**3.1 Single-stage approach**

The structure of a switching fabric depends on the adopted sharing strategy of the Wavelength Converters. Two of them are reported in Figs 5 and 6.

 Fig. 5. Shared-Per-Wavelength Single-Stage Optical Switching Fabric.

They are related to two proposed main WC sharing strategies. In the first one, referred to as Shared-Per-Wavelength (SPW) (Eramo et al., 2008; 2009a;b), the WCs are partially shared. All of the packets arriving on a given wavelength share the same pool of converters. In the second one referred to as Shared-Per-Node (SPN) (Eramo et al., 2009c; Eramo, 2010),the WCs are fully shared and all of the arriving packets share the same pool of WCs. Next we illustrate the switching fabrics of the SPW and SPN switches.

The SPW switching fabric is illustrated in 5 and its operation mode is the following (Eramo et al., 2008; 2009a;b). A packet not requiring wavelength conversion is directly routed towards the Output Fibers (OF). On the contrary a packet needing the use of a WC will be directed to the pool of *rw* WCs dedicated for the wavelength on which the packet is arriving.

**SSM 1**u**K**

**3.2 Multi-stage approach**

**control signals**

{

Semiconductor Optical Amplifiers (SOA).

coupler fabricated in lithium niobate.

**S P L I T T E R** **control signals**

> **Semiconductor Optical Amplifier (SOA)**

**(a) (b)**

SOA-Based Optical Packet Switching Architectures 73

Fig. 7. Realization of 1 × *K* SSM (a) and *K* × 1 SSM (b) by means of splitters, couplers and

One of the most used Multi-Stage (MS) switching fabric is the BENES one. It belongs to a class of rearrangeably non blocking networks with 2 × 2 switching elements. Fig. 8.a shows a 8 × 8 BENES switch using 20 2 × 2 switching elements. It is one of the most efficient architectures in

1) 2 × 2 switching elements, with *P* being a power of 2 (Benes, 1965). A single 2 × 2 switch can be realized in SOA technology as shown in Fig. 8.b. It is made by four SOAs, two splitters and two couplers and enables connectivity in both the *bar* and *crossed* states similar to a directional

terms of used number of 2×2 switching elements. A *<sup>P</sup>* <sup>×</sup> *<sup>P</sup>* BENES switch requires *<sup>P</sup>*

**2**u**2 2**u**2 2**u**2 2**u**2 2**u**2**

**2**u**2 2**u**2 2**u**2 2**u**2 2**u**2**

**2**u**2 2**u**2 2**u**2 2**u**2 2**u**2**

**2**u**2 2**u**2 2**u**2 2**u**2 2**u**2**

switching fabric is illustrated in Fig. 9 in the case *N*=2, *M*=2 and *r*=2.

SOA technology based 2 × 2 switching element (b).

Fig. 8. 8 × 8 BENES switching architecture realized with 20 2 × 2 switching elements (a).

A switching fabric supporting *N* IF/OF, *M* wavelengths and fully shared *r* wavelength converters can be realized with an 2*NM* × 2*NM* BENES network. An example of BENES

The total number of splitters and couplers can be reduced as illustrated in the switch of Fig. 10. It is obtained by starting from the switch reported in Fig. 9 and by combining in the

**SSM K**u**1**

**control signals**

{

**C O U P L E R**

> **Semiconductor Optical Amplifier (SOA)**

> > <sup>2</sup> (2*log*2*P* −

**Semiconductor Optical Amplifier (SOA)**

**S C**

**Control signals**

**Coupler**

**C**

**S**

**a) b)**

**S**

**SplitterC**

**SOA**

**control signals**

**SOA 1**

**SOA j**

**SOA K**

Fig. 6. Shared-Per-Node Single-Stage Optical Switching Fabric.

The selection of either an OF or a WC is realized by means of a 1 × (*N* + *rw*) Space Switching Module (SSM) of the 1*st* SSM stage. Each *N* × 1 SSM of the 3*rd* SSM stage in Fig. 5 has the function to forward to a WC the packet selected by the control unit to be wavelength converted. After the conversion, the packets are sent to the OFs by means of a 1 × *N* SSM of the 4*th* SSM stage. The function of an (*N* + *rw*)*M* × 1 SSM of the 2*nd* SSM stage is to couple all of the packets directed to any OF.

