Sergey S. Stafeev

Analysis of the shape of a subwavelength focal spot for the linearly polarized light

By decomposing a linearly polarized light field in terms of plane waves, the elliptic intensity distribution across the focal spot is shown to be determined by the E-vectors longitudinal component. Considering that the Poynting vectors projection onto the optical axis (power flux) is independent of the E-vectors longitudinal component, the power flux cross section has a circular form. Using a near-field scanning optical microscope (NSOM) with a small-aperture metal tip, we show that a glass zone plate (ZP) having a focal length of one wavelength focuses a linearly polarized Gaussian beam into a weak ellipse with the Cartesian axis diameters FWHM(x)=(0.44±0.02)λ and FWHM(y)=(0.52±0.02)λ and the (depth of focus) DOF=(0.75±0.02)λ, where λ is the incident wavelength. The comparison of the experimental and simulation results suggests that NSOM with a hollow pyramidal aluminum-coated tip (with 70° apex and 100 nm diameter aperture) measures the transverse intensity, rather than the power flux or the total intensity. The conclusion that the small-aperture metal tip measures the transverse intensity can be inferred from the Bethe-Bouwkamp theory.

Tight focusing with a binary microaxicon

Using a near-field scanning microscope (NT-MDT) with a 100 nm aperture cantilever held 1 μm apart from a microaxicon of diameter 14 μm and period 800 nm, we measure a focal spot resulting from the illumination by a linearly polarized laser light of wavelength λ=532 nm, with its FWHM being equal to 0.58λ, and the depth of focus being 5.6λ. The rms deviation of the focal spot intensity from the calculated value is 6%. The focus intensity is five times larger than the maximal illumination beam intensity.

Tight focus of light using micropolarizer and microlens

Using a binary microlens of diameter 14 μm and focal length 532 nm (NA=0.997) in resist, we focus a 633 nm laser beam into a near-circular focal spot with dimensions (0.35 ± 0.02)λ and (0.38 ± 0.02)λ (λ is incident wavelength) at full width half-maximum intensity. The area of the focal spot is 0.105λ(2). The incident light is a mixture of linearly and radially polarized beams generated by reflecting a linearly polarized Gaussian beam at a 100  μm × 100  μm four-sector subwavelength diffractive optical microelement with a gold coating. The focusing of a linearly polarized laser beam (the other conditions being the same) is found to produce an elliptical focal spot measuring (0.40 ± 0.02)λ and (0.50 ± 0.02)λ. To our knowledge, this is the first implementation of subwavelength focusing of light using a pair of micro-optic elements (a binary microlens and a micropolarizer).

Subwavelength focusing of laser light by microoptics

Near-field scanning optical microscope (NSOM) measurements revealed that a linearly polarized Gaussian beam of wavelength λ = 532 nm focused with a binary zone plate (ZP) of focal length λ, radius 7 μm, and groove depth 510 nm, fabricated in hydrogen silsesquioxane, produces a focal spot of size FWHM = (0.44 ± 0.02)λ, with the side lobes being lower than 10% of the intensity peak in the focus. Replacing the incident 532 nm wavelength with a 633 nm wavelength resulted in a 1.8 times shorter focal length and a tighter (in terms of wavelengths) focal spot of FWHM = (0.40 ± 0.02)λ. This value is smaller than the scalar diffraction-limited size in vacuum, FWHM = 0.51λ. This is the smallest focal spot so far experimentally obtained for a binary phase ZP and the root-mean-square deviation of the experimental curve from a FDTD simulation is 5%. We show that the metallic pyramid-shaped cantilever with a 100-nm-hole in the tip that is used in the NSOM is only able to detect the transverse electric field component. The FDTD simulation showed such a cantilever to be over 3 times more sensitive to the transverse electric field component than to the longitudinal one. Using the Richards–Wolf (RW) formulae, the near-focus intensity distribution can be calculated with 6% error for focal lengths larger than 4λ. It is usually assumed that the Debye theory and the RW formulae are only valid for focal lengths much larger than the incident wavelength. By FDTD simulation, we showed that when illuminating the ZP by a radially (rather than linearly) polarized beam, a decrease in the focal spot transverse size did not result in a substantially reduced total volume of focus (4%).

