Nándor Bokor

High-numerical-aperture focusing of radially polarized doughnut beams with a parabolic mirror and a flat diffractive lens

Recently, Dorn et al. [Phys. Rev. Lett. 91, 233901 (2003)] demonstrated the significance of radially polarized doughnut beams in obtaining very small focal spots (with an area of approximately 0.26 lambda2) with high-numerical-aperture (NA) aplanatic microscope objectives. We propose two simple alternative ways to focus such radially polarized beams: a parabolic mirror and a flat diffractive lens. Because of their large apodization factor for a high NA, a significant further reduction in spot area (up to a factor of 1.76 at a NA of 1) compared with the aplanatic system can be achieved.

Toward a spherical spot distribution with 4π focusing of radially polarized light

The properties of the focal spot for 4pi focusing with radially polarized light are presented for various apodization factors. With a focusing system satisfying the Herschel condition, sharp focal spots with almost-perfect spherical symmetry (leading to equal axial and transverse resolution) and extremely low sidelobes are achieved.

Investigation of polarization effects for high-numerical-aperture first-order Laguerre-Gaussian beams by 2D scanning with a single fluorescent microbead

The focal intensity distribution of strongly focused (NA=0.9) first order Laguerre-Gaussian doughnut beams is investigated experimentally for three different polarizations: linear, and left-handed circular and right-handed circular. The investigations are done by 2-dimensional scanning the focal plane with of a 100nm diameter fluorescent microbead, and measuring the fluorescence signal. The results are shown to be in excellent agreement with theoretical predictions, and demonstrate the superiority of one of the circular polarizations to achieve a sharp dark central spot.

Generation of a hollow dark spherical spot by 4pi focusing of a radially polarized Laguerre-Gaussian beam

The properties of the focal spot for 4pi focusing with radially polarized first-order Laguerre-Gaussian beams are calculated. It is shown that a focal spot that has an extremely sharp dark region at the center and an almost-perfect spherical symmetry can be achieved. When such a hollow dark spherical spot is used in 4pi fluorescence depletion microscopy, an axial FWHM spot size of approximately 39 nm and a transverse FWHM spot size of approximately 64 nm can be achieved simultaneously in a practical system.

Investigation of the center intensity of first- and second-order Laguerre-Gaussian beams with linear and circular polarization

The vectorial Debye integral shows that tightly focused Laguerre-Gaussian (LG) beams have a residual intensity at the focal point for linear polarization, for a topological charge of m=1 and 2. We measured the shapes of linearly and circularly polarized LG beams and found that a central intensity appeared at m=1 and 2 for linear and right-handed circular polarization, however, it is completely canceled for left-handed circular polarization. In general, when the orbital angular momentum of the LG beam is parallel to the spin angular momentum of the photons, zero intensity is always achieved at the focus.

Construction of super-resolution microscope based on cw laser light source

We constructed a super-resolution microscope system based on a cw laser light source. Electro-optical modulators convert the cw laser light into a light pulse with a width of 15ns and provide a repetition rate of 100kHz. The performance of the microscope was evaluated using 100nmϕ fluorescence microbeads. The fluorescence signal from the beads can be detected with very low statistical fluctuation. The super-resolution image was obtained with better signal to noise ratio compared with that given by a pulse laser light source with a repetition rate of several tens of hertz. The fluorescent size of the beads was 150nm, which is 2.3 times smaller than the diffraction limit. Experimental results confirmed that the two-point resolution also overcomes the diffraction limit. The constructed system is expected to become a commercial microscope.

Measurement of contrast transfer function in super-resolution microscopy using two-color fluorescence dip spectroscopy

The contrast transfer function (CTF) of super-resolution microscopy was quantitatively investigated using a fluorescent scale. The scale has minute fluorescent line patterns, finer than 100 nm, and is suitable for measuring CTF in super-resolution microscopy. The measured CTF shows that super-resolution microscopy can indeed improve the optical properties of fluorescent images and enable us to observe a structure with the spatial resolution overcoming the diffraction limit. From the CTF, it has been found that super-resolution microcopy can resolve a 100 nm line-and-space pattern and provides a contrast of 10%. The CTF corresponds to a PSF with a full-width at half-maximum (FWHM) of 130 nm. An evaluation using a 100 nmφ fluorescent bead consistently supports the results given by the CTF for super-resolution microscopy.

Light collimation, imaging, and concentration at the thermodynamic limit

A new type of optical instrument, the curved hologram, is introduced that allows us the unique opportunity to independently control its spatial phase function and its shape (whereas in reflecting or refracting optical elements the shape uniquely determines the spatial phase function). We show how proper design of the hologram shape (using a simple analytic procedure) yields perfect uniform collimation and also collimation and concentration of diffuse (monochromatic) light at the thermodynamic limit of brightness conservation. The results of our experimental demonstration as well as those of our numerical ray-tracing simulations verify our design.

Solving the inverse problem of high numerical aperture focusing using vector Slepian harmonics and vector Slepian multipole fields

Abstract A technique using vector Slepian harmonics and vector Slepian multipole fields is presented for a general treatment of the inverse problem of high numerical aperture focusing. A prescribed intensity distribution or electric field distribution in the focal volume is approximated using numerical optimization and the corresponding illuminating field at the entrance pupil is constructed. Three examples from the recent literature are chosen to illustrate the method.

Laguerre-Gaussian radial Hilbert transform for edge-enhancement Fourier transform x-ray microscopy.

An efficient technique to achieve isotropic edge enhancement in optics involves applying a radial Hilbert transform on the object spectrum. Here we demonstrate a simple setup for isotropic edge-enhancement in soft-x- ray microscopy, using a single diffractive Laguerre-Gaussian zone plate (LGZP) for radial Hilbert transform. Since the LGZP acts as a beam-splitter, diffraction efficiency problems usually associated with x-ray microscopy optics are not present in this system. As numerically demonstrated, the setup can detect optical path differences as small as lambda/50 with high contrast.