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arXiv:1309.0538 · Physical Review A

Optical bistability in one-dimensional doped photonic crystals with spontaneously generated coherence

Shahnaz Aas, Özgür Esat Müstecaplıoğlu

Published Nov 26, 2013• 16 citations
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Abstract

We investigate optical bistability in a multilayer one-dimensional photonic crystal where the central layer is doped with $\ensuremath{\Lambda}$-type three-level atoms. We take into account the influence of spontaneously generated coherence when the lower atomic levels are sufficiently close to each other, in which case Kerr-type nonlinear response of the atoms is enhanced. We calculate the propagation of a probe beam in the defect mode window using the numerical nonlinear transfer matrix method. We find that Rabi frequency of a control field acting on the defect layer and the detuning of the probe field from the atomic resonance can be used to control the size and contrast of the hysteresis loop and the threshold of the optical bistability. In particular we find that at the optimal spontaneously generated coherence, a three orders of magnitude lower threshold can be achieved relative to the case without the coherence.

DOI
10.1103/physreva.88.053846

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We investigate optical bistability in a multilayer one-dimensional photonic crystal where the central layer is doped with \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-type three-level atoms. We take into account the influence of spontaneously generated coherence when the lower atomic levels are sufficiently close to each other, in which case Kerr-type nonlinear response of the atoms is enhanced. We calculate the propagation of a probe beam in the defect mode window using the numerical nonlinear transfer matrix method. We find that Rabi frequency of a control field acting on the defect layer and the detuning of the probe field from the atomic resonance can be used to control the size and contrast of the hysteresis loop and the threshold of the optical bistability. In particular we find that at the optimal spontaneously generated coherence, a three orders of magnitude lower threshold can be achieved relative to the case without the coherence.
In this paper, we investigate optical properties of a multilayer one-dimensional photonic crystal, where the central layer is doped with one of different kinds of three-level atomic systems, e.g., Vee, Λ, upper coupling ladder, and lower coupling ladder. Then, the control of optical bistability properties of the photonic crystal, by Rabi frequency of the coupling field, spontaneously generated coherence, and probe detuning, is studied. We discuss the advantages and disadvantages of different systems' optical properties. It is shown that the investigated photonic crystals have a bistability property as well as full transparency. Also, the photonic crystals show some amplification in transmission and even reflection of the probe field.
We investigate the property of optical bistability in a photonic-crystal one-atom laser when nonlinear microcavity is present. The physical system consists of a coherently driven two-level light emitter strongly coupled to a high-quality microcavity which is embedded within a photonic crystal and another coherent probing field which has incident into the microcavity. In our case, the microcavity is fabricated by nonlinear material and placed as an impurity in photonic crystal. This study reveals that such a system can exhibit optical bistability. The dependence of threshold value and hysteresis loop on the photonic band gap of the photonic crystal, driving field Rabi frequency and dephasing processes, are studied. Our results clearly illustrate the ability to control optical bistability through suitable photonic-crystal architectures and external coherent driving field, and this study suggests that in a photonic-crystal nonlinear microcavity, the one-atom laser acts as an effective controllable bistable device in the design of all-light digital computing systems in the near future.
We study the optical bistable properties in one-dimensional photonic crystal with symmetric structure (AB)N(D)M(BA)N, where A is high refractive index medium, B is low refractive index medium, D is defect layer, N is the number of layer periods at the left and right of the defect layer. M determines the thickness of the defect layer with Kerr medium. First, we analyze mechanisms producing bistability by the structure consisted of a nonlinear layer sandwiched between Bragg reflectors. Then by using the transfer matrix method, we calculate numerically the threshold value of the bistability switching in one-dimensional photonic crystals with structure (AB)N(D)M(BA)N. The investigations show that the number of layer periods (N) and the thickness of the defect layer (M) influence the threshold value of the bistability switching. We confirm the parameter of the bistability switching to produce the lower threshold value.
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Optical bistability in a four-level inverted Y-type atom system inside an optical ring cavity is investigated numerically. Atomic density matrix equations are derived by the density matrix theory. The effect of the Spontaneously Generated Coherence( SGC) on threshold of the optical bistability is studied.When the probing field and controlling field are in two-photon resonance,the atoms are trapped on the two lower states,probing field is transparent and there is no bistability in the system. But when the probing field and coupling field or coupling field and controlling field are in two-photon resonance,there is the optical bistability in the system. Under condition of the stable state,SGC can make the interference destructive from two transition channels. Population distribution on the higher levels is enhanced,transparency window becomes narrow,and the threshold of the bistability becomes large.
We theoretically investigate optical bistability (OB) behaviour in a four-level atomic system confined in a unidirectional ring cavity. It is shown that OB can be controlled by adjusting the intensity of the coupling field and the value of the cooperativity parameter. More importantly, our numerical results show that the threshold intensity of OB can be reduced without decreasing the range of the hysteresis loop via adjusting the effect of spontaneously generated coherence (SGC) or the relative phase between two applied fields. The influence of the frequency detuning of the coupling field on the OB behaviour is also discussed.