J. Eur. Opt. Society-Rapid Publ. 21, 4( 2025) 35
Table 2. Comparison of the FRISP method with FDTD simulation of a microsphere with a diameter of 10 lm and a refractive index of n = 1.5.
Method
Position focal spot [ lm ] from sphere center
Deviation of position [%]
FWHM [ nm ]
Deviation of FWHM [%]
FDTD |
5.67 |
— |
399 |
— |
FRISP |
5.8 |
2.2 |
396 |
1.0 |
Figure 6. Schematic sketch of the optical setup for measuring the influence of a micro sphere on the intensity distribution of a plane wave.
Figure 5. Comparison of the FRISP method with a FDTD simulation of a microsphere with a diameter of 10 lm, a refractive index of n = 1.5 and a wavelength of 634 nm. The normalized intensity distribution of a simulated photonic nanojets generated by the microsphere along the propagation axis a) for the FRISP method and b) for a FDTD simulation with Ansys. c) Comparison of the intensity profiles at the focal spot position along the vertical dashed lines to determine the FWHM. d) Intensity profiles along the horizontal dashed lines through the center of the micro sphere.
equations with the FDTD method [ 17 ]. This leads to additional time savings during the preparation of the simulation and simplifies the consideration of correlations between the shape of the micro structure and its intensity distribution.
3.3
Experimental validation
In addition to the comparison with simulation results obtained in the literature, we also compare the FRISP approach with experimental results from measurements of the focusing properties of SiO 2 micro spheres with a diameter of 11 lm. The measurement of the intensity
distribution of the micro sphere was performed with a Keyence digital microscope VHX-7000 and a Keyence zoom objective VH-Z500T( zoom factor 5000 and NA = 0.82). For the illumination we used a laser diode( LP637-PA70) with a wavelength of 634 nm and a laser driver( CLD1010) from Thorlabs.
Figure 6 shows a schematic sketch of the optical setup for the measurement. The 3D intensity distribution consists of 200 separate 2D images with a vertical spacing of 85 nm. These images are then combined into a 3D stack of images. In order to correct for any lateral displacement of the images during the measurement process, a cross-correlation of the successive images was carried out.
Figure 7 shows the results of an experimental measurement and a simulation of a SiO 2 microsphere with a diameter of 11 lm. There is a strong similarity between the experimental and simulation results in terms of focal spot position and size. For areas inside the micro sphere there are some deviations between the simulated and measured intensity distribution. These deviations are caused by the effects of backscattering and reflection inside and at the boundaries of the micro sphere, which are not modeled by the FRISP approach. The similarity of the intensity distribution for the focal region of the microstructure confirms