Abstract

A topic of great current interest is the harnessing and enhancement of optical tweezer forces for trapping small objects of different sizes and shapes at relatively small powers. Here we demonstrate the stable trapping, inside the core of a hollow-core photonic crystal fiber (HC-PCF), of a mechanically compliant fused silica nanospike, formed by tapering a single-mode fiber (SMF). The nanospike is subwavelength in diameter over its ∼50  μm insertion length in the HC-PCF. Laser light, launched into the SMF core, adiabatically evolves into a mode that extends strongly into the space surrounding the nanospike. It then senses the presence of the hollow core, and the resulting optomechanical action and back-action results in a strong trapping force at the core center. The system permits lens-less, reflection-free, self-stabilized, and self-aligned coupling from SMF to HC-PCF with a demonstrated efficiency of 87.8%. The unique configuration also provides an elegant means of investigating optomechanical effects in optical tweezers, especially at very low pressures.

© 2016 Optical Society of America

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  23. J. Millen, T. Deesuwan, P. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nat. Nanotechnol. 9, 425–429 (2014).
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    [Crossref]
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2015 (1)

L. P. Neukirch, E. von Haartman, J. M. Rosenholm, and A. N. Vamivakas, “Multi-dimensional single-spin nano-optomechanics with a levitated nanodiamond,” Nat. Photonics 9, 653–657 (2015).
[Crossref]

2014 (2)

J. Millen, T. Deesuwan, P. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nat. Nanotechnol. 9, 425–429 (2014).
[Crossref]

J. Gieseler, R. Quidant, C. Dellago, and L. Novothy, “Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state,” Nat. Nanotechnol. 9, 358–364 (2014).
[Crossref]

2013 (4)

O. M. Marago, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013).
[Crossref]

G. Volpe, “Simulation of a Brownian particle in an optical trap,” Am. J. Phys. 81, 224–230 (2013).
[Crossref]

N. Descharmes, U. P. Dharanipathy, Z. Diao, M. Tonin, and R. Houdre, “Observation of backaction and self-induced trapping in a planar hollow photonic crystal cavity,” Phys. Rev. Lett. 110, 123601 (2013).
[Crossref]

J. Gieseler, L. Novotny, and R. Quidant, “Thermal nonlinearities in a nanomechanical oscillator,” Nat. Phys. 9, 806–810 (2013).
[Crossref]

2012 (2)

T. A. Birks, B. J. Mangan, A. Diez, J. L. Cruz, and D. F. Murphy, ““Photonic lantern” spectral filters in multi-core fiber,” Opt. Express 20, 13996–14008 (2012).
[Crossref]

J. Gieseler, B. Deutsch, R. Quidant, and L. Novotny, “Subkelvin parametric feedback cooling of a laser-trapped nanoparticle,” Phys. Rev. Lett. 109, 103603 (2012).
[Crossref]

2011 (3)

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

K. Dholakia and T. Cizmar, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[Crossref]

T. C. Li, S. Kheifets, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nat. Phys. 7, 527–530 (2011).
[Crossref]

2010 (2)

G. Volpe, L. Helden, T. Brettschneider, J. Wehr, and C. Bechinger, “Influence of noise on force measurements,” Phys. Rev. Lett. 104, 170602 (2010).
[Crossref]

T. Li, S. Kheifets, D. Medellin, and M. G. Raizen, “Measurement of the instantaneous velocity of a Brownian particle,” Science 328, 1673–1675 (2010).
[Crossref]

2009 (2)

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

P. T. Rakich, M. A. Popovic, and Z. Wang, “General treatment of optical forces and potentials in mechanically variable photonic systems,” Opt. Express 17, 18116–18135 (2009).
[Crossref]

2008 (1)

K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5, 491–505 (2008).
[Crossref]

2007 (1)

2006 (1)

2004 (1)

2000 (2)

T. A. Birks, J. C. Knight, and T. E. Dimmick, “High-resolution measurement of the fiber diameter variations using whispering gallery modes and no optical alignment,” IEEE Photon. Technol. Lett. 12, 182–183 (2000).
[Crossref]

A. Ashkin, “History of optical trapping and manipulation of small-neutral particle, atoms, and molecules,” IEEE J. Sel. Top. Quantum Electron. 6, 841–856 (2000).
[Crossref]

1994 (2)

1991 (1)

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: adiabaticity criteria,” IEE Proc. J. 138, 343–354 (1991).

