In this work, we study the influence of disorder on the omnidirectional bandgap in a one dimensional stack of alternating positive and dispersive negative index materials. We achieve this through using the transfer matrix method to study wave propagation properties. In the case where the number of periods becomes infinitely large, the limit of the transmittance is derived from the trace of the matrix, and thus reducing the calculation complexity. The origin of the transmission resonances and their relation with the field localization for random systems are analyzed and compared with that of the periodic case. Our result shows that the zero average refractive index bandgap is not affected by small disorders in layer thickness or refractive index, and thus the multilayer stack is robust against fabrication. The finding is expected to achieve potential applications in optoelectronic sensor devices such as omnidirectional reflectors in airplane radomes. We also show that a random mixture of positive and dispersive negative index materials in an equal ratio always possesses a zero average refractive index bandgap.
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