| Because of the global traffic improve rapidly, everyone began to research optical computer and all-optical Network (All Optical Network, AON).People have a great requirements, therefore slow light effect is a hot research in recent years. Slow light signal propagation velocity can achieve optical signal storage, Optical computer will birth in the future all optical network. Under the different experiments, this method can change the signal propagation velocity of light in different ways, eventually we can get super slow (fast) light.In this article use1480nm pump, erbium-doped fiber Bragg grating (erbium doped fiber Bragg grating, EDFBG) to implement the principle of slow light effect, from the theoretical formula derived in the first place, and then through the mathematical simulation of the mat lab from analog graphics is analyzed.The energy level diagram of figure1is a Er3+, in which the level4I15/2,4I13/2,4I11/2is a three-level structure,1480nm pump action, Er3+in the ground state4I15/2after a relaxation time transition to metastable4I13/2, finally formed the population inversion, and1535nm detecting light excitation level4will happen between4I15/2-4I13/2-Formula, n(z)=no[1+2hcos(2πz/T+φ)],0<z<L for grating refractive index modulation, n0is the average refractive index grating, z is axial, h and φ are refractive index modulation and phase modulation depth (usually h<<1), L is the length of the grating, and T is the grating modulation cycle.Frequency of FBG and detecting light frequency approximately equal field strength formula: u(z) and v(z)is the forward and reverse transmission light amplitude value, kB is FBG propagation constant.When detecting light propagation of FBG is coupled-mode equation:Two boundary conditions:z=0at the grating incidence end detecting light into the gratings are entirely, u(0,ε)=√I0,(" enter the grating detection light intensity).In the end of the grating z=L output light reflected light is there v(L,δ)=0.The grating t is the transmission coefficient t(δ)=u(L,δ)/u(0,δ).Exists when detecting light group delay τg(δ), group delay is the transmission coefficient of phase of detecting light frequency derivative, on the depth of modulation is uniform fiber Bragg grating (q is constant) cycle. Solutions (4-6) type fiber Bragg grating, and consider the detecting light transmittance expression, the expression of the group delay: k=√q2-g2; g=(δ+gr)+igi, The last transmission group velocity of light using this formula to express vg=L/τg.Group of refractive index isng=c/vg.The transmission coefficientt(δ) and corresponding refractive index curve can be obtained, as shown in figure2.From figure2can be found in the index of refraction exist severe change of the area, in the frequency detuning of transmitted light group velocity will happen very big change.In figure2values of parameters are as follows:L=2cm, c=3×108m/s,λp=980nm, λpro=1533.8nm, Pth=0.8mW, Pp=4.0mW, ωB=2π×195.58THz, ωpro=2π×199.59THz, τ=10ms, r=1.0×10-2,σe=4.8×10-25m2,σa=5.8×10-25m2, N=8×1025, h=2.345×10-4。Figure3vg/c and δωpro is changing with the curve, a and b, respectively corresponding to the fast and slow light.Since the transmission changes the speed of light, which is what parameters will affect the magnitude of change quantity? What parameters will determine the type of transmitted light (slow or fast light)? By changing the parameters of a certain size, transmission change the amount of the group velocity of light. We can find that the transmitted light group velocity and the length of the grating L, doping concentration N, pump power Pp and grating refractive index modulation of h. Figure4and figure5for the relation curve between them.Figure2(solid line) and the transmission coefficient index (dashed line) and the frequency detuning ωpro-ωB of the curve. Figure3. vg/c along with δωpro the change of curve. Figure3a:parameter value is constant, the transmission was the super fast light. Figure3b:h=2.345x10-5other parameters unchanged transmission was the super slow light.Figure4:vg/c with the grating length L (a), the pump power Pp (c), h(d) grating, grating refractive index modulation,N(b) doping concentration, simulation graphics other parameters are constant values.We got through changing the four graphs, A:when the length of the FBG increases gradually, a transmission light group velocity ratio between the speed of light from above1to change to1and then continue to rise.Concluding is that increasing the length of the FBQ of which the emergent light of the speed of light would increases with the length of the transition from slow to fast light. B:when the pump power is less than1mw is inversely proportional to the two, both when pump power is greater than1mw is proportional to the. According to the vg/c value that is less than1.That isthe transmission group velocity of light is always less than the speed of light, then transmitted light is superslow light. C according to the graphics transmission at the start of the group velocity of light with the grating refractive index modulation depth and gradually increase is proportional to the increase, but in the modulation depth is approximately0.12×10-4position when they started to change as the inverse relationship, and the position of the ordinate approximation numerical4changes gradually abate, graphics is similar to a horizontal line. From vg/c the shift from less than1until the change is greater than1, the transmission will become a super fast from super slow light. D according to