1986 (1)

1983 (1)

M. Christen, “Air and gas damping of quartz tuning forks,” Sens. Actuators 4, 555–564 (1983).
[Crossref]

Anders, J.

J. Millen, T. Deesuwan, P. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nat. Nanotechnol. 9, 425–429 (2014).
[Crossref]

Ashkin, A.

A. Ashkin, “History of optical trapping and manipulation of small-neutral particle, atoms, and molecules,” IEEE J. Sel. Top. Quantum Electron. 6, 841–856 (2000).
[Crossref]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
[Crossref]

Barker, P.

J. Millen, T. Deesuwan, P. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nat. Nanotechnol. 9, 425–429 (2014).
[Crossref]

Bechinger, C.

G. Volpe, L. Helden, T. Brettschneider, J. Wehr, and C. Bechinger, “Influence of noise on force measurements,” Phys. Rev. Lett. 104, 170602 (2010).
[Crossref]

Birks, T. A.

Bjorkholm, J. E.

Black, R. J.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: adiabaticity criteria,” IEE Proc. J. 138, 343–354 (1991).

Block, S. M.

Brettschneider, T.

G. Volpe, L. Helden, T. Brettschneider, J. Wehr, and C. Bechinger, “Influence of noise on force measurements,” Phys. Rev. Lett. 104, 170602 (2010).
[Crossref]

Christen, M.

M. Christen, “Air and gas damping of quartz tuning forks,” Sens. Actuators 4, 555–564 (1983).
[Crossref]

Chu, S.

Cizmar, T.

K. Dholakia and T. Cizmar, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[Crossref]

Cruz, J. L.

Deesuwan, T.

J. Millen, T. Deesuwan, P. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nat. Nanotechnol. 9, 425–429 (2014).
[Crossref]

Dellago, C.

J. Gieseler, R. Quidant, C. Dellago, and L. Novothy, “Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state,” Nat. Nanotechnol. 9, 358–364 (2014).
[Crossref]

Descharmes, N.

N. Descharmes, U. P. Dharanipathy, Z. Diao, M. Tonin, and R. Houdre, “Observation of backaction and self-induced trapping in a planar hollow photonic crystal cavity,” Phys. Rev. Lett. 110, 123601 (2013).
[Crossref]

Deutsch, B.

J. Gieseler, B. Deutsch, R. Quidant, and L. Novotny, “Subkelvin parametric feedback cooling of a laser-trapped nanoparticle,” Phys. Rev. Lett. 109, 103603 (2012).
[Crossref]

Dharanipathy, U. P.

N. Descharmes, U. P. Dharanipathy, Z. Diao, M. Tonin, and R. Houdre, “Observation of backaction and self-induced trapping in a planar hollow photonic crystal cavity,” Phys. Rev. Lett. 110, 123601 (2013).
[Crossref]

Dholakia, K.

K. Dholakia and T. Cizmar, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[Crossref]

Diao, Z.

N. Descharmes, U. P. Dharanipathy, Z. Diao, M. Tonin, and R. Houdre, “Observation of backaction and self-induced trapping in a planar hollow photonic crystal cavity,” Phys. Rev. Lett. 110, 123601 (2013).
[Crossref]

Diez, A.

Dimmick, T. E.

T. A. Birks, J. C. Knight, and T. E. Dimmick, “High-resolution measurement of the fiber diameter variations using whispering gallery modes and no optical alignment,” IEEE Photon. Technol. Lett. 12, 182–183 (2000).
[Crossref]

Dziedzic, J. M.

