1. Modelling the sharp focusing of laser light Voronezh, 2010 Sergey Stafeev Samara State Aerospace University Image Processing System Institute REC-14, Samara

2. 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 = 0.35 λ [Opt.Lett. - 2009. - Vol.34, no.8. - P.1180-1182], FWHM = 0.4 λ [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

3. 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 E r, E z and H φ (1) (2)

4. Refractive microaxicon Focusing of r adially-polarized mode R- TEM 01 (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-TEM 01  FWHM=0.30λ  HMA=0.071λ 2

5. Instantaneous distributions of the amplitude E r and E z for diffraction of the R-TEM 01 laser mode by the refractive microaxicon The Intensity and FWHM of the focal spot as a function of axicons height ErEr EzEz Refractive microaxicon: 3D modelling the intensity distribution in focal plane the intensity distribution along axicon axis

6. Binary microaxicon  FWHM = 0.39λ  HMA= 0.119λ 2 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 r adially-polarized mode R- TEM 01 using binary microaxicon

7. 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 3.5 λ to 4.5 λ with a 2-um period for the axicon with period 4um.  The minimal diameter of focal spot equal to 3.6 λ (FWHM=1.2 λ ) 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 =532 nm )

8. 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-TEM 01 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=0.30 λ and axial spot size at half-intensity FWHM z =0.12 λ. The focal spot area at half- intensity equals HMA=0.071 λ 2.  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 3.5 λ to 4.5 λ with a 2-um period for the axicon with period 4um.  The results of numerical simulation agree with experiment