scholarly journals Energy flows in tight focus of optical vortices

2021 ◽  
Vol 2103 (1) ◽  
pp. 012162
Author(s):  
S S Stafeev ◽  
V V Kotlyar
Keyword(s):  
Optical Axis ◽  
Numerical Aperture ◽  
Longitudinal Component ◽  
Orbital Energy ◽  
Optical Vortices ◽  
Absolute Value ◽  
Energy Flows ◽  
Tight Focusing ◽  
Left Circular Polarization ◽  
532 Nm

Abstract In this paper we investigated tight focusing of optical vortex with topological charge m = 2 and left circular polarization. The simulation was based on Richards-Wolf equation. Light with wavelength 532 nm was focused by aplanatic lens with numerical aperture NA=0.95. It was shown that the longitudinal component of Poynting vector has negative values on the optical axis. The reason of the energy backflow is due to the fact that the projection of the spin flow onto the optical axis is negative and exceeds in absolute value the projection of the orbital energy flow, which is always positive.

scholarly journals Longitudinal component of the Poynting vector of a tightly focused optical vortex with circular polarization

2018 ◽  
Vol 42 (2) ◽  
pp. 190-196 ◽  
Author(s):  
S. S. Stafeev ◽  
A. G. Nalimov
Keyword(s):  
Circular Polarization ◽  
Intensity Distribution ◽  
Poynting Vector ◽  
Fdtd Method ◽  
Numerical Aperture ◽  
Longitudinal Component ◽  
Optical Vortices ◽  
Diffractive Lens ◽  
532 Nm ◽  
Topological Charges

We numerically investigated the focusing of optical vortices with the wavelength ? = 532 nm and right-hand circular polarization by using a diffractive lens with the numerical aperture NA = 0.95. The simulation was carried out using the Richards-Wolf formulae and the FDTD-method. The focusing of optical vortices with topological charges equal to ±1 and ±2 was investigated. It was shown that the focusing of optical vortices with circular polarization by a wide-aperture diffractive lens can produce an intensity distribution with the negative value of the longitudinal component of the Poynting vector.

scholarly journals Toroidal Vortices of Energy in Tightly Focused Second-Order Cylindrical Vector Beams

Photonics ◽  
2021 ◽  
Vol 8 (8) ◽  
pp. 301
Author(s):  
Sergey S. Stafeev ◽  
Elena S. Kozlova ◽  
Victor V. Kotlyar
Keyword(s):  
Critical Points ◽  
Saddle Points ◽  
Numerical Aperture ◽  
Second Order ◽  
Optical Vortices ◽  
Annular Aperture ◽  
Toroidal Surface ◽  
Toroidal Vortices ◽  
532 Nm ◽  
Topological Charges

In this paper, we simulate the focusing of a cylindrical vector beam (CVB) of second order, using the Richards–Wolf formula. Many papers have been published on focusing CVB, but they did not report on forming of the toroidal vortices of energy (TVE) near the focus. TVE are fluxes of light energy in longitudinal planes along closed paths around some critical points at which the flux of energy is zero. In the 3D case, such longitudinal energy fluxes form a toroidal surface, and the critical points around which the energy rotates form a circle lying in the transverse plane. TVE are formed in pairs with different directions of rotation (similar to optical vortices with topological charges of different signs). We show that when light with a wavelength of 532 nm is focused by a lens with numerical aperture NA = 0.95, toroidal vortices periodically appear at a distance of about 0.45 μm (0.85 λ) from the axis (with a period along the z-axis of 0.8 μm (1.5 λ)). The vortices arise in pairs: the vortex nearest to the focal plane is twisted clockwise, and the next vortex is twisted counterclockwise. These vortices are accompanied by saddle points. At higher distances from the z-axis, this pattern of toroidal vortices is repeated, and at a distance of about 0.7 μm (1.3 λ), a region in which toroidal vortices are repeated along the z-axis is observed. When the beam is focused and limited by a narrow annular aperture, these toroidal vortices are not observed.

scholarly journals Investigation of the influence of amplitude spiral zone plate parameters on produced energy backflow

2019 ◽  
Vol 43 (6) ◽  
pp. 1093-1097
Author(s):  
E.S. Kozlova
Keyword(s):  
Time Domain ◽  
Finite Difference Time Domain ◽  
Energy Flow ◽  
Optical Axis ◽  
Longitudinal Component ◽  
Zone Plate ◽  
Optical Vortices ◽  
Relief Height ◽  
Vortex Beams ◽  
Difference Time

Investigation of the influence of parameters of silver, aluminum, gold, and chromium spiral zone plates on the longitudinal component of Umov-Pointing vector in produced optical vortices by using the frequency-dependent finite-difference time-domain method is presented. It is shown that the aluminum spiral zone plate with a relief height of 50 nm gives an optical vortex with the smallest longitudinal component of Umov-Pointing vector on the optical axis. The gold spiral zone plate is the least effective for the formation of vortex beams with a reverse energy flow.

scholarly journals Topological charge of optical vortices and their superpositions

