Abstract:
The object of the present invention is to provide a full-mesh optical wavelength division multiplexing transmission network device which is capable of exhibiting excellent communication quality and being mass produced, by reducing the accumulation number of coherent crosstalk lights, without any modification of constituent components constituting the conventional one. In the full-mesh optical wavelength division multiplexing transmission network device, provided is an N×N wavelength multi/demultiplexer having a periodic wavelength demultiplexing property in input/output combination, which performs input/output from/to first and second I/O port groups for optical signals and allows lightwaves traveling in opposite directions not to interfere with each other within the circut, thus reducing the accumulation number of coherent crosstalk lights in WDM wavelength lights and improving S/N of a received light. Particularly, by preventing the accumulation of adjacent crosstalk lights, communications with higher quality can be achieved.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a full-mesh optical wavelength division multiplexing transmission network transmission device for transmitting a plurality of optical signals wavelength-division multiplexed among a plurality of transmitting and receiving apparatuses. 
     This specification is based on Japanese Patent Application (No. 11(1999)-229174) to Japan Patent Office, and contents described in this Japanese Patent Application will be incorporated as a part of this specification. 
     2. Descriptions of the Related Art 
     An optical wavelength division multiplexinging (WDM) transmission system, which transmits a plurality of optical signals on one optical fiber by allocating the signals to different wavelengths, can increase significantly the capacity of its transmission path. In addition, the optical WDM transmission system can perform wavelength addressing which is capable of allocating the destination information relating to the optical signals to the respective wavelengths. Furthermore, a star-type WDM system, in which an N×N wavelength multi/demultiplexer having a periodic wavelength demultiplexing property in input/output combination is arranged in the center so as to connect N transmitting and receiving apparatuses therebetween, can realize a full-mesh WDM transmission network device capable of interconnecting the apparatus through independent N×N signal paths by using only N wavelengths optical signals. 
     FIG. 25 is a block diagram for explaining a schematic constitution of a conventional full-mesh WDM transmission network device. Referring to FIG. 25, reference numerals  1  to  4  denote transmitting and receiving apparatuses;  5  to  8 , transmitters for sending WDM signals (wavelength λ K :K=1, 2, . . . , N);  9  to  12 , receivers for receiving the WDM signals (wavelength λ K :K=1, 2, . . . , N);  13  to  16 , 1×N wavelength multiplexers for multiplexing optical signals having different N wavelengths onto one optical fiber,  17  to  20 , 1×N wavelength demultiplexing circuits for demultiplexing the WDM signals wavelength-multiplexed on one optical fiber, into signals having N wavelengths;  21 , an N×N wavelength multi/demultiplexer having a periodic wavelength demultiplexing property in input/output combination, which has a first I/O port group ( 1 ,  2 , . . . , N on the left side) composed of N ports and the opposing second I/O port group ( 1 ,  2 , . . . , N on the right side) composed of N ports; and  22  to  29 , optical fibers for optically connecting the transmitting and receiving apparatuses  1  to  4 , to the I/O ports of the N×N wavelength multi/demultiplexer  21 . In the optical fibers  22  to  29 , the wavelengths λ K  (K=1, 2, . . . , N) of the WDM signals propagating on the optical fibers, the signals being wavelength-multiplexed, and the directions of the WDM signals to be transmitted, which are indicated by arrows, are shown. 
     In this prior art 1×N AWGs (arrayed-waveguide grating wavelength multi/demultiplexer) each having a first I/O port composed of one port and a second I/O port group composed of N ports facing the one first I/O port are used as the 1×N wavelength multiplexers  13  to  16  and the 1×N wavelength demultiplexing circuits  17  to  20 . An N×N AWG having a first I/O port group composed of N ports and a second I/O port group composed of N ports facing the first I/O port group and having a periodic wavelength demultiplexing property in input/output combination is used as the N×N wavelength multi/demultiplexer  21 . 
     FIG. 26 is a table showing a periodic wavelength demultiplexing property in input/output combination for N×N AWG (N=8), and a port connection rule between the transmitting and receiving apparatus and the AWG in the conventional full-mesh WDM transmission network device. The N×N AWG having the wavelength demultiplexing property of the periodic input/output relation can be realized by a method recorded in Japanese Patent Application No. 10(1998)-210679, and the like. The wavelength demultiplexing property between eight ports of the first input/output group of the N×N AWG and eight ports of the second input/output group thereof is periodic as shown by the wavelength λ K  (K=1, 2, . . . , 8) in FIG.  26 . 
