Nano-jet related to Bessel beams and to super-resolutions in microsphere optical experiments

Abstract

The appearance of a Nano-jet in the microsphere optical experiments is analyzed by relating this effect to non-diffracting Bessel beams. By inserting a circular aperture with a radius of subwavelength dimension in the EM waist, and sending the transmitted light into a confocal microscope, the EM oscillations by the different Bessel beams are avoided. On this constant EM field evanescent waves are superposed. While this effect improves the optical-depth of the imaging process, the object fine-structures are obtained, from the modulation of the EM fields by the evanescent waves. The use of a combination of the microsphere optical system with an interferometer for phase contrast measurements is described.

Super-Resolution of Nano-Materials and Quantum Effects Obtained by Microspheres

“…Since the incident angle I  with the corresponding crossing angle  is changing as a function of the incident point on the microsphere, one may get a perfect outcome by the superposition of Bessel functions and changing it continuously as a function of the incident angle. An estimate of the width of the nanojet, which is in agreement with the experiment was given earlier [94] by using Eq. (26) with an average value for the parameter  .…”

“…The present idea is that we have to take into account the spherical symmetry by superposing Bessel beams on the trajectory of geometric optics. As the spherical Bessel beam depends on the angle  , we need to solve the physical optics wave function ( , , ) zt  , in cylindrical coordinates [93][94][95]. The exponential function describes non-diffracted propagation in the z direction for one Bessel beam, where z is the distance from the focal plane of this wave,  is the distance from the symmetric axis and  is given by Eq.…”

“…23 . 26Since we have rays with different crossing angle  , we need to use superposition of the solutions (23)(24)(25) with continuous values of  and with different weight parameters [94]. The nanojet is obtained in such a qualitative description by the superposition of the different bright cores.…”

“…The nanojet is obtained in such a qualitative description by the superposition of the different bright cores. The radius over incident angles corresponds approximately to the width of the nanojet [94]. However, more rigorous results are obtained by Mie theory calculations.…”