The SPW sharing strategy (Eramo et al., 2009c; Eramo, 2010) allows for a reduction in the switching fabric complexity, improving the scalability. As a matter of fact, the SSMs of the 1*st* and 3*rd* stage have reduced complexity with respect to the ones of the SPN reference switch diagrammed in Fig. 6 with *r* denoting the total number of shared WCs. This is due to the fact that *rw*, number of WCs shared per wavelength in SPW switch, is much smaller than *r*, the number of WC shared in SPN switch. The reduction in switching fabric complexity of the SPW switch leads to a smaller signal attenuation and consequently to a smaller SSM power consumption.

We report in Fig. 7.a and Fig. 7.b an example of realization of 1×*K* SSM and *K*×1 SSM respectively by means of splitters, couplers and Semiconductor Optical Amplifiers (SOA). The input of an 1×*K* SSM is switched to the output #*j* by turning on SOA #*j* and turn off the remaining SOAs. The SOA in the *K*×1 SSM is activated when at least one input signal has to be coupled.

Fig. 7. Realization of 1 × *K* SSM (a) and *K* × 1 SSM (b) by means of splitters, couplers and Semiconductor Optical Amplifiers (SOA).

### **3.2 Multi-stage approach**

6 Optical Amplifier

**4th SSM** 

**SSM 1**u**N**

*# r*

**SSM 1**u**N**

*# 1*

O

O

O

O

**From**

**Wavelength**

**Converters**

all of the packets directed to any OF.

consumption.

be coupled.

*<sup>1</sup>* **SSM 1**u**(N+r)**

*<sup>M</sup>* **SSM 1**u**(N+r)**

*<sup>1</sup>* **SSM 1**u**(N+r)**

*<sup>M</sup>* **SSM 1**u**(N+r)** 1

**1st SSM** 

**Stage**

*N+r N N+1*

1

*N+r N N+1*

1

*N+r N N+1*

1

*N+r N N+1*

1

*N*

1

*N*

**Stage**

Fig. 6. Shared-Per-Node Single-Stage Optical Switching Fabric.

The selection of either an OF or a WC is realized by means of a 1 × (*N* + *rw*) Space Switching Module (SSM) of the 1*st* SSM stage. Each *N* × 1 SSM of the 3*rd* SSM stage in Fig. 5 has the function to forward to a WC the packet selected by the control unit to be wavelength converted. After the conversion, the packets are sent to the OFs by means of a 1 × *N* SSM of the 4*th* SSM stage. The function of an (*N* + *rw*)*M* × 1 SSM of the 2*nd* SSM stage is to couple

The SPW sharing strategy (Eramo et al., 2009c; Eramo, 2010) allows for a reduction in the switching fabric complexity, improving the scalability. As a matter of fact, the SSMs of the 1*st* and 3*rd* stage have reduced complexity with respect to the ones of the SPN reference switch diagrammed in Fig. 6 with *r* denoting the total number of shared WCs. This is due to the fact that *rw*, number of WCs shared per wavelength in SPW switch, is much smaller than *r*, the number of WC shared in SPN switch. The reduction in switching fabric complexity of the SPW switch leads to a smaller signal attenuation and consequently to a smaller SSM power

We report in Fig. 7.a and Fig. 7.b an example of realization of 1×*K* SSM and *K*×1 SSM respectively by means of splitters, couplers and Semiconductor Optical Amplifiers (SOA). The input of an 1×*K* SSM is switched to the output #*j* by turning on SOA #*j* and turn off the remaining SOAs. The SOA in the *K*×1 SSM is activated when at least one input signal has to

O*1*,... O*M*

**SSM (NM+r)**u**1**

**2nd SSM** 

**Stage**

**SSM (NM+r)**u**1**

1

*NM*

1

*NM*

**SSM NM**u**1**

*# 1*

**SSM NM**u**1**

*# r*

**3rd SSM** 

**Stage**

1

*NM+r*

1

*NM+r*

O*1*,... O*M*

**To**

**Wavelength**

**Converters**

One of the most used Multi-Stage (MS) switching fabric is the BENES one. It belongs to a class of rearrangeably non blocking networks with 2 × 2 switching elements. Fig. 8.a shows a 8 × 8 BENES switch using 20 2 × 2 switching elements. It is one of the most efficient architectures in terms of used number of 2×2 switching elements. A *<sup>P</sup>* <sup>×</sup> *<sup>P</sup>* BENES switch requires *<sup>P</sup>* <sup>2</sup> (2*log*2*P* − 1) 2 × 2 switching elements, with *P* being a power of 2 (Benes, 1965). A single 2 × 2 switch can be realized in SOA technology as shown in Fig. 8.b. It is made by four SOAs, two splitters and two couplers and enables connectivity in both the *bar* and *crossed* states similar to a directional coupler fabricated in lithium niobate.