     The N×N AWG is a circuit symmetrical with respect to the first I/O port group and the second I/O port group. For example, the multiplexed WDM signal wavelength λ K  (K=1, 2, . . . , 8) input from a predetermined port of the first I/O port group is wavelength-demultiplexed and output to each port of the second I/O port group. In contrast, the multiplexed WDM signal wavelength λ K  (K=1, 2, . . . , 8) input from a predetermined port of the second I/O port group is wavelength-demultiplexed and output to each port of the first I/O port group. 
     The arrows shown above the each wavelength λ K  in FIG. 26 express the relation of the input/output among the ports. The arrows toward the right mean that the first I/O port group side is used as an input port and the second I/O port group side is used as an output port, and the arrows toward the left mean that second I/O port group side is used as an input port and the first I/O port group is used as an output port. To be more specific, in the conventional full-mesh WDM transmission network device, the whole of the first I/O port group side is used as the input port, and the whole of the second I/O port group side is used as the output port. Although there are 64 (8×8) paths among 8×8 AWG ports, the 64 paths can be independently established at only 8 wavelengths by using of the periodic wavelength demultiplexing property as shown in FIG,  26 . 
     By connecting the I/O ports of the AWG to each transmitting and receiving apparatus, signals can be transmitted independently therebetween through all the paths which can be established among the eight transmitting and receiving apparatuses. Moreover, since a specified wavelength λ K  is allocated to the respective path, if a wavelength corresponding to a receiver is selected on the transmitter side, a wavelength addressing function to transmit the signal automatically to an objective receiver can be realized. 
     FIG. 27 is a diagram for explaining the wavelength addressing. In FIG. 27, reference numerals  31  to  38  denote eight transmitting and receiving apparatuses ( 1 ) to ( 8 ), and  39  denotes a 8×8 AWG. The wavelength demultiplexing property of the 8×8 AWG and the port connection rule between each of the transmitting and receiving apparatuses and the 8×8 AWG are described in FIG.  26 . An optical signal having a wavelength λ 2  transmitted from the transmitting and receiving apparatus ( 1 )  31  is guided to the port  1  of the first I/O port group of the 8×8 AWG  39 , and switched within the 8×8 AWG  39 . The optical signal is then sent to the transmitting and receiving apparatus ( 2 )  32  from the port  2  of the second I/O port group thereof. Similarly, a return signal λ 2  sent back from the transmitting and receiving apparatus ( 2 )  32  is transmitted to the transmitting and receiving apparatus ( 1 )  31  via the 8×8 AWG  39 . For example, optical signals λ 3  and λ 5  transmitted from the transmitting and receiving apparatus ( 1 )  31  are automatically delivered to the transmitter ( 3 )  33  and the transmitting and receiving apparatus ( 5 )  35 , respectively. 
     FIG. 28 is a graph showing atypical transmission spectrum property between certain input and output ports of the AWG fabricated as a silica-based planar lightwave circuit. Although a wavelength of an optical signal to be transmitted between the input and output ports is equal to λ K , other than this optical signal also an optical signal (λ 1 , λ 2 , . . . , λ K−1 , λ K+1 , . . . , λ N ) input from the same port can be scarcely transmitted therebetween. This is the noise called crosstalk light. An intensity ratio of the crosstalk light to the optical signal is approximately −30 dB with respect to a wavelength (λ K−1 , λ K+1 ) adjacent to the wavelength λ K , and approximately −40 dB with respect to other wavelengths (λ 1 , λ 2 , . . . , λ K−2 , λ K+2 , . . . , λ N ). 
     In the N×N AWG of the conventional full-mesh WDM transmission network device, the WDM signals of N wavelengths are input from all ports of the first I/O port group. For example, in the case of the 8×8 AWG having the wavelength demultiplexing property of the periodic input/output relation as shown in FIG. 26, the optical signal λ 5  (thick solid line) which is transmitted from the transmitting and receiving apparatus ( 1 )  31  and input to the 8×8 AWG via the port  1  of the first I/O port group (the port group on the left side of the 8×8 AWG) is output from the port  5  of the second I/O port group (the port group on the right side of the 8×8 AWG), and received by the transmitting and receiving apparatus ( 5 )  35 . 
