**8. Hybrid amplifiers**

There is one more method of utilizing fiber amplifiers for optimum utilization of available fiber bandwidth i.e. by way of using various combinations of optical amplifiers in different wavelength ranges. The amplifiers can be connected either in parallel or in series. This configuration is termed as Hybrid Amplifier which is highly viable for the above discussed cause. In parallel configuration, the DWDM signals are first demultiplexed into several wavelength-band groups with a coupler, then they are amplified by amplifiers that have gains in the corresponding wavelength band and then they are multiplexed again with a coupler. The parallel configuration is very simple and applicable to all amplifiers. However, it has disadvantages also e.g. an unusable wavelength region exists between each gain band originated from the guard band of the coupler. Also, the noise figure degrades due to the loss of the coupler located in front of each amplifier. On the contrary, the amplifiers connected in series have relatively wide gain band, because they do not require couplers. Hybrid configurations can be made by combination of the following:

 **EDFAs and FRAs:** It has been observed that the gain spectrum of FRAs can be tailored by adjusting the pump powers and pump wavelengths. So this property is used to increase the amplification bandwidth of EDFA [Thyagarajan& Kakkar 2004; Oliveira et.al.2007, Kaur &Gupta 2008].

Hybrid Fiber Amplifier 115

TDFA i.e. 3H6, 3H4 and 3F4, the other two levels of TDFA i.e. 3H5 and 3F2, 3 are ignored as the rate of their non radiation (τnr) to the corresponding levels are very high. Similarly, in case of EDFA, two levels 4I15/2, 4I13/2 is considered and level 4I11/2 is ignored for the same reasons. From the absorption and emission spectra, it is clear that the absorption and emission peaks of EDFA coincides at 1530nm, while the absorption peak of TDFA lies at 1430nm and emission peak of TDFA lies at 1460nm. Form the gain spectrum of EDFA, from which it is clear that EDFA has peak gain at 1530nm, beyond which the gain reduces slightly and remains flat almost until 1550nm. After that gain reduces sharply. This gain can be flattened by cascading TDFA with EDFA. Fig. 10 shows the flattened gain spectrum of Hybrid amplifier by cascading TDFA and EDFA. The thulium doped fiber (TDF) in first stage was forward pumped with a 1390nm pump laser diode (LD) and erbium doped fiber (EDF) in second stage is pumped with a 980nm LD. For efficient amplification the concentration of TDF +3 ions was kept very high (approx. 7500 ppm) [Percival & Williams 1994; Komukai et.al.1995]. Table 4 shows the

**Feature TDFA-EDFA EDFA-TDFA** 

F-ratio is calculated for the parameters mentioned in above Table 4. The calculated and

**variation D.F SS MS F-ratio Tabulated** 

The table 5 shows that the F-ratio is significant of 5% level which means that both hybrid configurations work differently. F-ratio is used to judge whether the difference among several sample means is significant or just a matter of sampling fluctuations. MS residual is always due to fluctuations of sampling and so serves as the basis for the significance test. The F-ratio is compared with its corresponding table value for the given degree of freedom at a specified level of significance. The table 5 shows that both the F-ratios are significant of 5% level which means that TDFA-EDFA amplifier work differently as compared with EDFA-TDFA amplifier. The gain spectrum of TDFA-EDFA is more widened as compared to that of EDFA-TDFA configuration. Since there is a large difference between the calculated and the table value of F. So, the null hypothesis is rejected. For WDM systems, TDFA-EDFA has a great impact as a hybrid amplifier as compared with EDFA-TDFA amplifier[Kaur & Gupta 2009]. As studied from the existing schemes, the amplification of DWDM signals using TDFA-EDFA hybrid

**samples** 1 1.5 1.5 .05 18.51

amplifiers have major problems and short comings which are as listed below:

20 dB for 1485nm-1550nm

**F-ratio (1,2)** 

range

range

**Noise Figure** <6Db <7dB

different characteristics of both configurations.

tabulated value of F-ratio is shown in Table 5.

