We analyze the performance of nanocrystal-Si (nc-Si) sensitized Er-doped waveguide amplifier using coupled nc-Si-Erbium rate equation, and suggest novel structures / operation methods which can be used to enhance its performance figures. With 2-dimensional modified propagation equation applied for the pump / signal waves along with modest assumptions on design parameters, we show that 10dB of gain with 0dBm input signal can be achieved with currently available pump LED power.
©2005 Optical Society of America
Out of many approaches developed so far to achieve low-cost micro amplifiers (amplets) for the access / metro network, Erbium doped waveguide amplifier (EDWA) has been considered to be the most promising candidate due to its well known characteristics inherited from its relative, the EDFA. Unfortunately, there still exist two main drawbacks for EDWA/EDFA which hinder the ultimate performance/cost optimization for the amplet application: the need for an expensive pump laser tuned precisely to the narrow absorption band of an Er3+ ion, and the long interaction length between pump and signal resulting from the small pump absorption cross section.
A technique that has attracted a great attention as a possible solution to these problems is nanocrystal Si (nc-Si) sensitization of erbium [1–5] in which nc-Si, acting as a co-dopant to Er ions, absorbs pump photons, creates photo-carriers, and finally transfers the energy to nearby Er ions through an Auger-like process . As confirmed by numerous experimental reports, nc-Si differs from the other sensitizers for Erbium in that it has a strong, continuous, broad absorption band for the pump [1, 4, 5], and that it gives orders of magnitude larger effective excitation cross-section for the Er ion [2–5] enabling top pumping of the waveguide.
Additional advantage from the co-doping of nc-Si also comes from the enhanced Er emission cross-sections at 1.5μm, enabling high gain without the need of high Er concentration - thus avoiding the performance degradation from the quenching effect [3, 7, 8]. Following these observations, the possibility of achieving positive optical gain has been demonstrated / assessed in terms of both experimental [9, 10] and theoretical means [7, 11]. Still, the analysis so far has remained in the fundamental domain confirming the optical gain in a top-pumped, nc-Si sensitized Er waveguide, and not yet in the practical domain with a realistic device as a target.
In this paper, we provide, for the first time a detailed performance analysis of an nc-Si co-doped Er waveguide amplifier (NC-EDWA) that targets a real application. Saturation output power, required pump density, optical gain and noise figure has been assessed in terms of the device structure and input signal strength, utilizing a newly developed 2-dimensioanl propagation equation and employing a coupled nc-Si-Erbium rate equation. Results show a high feasibility of achieving 10dBm of output power with 0dBm of signal input signal, using an array of commercially available high-power blue-green LEDs as the top-pumping nc-Si excitation source.
2. Model equations
Although some of the detailed information on the nc-Si / Er interaction mechanism - such as energy migration and nanocluster surface defect states [12, 13] - is still missing, numerical model for overall amplification process has been already constructed and utilized in the previous study  to estimate the optimum material composition. Ignoring negligible effects (such as concentration induced quenching and excite state absorption) which are well suppressed in optimally manufactured samples [3, 8, 11], we simplified the coupled rate equation to concentrate on the investigation of amplifier performance as a function of device structure. In Fig. 1, we show the diagram for the reduced form of rate equation, in which we assume that energy transfer from nc-Si to Er occurs via the 4I11/2 energy level (980nm) of Erbium ions. This assumption is based on previous reports that 1, no PL line from energy states higher than 980nm have been observed [3, 9]; 2, excition luminescence from nc-Si generally overlap the 980 nm absorption band [14, 15]; and 3, quasi-resonant transfer of energy from nc-Si to Er3+ can occur via the 4I11/2 energy level . We note, however, that the result of the paper does not depend on the exact transfer mechanism, as long as there exist an “effective transfer rate” and “effective relaxation rate”. In the rate equation, h, Ni , , vs , na , nb , , vp , are Planck constant, Er ion density on ith energy level (1=4I15/2, 2=4I13/2, 3=4I11/2), effective signal intensity, signal frequency, ground/excited state NC-Si density, effective pump intensity, pump frequency, respectively. Other parameters are also listed in table 1. It should also be noted that in order to accommodate the effect of top-pumping configuration, we constructed a two dimensional propagation equation set for pump and signal/ASE beams (refer Fig. 2) modified from the conventional EDFA propagation equation , and calculated the signal / pump power evolution both for along waveguide length direction (signal/ASE) and waveguide height direction (pump). The parameters used in the analysis are summarized in table 1, taken from the previous experimental reports made by different research groups [7, 8, 9, 11 and 12]. The spectral profile of Erbium emission cross-section was obtained from the photoluminescence spectrum of nc-Si EDW. Applying the McCumber relation to the emission cross-section, we also obtained absorption cross-section profile of Erbium in the NC-EDW waveguide (Fig. 3). To avoid the possible quenching effect, we assumed a moderate doping concentration for Er ions (3×1019 cm-3) .
