Surface Plasmon Resonance Sensing at the Interface of Doppler Broadening Dielectric Medium and Graphene

Abstract

The sensitivity of the surface plasmon polariton wave (SPPs) is coherently controlled and modified at the interface of four-level Doppler broadening dielectric medium and graphene. The useful control over the sensitivity of the SPPs under the Doppler broadening dielectric medium with system and driving fields parameters is reported. The sensitivity of SPPs is a function of probe and control field detuning, control field Rabi frequency, and decay rates. The high value of sensitivity is reported to 2700 deg/RIU with phase and decay rate, while small value of sensitivity is investigated to 320 deg/RIU with control field detuning. The above results show useful applications in biosensor, data storage, waveguiding, and solar cells.

Appendix

The coupled rate equations are given as

$$\begin{aligned} \dot{\tilde{\rho _{13}}}=D_1\tilde{\rho _{13}}+\frac{i}{2}\Omega _1\tilde{\rho _{43}}-\frac{i}{2}\Omega _2\tilde{\rho _{12}}+\frac{i}{2}\Omega _p(\tilde{\rho _{33}}-\tilde{\rho _{11}}) \end{aligned}$$

(18)

$$\begin{aligned} \dot{\tilde{\rho _{43}}}=D_2\tilde{\rho _{43}}+\frac{i}{2}\Omega ^{*}_1\tilde{\rho _{13}}-\frac{i}{2}\Omega _2\tilde{\rho _{42}}-\frac{i}{2}\Omega _p\tilde{\rho _{41}} \end{aligned}$$

(19)

$$\begin{aligned} \dot{\tilde{\rho _{12}}}=D_3\tilde{\rho _{12}}+\frac{i}{2}\Omega _{2}\tilde{\rho _{13}}-\frac{i}{2}\Omega _{1}\tilde{\rho _{42}}-\frac{i}{2}\Omega _{p}\tilde{\rho _{32}} \end{aligned}$$

(20)

$$\begin{aligned} \dot{\tilde{\rho _{42}}}=\frac{i}{2}\Omega ^{*}_{1}\tilde{\rho _{12}}-\Omega ^{*}_{2}\tilde{\rho _{43}}-D_4\tilde{\rho _{42}} \end{aligned}$$

(21)

The parameters $A_{1-4}$ are written below:

$$\begin{aligned} D_1=i(\Delta _{pd}+kv)-\frac{G_{31}+G_{41}}{2} \end{aligned}$$

(22)

$$\begin{aligned} D_2=i(\Delta _{1}+\eta _{1}kv-\Delta _{pd}-kv) \end{aligned}$$

(23)

$$\begin{aligned} D_3=i(\Delta _{pd}+kv-\Delta _1-\eta _{2}kv)-\frac{G_{32}+G_{42}+G_{31}+G_{41}}{2} \end{aligned}$$

(24)

$$\begin{aligned} D_4=i(\Delta _{pd}+kv-\Delta _1-\eta _{1}kv-\Delta _2-\eta _{2}kv)-\frac{G_{32}+G_{42}}{2} \end{aligned}$$

(25)

$$\begin{aligned} B_1=i(\Delta _{pg}+kv-\Delta _4-\eta _{2}kv-\Delta _3-\eta _{1}kv)+\frac{G_{a}+G_{b}+G_{d}}{2} \end{aligned}$$

(26)

$$\begin{aligned} B_2=i(\Delta _{pg}+kv-\Delta _4-\eta _{2}kv)+\frac{G_{a}+G_{d}}{2} \end{aligned}$$

(27)

$$\begin{aligned} B_3=i(\Delta _{pg}+kv)+\frac{G_{a}+G_{b}+G_{d}}{2} \end{aligned}$$

(28)