Conditions of Perfect Imaging in Negative Refraction Materials with Gain

Figure 3

The “walk-off” angles as function of frequency 𝜔 in an active (pumped) NRM. The dashed line in all the plots shows the frequencies at which 𝑛′(𝜔)=−1. (a) The blue line is the spatial “walk-off” angle with the pumping rate of Γ_pump=0.21×10⁹ s⁻¹ at |𝑞_𝑥|=0.01|𝑞|. Both losses and the “walk-off” within the gain window are precisely canceled. (b) The 𝛿 angles obtained at the pumping rate of Γ_pump=0.21×10⁹ s⁻¹. The group velocities and phase velocities are strictly antiparallel in this case (𝛿=180^∘) at different |𝑞_𝑥| when 𝑛′(𝜔)=−1 (at 𝜔=121.28×10¹² s⁻¹). (c) The 𝛿 angles obtained at the pumping rate of Γ_pump=0.48×10⁹ s⁻¹. Even though at this pumping rate the NRM is turned into a light-amplifying medium, the spatial “walk-off” reappears and depends on the value of |𝑞_𝑥| when 𝑛^′(𝜔)=−1, which may lead to degradation of the optical performance of an NRM.

(a)

(b)

(c)