In order to precisely incorporate the effect of signal distribution in the waveguide, the propagation mode envelope profile was obtained independently by a commercial waveguide simulator (Rsoft, Photonic CAD Suite), assuming a rectangular waveguide structure (refractive indices of 1.464 and 1.459 for core and cladding, respectively). The entire volume of doped core was divided into 20 × 20 × 500 segments of spatial slots for accurate calculation of the inversion, pump, signal and ASE power at each slot. Numerical analysis was carried out over the spectral range of 1500 to 1610nm with 1nm resolution including ASE, assuming uniform doping of the NC-Si and Er in the core. Comparison of the result to previous experimental reports [8, 9] showed reasonable agreement (within ~ 1dB) in the behaviors of performance factors, considering the measurement errors including the misalignment of pump beam, and coupling of the signal to the air-clad ridge waveguide used in the past experiment.
3. Performance analysis
To test the feasibility of the NC-EDWA for amplet applications, we started with a waveguide structure with core dimension of 7 × 7 μm2, targeting a modest gain of 10dB for 0 dBm input signal power. The calculated gain values for 0dBm input signal power as a function of pump power and waveguide length are shown as dashed lines in Fig. 4 (a). Considering the maximum pump intensity currently available from commercial high power LEDs (26.7 W/cm2 from Cree C460XT290), this Fig. shows that it is difficult to achieve the target performance (10dB gain for 0 dBm input signal) with a reasonable length (~ 5cm) of NC-EDWA. Dashed lines in Fig. 4(b) show the gain characteristics for 5cm waveguide as a function of input signal power. For example, though 10dB or even higher gain can be easily achieved for small signal (< -10dBm) with currently available LEDs, impractically higher LED pump intensity is required in order to satisfy 10dB of gain value for large input signal power.
One of the conceivable solution for gain enhancement would be increasing the (Er : NC-Si) doping concentration. However, in order to avoid concentration induced quenching and to investigate the effect of structure optimization without adjusting other parameters, we plot, as solid lines in Fig. 4, the gain values obtained from the same structure but with a pump reflector (100%) at the bottom. The gain improvement from the reuse of unabsorbed pump (estimated ~65%) is evident, but was not sufficient to compose a practical device with commercially available LED. Another non-trivial but novel approach for the performance enhancement is increasing the width of the waveguide (Fig. 5). By introducing an adiabatically tapered mode converter into / out of the amplifying region, it was possible to effectively increase the pump collection area (50μm × 5cm, Fig. 5). Roughly speaking, with the increased pump-collection area, NC-EDWA now can be considered as a parallel integration of amplet arrays, with enhanced saturation characteristics - lowering the requirement on the pump intensity. More importantly, this performance enhancement does not require any additional pump LED cost, since the width of light emission area of commercial LED is much wider than the width of expanded waveguide (250 μm vs 50 μm). To determine the reasonable range of the waveguide width, we calculated for waveguide length meeting the target performance (10dB gain with 0dBm input signal and 25W/cm2 pump intensity, for various waveguide widths. Fig. 6(a)).
