This paper presents an analytical model of the optical vortex scanning microscope. In this microscope the Gaussian beam with an embedded optical vortex is focused into the sample plane. Additionally, the optical vortex can be moved inside the beam, which allows fine scanning of the sample. We provide an analytical solution of the whole path of the beam in the system (within paraxial approximation)—from the vortex lens to the observation plane situated on the CCD camera. The calculations are performed step by step from one optical element to the next. We show that at each step, the expression for light complex amplitude has the same form with only four coefficients modified. We also derive a simple expression for the vortex trajectory of small vortex displacements.

An analytical model of an optical vortex microscope, in which a simple phase object was inserted into the illuminating beam, is presented. In this microscope, the focused vortex beam interacts with an object and transmits the corresponding information to the detection plane. It was shown that the beam at the detection plane can be separated analytically into two parts: a non-disturbed vortex part and an object beam part. The intensity of the non-disturbed part spreads out over the center; hence, the small disturbance introduced by the object can be detected at the image center. A first procedure for recovering information about the object from this set-up was proposed. The theory was verified experimentally.

The analytical solution for the propagation of the laser beam with optical vortex through the system of lenses is presented. The optical vortex is introduced into the laser beam (described as Gaussian beam) by spiral phase plate. The solution is general as it holds for the optical vortex of any integer topological charge, the off-axis position of the spiral phase plate and any number of lenses. Some intriguing conclusions are discussed. The higher order vortices are unstable and split under small phase or amplitude disturbance. Nevertheless, we have shown that off-axis higher order vortices are stable during the propagation through the set of lenses described in paraxial approximation, which is untypical behavior. The vortex trajectory registered at image plane due to spiral phase plate shift behaves like a rigid body. We have introduced a new factor which in our beam plays the same role as Gouy phase in pure Gaussian beam.

In our study, we describe the outcomes of the intercalation of different anthracycline antibiotics in double-stranded DNA at the nanoscale and single molecule level. Atomic force microscopy analysis revealed that intercalation results in significant elongation and thinning of dsDNA molecules. Additionally, using optical tweezers, we have shown that intercalation decreases the stiffness of DNA molecules, that results in greater susceptibility of dsDNA to break. Using DNA molecules with different GC/AT ratios, we checked whether anthracycline antibiotics show preference for GC-rich or AT-rich DNA fragments. We found that elongation, decrease in height and decrease in stiffness of dsDNA molecules was highest in GC-rich dsDNA, suggesting the preference of anthracycline antibiotics for GC pairs and GC-rich regions of DNA. This is important because such regions of genomes are enriched in DNA regulatory elements. By using three different anthracycline antibiotics, namely doxorubicin (DOX), epirubicin (EPI) and daunorubicin (DAU), we could compare their detrimental effects on DNA. Despite their analogical structure, anthracyclines differ in their effects on DNA molecules and GC-rich region preference. DOX had the strongest overall effect on the DNA topology, causing the largest elongation and decrease in height. On the other hand, EPI has the lowest preference for GC-rich dsDNA. Moreover, we demonstrated that the nanoscale perturbations in dsDNA topology are reflected by changes in the microscale properties of the cell, as even short exposition to doxorubicin resulted in an increase in nuclei stiffness, which can be due to aberration of the chromatin organization, upon intercalation of doxorubicin molecules.

Manipulation of micro- and nano-sized objects with optical tweezers is a well-established, albeit still evolving technique. While many objects can be trapped directly with focused laser beam(s), for some applications indirect manipulation with tweezers-operated tools is preferred. We introduce a simple, versatile micro-tool operated with holographic optical tweezers. The 40 µm long dumbbell-shaped tool, fabricated with two-photon laser 3D photolithography has two beads for efficient optical trapping and a probing spike on one end. We demonstrate fluids viscosity measurements and vibration detection as examples of possible applications.