Confining electromagnetic (e-m) modes in a tiny space is a desirable aspect for many applications including targeted material heating and light harvesting techniques. In this work, we report spatially squeezed e-m modes of a cavity resonator formed by the modified transformation optical (TO) medium. The proposed coordinate transformation scheme suggests curved contours of refractive index profile such that the e-m mode can be confined within the contours. The effective mode area for a TO cavity is at least 10 times smaller than the air-filled metallic cavity. The confined e-m modes of a proposed cavity are horizontally flattened but vertically squeezed of the dimension of λ/49. The material parameters of the proposed TO medium are approximated with non-magnetic and isotropic dielectric values. For an application aspect, squeezed mode of the TO cavity is used for targeted material heating, and it is demonstrated based on e-m thermal co-simulations. A tiny dielectric material placed at the squeezed part of the cavity mode is heated rapidly with the temperature rise of 2.350˚C/s (110˚C/s) for the single (dual) e-m source excitation with the peak electric field strength of 5 x 104 V/m. We further discuss how one can realize the proposed TO medium practically with a cell-grid approximation using photonic crystals and metamaterials.
1. Vučković, J., "Quantum optics and cavity QED with quantum dots in photonic crystals,", Note 2013, Stanford University, 2013. doi:10.1103/PhysRevA.75.063830
2. Ramakrishna, S. A., S. Guenneau, S. Enoch, G. Tayeb, and B. Gralak, "Confining light with negative refraction in checkerboard metamaterials and photonic crystals," Phys. Rev. A, Vol. 75, 063830, 2007. doi:10.1063/5.0027465
3. Yi, J., Z. Shi, D. Li, C. Liu, H. Sun, L. Zhu, X. Chen, and S. N. Burokur, "A metamaterial lens based on transformation optics for horizontal radiation of OAM vortex waves," J. Appl. Phys., Vol. 129, 2021. doi:10.1038/nmat1994
4. Tanaka, Y., J. Upham, T. Nagashima, T. Sugiya, T. Asano, and S. Noda, "Dynamic control of the Q factor in a photonic crystal nanocavity," Nature Mater., Vol. 6, 862-865, 2007. doi:10.2528/PIER00122803
5. Kishk, A. A., A. W. Glisson, G. P. Junker, W. M. Ave, and E. Segundo, "Bandwidth enhancement for split cylindrical dielectric resonator antennas," Progress In Electromagnetics Research, Vol. 33, 97-118, 2001. doi:10.1080/09500349608232782
6. Ward, A. J. and J. B. Pendry, "Refraction and geometry in Maxwell's equations," J. Mod. Opt., 773-793, 1996. doi:10.1364/JOSAB.27.001603
7. Teixeira, F. L., H. Odabasi, and K. F. Warnick, "Anisotropic metamaterial blueprints for cladding control of waveguide modes," J. Opt. Soc. Am. B, Vol. 27, 1603, 2010.
8. McCall, M., J. B. Pendry, V. Galdi, Y. Lai, S. A. R. Horsley, J. Li, J. Zhu, R. C. Mitchell-Thomas, O. Quevedo-Teruel, P. Tassin, V. Ginis, E. Martini, G. Minatti, S. Maci, M. Ebrahimpouri, Y. Hao, P. Kinsler, J. Gratus, J. M. Lukens, A. M. Weiner, U. Leonhardt, I. I. Smolyaninov, V. N. Smolyaninova, R. T. Thompson, M. Wegener, M. Kadic, and S. A. Cummer, "Roadmap on transformation optics," J. Opt., Vol. 20, No. 6, United Kingdom, 2018. doi:10.1016/S0079-6638(08)00202-3
9. Leonhardt, U. and T. G. Philbin, "Chapter 2 Transformation optics and the geometry of light," Prog. Opt., Vol. 53, 69-152, 2009. doi:10.1017/S0305004100012664
10. Van Dantzig, D., "The fundamental equations of electromagnetism, independent of metrical geometry," Math. Proc. Cambridge Philos. Soc., Vol. 30, 421-427, 1934. doi:10.1163/156939399X01104
11. Teixeira, F. L. and W. C. Chew, "Differential forms, metrics, and the reflectionless absorption of electromagnetic waves," Journal of Electromagnetic Waves and Applications, Vol. 13, 665-686, 1999. doi:10.1109/PROC.1981.12048
13. Rahm, M., D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell's equations," Photonics Nanostructures - Fundam. Appl., Vol. 6, 87-95, 2008. doi:10.1126/science.1125907
