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J. Eur. Opt. Society-Rapid Publ. 21, 4( 2025)
Figure 7. Experimental validation of the FRISP method with a SiO 2 micro sphere with a diameter of 11 lm. The normalized intensity distribution of a Photonic nanojet generated by a SiO 2 micro sphere along the propagation axis a) simulated and b) measured by an optical microscope. c) Comparison of the intensities along the centerline of the simulation a)( red) and the experiment b)( blue).
the validity of the FRISP approach for the simulation of photonic nanojets.
4 Conclusion
We present the FRISP method based on scalar diffraction theory which can simulate the focusing properties of microstructures with structure sizes < 50 lm and the corresponding photonic nanojets in the focal plane of the structure. Compared with standard FDTD-simulations, the computing time for such simulations with the FRISP approach is reduced by a factor of 135 and a conventional desktop computer can be used. In contrast with the significantly more computational-intensive FDTD simulations, the FRISP method has the limitation that it does not consider back reflections. FRISP method calculates only the forward propagation of the light, which leads to a deviation of the results between the FRISP method and FDTD simulations inside the microstructures. For regions outside the structure, especially for the shape, width( FWHM) and position of the focal spot, the FRISP method shows very good agreement with FDTD simulations. The errors for the focus position are in the range of 2.2 % and for the FWHM in the range of 1 %.
Consequently, the FRISP approach appears very suitable for the efficient simulation and iterative optimization of the focusing properties of optical micro structures, especially with respect to the geometry of photonic nanojets and near-field applications. Referring to [ 21, 22 ], we aim to extend the FRISP method in future work to incorporate the analysis of backward reflecting waves.
Acknowledgments
The authors are grateful to Reiner Klattenhoff( BIAS) for his technical support with the optical setup and experimental work.
Funding
The authors gratefully acknowledge the support of the Deutsche Forschungsgemeinschaft( DFG, German Research Foundation) for funding this work under the project“ Hochauflösende optische Mikroskopie mittels transmissiver Mikrostrukturen – HOMi- Trans”, grant no. 431605610.
Conflicts of interest The authors declare no conflicts of interest.
Data availability statement
The Data underlying the presented results and the used Matlab algorithms may be obtained from the authors upon a reasonable request.
Author contribution statement
Conceptualization, F. T. and C. F.; Data curation, F. T., M. A., R. E. B., M. F. O. H. and C. F.; Investigation, F. T., M. A., R. E. B. and M. F. O. H.; Methodology, F. T., M. A. and C. F.; Validation, F. T., M. A., R. E. B., M. F. O. H. and C. F.; Visualization, F. T., M. A., R. E. B. and M. F. O. H.; Formal Analysis, F. T., M. A., R. E. B., M. F. O. H. andC. F.; Writing— original draft, F. T., and C. F.; Funding acquisition, R. B. B.; Supervision, S. S. A. O, R. B. B. and C. F. All authors have read and agreed to the submitted version of the manuscript.
References
1 Chen Z, Taflove A, Backman V, Photonic nanojet enhancement of backscattering of light by nanoparticles: a potential novel visible-light ultramicroscopy technique, Opt. Express 12, 7, 1214 – 1220( 2004). https:// doi. org / 10.1364 / OPEX. 12. 001214.
2 Heifetz A, Kong SC, Sahakian AV, Taflove A, Backman V, Photonic nanojets, J. Comput. Theor. Nanosci. 6, 9, 1979 – 1992( 2009). https:// doi. org / 10.1166 / jctn. 2009.1254.
3 Darafsheh A, Photonic nanojets and their applications, J. Phys. Photon. 3, 2, 022001( 2021). https:// doi. org / 10.1088 / 2515-7647 / abdb05.
4 Wriedt T, Mie theory: a review, in The Mie Theory: Basics and Applications( Springer Berlin, Heidelberg, Germany, 2012), pp. 53 – 71. 5 Hulst HC, van de Hulst HC, Light Scattering by Small Particles( Courier Corporation, New York, 1981).
6 Luk’ yanchuk BS, Paniagua-Domínguez R, Minin I, Minin O, Wang Z, Refractive index less than two: photonic nanojets yesterday, today and tomorrow, Opt. Mater. Express 7, 6, 1820 – 1847( 2017). https:// doi. org / 10.1364 / OME. 7.001820.
7Taflove A, Oskooi A, Johnson SG, Advances in FDTD Computational Electrodynamics: Photonics and Nanotechnology( Artech House, Norwood, Massachusetts, 2013).