Quantum Interference Effects On Gain Leveling Of EDFAs With 1480 Pumping

EDFA (erbium-doped fiber amplifier) is one of the important devices in optical communication for it supports long distant transmission in dense wavelength division multiplexing (WDM) system. However, its uneven gain profile easily leads to crosstalk among the paths of with different wavelengths, thereby causing transmission error so that gain equalization for EDFA is particularly important by use of WDM systems. In this paper, we use EIT (Electromagnetically Induced Transparency) technique for gain leveling of EDFA in a two-level system with 1480nm pumping.For 1480nm pumping, the energy from the pump laser excites the erbium ions in the low lying Stark-split sublevels of the ⁴I_15/2manifold to the high lying Stark-split sublevels in the ⁴I_13/2manifold. Due to the rapid thermalization decay that transfer the erbium ions in the high lying Stark-split sublevels in the ⁴I_13/2manifold to low lying Stark-split sublevels, population inversion occurs between the energy sublevels of ⁴I_15/2 and ⁴I_13/2. Once the signal light at wavelengths with approximately between 1520 to 1560nm propagating along the EDFA, the amplification takes place between the low lying Stark-split sublevels of the ⁴I_13/2manifold and the high lying ones in the ⁴I_15/2. It is precisely that because of the stokes shift existing between the emission and the absorption bands of this transition, the light amplification can occurs from 1520nm to 1560nm. The energy schematic for EDFA is shown as in Fig .1: Electromagnetically induced transparency (EIT) is a process where the absorption profile of an atomic transition can be modified when the upper or lower level is coupled coherently to a third level by a strong laser field. As show in Fig.2:Due to the presence of a strong coherent field with frequencyωcand Rabi frequency ? c, the energy level 1 and 2 were split into doublets, Respectively, The susceptibility at the frequency of probe field induced by the strong field is reverse with the original gain spectrum as a filter does.The simplest treatment of EDFA considers the two-level amplification system with energy levels as shown in Fig.3, when it is pumped at 1480 nm. Level 1 is the ground level ⁴I_15/2a>nd level 2 is metastable level ⁴I_13/2, level |2a> and |2b> are the pumping and signal levels, respectively. The transitions between manifolds of level 2 to 1 are driven by the weak signal field with frequencyωsand amplitudeεsand the strong coherent field with frequencyωc and Rabi frequency ? c. Incoherent pump is corresponding to the transition |2b> - 1 and its pumping rate denotes asΛ. Without the strong field, Fig. 3 shows a typical two-level EDFA system with population inversion between manifolds of level |2a> and 1 due to the fast unradiative thermalization process within |2a> and |2b> . With the dipole approximation and the rotating wave approximation, the density matrix equations of this system can be written as: WhereΓa1,Γb1are the corresponding to radiative rates of the respective transitions;Γbais the nonradiative rate for the theomalization process; are frequency detunings between the fields and the respective transitions. We apply perturbation method to solve equations (1) which are valid to all order of coherent field and to first order to probe field in order to find the linear susceptibilities to the transition 2a - 1 in that the signal field is weak comparing with the coherent field. The density matrix elements are expressed as: Whereσ(0),σ(1)andσ( ? 1)are corresponding to zero order, one order and one order conjugated of the signal field. Inserting (2) into (1), and being noted that ,we have: Where The macroscopic polarization of the medium is P = Nμwhere N is the Er 3+ density andμ= tr(σμ) = (μ₂₁σ₁₂ +μ₁₂σ₂₁is average dipole moment. By the definition P =ε₀χ(ω_s)ε_s, we have the susceptibility of the signal field at frequencyωs: Inserting the expression ofσa(11) into (4) and we have: As we know that the gain-absorption coefficient of the probe is proportional to the imaginary part ofχ(ω_s), we need to discuss the imaginary part ofχ(ω_s)by using numerical solutions. In order to be fit to the experimental line shapes, we use Lorentzian fitting technique[55] toχ(ω_s) through a linear superposition of N Lorentzian line shapes of center wavelengthλ_i , line width (full wave, half maximum) ?λiand amplitude ai . With the expression of Li (λ_s ), the total susceptibility can be written as follow: We take Lorentzian fitting values from Table 4.2 in [55], reproduced in Table1. We draw the imaginary part of the total susceptibilityχvs. the wavelength of the signal field in Fig.4. It shows that the position of the gain peak emergy near to 1530 nm with the coherent fieldΩ= 0 (curve (a)). The peak gain excursion can be reduced by using a coherent field with a proper the intensity and frequency (curve (b) and (c)). The parameters for Fig.4 are chosen asΓba= 10Λ= 10; The other parameters are chosen as: (a)Ω= 0,Ωc= 0;(b)Ω= 0.8489c mΩ1 ,ωc= 6535.9c mΩ1; (c)Ω= 1.2732c mΩ1 ,ωc= 6535.9 cmΩ1. We see that a large laser intensity ( which is proportional toΩ) with a proper positive frequency detuningδ, benefits to the filter using EIT scheme we proposed here. In conclusion we prove that Electromagnetically Induced Transparency can be used as a filter to flat gain spectrum for two level erbium-doped fiber amplifier (EDFA) system with 1480nm pumping,by applying an addition strong coupling field.