Fig. 1. Structure of proposed model.The optical Stark beam is added to the cavity and a waveguide generated. The directions used in this paper are set by the coordinate.

Fig. 2. Two level excitonic states and their strong coupling with cavity photons when the OS beam is added.

Fig. 3. Effective refractive index versus OS shift “ $\Delta E_x^{{\sigma }^{+}}$ ”.

Fig. 4. Mode profile of polariton wavepacket for polarized OS beam when $\Delta E_x^{{\sigma }^{+}}$ = 5 meV. (a) Only one mode is supported at $\Delta {\text{E}}_{\text{x}}^{{\sigma }^{+}}$ = 5 meV. (b) A full map of the field distribution in the x-y plane at $\Delta {\text{E}}_{\text{x}}^{{\sigma }^{+}}$ = 5 meV.

Fig. 5. Mode profile and value of polarization degree ρ.(a) two modes are supported at $\Delta {\text{E}}_{\text{x}}^{{\sigma }^{+}}=\text{22}$ meV and $\Delta {\text{E}}_{\text{x}}^{{\sigma }^{-}}=\text{0}$ meV . (b) The full map of the field distribution in the x-yplane at $\Delta {\text{E}}_{\text{x}}^{{\sigma }^{+}}=\text{22}$ meV and $\Delta {\text{E}}_{\text{x}}^{{\sigma }^{-}}=\text{0}$ meV. (c) The modulation curves of ρ along the x-direction when y = 0 at $\Delta {\text{E}}_{\text{x}}^{{\sigma }^{+}}=\text{22}$ meV and $\Delta {\text{E}}_{\text{x}}^{{\sigma }^{-}}=\text{5}$ meV. (d) The full map of value $\rho$ in the x-y plane at $\Delta {\text{E}}_{\text{x}}^{{\sigma }^{+}}=\text{22}$ meV and $\Delta {\text{E}}_{\text{x}}^{{\sigma }^{-}}=\text{5}$ meV.

Fig. 6. Typical modulation curves of ρ along the waveguide (x direction) for y = 0. The black curve corresponds to $\Delta {\text{E}}_{\text{x}}^{{\sigma }^{+}}$ = 5 meV and $\Delta {\text{E}}_{\text{x}}^{{\sigma }^{-}}$ = 0 meV, the blue curve corresponds to $\Delta {\text{E}}_{\text{x}}^{{\sigma }^{+}}$ = 22 meV and $\Delta {\text{E}}_{\text{x}}^{{\sigma }^{-}}$ = 5 meV, the red curve corresponds to $\Delta {\text{E}}_{\text{x}}^{{\sigma }^{+}}$ = 5 meV and $\Delta {\text{E}}_{\text{x}}^{{\sigma }^{-}}$ = 22 meV.