     Furthermore, the optical signal λ 6  (thick broken line) which is transmitted from the transmitting and receiving apparatus ( 2 )  32  and input to the 8×8 AWG via the port  2  of the first I/O port group is output from the port  5  of the second I/O port group, and received by the transmitting and receiving apparatus ( 5 )  35 . At this time, crosstalk light (thin solid line) of the optical signal λ 5 , which is transmitted from the transmitting and receiving apparatus ( 2 )  32  and input via the port  2  of the first I/O port group, is also output from the port  5  of the second input/output group. Similarly, crosstalk lights of the optical signal λ 5  transmitted from other transmitting and receiving apparatuses are also output from the port  5  of the second I/O port group. As a result, one optical signal λ 5  and seven crosstalk lights having the equal wavelength are output from the port  5  of the second I/O port group. The crosstalk lights having equal wavelengths are called coherent crosstalk lights. At this time, since the coherent crosstalk lights from the port  2  and the port  8  of the first I/O port group, that is, the ports cyclically adjacent to the port to which the optical signal λ 5 is input, are crosstalk light from the adjacent wavelength (adjacent crosstalk light), these coherent crosstalk lights show intensities stronger than those of other five coherent lights. 
     Like the N×N AWG in the conventional full-mesh WDM transmission network device, when N optical signals having the equal wavelength are input from the same I/O port group side, N−1 coherent crosstalk lights always occur. Moreover, since the coherent crosstalk light is the noise having a wavelength equal to that of the optical signal, the optical signal and the noise cannot be separated from each other by a wavelength demultiplexing circuit of the transmitting and receiving apparatus, and the noise may increase owing to the interference of the plurality of coherent crosstalk lights. 
     In the conventional full-mesh WDM transmission network device, a certain WDM wavelength light received by the transmitting and receiving apparatus is a sum of one optical signal and N−1 coherent crosstalk lights, and two waves among these waves are the adjacent crosstalk lights. If the optical signal has the longest wavelength λ N  or the shortest wavelength λ 1 , one wavelength is the adjacent crosstalk light. Accordingly, a signal noise ratio S/N is expressed as follows: 
     
       
         S/N= P   Signal /[2 PAdjCT +( N −3) P   othCT ]  (1) 
       
     
     where P AdjCT , P OthCT  and P Signal  are the adjacent crosstalk light intensity, the non-adjacent crosstalk light intensity and the signal light intensity. Assuming that P AdjCT /P Signal  is equal to −30 dB and P OthCT /P Signal  is equal to −40 dB, S/N is 27 dB when N=4, 26 dB when N=8, and 25 dB when N=16. 
     As taught by the formula (1), in the conventional full-mesh WDM transmission network device noises created by the coherent crosstalk lights are accumulated with an increase in the number N of the transmitting and receiving apparatuses connected, so that S/N of the WDM wavelength light decreases. This implies that communication quality of the system deteriorates along with scale expansion. In contrast, a system satisfying a predetermined communication quality standard is limited in its scale. This is a serious problem in designing the system. 
     SUMMARY OF THE INVENTION 
     The present invention was made in view of such problems, and the object of the present invention is to provide a large scale full-mesh optical wavelength division multiplexing transmission network device which reduces the accumulation number of coherent crosstalk lights that cause noise, and has a communication quality more excellent than the conventional full-mesh optical wavelength division multiplexing transmission network device, without any modification of constituent components constituting the conventional one. The constituent components include a transmitter, a receiver, a 1×N wavelength multi/demultiplexer, an N×N wavelength multi/demultiplexer, and an optical fiber. 
     The full-mesh optical wavelength division multiplexing transmission network device of the present invention comprises N transmitting and receiving apparatuses; and an N×N wavelength multi/demultiplexer having a first I/O port group composed of N ports connected to a different one of said N transmitting and receiving apparatuses and a second I/O port group composed of N ports connected to a different one of said N transmitting and receiving apparatuses, wherein an optical signal having a different wavelength for each port of the second I/O port group among optical signals having N kinds of wavelength is transmitted between any one of the ports of the first I/O port group and each port of the second I/O port group; an optical signal having a different wavelength for each port of the first I/O port group among optical signals having N kinds of wavelength is transmitted between any one of the ports of the second I/O port group and each port of the first I/O port group; as a result, N port combinations for transmitting optical signals having an equal wavelength exist for each wavelength, among N×N port combinations made by the N ports of the first I/O port group and the N ports of the second I/O ports; among the N port combinations for transmitting the optical signals having the equal wavelength, in M port combinations the optical signals are transmitted from the first I/O port group to the second I/O port group, and in N−M port combinations the optical signals are transmitted from the second I/O port group to the first I/O port group; and the port of the second I/O port group for receiving the optical signal from the port of the first I/O port group connected to the any one of the transmitting and receiving apparatuses and the port of the first I/O port group for receiving the optical signal from the port of the second I/O port group connected to the any one of the transmitting and receiving apparatuses are connected to the different transmitting and receiving apparatus. 
     In the optical wavelength division multiplexing transmission network device of the invention, N is preferably an even number and M is equal to N/2. 