diagram at the beginning of the doping concentration is higher, the grating with transmission group velocity of light is directly proportional to the greater the relative relations. In doping concentration, N=5.35×1026, however, when the inversely proportional relationship between them. In doping concentration forN=4.8×1026betweenZ=5.8×1026get super fast the rest of the range is super slow light.Figure5different L (a), N (b), Pp (c), h (d), along with the diagram.A fiber Bragg grating length respectively A:L=2.5cm,2.0cm,1.5cm and1.0 cm,1-4and relatively; B:fiber grating doping concentration respectively for N=1×1026,2×1025,4×10258×10251-4relatively; C:fiber grating pump power values respectively Pp=8mW,4mW,2mW,1mW corresponding to each other; D:fiber grating modulation depth h=4.345×10-5,6.345×10-5,8.345×10-5,10.345×10-51-4and relatively; Other parameters value unchanged. Matlab simulation diagram is mixed dysprosium fiber Bragg gratings: values of parameters are as follows:L=2cm, c=3×108m/s, λp=1240nm, λo=1300nm, P,h=0.8mW, Pp=4.0mW, ωB=2π×195.58THz,ωpro=2π×199.59THz, τ=10ms, r=1.0×10-2,σe=1.7×10-24m2,σa=2.8×10-24m2, N=3.2×1025, h=2.345×10-4。Figure6. vb/c along with δωpro the change of curve. Figure6a:parameter value is constant, the transmission was the super fast light. Figure6b:h=2.345x10-5other parameters unchanged transmission was the super slow light.Figure7:vg/c with the grating length L (a), the pump power Pp (c), h(d) grating, grating refractive index modulation,N(b) doping concentration, simulation graphics other parameters are constant values. We got through changing the four graphs, A:when the length of the FBG increases gradually, a transmission light group velocity ratio between the speed of light from above1to change to1and then continue to rise.Concluding is that increasing the length of the FBQ of which the emergent light of the speed of light would increases with the length of the transition from slow to fast light. B:when the pump power is less than5mw is inversely proportional to the two, both when pump power is greater than5mw is proportional to the. According to the vg/c value that is less than1.That isthe transmission group velocity of light is always less than the speed of light, then transmitted light is superslow light. C according to the graphics transmission at the start of the group velocity of light with the grating refractive index modulation depth and gradually increase is proportional to the increase, but in the modulation depth is approximately0.03×10-3position when they started to change as the inverse relationship, and the position of the ordinate approximation numerical4changes gradually abate, graphics is similar to a horizontal line. From vg/c the shift from less than1until the change is greater than1, the transmission will become a super fast from super slow light. D according to diagram at the beginning of the doping concentration is higher, the grating with transmission group velocity of light is directly proportional to the greater the relative relations. In doping concentration, N=7.2×1026, however, when the inversely proportional relationship between them. In doping concentration forN=5.8×1026betweenZ=8.1×1026get super fast the rest of the range is super slow light. Figure8different L (a), N (b), Pp (c), h (d), along with the diagram.A fiber Bragg grating length respectively A:L=2.5cm,2.0cm,1.5cm and1.0cm,1-4and relatively; B:fiber grating doping concentration respectively for N=1×1026,2×1025,4×10258×10251-4relatively; C:fiber grating pump power values respectively Pp=8mW,4mW,2mW,1mW corresponding to each other;D:fiber grating modulation depth h=4.345×10-5,6.345×10-5,8.345×10-5,10.345×10-5From simulation graphics we know EDFBG ang DDFBG allow detecting light propagation speed change, eventually producing light fast (slow). Which produces light fast (slow) is mainly affected by four factors:the grating length L, grating N doping concentration, pump power Pp, grating refractive index modulation h.1.The group velocity of the transmission light and grating length change is proportional to the relationship, as L increases gradually. However in the N, Pp and h diagram has a turning point, in the turning point on the right side of the transmission light group velocity increases gradually with three parameters, the turning point in the left side is the opposite.2.Determine transmission was the fast (slow) light is the main factors L, N and h, Pp. Can be seen from figure4, figure a, c, d in fast (slow) has a light, figure b slow light, so, when others parameter values must be numerical change make Pp transmission was the slow light has been form is the same. DDFBG four parameters change rule summary is as follows:1.Through the figure7we get four graphs change:A:when the length of the FBG increases gradually, the speed of light would increases with the length of the transition from slow to fast light. B:according to the vg/c value that is less than1, which is transmitted light group velocity is always less than the speed of light, then transmitted light is superslow light.Cand D:according to graph transmission grating refractive index modulation depth increases the group velocity of light how fast light are among the different values.2. Determine transmission was the fast (slow) light is the main factors L, N, h, Pp. As can be seen from the figure8and figure a, b, c, d, has a fast (slow) light, in the other parameter values unchanged. |
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