As the mode conversion loss can be made very small (< ~0.1dB) with the introduction of the tapered structure, a waveguide width of 50μm was sufficient for the NC-Si EDWA to meet the target of a realistic amplet application with the current LED technology. The small signal gain and saturation characteristic for various widths of adiabatic NC-EDWA is also shown in Fig. 6(b). It should be pointed out that the small signal gain enhancement of the wider waveguide is mainly due to the increased core-mode overlap (Fig. 6 (a)). On the other hand, the increase in the saturation input power is mainly due to both the decrease in signal intensity in the expanded core, and increase in the incident pump power to the expanded pump collection area. The performance of NC-Si EDWA with 50×7μm2 active core with and without the bottom mirror is shown in Fig. 7 (solid and dashed line, respectively). As shown in this Fig., with 50×7μm2 active core and bottom mirror for the pump reflection, only 15.8 W/cm2 (8.8 W/cm2 for 100μm width) of pump intensity was sufficient to meet the target operating condition.
In Fig. 8 we also compare the inversion distributions of NC-Si EDWA, for the 4 types of EDWA structures under investigation. 0dBm input signal, 5cm gain medium and 25W/cm2 top-coupled pump intensity to the waveguide were assumed. As expected, mirrored waveguide with 50×7 μm2 core exhibited the highest inversion over the whole gain medium. Fig. 8(b)–(e) illustrates the spatial inversion distributions over the cross-sectional area of the waveguide, measured at 1 cm from the input of the amplifying section. The effect of pump reflection mirror on the increased inversion at the waveguide bottom (Fig. 8(c), 8(e)), and the effect of mode expansion (Fig. 8(d), 8(e)) is evident. As another key performance factor, we also calculated noise figures for different NC-Si EDWA structure. 6.9, 6.44, 5.23, 4.79 dB of NF (at 4.86, 5.67, 10.59, 12.02 of gain) have been obtained for 7×7, mirrored 7×7, 50×7, mirrored 50×7 μm2 waveguide structures, respectively. As an additional advantage achieved by the top-pumping configuration, we note that the inversion distribution of NC-Si EDWA can be easily adjusted by controlling intensity of each LED in the array , for example, to achieve even better noise figure performances.
Finally, noting that there exist some uncertainties in the parameter values depending on the material preparation method/conditions, we also investigated the tolerance in the material parameter values achieving reasonable performance figures (with the given optimal NC-Si EDWA structure, 7 μm × 50 μm × 5cm with bottom mirror). Fig. 9 shows the gain and NF contour of NC-Si EDWA, plotted as a function of Er lifetime, signal emission/absorption cross-section, NC-Si to Er coupling coefficient, and pump absorption cross section. For the given target performance (10dB gain with low NF (~5dB) for 0dBm input, 25W/cm2 pump) of NC-Si EDWA, it was found that there exist sufficient margin for the variations in the material parameter values (shaded region in the Fig., cross mark: parameter value in table 1). For the change of only one parameter value out of four, ±40, ±43, ±60, ±64% of tolerance was estimated for the coupling coefficient, signal cross-section, lifetime and pump absorption cross-section respectively. Especially for the consideration of precise signal cross-section value under debate (5e-21 ~ 6e-19 cm2, [8, 9, 11, 20, 21]), the minimum signal cross-section required to achieve the target performance was found to be 3.4e-20 cm2, under the given amplet structure and material parameters.
To summarize, we have analyzed the performance of NC-EDWA in terms of their device structure, and suggested also novel means of increasing its performance factors. Analysis has been carried out utilizing a modified signal / pump propagation equation to accommodate the top-pumping condition, and employing a coupled Nc-Si-Erbium rate equation. For 4 types of EDWA (rectangular core without/with mirror and expanded core without/with mirror), 130.4 W/cm2, 90.6 W/cm2, 21.9 W/cm2 and 15.8 W/cm2 of pump intensity was required to achieve 10dB of gain with 0 dBm of input signal power. The noise figure stayed well below 5dB for the suggested structures. Considering the pump intensity / cost available from a commercial LED, it is expected that the NC-EDWA possesses good feasibility to work as a future cost-effective, small form factor amplet arrays for metro application.
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