**Samples** 2 39.6 29.9

**Total** 3 41.1

Table 5. F-Measure Results

**Source of** 

**Between** 

**Within** 

**Gain** 25 dB for 1456nm-1556nm

Table 4. Features of TDFA-EDFA & EDFA-TDFA Amplifiers


Out of these, one of the-state-of-art hybrid amplifiers is TDFA -EDFA configuration. It is observed that for TDFA-EDFA configuration, the total gain of hybrid amplifier is given as product of gain of TDFA and gain of EDFA. The gain bandwidth is extended by cascading EDFA with TDFA. When EDFA is cascaded with TDFA in series, the total gain of hybrid amplifier is given by product of individual gains of each amplifier.The gain of TDFA is given as

$$\mathbf{G}\_{\mathrm{T}(\boldsymbol{\lambda})} = \exp\Big[\Big(\sigma\_{\mathrm{T}(1480)}\mathrm{NT}\_{2-\sigma\mathrm{T}(1990)}\mathrm{NT}\_{1-\sigma\mathrm{T}(800)}\mathrm{NT}\_{0}\Big)\Big] \Big(\eta\_{\mathrm{T}}\,\mathrm{L}\_{\mathrm{T}}\Big) \tag{8}$$

The gain of EDFA is given as:

$$\mathbf{G}\_{\mathbb{E}\left(\mathcal{A}\right)} = \exp\left[\left(\sigma\_{\mathbb{E}\left(1530\right)} \mathrm{NE}\_{2-\sigma\mathbb{E}\left(1480\right)} \mathrm{NE}\_{1}\right)\left(\eta\_{\mathrm{E}} \mathrm{L}\_{\mathrm{E}}\right)\right] \tag{9}$$

This means the total gain of hybrid amplifier is given as:

$$\begin{split} \mathbf{G}\_{\left(\lambda\right)} &= \mathbf{G}\_{\mathbf{T}\left(\lambda\right)} \mathbf{X} \mathbf{G}\_{\mathbf{E}\left(\lambda\right)} = \\ &= \exp\left[ \left( \sigma\_{\mathbf{T}\left(1480\right)} \mathbf{N} \mathbf{T}\_{2\cdot\sigma\mathbf{T}\left(1390\right)} \mathbf{N} \mathbf{T}\_{1\cdot\sigma\mathbf{T}\left(800\right)} \mathbf{N} \mathbf{T}\_{0} \right) \left( \eta\_{\mathbf{T}} \mathbf{L}\_{\mathbf{T}} \right) \right] \mathbf{X} \exp\left[ \left( \sigma\_{\mathbf{E}\left(1530\right)} \mathbf{N} \mathbf{E}\_{2\cdot\sigma\mathbf{E}\left(1480\right)} \mathbf{N} \mathbf{E}\_{1} \left( \eta\_{\mathbf{E}} \mathbf{L}\_{\mathbf{E}} \right) \right) \right] \end{split} \tag{10}$$

In the above equations, σT(1480), σT(1390) and σE(980) denotes cross-sections of excited state absorption, stimulated emission and ground state emission of TDFA. Similarly, σE(1530), σE(1480) represents the respective cross sections of EDFA. ηT and ηE represents the confinement factors of TDFA and EDFA respectively.

The above stated mathematical equations clearly illustrate the fact that the gain of hybrid amplifier broadens from 1460 nm to 1530 nm wavelength range. Further there is a noticeable reduction in the noise figure correspondingly in the hybrid amplifier. This affects in the gradual increase in the number of transmission channels of DWDM system, thereby increasing the overall transmission capacity of the optical communication system. The statistical analysis of TDFA-EDFA hybrid amplifier and EDFA-TDFA hybrid amplifier is done. The configuration TDFA-EDFA means the hybrid amplifier in which TDFA is in first stage and EDFA is in second stage, whereas configuration EDFA-TDFA means EDFA is in first stage and TDFA is in second stage. For this analysis, it is assumed that both fibers have step refractive index homogeneously broadened spectrum of thulium and erbium ions. We consider three levels of

 **TDFAs and FRAs**: Combining FRAs with TDFAs is very effective approach, because FRAs can provide any gain bandwidth by selecting the appropriate pump wavelengths. However, a drawback with FRAs is that double Rayleigh scattering (DRS) degrades the amplified signals [Percival & Williams 1994; Komukai et.al.1995,2001; Royet.al.2002and

 **TDFA**s **and EDFAs:** Hybrid amplifiers consisting of all rare –earth –doped- fiber amplifiers are easier to utilize than those incorporating FRAs, because these are free from DRS. These hybrid amplifiers are relatively simple in gain spectra control [Sakamoto et.al.2006 and Kaur & Gupta 2010]. Hybrid doped fiber amplifiers with different gain bandwidths have attracted a large interest for increasing the transmission capacity of long haul wavelength multiplexed optical communication systems in C-

Out of these, one of the-state-of-art hybrid amplifiers is TDFA -EDFA configuration. It is observed that for TDFA-EDFA configuration, the total gain of hybrid amplifier is given as product of gain of TDFA and gain of EDFA. The gain bandwidth is extended by cascading EDFA with TDFA. When EDFA is cascaded with TDFA in series, the total gain of hybrid amplifier is given by product of individual gains of each amplifier.The gain of TDFA is