2020 ◽  
Vol 44 (2) ◽  
pp. 145-154
Author(s):  
V.V. Kotlyar ◽  
A.A. Kovalev ◽  
A.V. Volyar
Keyword(s):  
Finite Number ◽  
Topological Charge ◽  
Optical Axis ◽  
Weight Coefficient ◽  
Optical Vortex ◽  
Optical Vortices ◽  
Vortex Center ◽  
Absolute Value ◽  
The Individual ◽  
Weight Coefficients

An optical vortex passed through an arbitrary aperture (with the vortex center found within the aperture) or shifted from the optical axis of an arbitrary axisymmetric carrier beam is shown to conserve the integer topological charge (TC). If the beam contains a finite number of off-axis optical vortices with different TCs of the same sign, the resulting TC of the beam is shown to be equal to the sum of all constituent TCs. For a coaxial superposition of a finite number of the Laguerre-Gaussian modes (n, 0), the resulting TC equals that of the mode with the highest TC (including sign). If the highest positive and negative TCs of the constituent modes are equal in magnitude, then TC of the superposition is equal to that of the mode with the larger (in absolute value) weight coefficient. If both weight coefficients are the same, the resulting TC equals zero. For a coaxial superposition of two different-amplitude Gaussian vortices, the resulting TC equals that of the constituent vortex with the larger absolute value of the weight coefficient amplitude, irrespective of the relation between the individual TCs.

ON OPTIMUM PUPIL FIELDS WITH MAXIMUM ELECTRIC FIELD COMPONENT IN FOCUS

2010 ◽  
Vol 19 (01) ◽  
pp. 189-201
Author(s):  
H. P. URBACH ◽  
S. F. PEREIRA ◽  
D. J. BROER
Keyword(s):  
Electric Field ◽  
Field Component ◽  
Optical Axis ◽  
Focal Point ◽  
Longitudinal Component ◽  
Electric Field Component ◽  
Incident Power ◽  
Entrance Pupil ◽  
Maximum Electric Field ◽  
High Na Lens

The field in the entrance pupil of a high NA lens can be optimized such that, for given incident power, the electric field component in a given direction in the focal point is maximum. If the field component is chosen parallel to the optical axis, the longitudinal component is maximized and it is found that the optimum longitudinal component is narrower than the Airy spot. We discuss how this can be used to obtain higher resolution in photolithography when a resist is used that is sensitive to only the longitudinal component. We describe a proposition for realizing such resist.

scholarly journals Strongly Focused Circularly Polarized Optical Vortices Regulated by a Fractal Conical Lens

2019 ◽  
Vol 10 (1) ◽  
pp. 28
Author(s):  
Zhirong Liu ◽  
Kelin Huang ◽  
Anlian Yang ◽  
Xun Wang ◽  
Philip H. Jones
Keyword(s):  
Angular Momentum ◽  
Optical Tweezers ◽  
Numerical Aperture ◽  
Optical Element ◽  
Optical Vortex ◽  
Optical Vortices ◽  
Circularly Polarized ◽  
Strong Focusing ◽  
New Type ◽  
Vortex Beams

In this paper, a recently-proposed pure-phase optical element, the fractal conical lens (FCL), is introduced for the regulation of strongly-focused circularly-polarized optical vortices in a high numerical aperture (NA) optical system. Strong focusing characteristics of circularly polarized optical vortices through a high NA system in cases with and without a FCL are investigated comparatively. Moreover, the conversion between spin angular momentum (SAM) and orbital angular momentum (OAM) of the focused optical vortex in the focal vicinity is also analyzed. Results revealed that a FCL of different stage S could significantly regulate the distributions of tight focusing intensity and angular momentum of the circularly polarized optical vortex. The interesting results obtained here may be advantageous when using a FCL to shape vortex beams or utilizing circularly polarized vortex beams to exploit new-type optical tweezers.

scholarly journals Minimal Focal Spot Size Measured Based on Intensity and Power Flow

Sensors ◽  
2021 ◽  
Vol 21 (16) ◽  
pp. 5505
Author(s):  
Victor V. Kotlyar ◽  
Sergey S. Stafeev ◽  
Vladislav D. Zaitsev
Keyword(s):  
Linear Polarization ◽  
Energy Flow ◽  
Power Flow ◽  
Focal Spot ◽  
Spot Size ◽  
Optical Vortices ◽  
Focal Spot Size ◽  
Minimum Diameter ◽  
Circular Symmetry ◽  
Energy Flows

It is shown, theoretically and numerically, that the distributions of the longitudinal energy flow for tightly focused light with circular and linear polarization are the same, and that the spot has circular symmetry. It is also shown that the longitudinal energy flows are equal for optical vortices with unit topological charge and with radial or azimuthal polarization. The focal spot has a minimum diameter (all other characteristics being equal), which is measured based on the intensity of an optical vortex with azimuthal polarization. The diameter of the focal spot calculated from the energy flow for light with circular or linear polarization is slightly larger (by a fraction of a percentage). The magnitude of the diameter based on the intensity plays a role in the interaction of light with matter, and the magnitude of the diameter based on the energy flux affects the resolution in optical microscopy which is crucial in sensorial applications.

Sign in / Sign up

Export Citation Format

Share Document