. St. J. Russell, “Optomechanical self-channeling of light in a suspended planar dual-nanoweb waveguide,” Phys. Rev. Lett. 108(9), 093903 (2012).
[Crossref] [PubMed]

Bjorkholm, J. E.

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, “Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure,” Phys. Rev. Lett. 55(1), 48–51 (1985).
[Crossref] [PubMed]

Black, R. J.

J. L. Archambault, R. J. Black, S. Lacroix, and J. Bures, “Loss calculations for antiresonant wave-guides,” J. Lightwave Technol. 11(3), 416–423 (1993).
[Crossref]

Blondy, J. M.

Bures, J.

J. L. Archambault, R. J. Black, S. Lacroix, and J. Bures, “Loss calculations for antiresonant wave-guides,” J. Lightwave Technol. 11(3), 416–423 (1993).
[Crossref]

Butsch, A.

J. R. Koehler, R. E. Noskov, A. A. Sukhorukov, A. Butsch, D. Novoa, and P. St. J. Russell, “Resolving the mystery of milliwatt-threshold opto-mechanical self-oscillation in dual-nanoweb fiber,” APL Photonics 1(5), 056101 (2016).
[Crossref]

A. Butsch, C. Conti, F. Biancalana, and P. St. J. Russell, “Optomechanical self-channeling of light in a suspended planar dual-nanoweb waveguide,” Phys. Rev. Lett. 108(9), 093903 (2012).
[Crossref] [PubMed]

Cable, A.

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, “Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure,” Phys. Rev. Lett. 55(1), 48–51 (1985).
[Crossref] [PubMed]

Chafer, M.

Chang, D. E.

L. Neumeier, R. Quidant, and D. E. Chang, “Self-induced back-action optical trapping in nanophotonic systems,” New J. Phys. 17(12), 123008 (2015).
[Crossref]

Chen, Y.

Chu, S.

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, “Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure,” Phys. Rev. Lett. 55(1), 48–51 (1985).
[Crossref] [PubMed]

Conti, C.

A. Butsch, C. Conti, F. Biancalana, and P. St. J. Russell, “Optomechanical self-channeling of light in a suspended planar dual-nanoweb waveguide,” Phys. Rev. Lett. 108(9), 093903 (2012).
[Crossref] [PubMed]

Debord, B.

Edavalath, N. N.

Eftekhari, F.

M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys. 5(12), 915–919 (2009).
[Crossref]

Frosz, M. H.

Gerome, F.

Girvin, S. M.

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452(7183), 72–75 (2008).
[Crossref] [PubMed]

Gordon, R.

M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys. 5(12), 915–919 (2009).
[Crossref]

Günendi, M. C.

Harris, J. G. E.

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452(7183), 72–75 (2008).
[Crossref] [PubMed]

Hollberg, L.

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, “Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure,” Phys. Rev. Lett. 55(1), 48–51 (1985).
[Crossref] [PubMed]

Hugonnot, E.

Jayich, A. M.

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452(7183), 72–75 (2008).
[Crossref] [PubMed]

Juan, M. L.

M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys. 5(12), 915–919 (2009).
[Crossref]

Kippenberg, T. J.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

Koehler, J. R.

J. R. Koehler, R. E. Noskov, A. A. Sukhorukov, A. Butsch, D. Novoa, and P. St. J. Russell, “Resolving the mystery of milliwatt-threshold opto-mechanical self-oscillation in dual-nanoweb fiber,” APL Photonics 1(5), 056101 (2016).
[Crossref]

Lacroix, S.

J. L. Archambault, R. J. Black, S. Lacroix, and J. Bures, “Loss calculations for antiresonant wave-guides,” J. Lightwave Technol. 11(3), 416–423 (1993).
[Crossref]

Marquardt, F.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452(7183), 72–75 (2008).
[Crossref] [PubMed]

Maurel, M.

Ménard, J.-M.

Neumeier, L.

L. Neumeier, R. Quidant, and D. E. Chang, “Self-induced back-action optical trapping in nanophotonic systems,” New J. Phys. 17(12), 123008 (2015).
[Crossref]

Noskov, R. E.

