Erbium-doped fiber amplifiers are essential devices in current high capacity fiber-optic telecommunication systems that are based on wavelength division multiplexing (WDM)technology [1]. Commonly used silica-based EDFAs are known to provide sufficient signal gain over an amplification bandwidth of ~30 nm in the C or the L bands,depending on the configuration. Even though the conventional silica-based EDFAs are well-suited for current WDM systems, there has been extensive work done in order to increase the EDFA gain bandwidth, due to the ever increasing demand for the expansion of data transmission capacity that has been caused by the large increase in the amount of data traffic on the Internet.

Ultra-wideband EDFAs that can cover a gain bandwidth of more than 50 nm have been successfully demonstrated using EDFs based on non-silica host materials, such as tellurite [2], bismuth oxide [3], and antimony silicate [4].Among the non-silica host material-based EDFs, the tellurite and bismuth oxide based ones are known to be capable of providing sufficient signal gain over the C and the L bands. The demonstrated gain bandwidth of tellurite and bismuth oxide EDFAs was ~70 nm, whereas the bandwidth of the antimony silicate EDFAs was ~50 nm. Another benefit of the tellurite and bismuth oxide EDFs is found in their high erbium doping concentration, which is enabled by the host materials’ high solubility to erbium ions. This feature is useful in the creation of compact fiber amplifiers with short fiber lengths.

Compared to both the antimony silicate-based and the tellurite-based EDFs, a huge benefit in using bismuth oxidebased EDFs is the fact that they can be readily spliced to conventional silica fibers using a commercially available fusion splicer with a splicing loss of less than 0.5 dB [3].This shows that bismuth oxide EDFs are superior to the other new host materials in terms of the ease of integration with pre-existing silica fiber-based communication systems.

One concern in realizing high-performance ultra-broadband amplifiers using bismuth oxide EDFs is the limitation in the amplification performance due to the various inhomogeneous and nonlinear effects caused by the high erbium concentration and the large host material nonlinearity. A range of experimental and theoretical studies on such effects as four wave mixing [3], cooperative up-conversion [5], pump excited state absorption (ESA) [6], and signal ESA [7] have been carried out.

In addition to the above-mentioned effects, another important effect that needs to be investigated is the pairinduced quenching (PIQ). The PIQ is an inhomogeneous phenomenon caused by clustered ions when the Er³⁺ ions are not evenly distributed. The PIQ is known to be strongly dependent on the host material; it is always observed in highly Er³⁺-doped fibers [8]. In an ion pair,one ion (donor) transfers its energy to the other (acceptor)when both of them are excited. The donor ion relaxes to its ground state, whereas the acceptor ion jumps to a higher energy level and relaxes back to its metastable state[9]. The PIQ can thereby cause EDFA performance degradation, such as gain reduction.

In this paper, we investigate the PIQ effect in a bismuth oxide-based EDFA in both a theoretical and an experimental manner. In the theoretical analysis we used a 6-level amplifier model that incorporates cooperative upconversion,PIQ, pump ESA, and signal ESA. In a comparison between the numerically calculated and experimentally measured gain and noise figure (NF) values, the relative number of paired ions is estimated to be ~ 6.02% in a commercially available bismuth oxide-based EDF. The impacts of the PIQ on the gain and the NF were also investigated.

This paper is organized as follows: In Section II the theoretical model used for this investigation is presented.In Section III the relative number of ion pairs in a commercially available bismuth oxide EDF is estimated, by comparing the numerically calculated gain and NF values with the experimentally measured ones. In Section IV, the PIQ is shown to be a significant degradation factor in the gain and NF performance. This is done by comparing the numerical and experimental output gains both with and without the PIQ. In Section V our conclusions are drawn from the obtained results.

For the numerical simulation, the bismuth oxide EDFA was assumed to be a six level system composed of the ⁴I_15/2, ⁴I_13/2, ⁴I_11/2, ⁴I_9/2, ⁴S_3/2, and ⁴F_7/2 states, as shown in Fig. 1. The EDFA model included the PIQ effects, the homogeneous cooperative up-conversion, the pump ESA,and the signal ESA [7],[10-13]. In the model, the effects of the pump (P_p), signal (P_s), and amplified spontaneous emission (ASE) (P_ASE) power on the populations in the energy level system were represented by the following two separate rate equations. The clustered ions were assumed to be pairs.

