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In this work, we numerically demonstrate an all-optical tunable Fano resonance in a fishnet metamaterial(MM) based on a metal/phase-change material(PCM)/metal multilayer. We show that the displacement of the elliptical nanoholes from their centers can split the single Fano resonance (FR) into a double FR, exhibiting higher quality factors. The tri-layer fishnet MMswith broken symmetry accomplishes a wide tuning range in the mid-infrared(M-IR) regime by switching between the amorphous and crystalline states of the PCM (Ge2Sb2Te5). A photothermal model is used to study the temporal variation of the temperature of the Ge2Sb2Te5 film to show the potential for switching the phase of Ge2Sb2Te5 by optical heating. Generation of the tunable double FR in this asymmetric structure presents clear advantages as it possesses a fast tuning time of 0.36 ns, a low pump light intensity of 9.6 μW/μm2, and a large tunable wavelength range between 2124 nm and 3028 nm. The optically fast tuning of double FRs using phase change metamaterials(PCMMs) may have potential applications in active multiple-wavelength nanodevices in the M-IR region. [ABSTRACT FROM AUTHOR]