Surface plasmons are usually described as surface waves with either a complex wavevector or a complex frequency. When discussing their merits in terms of field confinment or enhancement of the local density of states, controversies regularly arise as the results depend on the choice of a complex wavevector or a complex frequency. In particular, the shape of the dispersion curves depends on this choice. When discussing diffraction of surface plasmon a scalar approximation is often used. In this work, we derive two equivalent vectorial representations of a surface plasmon field using an expansion over surface waves with either a complex wavevector or a complex frequency. These representations can be used to account for propagation and diffraction of surface waves. They can also be used to discuss the issue of field confinment and local density of states as they have a non-ambiguous relation with the two dispersion relations.
The electromagnetic modes of a GaAs quantum well between two AlGaAs barriers are studied. At the longitudinal optical phonon frequency, the system supports a phonon polariton mode confined in the thickness of the quantum well that we call epsilon-near-zero mode. This epsilon-near-zero mode can be resonantly excited through a grating resulting in a very large absorption localized in the single quantum well. We show that the reflectivity can be modulated by applying a voltage. This paves the way to a new class of active optoelectronic devices working in the midinfrared and far infrared at ambient temperature.
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