     In the optical wavelength division multiplexing transmission network device of the invention, wavelengths of all optical signals transmitted from any one of the ports of one I/O port group to the other I/O port group are preferably different from wavelengths of all optical signals transmitted from a port adjacent to the said one port of the one I/O port group to the other I/O port group. 
     In the optical wavelength division multiplexing transmission network device of the invention, the transmitting and receiving apparatus preferably further includes: N−M transmitters; M receivers; a 1×N wavelength multi-demultiplexer which demultiplexes an optical signal output from predetermined one port of the first I/O port group into M optical signals having different wavelengths, inputs the demultiplexed optical signals to the different receivers among the M receivers, multiplexes optical signals output from said N−M transmitters into one optical signal, and transmits the multiplexed optical signal to predetermined one port of the first I/O port group; M transmitters, N−M receivers; and a 1×N wavelength multi/demultiplexer which demultiplexes an optical signal output from predetermined one port of the second I/O port group into N−M optical signals having different wavelengths, inputs the demultiplexed optical signals to the different receivers among the N−M receivers, multiplexes optical signals output by said M transmitters into one optical signal, and transmits the multiplexed optical signal to predetermined one port of the first I/O port group. 
     According to the present invention, a full-mesh optical wavelength division multiplexing transmission network device can be realized, which is capable of reducing the accumulation number of coherent crosstalk lights that cause noise, exhibiting excellent communication quality, and being mass produced, without any modification of constituent components (the transmitters, the receivers the 1×N AWG, the N×N AWG and the optical fiber) constituting the conventional one. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram for explaining a schematic constitution of a first embodiment of the present invention; 
     FIG. 2 is a table showing a wavelength demultiplexing property and a port connection rule for an AWG of the first embodiment of the present invention; 
     FIG. 3 is a diagram for explaining coherent crosstalk light of the first embodiment of the present invention; 
     FIG. 4 is a diagram for explaining a wavelength addressing of the first embodiment of the present invention; 
     FIG. 5 is a block diagram for explaining a schematic constitution of a second embodiment of the present invention; 
     FIG. 6 is a table showing a wavelength demultiplexing property and a port connection rule for an AWG of the second embodiment of the present invention; 
     FIG. 7 is a diagram for explaining coherent crosstalk light of the second embodiment of the present invention; 
     FIG. 8 is a diagram for explaining a wavelength addressing of the second embodiment of the present invention; 
     FIG. 9 is a block diagram for explaining a schematic constitution of a third embodiment of the present invention; 
     FIG. 10 is a table showing a wavelength demultiplexing property and a port connection rule for an AWG of the third embodiment of the present invention; 
     FIG. 11 is a diagram for explaining coherent crosstalk light of the third embodiment of the present invention; 
     FIG. 12 is a diagram for explaining a wavelength addressing of the third embodiment of the present invention; 
     FIG. 13 is a block diagram for explaining a schematic constitution of a fourth embodiment of the present invention; 
     FIG. 14 is a table showing a wavelength demultiplexing property and a port connection rule for an AWG of the fourth embodiment of the present invention; 
     FIG. 15 is a diagram for explaining coherent crosstalk light of the fourth embodiment of the present invention; 
     FIG. 16 is a diagram for explaining a wavelength addressing of the fourth embodiment of the present invention; 
     FIG. 17 is a block diagram for explaining a schematic constitution of a fifth embodiment of the present invention; 
     FIG. 18 is a table showing a wavelength demultiplexing property and a port connection rule for an AWG of the fifth embodiment of the present invention; 
     FIG. 19 is a diagram for explaining coherent crosstalk light of the fifth embodiment of the present invention; 
     FIG. 20 is a diagram for explaining a wavelength addressing of the fifth embodiment of the present invention; 
     FIG. 21 is a block diagram for explaining a schematic constitution of a sixth embodiment of the present invention; 
     FIG. 22 is a table showing a wavelength demultiplexing property and a port connection rule for an AWG of the sixth embodiment of the present invention; 
     FIG. 23 is a diagram for explaining coherent crosstalk light of the sixth embodiment of the present invention; 
     FIG. 24 is a diagram for explaining a wavelength addressing of the sixth embodiment of the present invention; 
     FIG. 25 is a block diagram showing a schematic constitution of a conventional device; 
     FIG. 26 is a table showing a wavelength demultiplexing property of a conventional 8×8 AWG and a port connection rule; 
     FIG. 27 is a diagram for explaining a wavelength addressing of a conventional device; 
     FIG. 28 is a graph showing an example of a transmission spectrum characteristic between input/output ports of a silica-based planar AWG; and 
     FIG. 29 is a diagram for explaining coherent crosstalk light of the conventional device. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Embodiments of the present invention will be described below. 
