Double Tunable Photonic Band Gaps In A Quasi-∧-four-level System And Control Of The Propagations Of Light Pulses

This paper discusses that double tunable photonic stop bands can simultaneously appear when the dispersion property of the medium in a quasi-Λ-four-level atomic system is spatially modulated periodically by a resonant standing light field. Theoretical calculations show that efficient coherent control of two band gaps can be achieved by the intensity of the standing field and the distance of two metastable levels. The double band gaps can be used to control the propagations of two light pulses with different central frequencies. Because we can let two light signals with different frequencies either pass through or rebound and the pluses experience little energy loss and profile deformation. This system can be a efficient two channel all-optical routing scheme. It may have important applications in quantum information networks and it may also act as a frequency selector used to distinguish the desired signal from an abundance of stray pulses.The abstract is divided into two parts.Double tunable photonic band gaps in a quasi-Λ-four-level systemThe double tunable photonic band gaps are presented in a quasi-Λ-four-level atomic system driven by a standing wave in ultracold atom system .The atom energy level structure is showed in figure 1. The dielectric constant of the medium is spatially modulated periodically when the excited state and two metastable state are driven by a resonant standing field. The double tunable photonic band gaps are created in ultracold atom system. The structure of double band gaps can be controlled by the Rabi frequency of the coupling field and the distance of two metastable state levels. The most important meanings of my work is that we can simultaneously present double tunable photonic band gaps in theory. The pumping field is a standing wave formed by a coupling field and the reflection of the coupling field. Intensity of the pumping field is not zero at anywhere when the intensity of the forward wave and the backward wave are different which is caused by adjusting the reflector's reflection efficiency Rm (η≠0 )slightly. The absorption and standing wave .a-At the quasinodes; b-At the antinodes. The illustration is magnifying of the central part. The parameters areΩ0 = 10γ,Δ1 =Δ2=γ. dispersion will be modulated periodically by the pumping field when the signal field transmits the medium from the quasinodes to the antinodes. As showed in figure 2(a), there is strong absorption with step dispersion at resonance transition frequency at the quasinodes. This is just the opposition at the antinodes which is showed in figure 2(b). There are two wide transparent windows where the dispersion maintains invariable basically in both sides of the resonance transition frequency. So the univariate periodic structure with periodically absorption and dispersion is formed. And the photonic band gaps appear.The real part and imaginary part of the Block wave vector are showed in figure 3. There are two regions where the real part and imaginary part of the Block wave vector satisfy the condition: ' , "0aκ=πκ≠.The incident wave can not match the transmission solution in the two regions. The incident light can not transmit the medium because the density of states of the wave attenuates rapidly. As there is no absorption in these regions , the probe light reflects and forms the band gaps.Now I will simulate the property of reflection and transmission of the probe light with transmission matrix in finite medium. The transparent windows are formed in our model beside the resonance point which is showed in figure 2. The dispersion is modulated periodically by the pumping field. The double photonic band gaps are formed because of more strong reflection caused by multiple reflections between adjacent atomic shells. The reflection is showed in figure 4(a), figure 4(b) show the structure of the transmission. Comparing with Artoni's work we obtain double outstanding band gaps. The index of reflection can reach 95%, and this scheme can be used to all-optical double channel router.The photonic band gaps will become wide when the ratio of reflection of different medium is increased for man-made photonic crystal. But the reflection will not change as soon as the man-made photonic crystal is manufactured. So the structure of the band gaps is confirmed. But the character of the band gaps can change by the changing of some parameters in our model. The calculation shows that the ratio of reflection of adjacent medium will be bigger when the Rabi frequency of the coupling field is increased. So the double photonic band gaps will be wider. This is showed in figure 5. Moreover we can change the distance of the metastable states 2 , 3 to influence the position of the band gaps which is showed in figure 6. As the increasing of the distanceΔ,the transparent windows created by double photon resonance will depart the resonance point ,and the double band gaps will move at the same time.Control of the propagations of two light pulses with different central frequencies by double tunable photonic band gapsThe width and position of this double band gaps with high index of reflection are tunable. This model will have potential application to control the propagations of two light pulses with different central frequencies. The width of the double band gaps can be controlled by the intensity of the coupling field. So we can make the whole pulse envelope between the band gaps. We can control the propagations of the light pulses by changing the distance of metastable levels and switching on or off the reflection of the coupling fields. Pulse A transmits and pulse B reflects in figure 7(a) , and the index of transmission and reflection is very high which means that the pulse envelope is situated between the transparent windows or the band gaps. In figure 7(b), both pulse A and pulse B are reflected, but the index of reflection is weaker than that in figure 7(a) because the center of the pulse is near the edge of band gaps. The propagations of pulses that pulse A reflects and pulse B transmits in figure 7(c) is completely different with that in figure 7(a). The distance of two metastable levels in figure 7(d) is the same as that in figure 7(c) , the only difference is that the pumping field becomes travelling wave from standing wave which is formed by adjusting the reflection efficiency to zero. In this situation , the medium can not form periodical reflection structure. Moreover the pulse is located in the double transparent windows formed by the travelling wave, so the two pulses transmit the medium with very little loss which is showed in figure 7(d).Through the above discussion , we can control the propagations of two pulses with different center frequenciesΔp = ? 0.5γ,Δp =γby changing some conditions . Table 1 can describe the situation of figure 7 clearly. We still suppose that the pulse A with the center frequenciesΔp = ? 0.5γand pulse B with center frequenciesΔp =γ.If the pulse reflects we will denote it -,and the transmission +. Now we can simultaneously control the propagations of two pulses with different central frequencies. In figure 7 we research the propagations of central frequencies inΔp = - 0.5γandΔ_p =γ. Certainly we can control the propagations of different pulses with other central frequencies. If the central frequencies of the pulses change ,we can simultaneously control the propagations of two pulses by changing the distance of the metastable levels,the intensity of the coupling field and the switching on or off the reflection of the coupling field.In conclusion, we have got the following viewpoints:(1)We obtain simultaneously a double tunable photonic band gaps for the first time in ultracold atomic system which is theoretically discussed in a quasi-Λ-four-level model driven by a standing wave. So the light in band gaps can not transmit but be reflected. The width and position of the band gaps can be control by changing the intensity of the coupling field and the distance of the metastable levels.(2) We can simultaneously control the propagations of two pulses with different central frequencies in theory for the first time. We can let two light signals with different frequencies either pass through or rebound by changing the distance of the metastable levels,the intensity of the coupling field and the switching on or off the reflection of the coupling field. This system can be a efficient two channel all-optical routing scheme. It may have important applications in quantum information networks and it may also act as a frequency selector used to distinguish the desired signal from an abundance of stray pulses.