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IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 17, NO. 2, FEBRUARY 2005
Amplification Properties of Erbium-Doped Solid-Core Photonic Bandgap Fibers Changzhi Li, Yidong Huang, Member, IEEE, Wei Zhang, Yi Ni, and Jiangde Peng
Abstract—A novel erbium-doped photonic bandgap fiber (PBGF) with honeycomb cladding and down-doped solid-core is proposed in this letter. This fiber is more practicable than reported erbium-doped air-core PBGF due to its Gaussian-like field distribution and low confinement loss. Theoretical analysis shows that it can largely improve pump efficiency (gain-to-pump-power ratio) for small pump power and reduce the optimum fiber length by 20%–50% for a wide range of pump powers, compared with erbium-doped step-index fiber. Index Terms—Erbium-doped fiber (EDF), optical amplification, photonic bandgap (PBG), photonic crystal fiber (PCF).
I. INTRODUCTION
P
HOTONIC crystal fibers (PCFs), which conduct light through total internal reflection (TIR) or photonic bandgap (PBG) effect, have opened up new features for the guidance of light in both passive and active devices. For active devices, works have been reported about the improvement on amplification properties and the corresponding applications of doped PCF [1], [2]. Though few, numerical analyses were conducted for erbium-doped TIR-PCF with air holes arranged in a triangular pattern [3] and erbium-doped air-core honeycomb PBG fiber (PBGF) [4]. The latter is distinguished for incorporating the bandgap effect, which may lead to higher pump efficiency than the erbium-doped step-index fiber (SIF) and even the erbium-doped TIR-PCF. However, two shortcomings were noted for air-core honeycomb PBGF. First, the annular field distribution leads to problems for coupling with conventional fiber. Second, the rigorous structure requirements for avoiding large confinement loss make it difficult to be fabricated. For example, even if there are eight rings of (in total 456) air holes, confinement losses are still above 10 dB/m [5]. A recent study demonstrates that PBG can be formed and changed by properly doping different regions in the periodic lattice [6]–[8]. Using the down-doped solid region as defect and the erbium-doped region as the active region, an erbium-doped solid-core PBGF with honeycomb cladding is proposed here, for the first time to the authors’ knowledge. Our previous work [9] has demonstrated that solid-core PBGF has Gaussian-like field distribution and low confinement loss (e.g., 0.01 dB/m can be ), showing that it achieved by only 84 air holes with is more practicable than air-core PBGF. Also, solid-core PBGF Manuscript received May 26, 2004; revised September 20, 2004. The authors are with the Electronic Engineering Department, Tsinghua University, Beijing 100084, China (e-mail:
[email protected];
[email protected];
[email protected];
[email protected];
[email protected]). Digital Object Identifier 10.1109/LPT.2004.839373
Fig. 1. Effective index =k versus 3 when d=3 = 0:8. Inset: Down-doped solid-core PBGF structure.
has a lower air-filling fraction than triangular pattern and a solid core compared with its air-core counterpart, being more robust during splicing. This letter focuses on the amplification properties of erbium-doped solid-core PBGF, showing that PBG leads to advantages on pump efficiency and optimum fiber length over erbium-doped SIF. II. MODELING Er
-DOPED SOLID-CORE PBGF
The solid-core honeycomb PBGF is shown in the inset of Fig. 1, where a down-doped solid region (e.g., doped with Fluorine) was used as a defect in the periodic structure. The active region is formed by doping erbium. The refractive index of the codoped area is mainly decided by fluorine, thus, is almost the same as the index of other down-doped region. To ensure a fair and strict comparison with an erbium-doped SIF, the two kinds of erbium-doped fibers (EDFs) have the same erbium-doped of SIF and of PBGF area, while the index core radius are varied to find the optimum performance for each structure. To date, there is little data about the absorption–emission cross sections of fluorine–erbium codoping; here, the two kinds of fibers are assumed to have the same cross sections to concentrate comparison on the effects of different waveguiding mechanisms. All fiber parameters are listed in Table I. The effective versus the normalized longitudinal wave vector comindex in PBGF was calculated by the full vectorial plane ponent wave expansion method (PWM) [10], as shown in Fig. 1. The result demonstrates that guided mode exists in the bandgap when the core is down-doped, which signifies that light is confined by PBG effect.