     It should be noted that the embodiments described below do not limit the spirt and scope of the invention defined by the claims. 
     To achieve the object of the present invention, all combinations of features described in the embodiments are not always necessary. 
     Embodiment 1 
     FIG. 1 is a block diagram for explaining a first embodiment of the present invention, which shows a schematic constitution of a full-mesh WDM transmission network device of N=4. Referring to FIG. 1, reference numerals  41  to  44  denote a transmitting and receiving apparatus;  45  to  52 , a transmitter for sending a WDM signal (wavelength λ K : K=1, 2, 3, 4);  53  to  60 , a receiver for receiving a WDM signal (wavelength λ K : K=1, 2, 3, 4);  61  to  68 , a 1×4 wavelength multi/demultiplexer which multiplexes optical signals of two different wavelengths into one optical fiber and demultiplexes a WDM signal which is wavelength-multiplexed to one optical fiber, into two wavelengths;  69 , a 4×4 wavelength multi/demultiplexer having a first I/O port group ( 1  to  4  on the left side) composed of four ports and a second I/O port group ( 1  to  4  on the right side) composed of four ports, the 4×4 wavelength multi/demultiplexer having a periodic wavelength demultiplexing property in input/output combination; and  70  to  77 , an optical fiber for optically connecting each of the transmitting and receiving apparatuses  41  to  44  and each of the I/O ports of the 4×4 wavelength multi/demultiplexes  69 . In FIG. 1, shown are the wavelengths (λ K : K=1, 2, 3, 4) of the WDM signal wavelength-multiplexed and transmitted on the corresponding optical fiber  70  to  77 , and the transmission directions (arrow) thereof. 
     In this embodiment, as the 1×4 wavelength multi/demultiplexes  61  to  68 , a 1×4 AWG (array waveguide diffraction grating) wavelength multi/demultiplexer was used, and as the 4×4wavelength multi/demultiplexer  69 , a 4×4 AWG having a periodic wavelength demultiplexing property in input/output combination was used. Constituent components (a transmitter, a receiver, a 1×4 AWG, a 4×4 AWG and an optical fiber) constituting the full-mesh WDM transmission network device of this embodiment are the same as those of the prior art. Note that while the 1×4 AWG was used exclusively for the wavelength multiplexer or the wavelength demultiplexing circuit in the prior art in this embodiment of the present invention the 1×4 AWG is used for the wavelength multi/demultiplexer that performs the wavelength multiplexing and demultiplexing simultaneously. 
     FIG. 2 is a table showing a periodic wavelength demultiplexing property in input/output combination of the 4×4 AWG and a port connection rule between the transmitting and receiving apparatuses and the 4×4 AWG in this embodiment of the present invention. The wavelength demultiplexing property of the 4×4 AWG has the same periodicity as that of the prior art. Although the connection relation between the transmitting and receiving apparatuses and the first I/O port group of the 4×4 AWG is also the same as that of the prior art the connection relation between the transmitting and receiving apparatus and the second I/O port group of the 4×4 AWG is different from that of the prior art. Furthermore, unlike the prior art according to combinations of the 4×4 AWG ports and the wavelengths of the optical signals, some optical signals are input from the first I/O port group side and output to the second I/O port group side, and other optical signals are input from the second I/O port group side and output to the first I/O port group side. Thus optical signals input/output bidirectionally. 
     In this embodiment, two optical signals among the four optical signals having the equal wavelength are input from the first I/O port group side to the 4×4 AWG, and other two optical signals are input from the second I/O port group side thereto. Since the lightwaves which are traveling in opposite directions are independent from each other, the optical wave input from the first I/O port group side and the optical wave input from the second I/O port group side, which have the equal wavelength, never interfere with each other within the 4×4 AWG. Accordingly, the WDM wavelength light output from the port of the 4×4 AWG includes only one optical signal and one coherent crosstalk light. For example, as shown in FIG. 3, the light having the wavelength λ 3 , which is output from the port  2  of the second I/O port group, includes only the optical signal λ 3  (thick solid line) input from the port  2  of the first I/O port group and the crosstalk light (thin solid line) of the optical signal λ 3  input from the port  1  of the first I/O port group, and does not include the crosstalk lights of the optical signals λ 3  input from the ports  1  and  4  of the second I/O port group. Specifically, the accumulation number of the coherent crosswalk lights is reduced to one from three, which is the accumulation number in the prior art. 
