Numerical calculation of modes in dispersive and absorptive systems is performed using the finite element method. The dispersion is tackled in the frame of an extension of Maxwell's equations where auxiliary fields are added to the electromagnetic field. This method is applied to multidomain cavities and photonic crystals including Drude and Drude-Lorentz metals. Numerical results are compared to analytical solutions for simple cavities and to previous results of the literature for photonic crystals, showing excellent agreement. The advantages of the developed method lie in the versatility of the finite element method regarding geometries and in sparing the use of the tedious complex poles research algorithm. Hence, the complex spectrum of resonances of non-Hermitian operators and dissipative systems, like two-dimensional photonic crystals made of absorbing Drude metal, can be investigated in detail. The method is used to reveal unexpected features of their complex band structure. (C) 2016 Optical Society of America
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