14. Pendry, J. B., D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science, Vol. 312, 1780-1782, 2006. doi:10.3390/en3071335
15. Yang, J., M. Huang, C. Yang, J. Peng, and R. Zong, "Metamaterial electromagnetic superabsorber with arbitrary geometries," Energies, Vol. 3, No. 7, 1335-1343, 2010. doi:10.1063/1.5045489
16. Vasantharajan, G., N. Yogesh, and V. Subramanian, "Beam steering based on coordinate transformation of Fermat spiral configurations," AIP Adv., Vol. 9, 075217, 2019. doi:10.1103/PhysRevLett.105.266807
17. Fernandez-Domnguez, A. I., S. A. Maier, and J. B. Pendry, "Collection and concentration of light by touching spheres: A transformation optics approach," Phys. Rev. Lett., Vol. 105, 266807, 2010. doi:10.1103/PhysRevB.77.035122
18. Tsang, M. and D. Psaltis, "Magnifying perfect lens and superlens design by coordinate transformation," Phys. Rev. B, Vol. 77, 035122, 2008. doi:10.2528/PIER15112505
19. Dehdashti, S., H. Wang, Y. Jiang, Z. Xu, and H. Chen, "Review of black hole realization in laboratory base on transformation optics," Progress In Electromagnetics Research, Vol. 154, 181-193, 2015. doi:10.1103/PhysRevA.90.043812
20. Kadic, M., G. Dupont, S. Enoch, and S. Guenneau, "Invisible waveguides on metal plates for plasmonic analogs of electromagnetic wormholes," Phys. Rev. A, Vol. 90, 043812, 2014. doi:10.1103/PhysRevLett.100.063903
21. Rahm, M., S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical design of reflectionless complex media by finite embedded coordinate transformations," Phys. Rev. Lett., Vol. 100, 063903, 2008. doi:10.1016/j.ijleo.2010.10.023
22. Zhou, J., M. Li, L. Xie, and D. Liu, "Design of a new kind of polarization splitter based on transformation optics," Optik, Vol. 122, 1672-1675, 2011. doi:10.1063/1.5020204
23. Haddad, H., R. Loison, R. Gillard, A. Harmouch, and A. Jrad, "A combination of transformation optics and surface impedance modulation to design compact retrodirective reflectors," AIP Adv., Vol. 8, 025114, 2018. doi:10.1364/OE.417678
24. Pakniyat, S., S. Jam, A. Yahaghi, and G. W. Hanson, "Reflectionless plasmonic right-angled waveguide bend and divider using graphene and transformation optics," Optics Express, Vol. 29, No. 6, 9589-9598, 2021.
25. Xu, L. and H. Chen, "Conformal transformation optics," Nat. Photonics, Vol. 9, 15-23, 2014. doi:10.1364/OE.18.006089
26. Chang, Z., X. Zhou, J. Hu, and G. Hu, "Design method for quasi-isotropic transformation materials based on inverse Laplace's equation with sliding boundaries," Optics Express, Vol. 18, No. 6, 6089, 2010.
28. Yogesh, N., Q. Yu, and Z. Ouyang, "Single- and multi-beam confinement of electromagnetic waves in a photonic crystal open cavity providing rapid heating and high temperatures," Photonics Nanostructures - Fundam. Appl., Vol. 15, 89-98, 2015. doi:10.1364/OE.22.002725
29. Cao, Y., J. Xie, Y. Liu, and Z. Liu, "Modeling and optimization of photonic crystal devices based on transformation optics method," Optics Express, Vol. 22, 2725-2734, 2014. doi:10.1063/1.4794940
30. Yan, S. and G. A. E. Vandenbosch, "Compact circular polarizer based on chiral twisted double split-ring resonator," Appl. Phys. Lett., Vol. 102, 103503, 2013. doi:10.2528/PIER12050206
31. Yogesh, N. and V. Subramanian, "Spatial beam compression and effective beam injection using triangular gradient index profile photonic crystals," Progress In Electromagnetics Research, Vol. 129, 51-67, 2012. doi:10.1002/adma.201605198
32. Zhou, N., C. Liu, J. A. Lewis, and D. Ham, "Gigahertz electromagnetic structures via direct ink writing for radio-frequency oscillator and transmitter applications," Adv. Mater., Vol. 29, No. 15, 1605198, 2017. doi:10.1002/adma.201800940
33. Velasco-Hogan, A., J. Xu, and M. A. Meyers, "Additive manufacturing as a method to design and optimize bioinspired structures," Adv. Mater., Vol. 30, No. 52, 1800940, 2018.
34. Poyanco, J. M., F. Pizarro, and E. Rajo-Iglesias, "Wideband hyperbolic flat lens in the Ka-band based on 3D-printing and transformation optics," Appl. Phys. Lett., Vol. 118, 2021.