volume | PIER Journals

Abstract

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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. Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

12. Deschamps, G. A., "Electromagnetics and differential forms," Proc. IEEE, Vol. 69, 676-696, 1981.
doi:10.1016/j.photonics.2007.07.013 Google Scholar

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 Google Scholar

14. Pendry, J. B., D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science, Vol. 312, 1780-1782, 2006.
doi:10.3390/en3071335 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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. Google Scholar

25. Xu, L. and H. Chen, "Conformal transformation optics," Nat. Photonics, Vol. 9, 15-23, 2014.
doi:10.1364/OE.18.006089 Google Scholar

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. Google Scholar

27. Whiteman, J. R., The Mathematics of Finite Elements and Applications, John Wiley and Sons, 1998, http://www.comsol.com.
doi:10.1016/j.photonics.2015.04.003

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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. Google Scholar

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. Google Scholar

Mr. ASRAFALI BARKATHULLA

Dr. Chakravarthy Venkateswaran

Dr. Natesan Yogesh