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, 915–919 (2009).
[Crossref]

Farwell, S. G.

Ferrari, A. C.

O. M. Marago, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013).
[Crossref]

Gieseler, J.

J. Gieseler, R. Quidant, C. Dellago, and L. Novothy, “Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state,” Nat. Nanotechnol. 9, 358–364 (2014).
[Crossref]

J. Gieseler, L. Novotny, and R. Quidant, “Thermal nonlinearities in a nanomechanical oscillator,” Nat. Phys. 9, 806–810 (2013).
[Crossref]

J. Gieseler, B. Deutsch, R. Quidant, and L. Novotny, “Subkelvin parametric feedback cooling of a laser-trapped nanoparticle,” Phys. Rev. Lett. 109, 103603 (2012).
[Crossref]

Gonthier, F.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: adiabaticity criteria,” IEE Proc. J. 138, 343–354 (1991).

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, 915–919 (2009).
[Crossref]

Gucciardi, P. G.

O. M. Marago, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013).
[Crossref]

Guffey, M. J.

Guyot-Sionnest, P.

Helden, L.

G. Volpe, L. Helden, T. Brettschneider, J. Wehr, and C. Bechinger, “Influence of noise on force measurements,” Phys. Rev. Lett. 104, 170602 (2010).
[Crossref]

Henry, W. M.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: adiabaticity criteria,” IEE Proc. J. 138, 343–354 (1991).

Houdre, R.

N. Descharmes, U. P. Dharanipathy, Z. Diao, M. Tonin, and R. Houdre, “Observation of backaction and self-induced trapping in a planar hollow photonic crystal cavity,” Phys. Rev. Lett. 110, 123601 (2013).
[Crossref]

Jones, P. H.

O. M. Marago, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013).
[Crossref]

Juan, M. L.

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5, 349–356 (2011).
[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, 915–919 (2009).
[Crossref]

Kheifets, S.

T. C. Li, S. Kheifets, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nat. Phys. 7, 527–530 (2011).
[Crossref]

T. Li, S. Kheifets, D. Medellin, and M. G. Raizen, “Measurement of the instantaneous velocity of a Brownian particle,” Science 328, 1673–1675 (2010).
[Crossref]

Kim, H. Y.

Knight, J. C.

T. A. Birks, J. C. Knight, and T. E. Dimmick, “High-resolution measurement of the fiber diameter variations using whispering gallery modes and no optical alignment,” IEEE Photon. Technol. Lett. 12, 182–183 (2000).
[Crossref]

Lacroix, S.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: adiabaticity criteria,” IEE Proc. J. 138, 343–354 (1991).

Li, T.

T. Li, S. Kheifets, D. Medellin, and M. G. Raizen, “Measurement of the instantaneous velocity of a Brownian particle,” Science 328, 1673–1675 (2010).
[Crossref]

Li, T. C.

T. C. Li, S. Kheifets, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nat. Phys. 7, 527–530 (2011).
[Crossref]

Liu, M.

Liu, M. Z.

Lou, J. Y.

Love, J. D.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: adiabaticity criteria,” IEE Proc. J. 138, 343–354 (1991).

Mangan, B. J.

Marago, O. M.

O. M. Marago, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013).
[Crossref]

Mazur, E.

Medellin, D.

T. Li, S. Kheifets, D. Medellin, and M. G. Raizen, “Measurement of the instantaneous velocity of a Brownian particle,” Science 328, 1673–1675 (2010).
[Crossref]

Millen, J.

J. Millen, T. Deesuwan, P. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nat. Nanotechnol. 9, 425–429 (2014).
[Crossref]

Murphy, D. F.

Nagy, A.

K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5, 491–505 (2008).
[Crossref]

Neukirch, L. P.

L. P. Neukirch, E. von Haartman, J. M. Rosenholm, and A. N. Vamivakas, “Multi-dimensional single-spin nano-optomechanics with a levitated nanodiamond,” Nat. Photonics 9, 653–657 (2015).
[Crossref]

Neuman, K. C.

