An envelope-function approach for a one-dimensional photonic crystal   containing single negative materials
  An envelope function approach is used to study the wave propagation in a one-dimensional Photonic Crystal containing single negative layers. This approach enables one to obtain the analytic expressions of the parameters of an equivalent effective medium. From these parameters, it is seen that the periodic structure appears to be an equivalent left-handed medium for the envelope function. For the nonlinear wave propagation the phenomenon of bistability and gap soliton formation near the edges of the zero-phi gap is discussed. 
Munazza Zulfiqar Ali and Tariq Abdullah