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.
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