G exp NT NT NT L T( )

 

 T(1480) 2 T(1390) 1 T(800) 0 T T 

E(1530) 2 E(1480) 1 E E

 

G exp [ NE NE L E ( )

T(1480) 2- T(1390) 1- T(800) 0 T T E(1530) 2- E(1480) 1 E E

 

=exp ( NT NT NT )( L ) X exp ( NE NE ( L )

 

In the above equations, σT(1480), σT(1390) and σE(980) denotes cross-sections of excited state absorption, stimulated emission and ground state emission of TDFA. Similarly, σE(1530), σE(1480) represents the respective cross sections of EDFA. ηT and ηE represents the

The above stated mathematical equations clearly illustrate the fact that the gain of hybrid amplifier broadens from 1460 nm to 1530 nm wavelength range. Further there is a noticeable reduction in the noise figure correspondingly in the hybrid amplifier. This affects in the gradual increase in the number of transmission channels of DWDM system, thereby increasing the overall transmission capacity of the optical communication system. The statistical analysis of TDFA-EDFA hybrid amplifier and EDFA-TDFA hybrid amplifier is done. The configuration TDFA-EDFA means the hybrid amplifier in which TDFA is in first stage and EDFA is in second stage, whereas configuration EDFA-TDFA means EDFA is in first stage and TDFA is in second stage. For this analysis, it is assumed that both fibers have step refractive index homogeneously broadened spectrum of thulium and erbium ions. We consider three levels of

  (8)

(9)

(10)

 

 

Aozasa et.al.2002].

band and L-band.

The gain of EDFA is given as:

( ) T( ) E( )

G =G XG =

 

This means the total gain of hybrid amplifier is given as:

confinement factors of TDFA and EDFA respectively.

 

 

given as

TDFA i.e. 3H6, 3H4 and 3F4, the other two levels of TDFA i.e. 3H5 and 3F2, 3 are ignored as the rate of their non radiation (τnr) to the corresponding levels are very high. Similarly, in case of EDFA, two levels 4I15/2, 4I13/2 is considered and level 4I11/2 is ignored for the same reasons. From the absorption and emission spectra, it is clear that the absorption and emission peaks of EDFA coincides at 1530nm, while the absorption peak of TDFA lies at 1430nm and emission peak of TDFA lies at 1460nm. Form the gain spectrum of EDFA, from which it is clear that EDFA has peak gain at 1530nm, beyond which the gain reduces slightly and remains flat almost until 1550nm. After that gain reduces sharply. This gain can be flattened by cascading TDFA with EDFA. Fig. 10 shows the flattened gain spectrum of Hybrid amplifier by cascading TDFA and EDFA. The thulium doped fiber (TDF) in first stage was forward pumped with a 1390nm pump laser diode (LD) and erbium doped fiber (EDF) in second stage is pumped with a 980nm LD. For efficient amplification the concentration of TDF +3 ions was kept very high (approx. 7500 ppm) [Percival & Williams 1994; Komukai et.al.1995]. Table 4 shows the different characteristics of both configurations.



F-ratio is calculated for the parameters mentioned in above Table 4. The calculated and tabulated value of F-ratio is shown in Table 5.


Table 5. F-Measure Results

The table 5 shows that the F-ratio is significant of 5% level which means that both hybrid configurations work differently. F-ratio is used to judge whether the difference among several sample means is significant or just a matter of sampling fluctuations. MS residual is always due to fluctuations of sampling and so serves as the basis for the significance test. The F-ratio is compared with its corresponding table value for the given degree of freedom at a specified level of significance. The table 5 shows that both the F-ratios are significant of 5% level which means that TDFA-EDFA amplifier work differently as compared with EDFA-TDFA amplifier. The gain spectrum of TDFA-EDFA is more widened as compared to that of EDFA-TDFA configuration. Since there is a large difference between the calculated and the table value of F. So, the null hypothesis is rejected. For WDM systems, TDFA-EDFA has a great impact as a hybrid amplifier as compared with EDFA-TDFA amplifier[Kaur & Gupta 2009]. As studied from the existing schemes, the amplification of DWDM signals using TDFA-EDFA hybrid amplifiers have major problems and short comings which are as listed below:

