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Diffraction grating equation a level11/23/2023 ![]() ![]() It has been shown that by applying a standing-wave beam, the higher order Fraunhofer diffraction can be obtained for a probe light due to the modulation of the refractive index. Two dimensional electromagnetically induced grating (2D EIG) has been also studied in a four-level double Λ-type atomic system via incoherent pumping field 19. The relative phase between applied fields due to the presence of SGC can influence the diffraction efficiency of the phase grating. It was shown that the SGC can adjust the diffraction efficiency of high order patterns in the presence of incoherent pumping field. The effect of SGC on EIG pattern in a four-level N-type atomic system was also investigated 18. The diffraction efficiency of weak probe light can transfer from zero-order to higher-order components. It was shown that as a result of the SGC, it is possible to achieve an enhanced nonlinear refraction with zero linear absorption. In another work by Gao 17, the SGC effect on Kerr nonlinearity and EIG of four-level atomic system were investigated. Considering a three-level atomic system in the Λ configuration with two closely-lying lower levels and in the presence of spontaneously generated coherence (SGC), it has been found that the diffraction efficiency of phase grating can be enhanced due to the presence of SGC. The coherent control of the EIG patterns via spontaneous emission has been studied by Xie et al. Many proposals have been suggested to investigate the EIG in various media 10, 11, 12, 13, 14, 15. The EIG is due to a periodic spatial modulation of absorption and dispersion of an atom. An important and favorable phenomenon arising from interaction of a standing-wave field with the EIT medium is known as electromagnetically induced grating (EIG) 9. It is known that the electromagnetically induced transparency (EIT) 1 leads to many appealing optical effects in quantum and nonlinear optics 2, 3, 4, 5, 6, 7, 8. Our proposed model may be useful for optical switching and optical sensors based on semiconductor nanostructures. The efficiency of phase grating for third-order of susceptibility is higher than phase grating for fifth-order susceptibility. ![]() When the coupling light is out of resonance, most of probe energy is transferred from zero-order to higher-order directions due to resonant tunneling effect. In resonance of coupling light, both amplitude and phase grating are formed in the medium due to enhancement of third-order and fifth-order probe absorption and dispersion. We investigate also the two-dimensional electromagnetically induced grating (2D-EIG) of the weak probe light by modulating the third-order and fifth-order susceptibilities. However, in off-resonance of coupling light, real parts of third-order and fifth-order susceptibilities enhance while the nonlinear absorption vanishes. In presence of the resonant tunneling and when the coupling light is in resonance with the corresponding transition, the real parts of third-order and fifth-order susceptibilities are enhanced which are accompanied by nonlinear absorption. It is found that the resonant tunneling can modulate the third-order and fifth-order of susceptibilities via detuning frequency of coupling light. We can solve for \(y_V\) and \(y_R\).We study the nonlinear optical properties in an asymmetric double AlGaAs/GaAs quantum well nanostructure by using an external control field and resonant tunneling effects. ![]()
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