Circuit Model of Parity-Time (PT ) Symmetric Waveguide Arrays

A circuit model is proposed for determining the characteristic modes (eigenvalues) of a periodic array of PT-symmetric (gain/loss coupled) waveguides. This model consists of a pair of coupled LC circuits, one with amplification resistance -R and the other with an equivalent attenuation. The band structure consists of two bands separated by a gap that depends on the value of the gain/loss (γ). In other words, one can control the size of bandgap and hence the allowed modes propagating within the PT array. For a critical value of gain/loss or (γ=γPT), the eigenvalues merge and the gap disappears. The corresponding results are in good agreement with the optical model results. The significance of this design lies with its tunability, high speed, and relative simplicity.