Hybrid Fiber Amplifier 117

It is clear with the configuration as shown in figure 10 that a wide bandwidth spectrum of nearly 100nm i.e. from 1460nm to 1560nm wavelength range is obtained. This also includes the 1510nm-1520nm range where EDFA as well as TDFA has no large gain for themselves. This is also observed that this gain is unflattened mainly from 1520nm to 1540nm region. This whole wavelength range is flattened by using a seven layer interference filter (TFF).A seven layer optical thin film filters consists of a stack of seven dielectric thin a film is used along with a cascaded TDFA and EDFA [Kaur & Gupta 2010]. There are so many ways to flatten the gain bandwidth of EFDA such as gain equalizers based on Mach-Zehnder optical filters, interference filters or long period grating and fluoride or tellurite based EDFA. The figure (11) shows a schematic diagram of a seven layer dielectric interference filter for gain flattening of hybrid amplifier consisting of cascaded TDFA with EDFA. A seven layer dielectric film is proposed as a gain equalizer. In figure (11) the shaded layer as high index layer having refractive index 2.4. The unshaded layer is a low index layer having refractive index as 1.46. The refractive index of fiber is assumed as 1.46. The third and sixth layer of this filter is half wavelength thick and all other layers have one fourth wavelength thickness. The filter is so designed that transmission loss occurs around the maximum gain of hybrid amplifier i.e. at 1531nm. The transmission loss is about 9dB. The flattened gain bandwidth of hybrid amplifier with the help seven layer deictic filter is shown in figure (12). The gain variation is less than ± 2.5% in the wavelength region of 1460-1560 nm. A [2X2] square matrix of a dielectric filter

[Matrix]= [M] = ∏��� � � ����� �

From equations (11) & (12), we get following equation for transmission

(����������(

����������������������������������������

Where mij are the components of the matrix [M]. Here we assume nfiber=1.46.Since the gain peak of hybrid amplifier occurs at 1530nm. So here we designed TFF such that the maximum transmission loss occurs at around the gain peak at wavelength 1530nm, which is observed as 9dB. In case of TE mode all parameters remain same except qx is replaced by px. It is clear from formula given in equation (13) that designing of interference filters with desired wavelength spectrum and transmittance is possible by selecting proper of layer of dielectric films, their thickness and refractive indices of core and cladding of the optical

� ����� � �����

� �

������� ����� � (11)

(12)

(13)

for TM mode is given as

fiber.

The transmission of a TFF is given as

T= �� � ��

T= � ���������


Although there are many improvements in gain spectrum of EDFA, but still the improved configurations are unable to provide enough bandwidth for emerging high quality parameters like gain, noise figure, amplified spontaneous emission etc. Therefore, there is a need to search for a new and versatile approach that enables an effective system with adequate bandwidth to accommodate large number of DWDM channels. One approach that can do the job is use of hybrid amplifier consisting of TDFA and EDFA in cascaded series combination. This hybrid amplifier is proven effective in DWDM systems. Several challenging points of research are realization and development of hybrid amplifiers, which can increase the bandwidth for S-band, C-band and L-band. The biggest challenge with hybrid amplifier is to maintain and offer high bandwidth in case of higher number of channels.

Fig. 10. Schematic Diagram of Cascaded TDFA-EDFA Hybrid amplifier using TFF

 The use of increasing number of channels in the present day DWDM optical networks requires a flat gain spectrum across the whole usable bandwidth. The unflattened gain spectrum of hybrid amplifiers implies that different channels of a DWDM system are amplified by different amounts. Hence a need is felt to broaden as well as flatten the

 It is observed that amplified spontaneous emission and its correction function for hybrid amplifiers have not been carried out leading to lesser gain and more noise of the signal. So, there is a need to analyze different parameters e.g. gain, noise figure,

 Hybrid amplifiers proposed till dates are using four or more than four amplifiers to achieve desirable gain, leading to higher complexity, noise. Hence there is a dire need to

 DWDM system till date are upto thirty two (32) channels but with lesser gain and high noise figure. The systems having adequate gain have been designed only upto eight (8) channels. Hence, there is a drastic need to increase the number of channels in DWDM

Although there are many improvements in gain spectrum of EDFA, but still the improved configurations are unable to provide enough bandwidth for emerging high quality parameters like gain, noise figure, amplified spontaneous emission etc. Therefore, there is a need to search for a new and versatile approach that enables an effective system with adequate bandwidth to accommodate large number of DWDM channels. One approach that can do the job is use of hybrid amplifier consisting of TDFA and EDFA in cascaded series combination. This hybrid amplifier is proven effective in DWDM systems. Several challenging points of research are realization and development of hybrid amplifiers, which can increase the bandwidth for S-band, C-band and L-band. The biggest challenge with hybrid amplifier is to maintain and offer high bandwidth in case of higher number of

amplified spontaneous emission of hybrid amplifier and its correction function. No scheme or algorithm has been designed to allow the hybrid amplifier to maintain a constant output signal power, independent of the optical wavelength and input power level. There are many occasions when constant optical signal power, independent of input power, is more desirable e.g. in an optical preamplifier in an optical receiver and

automatic power control cannot guarantee constant signal output power.

