Quadruple plasmon-induced transparency of polarization desensitization caused by the Boltzmann function

This study proposes a graphene metamaterial desensitized to the polarized angle to produce tunable quadruple plasmon-induced transparency (PIT). As a tool employed to explain the PIT, n-order coupled mode theory (CMT) is deduced for the first time and closely agrees with finite-difference time-domain (FDTD) simulations according to the quadruple PIT results in the case of n = 5. Additionally, the response of the proposed structure to the angle of polarized light is investigated. As a result, the Boltzmann function satisfied by the response of graphene strips to the polarization direction of incident light is proposed for the first time. Its property of polarization desensitization can be attributed to structural centrosymmetry, and conjugated variety which the Boltzmann functions result in. Therefore, a quintuple-mode modulation based on simultaneous electro-optical switch is realized by tuning Fermi levels within graphene. Its modulation degrees of amplitude and dephasing times are obtained. Given that the slow-light property is an important application of PIT, the n-order group index is thereby obtained. Hence, not only do the insights gained into polarization-desensitization structure provide new ideas for the design of novel optoelectronic devices, but also the results from the n-order CMT offer new research progress and references in theory.