This paper proposes to use an Aperiodic Fourier Modal Method (A-FMM) to model an outgoing photonic jet from a dielectric loaded waveguide ended by a tip with a specic shape. The proposed method has several advantages. First of all, the method is fast, which allows to manage optimization investigations. Secondly, the study excitation (and more particularly the impact of plan wave excitation) can be examined precisely. Using our modelling technique, we show, in comparison with an actual optimized elliptical tip, that an optimized rectangular tip improves energy concentration by 8% and reduces the calculation time by a factor of 10. Furthermore, A-FMM allows to show that plane wave excitation modifies the spatial distribution of the jet, especially in the case of TE polarization. This can explain the differences observed, in previous works, where only fundamental mode excitation was used in the modelling. To validate these general results, prototypes have been realized, and measurements in the microwave regime have been compared favorably with simulation results.
M. Kofi Edee,
"Numerical Study of a Photonic Jet with Aperiodic Fourier Modal Method and Experimental Validation," Progress In Electromagnetics Research C,
Vol. 88, 133-143, 2018. doi:10.2528/PIERC18100206
1. Chen, Z., A. Taflove, and V. Backman, "Photonic nanojet enhancement of backscattering of light by nanoparticles: A potential novel visible-light ultramicroscopy technique," Opt. Express, Vol. 12, No. 7, 1214-1220, 2004. doi:10.1364/OPEX.12.001214
2. Kong, S.-C., A. Sahakian, A. Taflove, and V. Backman, "Photonic nanojet-enabled optical data storage," Opt. Express, Vol. 16, No. 18, 13713-13719, 2008. doi:10.1364/OE.16.013713
3. Kong, S.-C., A. V. Sahakian, A. Heifetz, A. Taflove, and V. Backman, "Robust detection of deeply subwavelength pits in simulated optical data-storage disks using photonic jets," Applied Physics Letters, Vol. 92, No. 21, 211102, 2008. doi:10.1063/1.2936993
4. Itagi, A. V. and W. A. Challener, "Optics of photonic nanojets," J. Opt. Soc. Am. A, Vol. 22, No. 12, 2847-2858, Dec. 2005. doi:10.1364/JOSAA.22.002847
5. Lecler, S., Y. Takakura, and P. Meyrueis, "Properties of a three-dimensional photonic jet," Optics Letters, Vol. 30, No. 19, 2641-2643, Oct. 2005. doi:10.1364/OL.30.002641
6. Liu, C.-Y., "Photonic jets produced by dielectric micro cuboids," Appl. Opt., Vol. 54, No. 29, 8694-8699, Oct. 2015. doi:10.1364/AO.54.008694
7. Ju, D., H. Pei, Y. Jiang, and X. Sun, "Controllable and enhanced nanojet effects excited by surface plasmon polariton," Appl. Phys. Lett., Vol. 102, No. 171109, 2013.
8. Khaleque, A. and Z. Li, "Tailoring the properties of photonic nanojets by changing the material and geometry of the concentrator," Progress In Electromagnetics Research Letters, Vol. 48, 7-13, 2014. doi:10.2528/PIERL14052108
9. Lecler, S., H. Halaq, Y. Takakura, P. Gérard, B. Bayard, S. Robert, and B. Sauviac, "Jet photonique en sortie d’un guide d’onde: De nouvelles perspectives," (JNOG) Marseille, Juillet, France, 2011.
10. Takakura, Y., H. Halaq, S. Lecler, S. Robert, and B. Sauviac, "Single and dual photonic jets with tipped waveguides: An integral approach," IEEE Photonics Technology Letters, Vol. 24, No. 17, 1516-1518, 2012. doi:10.1109/LPT.2012.2206377
11. Takakura, Y., S. Lecler, B. Ounnas, S. Robert, and B. Sauviac, "Boundary impedance operator to study tipped parallel plate waveguides," IEEE Photonics Technology Letters, Vol. 62, No. 11, 5599-5609, 2014.
12. Zelgowski, J., A. Abdurrochman, F. Mermet, P. Pfeiffer, J. Fontaine, and S. Lecler, "Photonic jet subwavelength etching using a shaped optical fiber tip," Opt. Lett., Vol. 41, No. 9, 2073-2076, 2016. doi:10.1364/OL.41.002073
13. Ounnas, B., B. Sauviac, Y. Takakura, S. Lecler, B. Bayard, and S. Robert, "Single and dual photonic jets and corresponding backscattering enhancement with tipped waveguides: Direct observation at microwave frequencies," IEEE Photonics Technology Letters, Vol. 63, No. 12, 5612-5618, 2015.
14. Knop, K., "Photonic jet subwavelength etching using a shaped optical fiber tip," JOSA, Vol. 68, No. 9, 1206-1210, 1978. doi:10.1364/JOSA.68.001206
15. Lalanne, P. and G. M. Morris, "Highly improved convergence of the coupled-wave method for TM polarization," JOSA, Vol. 13, No. 4, 779-784, 1996. doi:10.1364/JOSAA.13.000779
16. Granet, G. and B. Guizal, "Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization," JOSA, Vol. 13, No. 5, 1019-1023, 1996. doi:10.1364/JOSAA.13.001019
17. Li, L., "Fourier modal method," Gratings: Theory and Numeric Applications, Evgeny Popov, Aix Marseille Université, 2014.
18. Li, L., "Use of Fourier series in the analysis of discontinuous periodic structures," JOSA, Vol. 13, No. 9, 1870-1876, 1996. doi:10.1364/JOSAA.13.001870
19. Granet, G., "Coordinate transformation methods," Gratings: Theory and Numeric Applications, Evgeny Popov, Aix Marseille Université, 2014.
20. Berenger, J.-P., "A perfectly matched layer for the absorption of electromagnetic waves," Journal of Computational Physics, Vol. 114, No. 2, 185-200, 1994. doi:10.1006/jcph.1994.1159
21. Plumey, J. P., K. Edee, and G. Granet, "Modal expansion for the 2D Green’s function in a non-orthogonal coordinates system," Progress In Electromagnetics Research, Vol. 59, 101-112, 2006. doi:10.2528/PIER05080701
22. Hyani, H., B. Sauviac, K. Edee, G. Granet, S. Robert, and B. Bayard, "Embout multi-guide pour la production de jet photonique appliqué á la détection dans des structures opaques," JCMM, France, 2018.