Mapping inter-element coupling in metamaterials: Scaling down to infrared

Abstract

Electrowetting based infrared lens using ionic liquids Appl. Phys. Lett. 99, 213505 (2011) Modulation of negative index metamaterials in the near-IR range Appl. Phys. Lett. 91, 173105 (2007) Mixed metal films with switchable optical properties Appl. Phys. Lett. 80, 1349Lett. 80, (2002 Population dynamics of the threemicron emitting level of Er3+ in YAlO3 J. Appl. Phys. 80, 6610 (1996) Experimental characterization of reactive ion etched germanium diffraction gratings at 10.6 μm Appl. Phys. Lett. 69, 3453 (1996) Additional information on J. Appl. Phys. The coupling between arbitrarily positioned and oriented split ring resonators is investigated up to THz frequencies. Two different analytical approaches are used, one based on circuits and the other on field quantities that includes retardation. These are supplemented by numerical simulations and experiments in the GHz range, and by simulations in the THz range. The field approach makes it possible to determine separately the electric and magnetic coupling coefficients which, depending on orientation, may reinforce or may cancel each other. Maps of coupling are produced for arbitrary orientations of two co-planar split rings resonant at around 2 GHz and then with the geometry scaled down to be resonant at around 100 THz. We prove that the inertia of electrons at high frequencies results in a dramatic change in the maps of coupling, due to reduction of the magnetic contribution. Our approach could facilitate the design of metamaterials in a wide frequency range up to the saturation of the resonant frequency. V C 2012 American Institute of Physics.

Coupling mechanisms of resonators in the THz regime

“…5b are equivalent to Q 2 /C and I 2 L, or twice the electric and magnetic energies, here C and L are the capacitance and inductance of the respective circuit and Q and I are the charge and current amplitudes. As it was already mentioned, electron's inertia in metals can not be disregarded in the THz range, and should be accounted for in the power balance by additional factor α for the current energy 11 . Dependences of the electric and magnetic energies Fig.…”

“…The relations for the capacitance and inductance of the nano-SRR are obtained from (9) and (10) The interaction strength between two circuits is described by coupling constants, which in return are defined as ratios of the interaction and stored energies 11,13 . In our case we deal with two types of interactions --the one between charges and the other one between currents -resulting in two coupling constants, with the values from expressions (5-6) and (8) …”

Resonant dynamics of arbitrarily shaped meta-atoms

“…However for many structures, interaction can be significant even at long distances, where retardation becomes significant 53 . Retardation introduces a phase factor which can greatly change the phase of the interaction constants [54][55][56] , and makes all stored energy quantities complex. This breaks the underlying physical assumptions of a Lagrangian model, and physical meaning can only be restored by including the full spectrum of plane waves, as per the system and bath approach discussed in Section II.…”

Surface polaritons in magnetic metamaterials from perspective of effective-medium and circuit models

“…15 On the other hand, spatial dispersion appears also as a result of an interaction between metamaterial elements by their electric and magnetic near fields. 16 In the metamaterial context, the subject has been developed extensively by Solymar, Shamonina, and co-authors (see e.g., Refs. [17][18][19][20] for magnetic coupling between split-ring resonators, although earlier studies were also conducted for other applications.…”