Energy Exchange at Degenerate Mixing of Four Fast TE2 Modes of a Thin Left-Handed Film on a Nonlinear Substrate

Managed Dispersion of Propagation Constants of TE2 Modes of a Thin Left-Handed Film on a Kerr Substrate near Frequencies of Group Velocity Zero

“…Along with this, investigations of guided mode propagation in thin lefthanded films have made it possible to reveal new dispersion properties that are absent in modes of righthanded films [4][5][6][7][8]. In the case of a left-handed film on a substrate with the Kerr effect, these properties lead to a change in the qualitative pattern of the mode interaction [9,10] as compared to the interaction of modes in a conventional right-handed film [11]. General properties of nonlinear planar waveguides based on left-handed metamaterials were studied in [6,7].…”

“…Using results of [6,7], one can obtain a dispersion equation that implicitly specifies propagation constants β of waveguide TE modes of a thin left-handed film with thickness h on a Kerr substrate as a function of frequency ω in the following form: (1) where are the dispersion dependences of relative dielectric permittivity and magnetic permeability of the film material [1][2][3][4][5][6][7][8][9][10]; ω p and ω m are the plasma resonance frequency and magnetic resonance frequency, respectively; μ c, s and ε c, s are the relative permeability and permittivity of the cover medium (subscript c) and undisturbed substrate (subscript s), respectively; c is the speed of light in vacuum; Δε s0 = n 2s P 0 δ(ω) are disturbances of the relative permittivity of the substrate at the interface with the film; n 2s is the Kerr coefficient; P 0 is the dimension of the light field intensity; and δ(ω) is a nonnegative function describing the variation in the light field intensity at the film-substrate interface (the intensity is equal to product P 0 δ(ω)) depending on frequency due to external managing. Note that the integration constant for the nonlinear equation for the transverse distribution of electric strength of the mode field in the substrate is expressed here in terms of the local intensity P 0 δ(ω), not in terms of the total power transported by the mode along the film, as in [6,7].…”