J. R. Koehler, R. E. Noskov, A. A. Sukhorukov, A. Butsch, D. Novoa, and P. St. J. Russell, “Resolving the mystery of milliwatt-threshold opto-mechanical self-oscillation in dual-nanoweb fiber,” APL Photonics 1(5), 056101 (2016).
[Crossref]

Novoa, D.

J. R. Koehler, R. E. Noskov, A. A. Sukhorukov, A. Butsch, D. Novoa, and P. St. J. Russell, “Resolving the mystery of milliwatt-threshold opto-mechanical self-oscillation in dual-nanoweb fiber,” APL Photonics 1(5), 056101 (2016).
[Crossref]

Pang, Y.

M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys. 5(12), 915–919 (2009).
[Crossref]

Pennetta, R.

Quidant, R.

L. Neumeier, R. Quidant, and D. E. Chang, “Self-induced back-action optical trapping in nanophotonic systems,” New J. Phys. 17(12), 123008 (2015).
[Crossref]

M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys. 5(12), 915–919 (2009).
[Crossref]

Roth, P.

Russell, P. St. J.

Scol, F.

Sukhorukov, A. A.

J. R. Koehler, R. E. Noskov, A. A. Sukhorukov, A. Butsch, D. Novoa, and P. St. J. Russell, “Resolving the mystery of milliwatt-threshold opto-mechanical self-oscillation in dual-nanoweb fiber,” APL Photonics 1(5), 056101 (2016).
[Crossref]

Thompson, J. D.

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452(7183), 72–75 (2008).
[Crossref] [PubMed]

Uebel, P.

Vincetti, L.

Wong, G. K. L.

Xie, S.

Zwickl, B. M.

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452(7183), 72–75 (2008).
[Crossref] [PubMed]

APL Photonics (1)

J. R. Koehler, R. E. Noskov, A. A. Sukhorukov, A. Butsch, D. Novoa, and P. St. J. Russell, “Resolving the mystery of milliwatt-threshold opto-mechanical self-oscillation in dual-nanoweb fiber,” APL Photonics 1(5), 056101 (2016).
[Crossref]

Biophys. J. (1)

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992).
[Crossref] [PubMed]

J. Lightwave Technol. (1)

J. L. Archambault, R. J. Black, S. Lacroix, and J. Bures, “Loss calculations for antiresonant wave-guides,” J. Lightwave Technol. 11(3), 416–423 (1993).
[Crossref]

Nat. Phys. (1)

M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys. 5(12), 915–919 (2009).
[Crossref]

Nature (1)

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452(7183), 72–75 (2008).
[Crossref] [PubMed]

New J. Phys. (1)

L. Neumeier, R. Quidant, and D. E. Chang, “Self-induced back-action optical trapping in nanophotonic systems,” New J. Phys. 17(12), 123008 (2015).
[Crossref]

Opt. Lett. (1)

Optica (3)

Phys. Rev. Lett. (2)

A. Butsch, C. Conti, F. Biancalana, and P. St. J. Russell, “Optomechanical self-channeling of light in a suspended planar dual-nanoweb waveguide,” Phys. Rev. Lett. 108(9), 093903 (2012).
[Crossref] [PubMed]

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, “Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure,” Phys. Rev. Lett. 55(1), 48–51 (1985).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

Other (1)

P. St. J. Russell, T. A. Birks, and F. D. Lloyd-Lucas, “Photonic Bloch Waves and Photonic Band Gaps,” Confined Electrons and Photons, E. Burstein and C. Weisbuch, eds., NATO ASI Series (Plenum Press), Vol. 340, 585–633 (1995).