Fig. 10. Schematic Diagram of Cascaded TDFA-EDFA Hybrid amplifier using TFF

minimize number of amplifiers in hybrid configuration.

gain spectrum of hybrid amplifier.

system.

channels.

It is clear with the configuration as shown in figure 10 that a wide bandwidth spectrum of nearly 100nm i.e. from 1460nm to 1560nm wavelength range is obtained. This also includes the 1510nm-1520nm range where EDFA as well as TDFA has no large gain for themselves. This is also observed that this gain is unflattened mainly from 1520nm to 1540nm region. This whole wavelength range is flattened by using a seven layer interference filter (TFF).A seven layer optical thin film filters consists of a stack of seven dielectric thin a film is used along with a cascaded TDFA and EDFA [Kaur & Gupta 2010]. There are so many ways to flatten the gain bandwidth of EFDA such as gain equalizers based on Mach-Zehnder optical filters, interference filters or long period grating and fluoride or tellurite based EDFA. The figure (11) shows a schematic diagram of a seven layer dielectric interference filter for gain flattening of hybrid amplifier consisting of cascaded TDFA with EDFA. A seven layer dielectric film is proposed as a gain equalizer. In figure (11) the shaded layer as high index layer having refractive index 2.4. The unshaded layer is a low index layer having refractive index as 1.46. The refractive index of fiber is assumed as 1.46. The third and sixth layer of this filter is half wavelength thick and all other layers have one fourth wavelength thickness. The filter is so designed that transmission loss occurs around the maximum gain of hybrid amplifier i.e. at 1531nm. The transmission loss is about 9dB. The flattened gain bandwidth of hybrid amplifier with the help seven layer deictic filter is shown in figure (12). The gain variation is less than ± 2.5% in the wavelength region of 1460-1560 nm. A [2X2] square matrix of a dielectric filter for TM mode is given as

$$\mathbf{[Matrix]} = \mathbf{[M]} = \Pi\_{\mathbf{x}=1} \mathbf{b} \begin{bmatrix} \cos \beta \mathbf{x} & \frac{j}{q} \sin \beta \mathbf{x} \\ jq \sin \beta \mathbf{x} & \cos \beta \mathbf{x} \end{bmatrix} \tag{11}$$

The transmission of a TFF is given as

$$\mathbf{T} = \left[ 1 + \frac{4R}{(1 - R)2} \sin^2(\frac{\phi}{2}) \right]^{-1} \tag{12}$$

From equations (11) & (12), we get following equation for transmission

$$\mathbf{T} = \left[ \frac{2 \ n \ fiber}{(m\_{11} + m\_{12} \iota\_{fiber}) n\_{fiber} \star\_{\left(m\_{21} + m\_{22} \iota\_{fiber}\right)}} \right]^2 \tag{13}$$

Where mij are the components of the matrix [M]. Here we assume nfiber=1.46.Since the gain peak of hybrid amplifier occurs at 1530nm. So here we designed TFF such that the maximum transmission loss occurs at around the gain peak at wavelength 1530nm, which is observed as 9dB. In case of TE mode all parameters remain same except qx is replaced by px. It is clear from formula given in equation (13) that designing of interference filters with desired wavelength spectrum and transmittance is possible by selecting proper of layer of dielectric films, their thickness and refractive indices of core and cladding of the optical fiber.

Hybrid Fiber Amplifier 119

Simulation of cascaded configuration of TDFA-EDFA

START

Specify population densities for GSA, ESA, ST, energy levels of and cross sections of TDFA, EDFA, range of I/P power, pump powers and operating wavelengths.

Calculation of gain

Is peak gain >28dB for wavelength ranging from 1460nm -1580nm?

Flattening of gain spectrum by selecting

**YES**

**YES**

Is Gain excursio n ≈ 1.5 ?

Calculate NF, ASE and ASE correction

Developing DWDM sysyem for 16 channels keeping into

Evaluation stage

END

considerstion of all possible impairments

gain flattening devices

**NO**

**NO**

Fig. 13. Flowchart Showing Simulation Process

factor

Fig. 11. Schematic Diagram of the dielectric multi-layer Interference Filter (TFF)

Fig. 12. Broadened and Flattened Gain Spectrum of Hybrid Amplifier