The Singled Ion Rate Equations

where N₁^s, N₂^s, N₃^s, N₄^s, N₅^s, and N6s represent the number of singled erbium ions in the ⁴I_15/2, ⁴I_13/2, ⁴I_11/2, ⁴I_9/2, ⁴S_3/2, and ⁴F_7/2 states, respectively. m is the number of ions within a cluster (2 for paired ions) and k is the relative number of clusters. A₂₁ and A₅₁ are the spontaneous emission rates from ⁴I_13/2 and ⁴S_3/2 to ⁴I_15/2, respectively. C_up is the up-conversion coefficient. A₃₂ is the non-radiative decay rate from the ⁴I_11/2 state to ⁴I_13/2, whereas A₄₃ is the non-radiative decay rate from ⁴I_9/2 to ⁴I_11/2. A₅₄ is the non-radiative decay rate from the ⁴S_3/2 state to ⁴I_9/2, whereas A₆₅ is the non-radiative decay rate from ⁴F_7/2 to ⁴S_3/2. R₁₃ and R₃₁ are the pump absorption and stimulated emission rates for 980 nm pumping, and R₁₂ and R₂₁ are the pump absorption and stimulated emission rates for 1480-nm pumping. W₁₂, W₂₁ are the signal absorption and stimulated emission rates. R₃₆ ^ESA and W₂₄ ^ESA are the pump and signal ESA rates, respectively. These rates are given in the following forms:

The superscripts of + and 1 indicate the relative beam propagation direction. σ_pa and σ_pe represent the absorption(a) and stimulated emission (e) cross-sections of the 980-nm pump, and σ_pa2 and σ_pe2 indicate the absorption (a) and stimulated emission (e) cross-sections of the 1480-nm pump, respectively. σ_sa and σ_se are the absorption (a) and stimulated emission (e) cross-sections of the signal (s). σ^ESA_Signal- is the signal ESA cross-section. Γ_s and Γ_p are the signal-to-core and pump-to-core overlap factor, respectively. r_m is the mode field radius of the EDF. h is Planck’s constant, v_p is the pump frequency and v_s is the signal frequency.

The Paired Ion Rate Equations

where N₁ ^p, N₂ ^p, N₃ ^p, N₄ ^p, N₅ ^p, and N₆ ^p represent the number of paired erbium ions in the ⁴I_15/2, ⁴I_13/2, ⁴I_11/2, ⁴I_9/2, ⁴S_3/2, and ⁴F_7/2 states, respectively. The absorption, stimulated emission, and spontaneous emission rates were assumed to be the same for the singled and paired ions. The signal ESA rate was also assumed to be the same for both cases.Subsequently, the total doping concentration N_t is given by:

where N₁, N₂, N₃, N₄, N₅, and N₆ are the number of total erbium ions in the ⁴I_15/2, ⁴I_13/2, ⁴I_11/2, ⁴I_9/2, ⁴S_3/2, and ⁴F_7/2 states, respectively.

The evolution of the pump, signal, and ASE powers along the EDF length can be described through the following propagation equations:

The Propagation Equations

where Δv is the spectral width of the ASE at v_s. α _p and α _s are the pump and signal propagation losses, respectively.The propagation equations were numerically solved with the population information at each level, which was obtained under steady state conditions.

The initial conditions for the numerical calculation are as follows:

The Initial Conditions

where L is the length of the EDF used.

The signal absorption and emission cross-sections used in this work were obtained from [14, 15]. The pump ESA Cross-section was assumed to be σ^ESA_pump ? 2×σ_pe as seen in[6]. Fig. 2 shows the stimulated emission, absorption, and signal ESA cross-sections used in this investigation. The

peak emission and absorption cross-sections are 9.43 × 10^-25 m² at 1532 nm and 8.31 × 10^-25 m² at 1530 nm, respectively.The signal ESA cross-section starts to appear at 1623 nm and increases monotonously up to 2.5 × 10^-25 m² at 1650 nm. The signal ESA cross-section σ^ESA_Signal was measured in our laboratory; further details on the signal ESA cross-section in bismuth oxide EDFs are fully described in [7]. The parameters of the bismuth oxide EDF used in this work are summarized in Table 1.

