Effect of loss on the dispersion relation of photonic and phononic crystals

@article{Laude2013EffectOL,
  title={Effect of loss on the dispersion relation of photonic and phononic crystals},
  author={V. Laude and Jose M Escalante and Alejandro Mart{\'i}nez},
  journal={Physical Review B},
  year={2013},
  volume={88},
  pages={2243021-2243028}
}
A theoretical analysis is made of the transformation of the dispersion relation of waves in artificial crystals under the influence of loss, including the case of photonic and phononic crystals. Considering a general dispersion relation in implicit form, an analytic procedure is derived to obtain the transformed dispersion relation. It is shown that the dispersion relation is generally shifted in the complex (k,ω) plane, with k the wave number and ω the angular frequency. The value of the shift… 

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* Electronic address: vincent.laude@femto-st.fr

    Within the frame of the viscoelastic model, δω| k /ω = ıF L/2 is almost a linear function of frequency