Comparison between CDF and EDF

The important optical parameters of the chromium-doped fiber (CDF) and a typical Erbium-doped fiber (EDF) are summarized in Table 5.4 [5.10]. The active ion concentration of a typical EDF is much higher than the CDF’s. This is because the Er ions in the silica host are naturally in the desired trivalent state. The highest Er doping concentration is limited by the interactions between the Er ions like up-conversion and concentration quenching. Unlike the EDF case, the Cr ions in the YAG host are initially in the trivalent state. A charge compensation mechanism is used to turn the oxidation state of some of the Cr ions into the quadrivalent state. The charge compensation efficiency for generating Cr⁴⁺ ions out of the Cr³⁺ ions is typically less than 6%. Most of the Cr ions still remain in the trivalent state. This charge compensation efficiency is the limiting factor of the Cr⁴⁺ concentration. As described in the previous section, the Cr ions evaporate out of the melt during the fiber growth process so the Cr⁴⁺ concentration of the fiber further decreases.

Table 5.4. Parameters of the CDF and a EDF, where is the absorption cross section for emission wavelength. ν

s

is assumed to be at the 1400-nm center emission wavelength for calculating [5.10].

s

σ

a

sat

Is

Parameter CDF EDF Unit

N0 3.2×10¹⁷ 80×10¹⁷ cm^-3

σ

a 22×10^-19 0.025×10^-19 @ 980 nm 0.018×10^-19 @ 1480 nm

cm²

σ

e 1.6×10^-19 0.050×10^-19 @ 1552 nm cm²

σ

e/

σ

a 0.073 2 @ 980n nm pump

2.78 @ 1480 nm pump

esap

σ 4.2 ×10^-19 — cm²

esas

σ 0.32 ×10^-19 — cm²

s

σ

a — 0.023×10^-19 @ 1552 nm cm²

τ

f 4.5 ~10000 μs

∆

λ

277 30 nm

sat

Ip 18.8×10³ 8.1×10³ @ 980 nm 7.5×10³ @ 1480 nm

W/cm²

sat

I 19.7×10s ² 2.56×10³ W/cm²

The pump absorption cross section and the signal emission cross section of the CDF are several orders of magnitude larger than those of the EDF. As shown in Eqs.

(2.7) and (2.8), the absorption constant and the gain constant are related to the products of the Cr⁴⁺ ion concentration and the corresponding cross sections. These products

σ

aNo and

σ

eNo of the CDF are 35 and 1.3 times larger than those of the EDF.

This implies that the required CDF length is shorter, which is favorable with consideration of the significant propagation losses of the CDF. The CDF length could be even shorter by increasing the Cr⁴⁺ doping concentration. However, for the application of fiber ASE light source, the relative magnitude of

σ

eNo compared to its own

σ

aNo product is more suitable for evaluation of its performance. The

σ

eNo

product of the CDF is about one third of its

σ

aNo product. If including the effect of the ESAs of the pump and ASE, the ratio of the ASE gain constant to the pump absorption constant becomes even smaller. As a result, before the forward and backward ASEs acquire sufficient gain the pump light in CDF already decays below its pump saturation intensity and has no ability to achieve population inversion within a short fiber length. Using the EDF as a reference, its

σ

eNo product is two times of the

σ

aNo product for 980 nm pump. Therefore the ASE can acquire enough gain while it propagates along the gain fiber. The

σ

e /

σ

a ratio is a useful parameter in evaluating an optical material for a fiber ASE source or amplifier. Although broad emission bandwidth is very attractive, the light amplification ability of the Cr⁴⁺:YAG is not so strong as its

σ

e /

σ

a ratio is only 0.073. For EDF, the

σ

e /

σ

a ratios are 2 and 2.78 for 980 nm and 1480 nm pumps, respectively. In order to extent the CDF length that the pump light can deliver its power along and thus improve the ASE powers, the bi-directional pumping scheme is suitable. In addition, since our CDF has a double-cladding structure, cladding pump scheme is useful in relieving the pump absorption while keeping the same gain constant since both the forward and backward ASEs are only propagating in the core. Incorporating a high reflectivity mirror at the input end of the CDF will improve the ASE efficiency because the backward ASE is reflected and can experience more gain as it travels backward through the CDF.

The lifetime of the CDF is about three orders of magnitude shorter than that of the EDF. The pump power for EDF can be as low as a few tens of milliwatts but still maintaining a good optical efficiency due to the long lifetime of the Er ion. For CDF, the much shorter lifetime of the excited Cr⁴⁺ ions leads to a faster spontaneous emission rate. As a consequence, a faster pumping rate is required for the CDF to maintain the excited state population. The saturation intensities described below are useful in evaluating the optical materials as gain media:

,

f a sat p p

I h

τ σ

=

ν ^(5.7)

,

f e sat s s

I h

τ σ

= ν

(5.8)

where and are the saturation intensities of the pump and ASE,

ν

s is the emission frequency. As shown in Table 5.4, the pump saturation intensity of the CDF is about two times larger than that of the EDF. The much larger cross-sections of CDF compensate the drawback of its short lifetime. So the much shorter lifetime of the CDF does not cause a serious issue in achieving population inversion. But when taking into consideration that the core diameter of the CDF is much larger than the EDF’s, which can be as small as 3~4 μm, the pump power of CDF will be much larger.

In our calculation, the pump power for the CDF should be at least in the order of watt level to have a better ASE output power. The low ASE efficiency of the CDF can be ascribed to the relatively small emission cross-section, compared with its own pump absorption cross-section.

sat

Ip I_s^sat

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