Modelling the sharp focusing of laser light

Voronezh, 2010

Sergey StafeevSamara State Aerospace University Image Processing System Institute

REC-14, Samara

Introduction Decreasing the focal spot size is critical in lithography,

optical memory and micromanipulation Sharp focusing is a reaching a minimal focal spot size

beyond the diffraction limits.

Recently plasmons with FWHM = 0.35λ [Opt.Lett. - 2009. - Vol.34, no.8. - P.1180-1182], FWHM = 0.4λ [Opt. Lett. - 2009. - vol.34, no12. - p.1867-1869] had been obtained.

In this research we used two types of axicons: refractive and diffractive which were illuminated by radially polarized light

Radial-FDTD FDTD = finite

difference time domain

This method involves the numerical solution of Maxwell's equations in cylindrical coordinate system

We used a modification for a radially polarized light (R-FDTD)

There are three equations with three components Er, Ez and Hφ

z

jiHjiH

t

jiEjiEji

nnnr

nr

)21

,21

()21

,21

(),21

(),21

(),

2

1(

2

1

0,2

1

0,10,0,

0

r

jiHirjiHir

irt

jiEjiEji

nnnz

nz

)21

,21

()21

()21

,21

()21

(

)(

1)21

,()21

,()2

1,(

2

1

0,2

1

0,10,0,

0

r

jiEjiE

z

jiEjiE

t

jiHjiH nz

nz

nr

nr

nn

)21

,()21

,1(),21

()1,21

()21

,21

()21

,21

( 0,0,0,0,2

1

0,2

1

0,

0

,0 ,00 ,0

rr

H EE

z t

,0 ,00 ,0

1 zz

rH EE

r r t

,0,0 ,00

r z HE E

z r t

(1)

(2)

tt

Refractive microaxiconFocusing of radially-polarized mode R-TEM01

(3)

using refractive (conical) microaxicon

Radial section of a conical glass (n=1.5) microaxicon of radius R =

7 µm and height h = 6 µm

The (absolute value of) radial component of the electric field strength of the mode R-TEM01

FWHM=0.30λ HMA=0.071λ2

2

2

exp)(rr

erE rr

Instantaneous distributions of the amplitude Er and Ez for diffraction of the R-TEM01 laser mode by the refractive

microaxicon

The Intensity and FWHM of the focal spot as a function of axicons height

Er Ez

Refractive microaxicon: 3D modelling

the intensity distribution in focal plane

the intensity distribution along axicon axis

Binary microaxicon

FWHM = 0.39λ HMA= 0.119λ2

binary axicon with step height 633nm, period 1.48um, index of refraction n =

1.5

the intensity distribution along axicon axis

the intensity distribution in focal plane (on the axicons surface)

Focusing of radially-polarized mode R-TEM01 using binary microaxicon

Manufacture and experiment Three diffractive binary axicons

of periods 4 µm, 6 µm, and 8 µm and height 500nm were fabricated on silica substrate (n=1.46) using a laser writing system CLWS-200 (bought with CRDF money) and plasmo-chemical etching.

Diameter of the focal spot in the near-zone (z<40um) varies from 3.5λ to 4.5λ with a 2-um period for the axicon with period 4um.

The minimal diameter of focal spot equal to 3.6λ (FWHM=1.2λ)

An oblique image of the central part of the binary axicon of period 8 µm,

produced with the Solver Pro microscope (bought with CRDF money).

The diameter of the light spot on the axis (in wavelengths) as a function of distance from

binary axicons with period 4µm

Diffraction pattern and radial section of the intensity distribution recorded with the CCD-camera from the axicons with period 4 µm at different distances: 5 µm and 2 µm (λ=532nm)

Conclusions We have numerical shown that when illuminating a

conical glass microaxicon of base radius 7 µm and height 6 µm by a radially polarized laser mode R-TEM01 of wavelength λ =1 µm, in the close proximity (20 nm apart) to the cone apex, we obtain a sharp focus of transverse diameter at half-intensity FWHM=0.30λ and axial spot size at half-intensity FWHMz=0.12λ. The focal spot area at half-intensity equals HMA=0.071λ2.

Three diffractive binary axicons of periods 4 µm, 6 µm, and 8 µm and height 500nm were fabricated on silica substrate (n=1.46) using a laser writing system CLWS-200 (bought with CRDF money) and plasmo-chemical etching.

Diameter of the focal spot in the near-zone (z<40um) varies from 3.5λ to 4.5λ with a 2-um period for the axicon with period 4um.

The results of numerical simulation agree with experiment