     In this embodiment, since the two optical signals having the equal wavelength, which are input from the first I/O port group side, are input from the ports adjacent to each other and the optical signals input from the second I/O port group side are input from the ports cyclically adjacent to each other, one coherent crosstalk light included in the output WDM wavelength light from the 4×4 AWG is a crosstalk light contributed from an adjacent port. Accordingly, in the full-mesh WDM transmission network device of this embodiment S/N of the WDM wavelength light received is expressed as follows: 
     
       
         S/N= P   Signal   /P   AdjCT   (2) 
       
     
     S/N is equal to 30 dB when P Signal /P AdjCT  is assumed to be −30 dB, and the S/N is improved by 3 dB compared to 27 dB in the prior art. 
     FIG. 4 is a diagram for explaining wavelength addressing in this embodiment. In FIG. 4, reference numerals  81  to  84  denote four transmitting and receiving apparatuses, and reference numeral  85  denotes a 4×4 AWG. The wavelength demultiplexing property of the 4×4 AWG  85  and the connection relation between the transmitting and receiving apparatuses and the 4×4 AWG  85  are explained in FIG.  2 . For example, the optical signal having the wavelength λ 4 ,transmitted from the transmitting and receiving apparatus ( 1 )  81 , is guided to the port  3  of the second I/O port group in the 4×4 AWG  85 , and switched within the 4×4 AWG  85 . This optical signal is then sent to the transmitting and receiving apparatus ( 2 )  82  from the port  2  of the first I/O port group. Similarly, the return signal λ 2  returned from the transmitting and receiving apparatus ( 2 )  82  is guided to the port  2  of the second I/O port group in the 4×4 AWG  85 , and then sent to the transmitting and receiving apparatus ( 1 )  81  from the port  1  of the first I/O port group. 
     Furthermore, one of the two optical signals having the wavelength λ 1  returned from the transmitting and receiving apparatus ( 1 )  81  is guided to the port  3  of the second I/O port group in the 4×4 AWG  85 , and automatically delivered to the transmitting and receiving apparatus ( 3 )  83  from the port  3  of the first I/O port group. The other is guided to the port  1  of the first I/O port group in the 4×4 AWG  85 , and automatically delivered to the transmitting and receiving apparatus ( 4 )  84  from the port  1  of the second I/O port group. These two optical signals are transmitted from the transmitters  45  and  46  of the transmitting and receiving apparatus ( 1 )  41  in FIG.  1 . 
     As described above, the full-mesh WDM transmission network device in this embodiment uses the constituent components similar to those of the prior art, and keeps the similar wavelength addressing function, while reducing the accumulation number of the coherent crosstalk lights included in each WDM wavelength light to one from three, thus realizing higher quality communication. Specifically, the S/N of the received light is improved by 3 dB. 
     Note that the table shown in FIG. 2 is strictly an example, and other examples applicable to this embodiment exist. The way to prepare such tables will be explained below 
     (1) Connection of the First I/O Port 
     The port  1  of the first I/O port group is connected to the transmitting and receiving apparatus ( 1 ), and the port  2  is connected to the transmitting and receiving apparatus ( 2 ). The port  3  is connected to the transmitting and receiving apparatus ( 3 ), and the port  4  is connected to the transmitting and receiving apparatus ( 4 ). 
     (2) Determination of Directions of the Optical Signals 
     Direction of the optical signal in each column of the table (direction of the arrow) will be any one of the following cases 1 to 4: 
     Case 1. . . . The following optical signals will be directed to the right, and the remaining will be directed to the left. 
     the optical signal between the port  1  of the first I/O port group and the port  1  of the second I/O port group 
     the optical signal between the port  1  of the first I/O port group and the port  3  of the second I/O port group 
     the optical signal between the port  4  of the first I/O port group and the port  1  of the second I/O port group 
     the optical signal between the port  4  of the first I/O port group and the port  3  of the second I/O port group 
     the optical signal between the port  2  of the first I/O port group and the port  2  of the second I/O port group 
     the optical signal between the port  2  of the first I/O port group and the port  4  of the second I/O port group 
     the optical signal between the port  3  of the first I/O port group and the port  2  of the second I/O port group 
     the optical signal between the port  3  of the first I/O port group and the port  4  of the second I/O port group 
     Case 2. . . . The following optical signals will be directed to the right and the remaining will be directed to the left. 