Fig. 8. 8 × 8 BENES switching architecture realized with 20 2 × 2 switching elements (a). SOA technology based 2 × 2 switching element (b).

A switching fabric supporting *N* IF/OF, *M* wavelengths and fully shared *r* wavelength converters can be realized with an 2*NM* × 2*NM* BENES network. An example of BENES switching fabric is illustrated in Fig. 9 in the case *N*=2, *M*=2 and *r*=2.

The total number of splitters and couplers can be reduced as illustrated in the switch of Fig. 10. It is obtained by starting from the switch reported in Fig. 9 and by combining in the

of Optical Packet Switching. First of all we introduce a SOA's power consumption model in Section 4.1 able to evaluate the power consumption as a function of the main SOA's parameters (current, forward polarization voltage, material loss, gain,··· ). Analytical models are introduced in Section 4.2 to evaluate the power consumption of Synchronous SPN (SSPN) Optical Packet Switches equipped with SS and MS switching fabric. Similar models have been introduced for the asynchronous case (Eramo et al., 2009c; Eramo, 2010) and when the SPW sharing strategy is adopted (Akar et al., 2011; Eramo et al., 2011). Some numerical results reporting the power consumption of Optical Packet Switches are illustrated in Section 4.3.

SOA-Based Optical Packet Switching Architectures 75

The SOA's power consumption model illustrated in (Hinton et al., 2008) is adopted; the SOA's

where *Vb* is the SOA forward bias voltage, *ib* is the polarization current, Γ*SOA* is the confinement factor, *αSOA* is the material loss, *LSOA* is the length and *it* is the transparency

*it* <sup>=</sup> *qwSOAdSOALSOAN*<sup>0</sup>

where *wSOA* is the SOA active region effective width, *dSOA* is the active region depth, *q* = 1.6 <sup>×</sup> <sup>10</sup>−9*<sup>C</sup>* is the electronic charge, *<sup>N</sup>*<sup>0</sup> is the conduction band carrier density required for

The analytical evaluation of the OPS power consumption is carried out as a function of the main switch and traffic parameters (Eramo, 2010; Eramo et al., 2011). We propose two analytical models to evaluate the power consumption of synchronous Optical Packet Switches equipped with Single-Stage and BENES switching fabric in Sections 4.2.1 and 4.2.2

In evaluating the various power consumption in the SS-SSPN Optical Packet Switch we notice

• there are as many turned on synchronizers in the synchronization stage as the number

• there are as many turned on SOAs in 1*st* stage as the number *Na*(*t*) of packets forwarded; • the number of turned on SOAs in both 2*nd* stage and 3*rd* stage equals the number *Nc*(*t*) of

• there are as many active turned on SOAs in 4*th* SSM stage as the number *Nd*(*t*) of OFs in

**4.2.1 Analytical evaluation of the power consumption in SSPN OPS equipped with**

*lnG* <sup>Γ</sup>*SOAαSOALSOA*

 1 +

*SOA* of the SOA needed to provide the gain *G*.

*<sup>τ</sup>* (2)

*it* (1)

**4.1 SOA's power consumption model**

*SOA* can be expressed as follows:

*Pal*,*<sup>G</sup>*

current given by:

**4.2 Analytical models**

**single-stage fabric switching**

from Figs 1,6 that at time *t*:

converted packets;

*Na*(*t*) of packets forwarded;

which at least one packet is directed;

respectively.

power consumption equals the supply power *Pal*,*<sup>G</sup>*

*Pal*,*<sup>G</sup>*

transparency, *τ* is the carrier spontaneous decay lifetime.

*SOA* = *Vbib* = *Vb*

Fig. 9. BENES Optical Packet Switch realized with splitters, couplers and SOAs (*N*=2, *M*=2, *r*=2).

adjacent stages with a 3dB Directional Coupler (DC) the output couplers on the left-hand and the input splitters on the right-hand.

Fig. 10. BENES Optical Packet Switch realized with splitters, directional couplers, couplers and SOAs (*N*=4, *M*=2, *r*=2).
