nanoscale simulations laboratory department of mechatronics gwangju institute of science and...

Nanoscale Simulations LaboratoryNanoscale Simulations LaboratoryDepartment of MechatronicsDepartment of Mechatronics

Gwangju Institute of Science and Technology (GIST), KOREAGwangju Institute of Science and Technology (GIST), KOREA

이 용 구

Calculation of optical trapping forces summary

Yong-Gu Lee

나노 시뮬레이션 연구실Nanoscale Simulations Laboratory나노 시뮬레이션 연구실Nanoscale Simulations Laboratory

Rayleigh, Mie, and Ray-optics regimes

With Rayleigh scattering, the electric field is assumed to be invariant in the vicinity of the particle

Taken from the course notes of Radar Metrology by Prof. Bob Rauber (UIUC)http://www.atmos.uiuc.edu/courses/atmos410-fa04/presentations.html


Electromagnetic forces

+

S N

Moving + charge

Current flow direction

Electric force Magnetic force


Electromagnetic forces

3 2 2 2

2 2 2 2

coulombs volts kilogram[ ]

meter meter second meter

amperes webers kilogram[ ]

meter meter second meter

: Electric vector

: Magnetic vector

: free charge density

: electric curr

e

V

m

V

E F E

J B F J B

E

B

J ent density


Dielectric material (유전체 )

Dielectric material: poor conductor of electricity but an efficient supporter of electrostatic fields

Examples are: porcelain (ceramic), mica, glass, plastics, and the oxides of various metals. Dry air is an excellent dielectric. Distilled water is a fair dielectric. A vacuum is an exceptionally efficient dielectric.

Metals can be thought as dielectric at their outermost shells


Induced electric field in a dielectric object

E1

Incidentplanewave

DielectricSphere

+

-

-

+


Potential due to dipole

DielectricSphere

22

1 1 cos, higher order terms.

4 4

: Electric permittivity

q: Electric charge

: Charge separation

q qlr

r r r

l

- charge

+ charge2r

r

,r


Electric field inside dielectrics

2 12 1

(1) is continuous everywhere

(2) 0 across a surface bounding two dielectrics;

it is assumed that the interface of the dielectric bears no charge,

(3)

n n

E

21 0 0 0 1

1 2

3ˆ where

2E

E E E e2

1

Image from: Julius Adams Stratton, Electromagnetic theory, McGraw-Hill Book Company Inc. 1941


Gradient force (Rayleigh regime)

1 1 0

2 1 21 1 2 1 0

1 2

1

23 2 2

1 2 0 2

2 3 223 2 1 2

1 2 0 2 2

The energy of this polarized sphere in the external field is

1U

2

3

2

,

1 1, 4 ,

2 2

1 2 1

2 2

V

grad

grad grad T T

dv

t U

mt r n E t

m

m r n mr n E I

m c m

P E

P E E

F r

F r F r r

r r

1 2/m n n


Scattering force (Rayleigh regime)

Incidentplanewave

DielectricSphere

Scattered sphericalwave

2

,

/

where is the cross section for

the radiation pressure of the particles

pr Tscat

pr

C t

c n

C

S r

F r


Calculating Cpr

Maxwell’s equation

Decouple Maxwell’s equation

through Electric Hertz vector

Introduce the spherical scattering

geometry

Solve the decoupled

Maxwell’s equation for the scattering

cross section

Green’s function


This slide is taken from the lecture notes of Optical Tweezers in Biology by Prof. Dmitri Petrov https://www.icfo.es/courses/biophotonics2006/html/


Mie (scattering) theory

Spherical harmonics: Waves in spherical structures

Maxwell’s equation

Decouple Maxwell’s equation through Electric &

Magnetic Hertz vector

Solve the decoupled

Maxwell’s equation for the scattering

cross section

Spherical harmonics


Ray optics regime

Z

Y

O

PR

P

PT

PT R

PT R

2

22

2β

αα+β

β

θθ

r

r

θ-rΠ-2(θ-r)

θ

θ

r

θ-r

r

Π-(θ+r)

Angles measured

+z

+y Medium index of refraction n1

Sphere index of refraction n2


Metal trapping

An electronic field attenuates e-times in the skin layer

This slide is adapted from the lecture notes of Optical Tweezers in Biology by Prof. Dmitri Petrov https://www.icfo.es/courses/biophotonics2006/html/

nanoscale simulations laboratory department of mechatronics gwangju institute of science and...

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