Gaussian Pulse Distortion in a Nonlinear Induced Kerr Atomic Medium

Abstract

The Gaussian pulse propagation is investigated in an atomic medium under Kerr nonlinearity effect. The pulse intensity is reduced from $100\%$ to $3\%$ as the propagation distance of the medium L= 100 cm. The pulse shows large phase shift within the medium due to large delay. The large phase shift and delay have significant applications, but the pulse intensity is dropped and energy is lost with cross-Kerr nonlinearity in the medium. Time holes are investigated due to rapid distortion and phase shifts in time where the pulse intensity is vanished. The pulse is split into large and small delay and phase shifts. The modified results may have significant applications in photo cell devices, self- and cross-phase modulation and disadvantage in communication systems.

Appendix

$$\begin{aligned} \overset{\cdot }{\overset{\sim }{\rho }}_{45}= & \; B_1\widetilde{\rho }_{45} +\frac{i}{2}G_2^{*}\widetilde{\rho }_{25}-\frac{i}{2}G_{1c} \widetilde{\rho }_{41}-\frac{i}{2}G_2 \widetilde{\rho }_{43}+\frac{i}{2}G_p( \widetilde{\rho }_{55}- \widetilde{\rho }_{44}) \\ \overset{\cdot }{\overset{\sim }{\rho }}_{41}= & \; B_2\widetilde{\rho }_{41} +\frac{i}{2}G_2^{*}\widetilde{\rho }_{21}-\frac{i}{2}G^*_{1c} \widetilde{\rho }_{45}+\frac{i}{2}G_p \widetilde{\rho }_{51}\\ \overset{\cdot }{\overset{\sim }{\rho }}_{43}= & \; B_3\widetilde{\rho }_{43} +\frac{i}{2}G_2^{*}\widetilde{\rho }_{23}-\frac{i}{2}G^*_{2c} \widetilde{\rho }_{45}+\frac{i}{2}G_p \widetilde{\rho }_{53}\\ \overset{\cdot }{\overset{\sim }{\rho }}_{25}= & \; B_4\widetilde{\rho }_{25}+\frac{i}{2}G_2\widetilde{\rho }_{45}-\frac{i}{2}G_{1c} \widetilde{\rho }_{21}-\frac{i}{2}G_{2c} \widetilde{\rho }_{23}-\frac{i}{2}G_{p} \widetilde{\rho }_{24}\\ \overset{\cdot }{\overset{\sim }{\rho }}_{21}= & \; B_5\widetilde{\rho }_{21} +\frac{i}{2}G_2\widetilde{\rho }_{41}-\frac{i}{2}G^*_{1c} \widetilde{\rho }_{25}\\ \overset{\cdot }{\overset{\sim }{\rho }}_{23}= & \; B_6\widetilde{\rho }_{23} +\frac{i}{2}G_2\widetilde{\rho }_{43}-\frac{i}{2}G^*_{2c} \widetilde{\rho }_{25} \end{aligned}$$

where

$$\begin{aligned} B_1= & \; (i\Delta _p-\frac{\Gamma _{54}}{2})\\ B_2= & \; (i\Delta _p-i1_c)-\frac{1}{2}(\Gamma _{51}+\Gamma _{54})\\ B_3= & \; (i\Delta _p-i2_c)-\frac{1}{2}(\Gamma _{53}+\Gamma _{54})\\ B_4= & \; i(\Delta _p+\Delta _2)\\ B_5= & \; i(\Delta _2+\Delta _p-\Delta _{1c})-\frac{1}{2}\Gamma _{51} \end{aligned}$$

and

$$\begin{aligned} B_6=i(\Delta _p+\Delta _2-\Delta _{2c})-\frac{1}{2}\Gamma _{53} \end{aligned}$$