Curved laser microjet in near field

With the use of the finite-difference time-domain-based simulation and a scanning near-field optical microscope that has a metal cantilever tip, the diffraction of a linearly polarized plane wave of wavelength λ by a glass corner step of height 2λ is shown to generate a low divergence laser jet of a root-parabolic form: over a distance of 4.7λ on the optical axis, the beam path is shifted by 2.1λ. The curved laser jet of the FWHM length depth of focus=9.5λ has the diameter FWHM=1.94λ over the distance 5.5λ, and the intensity maximum is 5 times higher than the incident wave intensity. The discrepancy between the analytical and the experimental results amounts to 11%.

Subwavelength micropolarizer in a gold film for visible light

We have designed and fabricated a 100  μm×100  μm four-sector binary subwavelength reflecting polarization microconverter in a gold film. Using finite-difference time-domain-aided numerical simulations and experiments, the micropolarizer was shown to convert an incident linearly polarized Gaussian beam of wavelength 532 nm into an azimuthally polarized beam. Conditions for generating on-axis regions of nonzero intensity when using propagating optical vortices with different initial polarization were deduced. By putting a spiral phase plate into an azimuthally polarized beam, the intensity pattern was shown to change from diffraction rings to a central peak.

Microlens-aided focusing of linearly and azimuthally polarized laser light

We have investigated a four-sector transmission polarization converter (4-SPC) for a wavelength of 633 nm, that enables the conversion of a linearly polarized incident beam into a mixture of linearly and azimuthally polarized beams. It was numerically shown that by placing a Fresnel zone plate of focal length 532 nm immediately after the 4-SPC, the incident light can be focused into an oblong subwavelength focal spot whose size is smaller than the diffraction limit (with width and breadth, respectively, measuring FWHM = 0.28λ and FWHM = 0.45λ, where λ is the incident wavelength and FWHM stands for full-width at half maximum of the intensity). After passing through the 4-SPC, light propagates in free space over a distance of 300 μm before being focused by a Fresnel zone plate (ZP), resulting in focal spot measuring 0.42λ and 0.81λ. The focal spot was measured by a near-field microscope SNOM, and the transverse E-field component of the focal spot was calculated to be 0.42λ and 0.59λ. This numerical result was verified experimentally, giving a focal spot of smaller and larger size, respectively, measuring 0.46λ and 0.57λ. To our knowledge, this is the first implementation of polarization conversion and subwavelength focusing of light using a pair of transmission micro-optic elements.

Thin high numerical aperture metalens

We designed, fabricated, and characterized a thin metalens in an amorphous silicon film of diameter 30 µm, focal length equal to the incident wavelength 633 nm. The lens is capable of simultaneously manipulating the state of polarization and phase of incident light. The lens converts a linearly polarized beam into radially polarized light, producing a subwavelength focus. When illuminated with a linearly polarized Gaussian beam, the lens produces a focal spot whose size at full-width half-maximum intensity is 0.49λ and 0.55λ (λ is incident wavelength). The experimental results are in good agreement with the numerical simulation, with the simulated focal spot measuring 0.46λ and 0.52λ. This focal spot is less than all other focal spots obtained using metalenses.

Elongated Photonic Nanojet from Truncated Cylindrical Zone Plate

Previously (Chen et al., 2004), it was shown that dielectric cylinder can form focal spots with small diameters and long depth. This type of focal spot was called photonic nanojet. In this paper, it was shown that dielectric cylinder of radius 595 nm (1.12 of wavelength) forms near the surface a photonic nanojet with diameter equal to 0.31 of wavelength and depth of focus equal to 0.57 of wavelength. Adding truncated concentric rings with radiuses equal to radiuses of zone plate to the cylinder increases the depth of focus to 1.18 of the wavelength. The diameter and intensity of focal spot near the cylinder surface remain unchanged.

High Resolution through Graded-Index Microoptics

By solving Helmholtz equations, relationships to describe propagating modes in an arbitrary graded-index planar waveguide are derived. We show that in the quadratic- and secant-index waveguides a minimal mode width is 0.4, where is the wavelength in free space and is the refractive index on the fiber axis. By modeling in FullWAVE, we show that the high-resolution imaging can be achieved with half-pitch graded-index Mikaelian microlenses (ML) and Maxwell’s “fisheye” lenses. It is shown that using a 2D ML, the point source can be imaged near the lens surface as a light spot with the full width at half maximum (FWHM) of 0.12λ. This value is close to the diffraction limit for silicon () in 2D media λ. We also show that half-pitch ML is able to resolve at half-maximum two close point sources separated by a 0.3λ distance.