optical forces – part ii · forces due to fluctuating fields! forces arise due to correlated...
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Optical Forces – part II 28/11/2014
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Scattering force Proportional to number of incident photons and scattering cross section
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Refraction and reflection of light rays gives forces Fa and Fb whose vector sum is always restoring
Optical Force on a microsphere
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Optical forces in the Dipole Approximation
Optical Force:
Time-average:
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thus:
0(for non-relativistic speeds)
time-average:
Dipole Approximation
ARRANGING ..
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/ 1 + sin(2!t)
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Optical forces in the Dipole Approximation
Time-average:
Monochromatic fields:
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Small particles :
Trapping efficiency :
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OPTICAL TWEEZERS
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Today
Trapping with near fields
Backaction effects
Maxwell stress tensor
Fluctuation induced forces
Trapping of atoms
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Trapping with Near fields
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Optical forces in the Dipole Approximation
(Monochromatic fields)
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Trapping with Near fields
z
xy
Refraction
Snell’s law:
z
xy
Total internal reflection (TIR)
Evanescent fields
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Trapping with Near fields
z
xy
Forces:
Energy flow only along x:
Field enhancement
Evanescent wave in z localization
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Kawata, S. et al. Movement of micrometer-sized particles in the evanescent field of a laser beam. Opt. Lett. 17, 772–774 (1992).
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Surface mode corresponds to pole of transmission coefficient
Field is enhanced at the boundary
Stronger field enhancement with metals (negative ε)
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Excitation of SPPs through thin metal film
k of photon in air is always < k of SPP
no excita>on of SPP is possible
Excita>on of SPP through thin film
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Travelling wave Standing wave Local field enhancement
Plasmonic Excitations
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Intensity around sphere (dipole near field)
Approximate structure with a dipole
Plasmonic Trapping
Optical potential: Optical Force:
Field enhancement localization
Remember (planar interface):
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Optical potential:
rt = ro = 5nm εp = 2.5 εm = 1.77 f = 3000
Plasmonic Trapping
Novotny et al. Theory of nanometric optical tweezers. Physical Review Letters 79, 645–648 (1997)
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Righini et al. Parallel and selective trapping in a patterned plasmonic landscape. Nature Physics 3, 477–480 (2007)
Plasmonic Trapping
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Trap off
Nature Photonics 5, 349 (2011)
Plasmonic Trapping
flow
trap particle
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Size dependent trapping
0 5 10 15 20 25 30
0.2
0.4
0.6
0.8
1.0
1.2
1.4
r0 (nm)
I 0(W
μm-2)
Small polarizability Large particle – tip distance
Optimum particle size for trapping
Minimum intensity to trap particle of radius r0 at r0 + rt
Design structures to trap specific particles (polarizability, size) => Sorting of particles
Required trap depth kBT
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d =3.55 µm d =4.88 µm
0 min 7 min 14 min
Size dependent trapping
Righini et al. Nature Physics 3, 477–480 (2007)
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Trapping of atoms
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Atomic polarizability : (appendix A)
Rabi frequency
decay rate
transition frequency
transition dipole
Intensities and saturation parameter:
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Trapping of atoms
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SODIUM ATOMS
numbers in figure
Doppler shift
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Backaction effects
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Optical Binding
Tatarkova et al. One-Dimensional Optically Bound Arrays of Microscopic Particles. Physical Review Letters 89, 283901 (2002)
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Self induced back-action
=> Cavity - optomechanics (next lecture)
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Maxwell stress tensor
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MAXWELL:
LORENTZ:
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Maxwell stress tensor
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+
Maxwell stress tensor
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Cooking it up
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cycle-average:
(LORENTZ)
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Finally …
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Forces acting on object B are entirely determined by the fields on a surface enclosing B
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Forces due to fluctuating fields
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Forces due to fluctuating fields
Fluctuating environment Fluctuating dipole
Forces arise due to correlated fluctuations in the particle and other bodies in the environment
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Time-averaged force:
Monochromatic:
Fluctuating forces are broadband
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Time – averaged force
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Consider one iteration of induced fields / dipole:
environment
G
α
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FLUCTUATION-DISSIPATION THEOREM:
Forces arise due to correlated fluctuations
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Environment
Compact form
Compact form
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Calculation of force when the environment is a single dipole
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Reminder: Greens function for environment = dipole
Field at r due to dipole at r1:
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Force between two fluctuating dipoles
The force is conservative
Casimir-Polder Potential
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Casimir-Polder Potential:
Short distances
Van der Waals potential:
Force between two fluctuating dipoles
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Forces due to fluctuating fields
Forces arise due to correlated fluctuations in the particle and other bodies in the environment
Force between two perfect conductors of area 1µm2 separated by 5nm: 2nN! ⇒ Gecko effect (millions of tiny kreatin hairs)
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Summary
Trapping with near fields field enhancement and strong localization lead to strong gradient forces
Backaction effects: Optical binding, Optomechanics
Maxwell stress tensor General treatment of optical forces
Fluctuation induced forces Correlated fluctuations
Trapping of atoms Frequency dependent polarizability, negative and positive forces, optical cooling