Optical Forces – part II · Forces due to ﬂuctuating ﬁelds! Forces arise due to correlated...

www.photonics.ethz.ch

Optical Forces – part II 28/11/2014


Scattering force Proportional to number of incident photons and scattering cross section


Refraction and reflection of light rays gives forces Fa and Fb whose vector sum is always restoring

Optical Force on a microsphere


Optical forces in the Dipole Approximation

Optical Force:

Time-average:

thus:

0(for non-relativistic speeds)

time-average:

Dipole Approximation

ARRANGING ..


/ 1 + sin(2!t)



Time-average:

Monochromatic fields:

Small particles :

Trapping efficiency :


OPTICAL TWEEZERS


Today

Trapping with near fields

Backaction effects

Maxwell stress tensor

Fluctuation induced forces

Trapping of atoms


Trapping with Near fields



(Monochromatic fields)



z

xy

Refraction

Snell’s law:

z

xy

Total internal reflection (TIR)

Evanescent fields




z

xy

Forces:

Energy flow only along x:

Field enhancement

Evanescent wave in z localization


Kawata, S. et al. Movement of micrometer-sized particles in the evanescent field of a laser beam. Opt. Lett. 17, 772–774 (1992).


Surface mode corresponds to pole of transmission coefficient

Field is enhanced at the boundary

Stronger field enhancement with metals (negative ε)


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


Travelling wave Standing wave Local field enhancement

Plasmonic Excitations


Intensity around sphere (dipole near field)

Approximate structure with a dipole

Plasmonic Trapping

Optical potential: Optical Force:

Field enhancement localization

Remember (planar interface):


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)


Righini et al. Parallel and selective trapping in a patterned plasmonic landscape. Nature Physics 3, 477–480 (2007)

Plasmonic Trapping


Trap off

Nature Photonics 5, 349 (2011)

Plasmonic Trapping

flow

trap particle

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



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)


Trapping of atoms

Atomic polarizability : (appendix A)

Rabi frequency

decay rate

transition frequency

transition dipole

Intensities and saturation parameter:


Trapping of atoms

SODIUM ATOMS

numbers in figure

Doppler shift

www.nano-optics.org www.photonics.ethz.ch


Backaction effects


Optical Binding

Tatarkova et al. One-Dimensional Optically Bound Arrays of Microscopic Particles. Physical Review Letters 89, 283901 (2002)


Self induced back-action

=> Cavity - optomechanics (next lecture)



MAXWELL:

LORENTZ:




+



Cooking it up

cycle-average:

(LORENTZ)


Finally …

Forces acting on object B are entirely determined by the fields on a surface enclosing B



Forces due to fluctuating fields



Fluctuating environment Fluctuating dipole

Forces arise due to correlated fluctuations in the particle and other bodies in the environment


Time-averaged force:

Monochromatic:

Fluctuating forces are broadband


Time – averaged force


Consider one iteration of induced fields / dipole:

environment

G

α


FLUCTUATION-DISSIPATION THEOREM:

Forces arise due to correlated fluctuations


Environment

Compact form

Compact form


Calculation of force when the environment is a single dipole


Reminder: Greens function for environment = dipole

Field at r due to dipole at r1:


Force between two fluctuating dipoles

The force is conservative

Casimir-Polder Potential


Casimir-Polder Potential:

Short distances

Van der Waals potential:

Force between two fluctuating dipoles



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)


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

Date post:	12-Jul-2020
Category:	Documents
Upload:	others
View:	1 times
Download:	0 times

Optical Forces – part II · Forces due to ﬂuctuating ﬁelds! Forces arise due to correlated...

Documents