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Figures (8)

Fig. 1
Fig. 1 Sketch of the planar system. A glass nanoplate of a thickness h is placed inside a hollow planar waveguide of width w. The optical modes propagate in the z-direction and the nanoplate is considered to be attached to imaginary springs, which in the absence of any optical forces will return the nanoplate (position y = η) to the base position y = ηB.
Fig. 2
Fig. 2 (a) Dimensionless optical pressure for five different values of nanoplate mode order m, plotted against nanoplate position. On resonance (m = 2) the forces are zero. As m deviates more and more from 2, the anti-resonance grows in strength, producing stronger and stronger optical forces. (b) The corresponding modal refractive indices. For m = 2 (dashed line) the nanoplate is fully transparent, i.e., it acts like an anti-reflection coating. As a result the refractive index does not vary with the position of the nanoplate.
Fig. 3
Fig. 3 Sketch Supermode field intensity profiles in the resonant and anti-resonant cases. The insets are magnified versions of the fields in the vicinity of the nanoplate. (a) Intensity profiles for two positions of an m = 2 resonant nanoplate (TE polarization). The profile of the hollow waveguide mode is almost unaffected by the nanoplate, which acts like an anti-reflection coating. (b) Intensity profiles for two positions of an m = 1.5 anti-resonant nanoplate (TE polarization). The supermode field profiles are strongly affected by the nanoplate, which acts like a strong reflector. The upper plot refers to point A in Fig. 2, and the lower plot to point B.
Fig. 4
Fig. 4 (a) Effects of laser detuning δkw on the optical pressure. Each value of m is exactly matched in the nanoplate at zero detuning, by adjusting hn (values shown). In every case, ηn = 0.52. (b) Optical pressure in the resonant case plotted versus nanoplate position in the vicinity of ηn = 0.52 for positive (blue) and negative (red) detuning. It is interesting that positive detuning from a zero creates a positive pressure and thus an anti-trap, whereas negative detuning creates a trap (shaded region in (a)). There is a close analogy with red and blue detuning of an atomic resonance.
Fig. 5
Fig. 5 Bistability in the position of a sprung anti-resonant nanoplate (m = 1.5, kw = 100) as the base position is varied (see Fig. 1). With the light turned off, the base and nanoplate positions coincide (dotted line). If the mechanical spring constant is set to zero, the nanoplate will be stably trapped at the position marked by the small white circle at the center. Although the optical and mechanical forces are balanced at the yellow circles, these positions are anti-traps. Note that the nanoplate touches the mirrors at the edges of the gray-shaded regions.
Fig. 6
Fig. 6 Schematic of the SR-PCF plus nanoplate system. Left: sketch of the whole structure. The diagonal distance between the capillaries is D, and the inner diameter and wall thickness of the capillaries are d and t. Right: Detail showing the nanoplate dimensions and orientation.
Fig. 7
Fig. 7 (a) The optical force acting on a vertically aligned nanoplate (per unit fiber length per Watt of launched power) plotted against its horizontal (upper) and vertical (lower) position. Within the gray shaded regions, complex surface states appear that strongly distort the forces (not studied in this paper). (b) Normalized distributions of the z component of Poynting vector for the three different nanoplate positions marked in (a). The scale-bar marks a length of 10λ.
Fig. 8
Fig. 8 (a) Spatial map of the optical torque acting on the nanoplate near core center. (b) Upper: Optical torque plotted against nanoplate orientation θ for the three nanoplate positions marked in (a). Lower: The curve for position A plotted on an expanded vertical scale. The vertical gray lines mark the positions of the capillary centers. The white circles label the rotationally stable trapping positions, and the red, unstable positions.

Tables (1)

Tables Icon

Table 1 Membrane mode order and thickness at which the membrane mode and the supermode have the same refractive index. As m = 2 is approached, the index changes very little.

Equations (9)

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

sin( p v (1 h n ))+(qcosAcosB q 1 sinAsinB)tan p g h n =0,
n R = n g 2 (mπ/(kw h n )) 2 , n R <1
σ net =σ( η n + h n /2)σ( η n h n /2),
σ ^ net = σ net c n sm S av ,
τ opt = r× σ net ds ,
d 2 f d y 2 +( k 2 n 2 (y) β 2 )f=0
f 1 = f 2 and ξ 1 d f 1 dy = ξ 2 d f 2 dy ,
σ( y n )= S av 2c n sm [ ( n sm 2 ξ 2 1 ) f 2 ( y n ) ξ 2 ( f ( y n ) k 2 w 2 ) 2 ]
0 1 ξ( y n ) f 2 ( y n )d y n =1

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