Arrayed waveguide grating based modular interconnection networks and methods for constructing and applying the same

1. A method for constructing an interconnection network, comprising:

providing N 1 N 2 ×1 wavelength multiplexers, labeled by L 0 , L 1 , . . . , L N _ −1 , for N 1 left nodes, an ith N 2 ×1 wavelength multiplexer having its jth input port connected with a jth port of an ith left node, and a jth port of the ith left node is associated with a wavelength

λ

[

i

+

j

]

N

1

,

wherein i=0, 1, . . . , N 1 −1, j=0, 1, . . . , N 2 −1;

providing N 2 1×N 1 wavelength demultiplexers labeled by R 0 , R 1 , . . . , R N 2 − 1 , for N 2 right nodes, a jth 1×N 1 wavelength demultiplexer having its ith output port connected separately with an ith port of a jth right node, and an ith port of a jth right node is associated with wavelength

λ

[

i

+

j

]

N

1

;

interconnecting the N 1 wavelength multiplexers on the left with the N 2 wavelength demultiplexers on the right via the N 1 ×N 2 AWG, the N 1 ×N 2 AWG having the N 1 input ports and the N 2 output ports, and being associated with the wavelength set Λ={λ 0 , λ 1 , . . . , λ N 1 −1 };

decomposing the N 1 ×N 2 AWG to a three-stage AWG network S A (n 1 , r 1 , m A , n 2 , r 2 ),

wherein the AWG network S A comprises N 1 =r 1 n 1 input ports on an input side, with each input port being a 1×n 2 wavelength demultiplexer, and N 2 =r 2 n 2 output ports on an output side, with each output port being an n 1 ×1 wavelength multiplexer, m A r 1 ×r 2 AWGs in the central stage, wherein r 1 =r 2 =r, n 1 =N 1 /r, n 2 =N 2 /r, and m A =n 1 n 2 ;

an ith input port is labeled by D A1 (α A , a A ), wherein α A =└i/n 1 ┘ and a A =[i] n 2 , and a jth output port is labeled by M A1 (β A , b A ), wherein β A =└j/n 2 ┘ and b A =[j] n 2 , and each of the AWGs in the central stage is labeled by G A1 (α A , b A ); the α A th input port of G A1 (α A , b A ) is connected with the b A th output port of D A1 (α A , a A ), the β A th output port of G A1 (α A , b A ) is connected with the α A th input port of M A1 (β A , b A ), and G A1 (α A , b A ) is associated with a wavelength subset

Λ

[

a

A

+

b

A

]

n

1

=

{

λ

[

a

A

+

b

A

]

n

1

⁢

r

+

k

|

k

=

0

,

1

,

…

⁢

,

r

-

1

}

;

replacing the ith N 2 ×1 wavelength multiplexer L i and the 1×n 2 wavelength demultiplexer D A1 (α A , a A ) with n 2 r×1 wavelength multiplexers, each of the r×1 wavelength multiplexers is labeled by D A2 (α A , a A , b A );

replacing the jth 1×N 1 wavelength demultiplexer R j and the n 1 ×1 wavelength multiplexer M A1 (β A , b A ) with n 1 r×1 wavelength demultiplexers, each of the r×1 wavelength demultiplexers being labeled by M A2 (β A , b A , α A ); and

associating each r 1 ×r 2 AWG, labeled by G A2 (α A , b A ), with a wavelength subset {λ k |k=0, 1, . . . , r−1};

wherein the output port of D A2 (α A , a A , b A ) is connected with the α A th input port of G A2 (α A ,b A ), and the input port of M A2 (β A , b A , α A ) is connected with the β A th output port of G A2 (α A , b A ).

2. An AWG-based modular interconnection network according to claim 1 , comprising:

left nodes, a number of the left nodes being N 1 , and each of the left nodes having N 2 ports,

right nodes, a number of the right nodes being N 2 , and each of the right nodes having N 1 ports,

an optical transceiver associated with a fixed wavelength on each port of the left and right nodes,

r×1 wavelength multiplexers, a number of the r×1 wavelength multiplexers being N 1 n 2 , each of the n 2 r×1 wavelength multiplexers having N 2 input ports being connected with the N 2 ports of one of the left nodes, and n 2 =N 2 /r,

1×r wavelength demultiplexers, a number of the 1×r wavelength demultiplexers being N 2 n 1 , each of the n 1 1×r wavelength demultiplexers having N 1 output ports being connected with the N 1 ports of one of the right nodes, and n 1 =N 1 /r, and

r×r AWGs connecting the r×1 wavelength multiplexers and the 1×r wavelength demultiplexer, a number of the r×r AWGs being n 1 n 2 , each of the r×r AWGs being associated with a wavelength subset {λ k |k=0, 1, . . . , r−1},

where N 1 ≧N 2 , N 1 and N 2 are integers that have a greatest common divisor r, and r>1.