     the optical signal between the port  2  of the first I/O port group and the port  1  of the second I/O port group 
     the optical signal between the port  2  of the first I/O port group and the port  3  of the second I/O port group 
     the optical signal between the port  3  of the first I/O port group and the port  1  of the second I/O port group 
     the optical signal between the port  3  of the first I/O port group and the port  3  of the second I/O port group 
     the optical signal between the port  1  of the first I/O port group and the port  2  of the second I/O port group 
     the optical signal between the port  1  of the first I/O port group and the port  4  of the second I/O port group 
     the optical signal between the port  4  of the first I/O port group and the port  2  of the second I/O port group 
     the optical signal between the port  4  of the first I/O port group and the port  4  of the second I/O port group 
     Case 3. . . . The following optical signals will be directed to the right, and the remaining will be directed to the left. 
     the optical signal between the port  1  of the first I/O port group and the port  1  of the second I/O port group 
     the optical signal between the port  1  of the first I/O port group and the port  3  of the second I/O port group 
     the optical signal between the port  2  of the first I/O port group and the port  1  of the second I/O port group 
     the optical signal between the port  2  of the first I/O port group and the port  3  of the second I/O port group 
     the optical signal between the port  3  of the first I/O port group and the port  2  of the second I/O port group 
     the optical signal between the port  3  of the first I/O port group and the port  4  of the second I/O port group 
     the optical signal between the port  4  of the first I/O port group and the port  2  of the second I/O port group 
     the optical signal between the port  4  of the first I/O port group and the port  4  of the second I/O port group 
     Case 4. . . . The following optical signals will be directed to the right, and the remaining will be directed to the left. 
     the optical signal between the port  3  of the first I/O port group and the port  1  of the second I/O port group 
     the optical signal between the port  3  of the first I/O port group and the port  3  of the second I/O port group 
     the optical signal between the port  4  of the first I/O port group and the port  1  of the second I/O port group 
     the optical signal between the port  4  of the first I/O port group and the port  3  of the second I/O port group 
     the optical signal between the port  1  of the first I/O port group and the port  2  of the second I/O port group 
     the optical signal between the port  1  of the first I/O port group and the port  4  of the second I/O port group 
     the optical signal between the port  2  of the first I/O port group and the port  2  of the second I/O port group 
     the optical signal between the port  2  of the first I/O port group and the port  4  of the second I/O I/O port group 
     (3) Connection of the Second I/O Port Group 
     In accordance with the direction of the optical signal, that is, the cases 1 to 4, each port of the second I/O port group and the transmitting and receiving apparatuses ( 1 ) to ( 4 ) are connected as follows: 
     For the cases 1 and 2. . . . The ports of the second I/O port group and the transmitting and receiving apparatuses ( 1 ) to ( 4 ) are connected in any one of the following manners: 
     The port  1  of the second I/O port group is connected to the transmitting and receiving apparatus ( 1 ), and the port  2  is connected to the transmitting and receiving apparatus ( 2 ). The port  3  is connected to the transmitting and receiving apparatus ( 4 ) and the port  4  is connected to the transmitting and receiving apparatus ( 3 ). 
     The port  1  of the second I/O port group is connected to the transmitting and receiving apparatus ( 4 ), and the port  2  is connected to the transmitting and receiving apparatus ( 2 ). The port  3  is connected to the transmitting and receiving apparatus ( 1 ) and the port  4  is connected to the transmitting and receiving apparatus ( 3 ). 
     The port  1  of the second I/O port group is connected to the transmitting and receiving apparatus ( 1 ), and the port  2  is connected to the transmitting and receiving apparatus ( 3 ). The port  3  is connected to the transmitting and receiving apparatus ( 4 ) and the port  4  is connected to the transmitting and receiving apparatus ( 2 ). 
     The port  1  of the second I/O port group is connected to the transmitting and receiving apparatus ( 4 ), and the port  2  is connected to the transmitting and receiving apparatus ( 3 ). The port  3  is connected to the transmitting and receiving apparatus ( 1 ) and the port  4  is connected to the transmitting and receiving apparatus ( 2 ). 
     The port  1  of the second I/O port group is connected to the transmitting and receiving apparatus ( 2 ), and the port  2  is connected to the transmitting and receiving apparatus ( 1 ). The port  3  is connected to the transmitting and receiving apparatus ( 3 ) and the port  4  is connected to the transmitting and receiving apparatus ( 4 ). 
     The port  1  of the second I/O port group is connected to the transmitting and receiving apparatus ( 3 ), and the port  2  is connected to the transmitting and receiving apparatus ( 1 ). The port  3  is connected to the transmitting and receiving apparatus ( 2 ) and the port  4  is connected to the transmitting and receiving apparatus ( 4 ). 
