**2. Optical amplifier**

An optical amplifier is a device that amplifies an optical signal directly, without the need to first convert it to an electrical signal. In the 1990's, optical amplifiers, which directly amplified the transmission signal, became widespread minimizing system intricacies and cost [7]. Many techniques have been proposed to improve the performance of FSO link like the amplification of signal [3].

To maintain the integrity of information sent from one location to another, optical amplifiers, such as doped fiber amplifiers (DFA), doped waveguide amplifiers (DWA), and semiconductor optical amplifiers (SOA), are utilized to extend transmission range for the cost-effective implementation of FSO and can be used for amplification of WDM network easily [4].

#### **2.1 Doped fiber amplifiers**

Doped fiber amplifiers (DFAs) are optical amplifiers that use a doped optical fiber as a gain medium to amplify an optical signal [8]. They are related to fiber lasers. The signal to be amplified and a pump laser are multiplexed into the doped fiber, and the signal is amplified through interaction with the doping ions. Er3+is one of the most commonly used doped ions in integrated photonics and the EDFA is one effective way to amplify light signal at optical communication window between 1500 to 1600 nm.

#### *2.1.1 Erbium doped fiber amplifier*

The erbium-doped fiber amplifier (EDFA) is the most deployed fiber amplifier as its amplification window coincides with the third transmission window of silicabased optical fiber and has demonstrated high gain, low noise, and full compatibility with DWDM signals. In general, EDFA works on the principle of stimulating the emission of photons. With EDFA, an erbium-doped optical fiber at the core is pumped with a laser at or near wavelengths of 980 nm and 1480 nm, and gain is exhibited in the 1550 nm region (**Figure 2**).

#### **2.2 Doped waveguide amplifier**

Waveguide amplifiers, in particular, are new integrated optical products well suited to metro/access applications. Some of the intrinsic benefits for using this later *Waveguide Amplifier for Extended Reach of WDM/FSO DOI: http://dx.doi.org/10.5772/intechopen.104790*

#### **Figure 2.**

*Erbium doped fiber amplifier block diagram.*

include their compactness, performance, flexibility, and lower-cost processing [9]. These integrated devices offer the prospect of combining passive and active components on the same substrate while producing compact and robust devices at lower cost than commercially available fiber-based counterpart. However, the way to implement all-optical network relies on the control of gain variation of amplifiers which is sensitive to total input power variation [1, 8].

#### *2.2.1 Erbium-doped waveguide amplifier*

The erbium-doped waveguide amplifier (EDWA) are planar waveguides doped with erbium ions and are excited similar to EDFAs. EDWAs integrate several functions and components onto a mass produced integrated circuit and have recently received considerable attention as a potential high-gain medium for optical amplification in the communication band (**Figure 3**) [8, 9].

## **3. Concentration quenching of erbium**

EDWAs are less efficient than EDFAs due to higher erbium concentration in the waveguide on the substrate. Greater erbium ion concentration causes more pumping power to quench to the system. Additionally, there is greater loss in waveguides than fibers. Concentration quenching is the reduction in quantum efficiency of a erbium ion as its concentration increases. It generally manifests itself by a shortening of the measured metastable level lifetime and occurs mostly through cross relaxation or co-operative up- conversion processes.

When the concentration levels are such that the separation between two erbium ions is greater than the diameter of an individual erbium ion then the up conversion process is called "homogeneous up conversion (HUC)". In addition to the abovementioned effects, another important effect that needs to be investigated is the pair induced quenching (PIQ). This later is an inhomogeneous phenomenon

**Figure 3.** *Erbium-doped waveguide amplifiers block diagram.*

**Figure 4.**

*Scheme of pair-induced quenching (PIQ) and up-conversion (HUC) processes in erbium-doped fiber amplifier.*

caused by clustered ions when the Er+3 the inter-ionic distance between two erbium ions becomes less and they come much closer to each other so as to form "clusters" [10]. This issue has been addressed by co-doping the erbium by ytterbium (Yb+3) (**Figure 4**).

### **4. Co doping with ytterbium ions to inhibit PIQ**

To increase the absorption cross section, ytterbium ions (Yb3+) are usually co-doped as a sensitizer. The introduction of ytterbium can effectively restrain the erbium Er3+ ion clusters, and reduce up-conversion nonlinear side effect. This can increase the total gain and the unit length gain greatly [11].

The performance of the Er3 + �Yb3+ co- doped waveguide amplifiers (EYDWA) is better than that of the EDWA, and the EYDWAs are therefore expected to be an attractive high-gain medium material for optical amplification because of their use as amplifiers in optical telecommunications and as compact light sources for eye-safe range finding in the 1.55 μm spectral range (**Figure 5**) [12, 13].

Ytterbium offers the advantage of a high absorption cross-section and a good spectral overlap of its emission with erbium 4 I11/2 absorption, leading to an efficient energy transfer from ytterbium to erbium.

The rate equations for Er+3 and Yb+3 population can be written as [14]:

$$\frac{d\mathbf{N}\_2}{dt} = -\mathbf{A}\_{21}\mathbf{N}\_2 - 2\mathbf{U}\_{up}\mathbf{N}\_2^2 + \mathbf{N}\_1\sigma\_{\rm s\varepsilon}\rho\_{\rm s} - \mathbf{N}\_2\sigma\_{\rm s\varepsilon}\rho\_{\rm s} + \chi\_{32}\mathbf{N}\_3 \tag{1}$$

$$\frac{d\mathbf{N}\_3}{dt} = -\mathbf{N}\_3 \sigma\_{p\epsilon} \rho\_p + \mathbf{N}\_1 \sigma\_{pu} \rho\_p + \mathbf{P} \mathbf{N}\_1 \mathbf{N}\_6 - P' \mathbf{N}\_3 \mathbf{N}\_5 - \mathbf{N}\_3 \sigma\_{32} + \chi\_{43} \mathbf{N}\_4 \tag{2}$$

$$\frac{d\mathbf{N}\_4}{dt} = \mathbf{C}\_{\rm up} N\_2^2 - \boldsymbol{\gamma}\_{43} \mathbf{N}\_4 \tag{3}$$

$$\sum\_{i}^{4} N = N\_{Er} \tag{4}$$

$$\frac{dN\_3}{dt} = PN\_1N\_6 - P'N\_3N\_5 - N\_5\sigma'\_{pa}\rho\_p + N\_6\sigma'\_{pa}\rho\_p + N\_6\sigma'\_{p\epsilon}\rho\_p + A\_{65}N\_6\gamma\_{43}N\_4 \tag{5}$$

$$\mathbf{N\_{Yb}} = \mathbf{N\_{5}} + \mathbf{N\_{6}} \tag{6}$$

where, N1, N2, N3 and N4 are the Er population densities (m�<sup>3</sup> ) of 4I15/2,4I13/ 2,4I1/2, 4I9/2 levels, respectively. The quantities N5, N6 are the Yb+3 population

**Figure 5.** *Energy level diagram of erbium and ytterbium system.*

densities (m�<sup>3</sup> ) of the 2F7/2 and 2F5/2 levels respectively. Whereas, *φp*, *φs*, *σ*<sup>0</sup> *pa*, *σ*<sup>0</sup> *pe*, A21, A65, *P*, P<sup>0</sup> , Cup are defined in **Table 1**.

The spontaneous emission rates of Er+3 and Yb+3 can be calculated by:

$$
\sigma\_d = \frac{h\gamma n}{C} B\_{12} \mathbf{g}\_{12}(\boldsymbol{\gamma}),\\\sigma\_\varepsilon = \frac{h\gamma n}{C} B\_{22} \mathbf{g}\_{21}(\boldsymbol{\gamma})\tag{7}
$$

where *g*12ð Þ*γ* and *g*21ð Þ*γ* are the normalized emission and absorption line shape respectively, n is the refractive index of the medium and *B*<sup>12</sup> and *B*<sup>21</sup> are the coefficients of transition. Then the signal gain G and total noise Figure NF are given by:

$$G = \exp\left[\int\_0^L \mathbf{g}(z)dz\right],$$

$$NF = 10\log\log\_{10}\left[\frac{1}{G} + \frac{P\_{ASE}}{Gh\gamma B\_0} - \frac{P\_{SSE}}{h\gamma B\_0}\right] \tag{8}$$


**Table 1.** *Parameter definition for equations.*

where γ is the signal frequency, Bo is the noise bandwidth, PASE and PSSE are the power of amplified spontaneous emission, and the power of source spontaneous emission, respectively.
