Objective With the increasing demand for high capacity and high speed information transmission, the transmission, storage, retrieval, transformation, and processing of optical information have become a very important research area in the field of information science. A grating is a type of optical device with a spatially-periodic structure. It has four main properties: dispersion, beam splitting, polarization, and phase matching. It is widely used in information processing, optical communication, optical storage, and other fields. However, when a grating is used in communications, it not only has a conversion efficiency and a conversion rate between optical and electrical signals, but also has the response rate of a mechanical structure, which has large effects on the signal transmission efficiency, bandwidth, and stability. Therefore, all-optical networks based on the all-optical switching technology have become a new focus of research. In all-optical networks, information transmission, transformation, and amplification do not need light-electricity conversion, and the optical structures are simple, reconfigurable with anti-interference capability, thus the utilization rate of network resources is improved. The core device of an all-optical network based on an all-optical switch has the advantages of stability, high capacity, and ultra-high speed, and thus, it has attracted more and more attention from researchers. Therefore, the purpose of this study is to realize all-optical control based on grating characteristics. We achieve a nearly-resonant gain grating effect that can be used to control light in real-time and thus all-optical control is realized.
Methods In an N-type four-level atomic system, the analytical expression of the polarization rate of the probe field was first calculated by the density matrix method under the steady-state condition based on the perturbation theory. Then, the propagation equation of the probe field was obtained using Maxwell's equations. From the analytical solution, the related factors affecting the diffraction efficiency of the probe field were analyzed, mainly including the Rabi frequencies and detunings of the modulation and coupling fields. In addition, it was seen that the transfer function of the interaction length between light and atoms also influenced the diffraction efficiency. We focused on the amplification and diffraction capacity of the probe field and generated the transmission functional curve of the probe field. The changes in diffraction intensity with Rabi frequencies, detunings of the modulation and coupling fields, and interaction length between light and atoms were also considered. A nearly-resonant gain grating with high gain and a strong diffraction ability was realized by identifying and adjusting the relevant parameters appropriately.
Results and Discussions A nearly-resonant gain grating effect is studied in an N-type four-level coherent atomic structure. The grating can not only amplify the light information, but can also actively control the light field in real-time and realize the modulation of the amplitude and phase at the same time to achieve all-optical control. When the coupling field is resonant and the probe and modulation fields are near resonance, they can regulate the gain and phase of the probe field so that the energy of the probe field is amplified and the high-order diffraction efficiency of the probe field can be significantly improved [Fig. 2(b)]. It is seen that the diffraction efficiency of the nearly-resonant gain grating goes beyond the theoretical limit of an ideal sinusoidal phase grating, and its diffraction efficiency is nearly three times that of a sinusoidal phase grating. In addition, during the change in the Rabi frequency of the modulation field, the atomic medium can continuously transform between the absorption and gain media [Fig. 3(a)]. Moreover, the modulation field has a threshold for the diffracted light during this process. When the intensity of the modulation field is less than the threshold, there is almost no diffracted light. When the intensity of the modulation field is greater than the threshold, the intensity of the each order diffracted light increases sharply (Fig. 6).
Conclusions We theoretically study a nearly-resonant gain grating in an N-type four-level atomic system. The results show that the energy of the probe field is amplified by four times under the combined action of the modulation and coupling fields when there is only amplitude modulation, and this is mainly concentrated in the zeroth-order diffraction direction. With the introduction of phase modulation, the coupling field plays an important role in the distribution of diffracted light, and more energy is distributed along the higher-order diffraction direction. In this process, for the first-order, second-order, and third-order diffracted light, there are thresholds for the modulation field, which are 0.28γ, 0.26γ, and 0.32γ, respectively. When the intensity of the modulation field is less than the threshold, there is almost no diffracted light, and when the intensity of the modulation field is above the threshold, the intensity of each order diffracted light increases dramatically. In addition, other factors affecting the high-order diffraction efficiency of the probe field are also studied. By adjusting the relevant parameters, a grating with high gain, strong diffraction capacity, and controllable threshold is obtained, which has broad applications in new photonic devices such as all-optical switches, all-optical routes, and all-optical logic gates.