K. C. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy,” Nat. Methods 5, 491–505 (2008).
[Crossref]

Novothy, L.

J. Gieseler, R. Quidant, C. Dellago, and L. Novothy, “Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state,” Nat. Nanotechnol. 9, 358–364 (2014).
[Crossref]

Novotny, L.

J. Gieseler, L. Novotny, and R. Quidant, “Thermal nonlinearities in a nanomechanical oscillator,” Nat. Phys. 9, 806–810 (2013).
[Crossref]

J. Gieseler, B. Deutsch, R. Quidant, and L. Novotny, “Subkelvin parametric feedback cooling of a laser-trapped nanoparticle,” Phys. Rev. Lett. 109, 103603 (2012).
[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, 915–919 (2009).
[Crossref]

Pannell, C. N.

Pelton, M.

Pesic, J.

Popovic, M. A.

Quidant, R.

J. Gieseler, R. Quidant, C. Dellago, and L. Novothy, “Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state,” Nat. Nanotechnol. 9, 358–364 (2014).
[Crossref]

J. Gieseler, L. Novotny, and R. Quidant, “Thermal nonlinearities in a nanomechanical oscillator,” Nat. Phys. 9, 806–810 (2013).
[Crossref]

J. Gieseler, B. Deutsch, R. Quidant, and L. Novotny, “Subkelvin parametric feedback cooling of a laser-trapped nanoparticle,” Phys. Rev. Lett. 109, 103603 (2012).
[Crossref]

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5, 349–356 (2011).
[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, 915–919 (2009).
[Crossref]

Raizen, M. G.

T. C. Li, S. Kheifets, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nat. Phys. 7, 527–530 (2011).
[Crossref]

T. Li, S. Kheifets, D. Medellin, and M. G. Raizen, “Measurement of the instantaneous velocity of a Brownian particle,” Science 328, 1673–1675 (2010).
[Crossref]

Rakich, P. T.

Righini, M.

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

Rosenholm, J. M.

L. P. Neukirch, E. von Haartman, J. M. Rosenholm, and A. N. Vamivakas, “Multi-dimensional single-spin nano-optomechanics with a levitated nanodiamond,” Nat. Photonics 9, 653–657 (2015).
[Crossref]

Russell, P. St. J.

Scherer, N. E.

Scherer, N. F.

Smith, G.

Stewart, W. J.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: adiabaticity criteria,” IEE Proc. J. 138, 343–354 (1991).

Svoboda, K.

Tong, L. M.

Tonin, M.

N. Descharmes, U. P. Dharanipathy, Z. Diao, M. Tonin, and R. Houdre, “Observation of backaction and self-induced trapping in a planar hollow photonic crystal cavity,” Phys. Rev. Lett. 110, 123601 (2013).
[Crossref]

Toussaint, K. C. J.

Vamivakas, A. N.

L. P. Neukirch, E. von Haartman, J. M. Rosenholm, and A. N. Vamivakas, “Multi-dimensional single-spin nano-optomechanics with a levitated nanodiamond,” Nat. Photonics 9, 653–657 (2015).
[Crossref]

Volpe, G.

G. Volpe, “Simulation of a Brownian particle in an optical trap,” Am. J. Phys. 81, 224–230 (2013).
[Crossref]

O. M. Marago, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8, 807–819 (2013).
[Crossref]

G. Volpe, L. Helden, T. Brettschneider, J. Wehr, and C. Bechinger, “Influence of noise on force measurements,” Phys. Rev. Lett. 104, 170602 (2010).
[Crossref]

von Haartman, E.

