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Lagrangians and Hamiltonians for the electrodynamics of Wire-SRR and single-resonance-chiral metamaterials

Last modified: 2012-01-04

#### Abstract

The Lagrangian densities for the electrodynamics of some dispersive metamaterials are proposed. The Euler-Lagrangian equations yield the correct Maxwell equations for the field

quantities E, B, D, H and the equations of motion for the polarization P and magnetization M. The Hamiltonians of the systems are then derived using the standard Legendre transform. The resultant Hamiltonians are the same as the energy densities derived in our previous publications. This confirms the correctness of the energy density formulas. The Hamiltonians, in principle can be quantized canonically to give the quantum descriptions of the low energy (long wavelength) electromagnetic excitations in these dispersive metamaterials.

quantities E, B, D, H and the equations of motion for the polarization P and magnetization M. The Hamiltonians of the systems are then derived using the standard Legendre transform. The resultant Hamiltonians are the same as the energy densities derived in our previous publications. This confirms the correctness of the energy density formulas. The Hamiltonians, in principle can be quantized canonically to give the quantum descriptions of the low energy (long wavelength) electromagnetic excitations in these dispersive metamaterials.