In order to estimate the relative number of paired ions(k) we used a numerical prediction method based on the comparison between the experimentally measured gain and NF values and the numerically predicted ones. The experimental setup for the measurement of the signal gain and the NF for a 2 m long bismuth oxide EDF is shown in Fig. 3. The bismuth oxide EDF used in this investigation was a commercially available one from Asahi Glass company, model number T1L-201P/31024-01. The bismuth oxide EDF was pumped using a 160-mW laser diode at 1480 nm using the forward pumping scheme. The tunable laser used as an input signal was a commercially available external cavity laser with a tuning range of 1490 ~ 1650 nm. The input signal power was fixed at 0 dBm. The signal gain and the NF were measured and numerically simulated at the signal wavelength of 1600 nm as the pump power was increased by 10-mW steps.

Fig. 4(a) shows the numerically calculated gains for the four different k values (0, 3, 6.02, and 9%), along with the experimentally measured ones. From the numerically calculated results, it is obvious that the signal gain significantly decreased as the k value increased. After trying to find the best fitting theoretical gain curve for the experimentally measured unknown variable k by using nonlinear least squares fitting, we found that the k = 6.02% led to the best fit. With respect to the NF, the same fitting procedure was used, as shown in Fig. 4(b). Interestingly, it was found from the numerically calculated NF curves that the NF remains fixed regardless of the relative number of paired ions. In addition, it was observed that the numerically calculated NF values agreed well with the experimentally measured ones.

In order to confirm the estimated k value (6.02%) we carried out an output spectrum comparison. Fig. 5 shows the numerically calculated spectra for the various k values along with the experimentally measured spectrum.

It is clearly evident from the graph that k = 6.02% gives the best theoretical fit to the experimentally measured spectrum.This indicates that the relative number of paired ions (k)in the bismuth oxide EDF used in this work is ~6.02%.

Finally, the impacts of the PIQ on the spectral gain and the NF were investigated. For this investigation, the experimental setup where the bismuth oxide-based EDF was pumped using a bidirectional pumping scheme is shown in Fig. 6. The forward pump power was 200 mW at 980 nm;the backward pump power was 160 mW at 1480 nm. The signal gain and the NF were measured and numerically simulated by sweeping the input signal beam wavelength from 1540 nm to 1635 nm by 5-nm steps in order to analyze the impacts of the PIQ. The input signal power was fixed at 0 dB m.

Fig. 7 shows the experimentally measured output spectrum along with the numerically calculated output spectrum based on k = 6.02%. It was evident that our numerical calculation agreed well with the experiment, even in the complicated bidirectional pumping case. Fig. 8(a) shows the signal gains for three different cases: (i) the experi

mental measurement, (ii) the numerical calculation with the PIQ, and (iii) the numerical calculation without the PIQ.The signal gain was observed to be reduced by ~5 dB over a gain bandwidth of ~90 nm from 1540 to 1630 nm,compared to the value that is supposed to be achieved without the PIQ.

Unlike the gain degradation dependent on the PIQ, the NF exhibited a completely different behavior. The NF was observed to remain unchanged at the wavelengths from 1560 to 1630 irrespective of the relative number of paired ions. This result is consistent with the observation found in Section III, where the NF at 1600 nm under the forward pumping scheme was fixed regardless of the relative number of paired ions. However, non-negligible NF degradation caused by the PIQ was observed at the 1540 ~ 1560 nm wavelengths. Such a spectral dependence of the NF degradation caused by the PIQ is believed to be due to the relative increase of the ion population at the metastable state despite the population inversion being unchanged.This effect needs to be further investigated

We have theoretically and experimentally investigated the pair-induced quenching effect in a commercially available bismuth oxide-based EDFA. By using the comparison between the numerically calculated and the experimentally measured gain values, the relative number of paired ions is estimated to be ~ 6.02% in the bismuth oxide EDF. The PIQ was observed to induce a ~5-dB gain reduction over a gain bandwidth of ~90 nm from 1540 to 1630 nm, compared to the value that is supposed to be achieved without the PIQ.Interestingly, NF degradation caused by the PIQ was observed only at the 1540 ~ 1560 nm wavelengths. This spectral dependence of the NF degradation caused by the PIQ needs to be further investigated.