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Supplementary Material (1)

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Figures (5)

Fig. 1.
Fig. 1. Optomechanically coupled silica nanospike and a HC-PCF. (a) 3D sketch of the experimental system. Inset: top, optical micrograph of a silica nanospike inserted into HC-PCF; bottom, SEM of the final section of the nanospike. (b) Left-hand plot: simulated adiabatic evolution of the nanospike mode (z component of Poynting vector is plotted) over the 50 μm insertion length, with the nanospike placed at the core center. The gray-shaded area represents the core wall, and the dashed curves indicate the local MFD. Right-hand plot: SEM of the HC-PCF structure along with the measured near-field profile of the mode excited by the nanospike. (c) Left-hand plot: measured local taper angle versus diameter for the whole pretaper and nanospike (blue open-circles) before insertion into the HC-PCF. The solid black line represents the adiabaticity criterion in free space. Right-hand plot: local taper angle versus diameter close to the tip of the nanospike when it is inserted 50 μm into the HC-PCF. The solid curves show the adiabaticity criteria for the “nanospike plus hollow core” structure with different offsets δ of the nanospike from the core center. The joined circles show the actual taper angle versus diameter. Adiabaticity is violated for δ=3  μm at a taper diameter of ∼160  nm.

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Fig. 2.
Fig. 2. Experimental setup. (a) Diagram of the measurement setup: PD, photodiode; PC, polarization controller; NS, nanospike; QPD, quadrant photodiode. (b) Typical Brownian motion spectrum at 10 μW input power, measured at 0.4 mbar and 0.32 μbar with the nanospike placed just outside the HC-PCF. (c) Measured spectral linewidth of thermal Brownian motion of the nanospike plotted against pressure. The dashed black line shows the linear fit to viscous damping.

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Fig. 3.
Fig. 3. Optical trapping force calculation and optical spring effect. (a) Simulated optical trapping force for 1 W of power plotted against the nanospike offset from the core center, calculated by integrating the Maxwell stress tensor (blue open-circles) and using response theory (blue dashed line). The red solid curve shows the trapping force when a focused Gaussian beam, with waist matching the MFD of the HC-PCF, is used. The orange dashed line plots the calculated effective mode index of the fundamental mode of a hollow core with a 150 nm glass strand placed inside. (b) Scaling of measured and simulated values of fR2−fm2 versus power for different values of base offset Δ from fiber axis. (c) Simulated Poynting vector distributions of the supermode at δ=1 and 3 μm for a hollow core containing a 150 nm glass strand. The bottom figures show the zoom-in around the strand. (d), (e) Measured Brownian motion spectra at (d) 0.4 mbar and (e) 0.32 μbar for several different power levels. The solid curves are fits to Lorentzian lineshapes.

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Fig. 4.
Fig. 4. Efficient coupling from SMF to HC-PCF. (a) Simulated mode-field diameter for a nanospike in free space (blue) and in the center of the hollow core (orange) for a core diameter of 12.1 μm. For tip diameters below ∼190  nm, the fundamental mode is guided mainly by the HC-PCF (gray-shaded area). The purple curve shows how the coupling efficiency varies with the final tip diameter when the nanospike is centered in the core. The solid purple dots show the coupling efficiencies measured for nanospikes with different final tip diameters. (b) Self-alignment and self-stabilization measured at atmospheric pressure, when the base of the nanospike is offset from the center by 0, 1, 2, 3, and 4 μm. Inset: transmitted signal recorded over 200 s at 450 mW (dark green) and 1 mW (bright green) when the nanospike is at the core center. The gray curve is the laser output monitored simultaneously (via PD1, scaled for comparison) at 450 mW, showing that the noise on the transmitted signal is caused by the laser.

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Fig. 5.
Fig. 5. Bistability and hysteresis of the transmission at atmospheric pressure. (a)–(d) Measured transmission at different input powers when the base of the nanospike is scanned from the central axis of the HC toward the core wall (blue) and then back (orange). The dashed arrows in (b) and (c) indicate the theoretical predicted switching points of the nanospike. Inset in (c): measured near-field mode profile for a value of Δ beyond the switching point. (e) Illustration of the bistability and hysteresis behavior due to the excitation of the LP11 mode of the “nanospike plus hollow core” structure.

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Equations (1)

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Fopt=Pc∫0L∂neff∂δdz,

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