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LI et al.: AMPLIFICATION PROPERTIES OF ERBIUM-DOPED SOLID-CORE PBGFs
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TABLE I FIBER PARAMETERS
Fig. 3. Gain versus pump power (1–100 mW) for various fiber configurations.
Fig. 2. Normalized radial field distributions of PBGF and SIF with different structure parameters.
The field distribution of solid-core PBGF was computed by PWM with a supercell containing 225 primitive cells, and the field distribution of SIF was calculated through a weekly guided approximation. To quantify the influence of field distribution on amplification properties, we applied the spatial-mode modeling of erbium-doped fiber [11] and took into account the variation along radial direction of metastable population
(1)
The parameters in (1) are defined in Table I. Taking into the population rate equations, a steady state solution can be obtained by Runge–Kutta algorithm. Amplified spontaneous emission (ASE) is calculated over 1500–1610 nm by assuming an equivalent ASE bandwidth with a 0.2-nm resolution. III. NUMERICAL RESULTS AND DISCUSSIONS The normalized field intensities in radial direction of PBGF and SIF with typical parameters are presented in Fig. 2. When exceeds 0.5, the fundamental mode of PBGF is Gaussian
Fig. 4. Maximum pump efficiency versus pump power for various fiber configurations in low pump power application.
like. As increases, fields are better confined, and the normalized pump and signal intensities get closer to each other. of SIF has an optimum value for But the index core radius each wavelength. The field will spread out as moves off this value. This implies that the overlap between dopant and optical , but the permode of PBGF can be enlarged by increasing formance of SIF may reach an extremum at the optimum value of . Simulation on amplification property shows that this value m. is The amplification property is first investigated by calculating signal gain along the fiber for pump power varying between 1–100 mW, which covers the typical applications of fiber communication networks. Results are presented in Fig. 3 as the maximum signal gain versus pump power. The maximum signal gain is found by optimizing the fiber length. It seems the maximum signal gain is insensitive to the change of fiber structure. Nevertheless, the gain difference may be significant for small pump powers. From this point of view, the pump efficiency (i.e., the maximum signal gain-to-pump-power ratio) for 0–10-mW pump power was calculated in Fig. 4. Compared with m, the solid-core SIF with optimum parameter varies PBGF improves the pump efficiency by 20%–70% as from 0.5 to 0.9, which means PBGF can minimize the pump
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IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 17, NO. 2, FEBRUARY 2005
IV. CONCLUSION The amplification properties of a novel erbium-doped PBGF with honeycomb cladding and down-doped solid-core were analyzed. Its Gaussian-like mode field and small confinement loss make practicable use of PBGF amplifier in optical networks. Compared with the erbium-doped SIF, it can improve the pump efficiency by 20%–70% for small pump power to obtain 10–20 dB gain, resulting in cheap and efficient optical amplifiers with a moderate gain to realize small-scale optical amplification. This is desirable as optical networks evolve from point-to-point configurations into more advanced network topologies. For a wide range of pump powers, the optimum fiber length can be reduced by 20%–50% under proper design of structure parameters. Fig. 5. Optimum fiber length versus pump power (1–100 mW) for various fiber configurations.
power needed for moderate gains ranging from 10 to 20 dB. The deciding factor is that PBGF can effectively limit pump and signal fields in the doped region so that ground-state ions can be excited to the upper state at a relatively low pump power, avoiding additional absorption of signal light. And this effect is quickly enhanced to a maximum as pump power increases. This is prohibitively difficult for SIF because it requires increasing the numerical aperture [12], which is limited by the codoping technique. However, as the pump power increases to a level large enough, the gain difference becomes negligible. This is because, although large overlap integral helps to effectively invert Er ions and boost the stimulated emission, the total amount of inverted ions and, thus, the signal gain become dominated by pump power and fiber length. Fig. 5 shows that the PBGF’s optimum fiber length, which corresponds to the maximum gain for pump power varying from increases and is shorter 1 to 100 mW, diminishes quickly as than the minimum value of SIFs. Even though the pump field is approximately the same distribution of PBGF with m, the larger overlap between as that of SIF with pump and signal fields enables PBGF to maintain an optimum length 20% shorter than that of SIF. The amplifier length can be reaches 0.9. further reduced to half of SIFs when
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