3. The method as claimed in claim 1 , further comprising:

replacing the AWG in the central stage with a module constituted of a network AWG of three stages.

4. A method for constructing an interconnection network, comprising:

providing N 1 N 2 ×1 wavelength multiplexers, labeled by L 0 , L 1 , . . . , L N 1 −1 , for N 1 left nodes, an ith N 2 ×1 wavelength multiplexer having its ith input port connected with a jth port of an ith left node, and a jth port of the ith left node is associated with a wavelength

λ

[

i

+

j

]

N

1

,

wherein i=0, 1, . . . , N 1 −1, j=0, 1, . . . , N 2 −1, and N 1 =KN 2 ;

providing N 2 1×N 1 wavelength demultiplexers labeled by R 0 , R 1 , . . . , R N 2 −1 , for N 2 right nodes, a jth 1×N 1 wavelength demultiplexer having its ith output port connected separately with an ith port of a jth right node, and an ith port of a jth right node is associated with wavelength

λ

[

i

+

j

]

N

1

;

interconnecting the N 1 wavelength multiplexers on the left with the N 2 wavelength demultiplexers on the right via the N 1 ×N 2 AWG, the N 1 ×N 2 AWG having the N 1 input ports and the N 2 output ports, and being associated with the wavelength set A={λ 0 , λ 1 , . . . , λ N 1 −1 };

decomposing the N 1 ×N 2 AWG to a two-stage network S B (K, N 2 , K, 1, N 2 ),

wherein each input port of the AWG network S B is a link, there are K N 2 ×N 2 AWGs in the central stage, and each output port is a K×1 wavelength multiplexer; the ith input port is labeled by D B1 (α B ,a B ), wherein α B =└i/N 2 ┘ and a B =[i] N 2 , the jth output port is labeled by M B1 (γ B ), wherein γ B =j, and each AWG in the central stage is labeled by G B1 (α B ), and the AWG in the central stage is associated with a wavelength subset Λ α B ={λ α B N 2 +k |k=0, 1, . . . , N 2 −1};

the α B th input port of G B1 (α B ) is thus D B1 (α B , a B ), the γ B th output port of G B1 (α B ) is connected with the α B th input port of M B1 (γ B );

denoting each of the N 1 ×1 wavelength multiplexers as D B2 (α 1 , a B );

replacing the jth 1×N 1 demultiplexer R j and the K×1 multiplexer M B1 (γ B ) with K N 2 ×1 wavelength multiplexers, each of the N 2 ×1 wavelength multiplexers being labeled by M B2 (γ B ,α B ); and

associating each N 2 ×N 2 AWG, labeled by G B2 (α B ), with a wavelength subset {λ k |k=0, 1, . . . , N 2 −1};

wherein D 2 (a B ,a B ) is connected with the α B th input port of G B2 (α B ), and M B2 (γ B ,α B ) is connected with the γ B th output port of G B2 (α B ).

5. An AWG-based modular interconnection network according to claim 4 , comprising:

left nodes, a number of the left nodes being N 1 , and each of the left nodes having N 2 ports,

right nodes, a number of the right nodes being N 2 , and each of the right nodes having N 1 ports,

an optical transceiver associated with a fixed wavelength on each port of the left or right node,

N 2 ×1 wavelength multiplexers, a number of the N 2 ×1 wavelength multiplexers being N 1 , and each of the N 2 ×1 wavelength multiplexers having N 2 input ports being connected with the N 2 ports of one of the left nodes;

1×N 2 wavelength demultiplexers, a number of the 1×N z wavelength demultiplexers being N 1 =KN 2 , and each of the K 1×N 2 wavelength demultiplexers having N 1 output ports being connected with the N 1 ports of one of the right nodes; and

N 2 ×N 2 AWGs connecting the N 2 ×1 wavelength multiplexers and the 1×N 2 wavelength demultiplexers, a number of the N 2 ×N 2 AWGs being K, and each of the N 2 ×N 2 AWGs being associated with a wavelength subset {λ i |i=0, 1, . . . , N 2 −1},

wherein N 1 =KN 2 .

6. The method as claimed in claim 4 , further comprising:

replacing the AWG in the central stage with a module constituted of a three-stage network of AWGs.