**2.3 Simulation procedure**

30 Selected Topics on Optical Amplifiers in Present Scenario

Optical powers and ASE propagating in the positive and negative directions are calculated at the boundaries of each section, while the total carrier density and local carrier changes caused by the CH and SHB processes are considered at the center of each

<sup>1</sup> (,) (,) (, )

 *Nz t Nz t Nz t ij ij ij*

(, ) ( , ) ( , ) ( , )+ ( ( , )) <sup>2</sup>

*Sz t Sz t <sup>I</sup> Nz t Nz t t RNz t v g eV*

*g ase g ase*

*v g v g*

the SOA, and experiencing an exponential amplification by a factor of (

the RHS, which can be assumed constant in a sufficiently small interval

Thus, basing upon the carrier density and the photon densities at the previous time step, we

where a linear interpolation is employed to estimate the photon densities of the input optical beam, co-propagating and counter-propagating ASEs at the center of each section. Similar method can be applied to (2) and (3), to calculate the local carrier density variations due to

The first term in the LHS of (7), describes the optical power propagating along the *z*-axis of

in the LHS, however, accounts for the optical power variation during the travelling time period in the section, which can be included using values obtained at last time step

Similar solutions can be given for the co-propagating and the counter-propagating ASEs, as

exp 1 ( , ) ( , )exp ( ( , ))

exp 1 ( , ) ( , )exp ( ( , ))

*ase i j ase* , and subjected to boundary conditions respectively,

 

 

*hc g z P z t P z t g z R Nz t*

1 1 1

*ase ase i j ase i j ase ase sp i j*

*hc g z P z t P z t g z R Nz t*

*Pz t Pz t* ( , ) ( , )exp ( , ) *i j ij* 11 1

1 1 1

 

*ase i j ase i j ase ase sp i j*

*t* is small enough, the left hand side (LHS) of (1) can be

*t t* (10)

1 11 1 11

 *gNz t z i j* 

<sup>1</sup> *Pz t P t* ( ,) () *j in j* (13)

 

 

<sup>1</sup> (,)0 *P zt ase j* (15a)

*ase ase*

*ase ase*

(, ) ( , ) (, ) ( , ) 2 2

*ase i j ase i j ase i j ase i j*

*S zt S z t S zt S z t*

1 11

*g* - 

*ij i j*

 

*int*), as shown in

*z*. The second term

int (12)

(14a)

(14b)

*ase*

*g*

*g*

(11)

1 1

(Bischoff, 2004). Therefore, a solution of (7) is,

where *Pin*(*tj*) denotes the input optical power at *tj*.

subjected to boundary condition,

where 1 int 

( ( , ), ) *g gNz t*

described in (8),

*ij ij ij g*

section. When the time interval

approximated by,

CH and SHB processes.

have,

So far, we have presented a detailed model of a single SOA. The simulation of the cascaded-SOA-switch can be completed by the following calculation procedure, where we use the case of 2 SOAs (turbo-switch) as the example:

