A negative refractive index lens can amplify the evanescent waves which
encode the high spatial frequencies, theoretically leading to unlimited
resolution. Motivated by this, we developed a formalism to calculate the
electric field of oscillating currents in a two general constituents composite
medium. We performed an exact calculation of the local electric field of an
oscillating dipole in a setup of an epsilon_1,mu_1 slab in an
epsilon_2,mu_2 host medium. We calculated the general electromagnetic
eigenstates of a flat-slab structure and used them to expand the electric
field. To facilitate the calculation we developed a procedure to treat
current sources analytically, enabling to readily explore the effect of
varying the dipole location and orientation and analyze volume currents.
The calculations of the lowest order eigenvalues showed that the high k
components are enhanced for the TM field when epsilon_1=-epsilon_2 and for
the TE field when mu_1=-mu_2, where the enhancement of the evanescent waves
starts from lower k values as we approach a setup with both
epsilon_1=-epsilon_2 and mu_1=-mu_2. The formalism can be applied to
analyze phenomena such as nonlinear response and Purcell effect.

References

[1] Phys. Rev. A 93, 063844 (16 pages), 2016. Electromagnetic eigenstates and the field of an oscillating point electric dipole in flat-slab composite structure,A. Farhi and D. J. Bergman.

[2]  SPIE Optics+Photonics, San Diego, [9547-63], 2015. Non-quasi-static eigenstates of Maxwell’s equations in a two-constituent composite medium and their application to a calculation of the local electric field of an oscillating dipole,A. Farhi and D. J. Bergman,

[3] SPIE Optics+Photonics, San Diego, [9921-13] (12 pages), 2016.General eigenstates of Maxwell's equations in a two-constituent composite medium and their application to a calculation of the local electric field in a flat-slab microstructure,A. Farhi and D. J. Bergman.