Grating structures made of materials which provide a high optical index contrast between the grating slabs and the surrounding medium have shown many extraordinary properties. The resonance of Bloch modes between the two grating interfaces and their coupling can be adjusted to obtain different and very promising properties in a large range of applications such as broadband mirrors, high-Q filters, planar lenses, circular polarizer... The development of VCSEL devices based on GaSb for a mid-infrared emission is still limited today at 2.6 µm. The high performances of high contrast grating (HCG) mirrors combined with a good polarization selectivity and a thickness lower than 2 µm should be very promising characteristics to enhance electrical, thermal and optical properties of VCSEL devices emitting above 2.3 µm and would allow spectroscopic measurements of polluting gas in the 2-3 µm wavelength range. In this paper, we present the design of a GaAs HCG to replace the top Bragg mirror of mid infrared based VCSEL. A robust optimization algorithm is used to find the best dimensions of the HCG structure for a VCSEL application. Thus, the homemade algorithm searches not only for the most efficient mirror but also for a robust design structure with large tolerances with respect to the errors of fabrication on the grating dimensions.