     The port  1  of the second I/O port group is connected to the transmitting and receiving apparatus ( 2 ), and the port  2  is connected to the transmitting and receiving apparatus ( 4 ). The port  3  is connected to the transmitting and receiving apparatus ( 3 ) and the port  4  is connected to the transmitting and receiving apparatus ( 1 ). 
     The port  1  of the second I/O port group is connected to the transmitting and receiving apparatus ( 3 ), and the port  2  is connected to the transmitting and receiving apparatus ( 4 ). The port  3  is connected to the transmitting and receiving apparatus ( 2 ) and the port  4  is connected to the transmitting and receiving apparatus ( 1 ). 
     For the cases 3 and 4. . . . Connection is made in any one of the following manners: 
     The port  1  of the second I/O port group is connected to the transmitting and receiving apparatus ( 1 ), and the port  2  is connected to the transmitting and receiving apparatus ( 3 ). The port  3  is connected to the transmitting and receiving apparatus ( 2 ) and the port  4  is connected to the transmitting and receiving apparatus ( 4 ). 
     The port  1  of the second I/O pot group is connected to the transmitting and receiving apparatus ( 2 ), and the port  2  is connected to the transmitting and receiving apparatus ( 3 ). The port  3  is connected to the transmitting and receiving apparatus ( 1 ) and the port  4  is connected to the transmitting and receiving apparatus ( 4 ). 
     The port  1  of the second I/O port group is connected to the transmitting and receiving apparatus ( 1 ), and the port  2  is connected to the transmitting and receiving apparatus ( 4 ). The port  3  is connected to the transmitting and receiving apparatus ( 2 ) and the port  4  is connected to the transmitting and receiving apparatus ( 3 ). 
     The port  1  of the second I/O port group is connected to the transmitting and receiving apparatus ( 2 ), and the port  2  is connected to the transmitting and receiving apparatus ( 4 ). The port  3  is connected to the transmitting and receiving apparatus ( 1 ) and the port  4  is connected to the transmitting and receiving apparatus ( 3 ). 
     The port  1  of the second I/O port group is connected to the transmitting and receiving apparatus ( 3 ), and the port  2  is connected to the transmitting and receiving apparatus ( 1 ). The port  3  is connected to the transmitting and receiving apparatus ( 4 ) and the port  4  is connected to the transmitting and receiving apparatus ( 2 ). 
     The port  1  of the second I/O port group is connected to the transmitting and receiving apparatus ( 4 ), and the port  2  is connected to the transmitting and receiving apparatus ( 1 ). The port  3  is connected to the transmitting and receiving apparatus ( 3 ) and the port  4  is connected to the transmitting and receiving apparatus ( 2 ). 
     The port  1  of the second I/O port group is connected to the transmitting and receiving apparatus ( 3 ), and the port  2  is connected to the transmitting and receiving apparatus ( 2 ). The port  3  is connected to the transmitting and receiving apparatus ( 4 ) and the port  4  is connected to the transmitting and receiving apparatus ( 1 ). 
     The port  1  of the second I/O port group is connected to the transmitting and receiving apparatus ( 4 ), and the port  2  is connected to the transmitting and receiving apparatus ( 2 ). The port  3  is connected to the transmitting and receiving apparatus ( 3 ) and the port  4  is connected to the transmitting and receiving apparatus ( 1 ). 
     The table is completed by the above-described manners (1) to (3). The table completed in such ways satisfies the following conditions {circle around (1)} to {circle around (5)}. Note that in this embodiment N is four. 
     {circle around (1)} The ports  1  to N of the first I/O port group are connected to different transmitting and receiving apparatuses among the transmitting and receiving apparatuses ( 1 ) to (N), respectively. Moreover, the ports  1  to N of the second I/O port group are connected to different transmitting and receiving apparatuses among the transmitting and receiving apparatuses ( 1 ) to (N), respectively. 
     {circle around (2)} The input/output combinations between the first and second I/O port groups have the periodic wavelength demultiplexing property. To be more specific, each of N optical signals, which has a different wavelength from the others, is transmitted at each of N paths between any one of the ports of the first I/O port group and N ports of the second I/O port group. Moreover, each of N optical signals, which has a different wavelength from the others, is transmitted at each of N paths between any one of the ports of the second I/O port group and N ports of the first I/O port group. As a result, among N×N port combinations made by the N ports of the first I/O port group and the N ports of the second I/O port group, there are N port combinations for each wavelength, through which optical signals having the same wavelength are transmitted. 
     {circle around (3)} Among the N port combinations made by any one of the ports of the first I/ 0  port group and each port of the second I/O port group, the optical signals are transmitted from the first I/O port group to the second I/O port group through the N/2 port combinations, and the optical signals are transmitted from the second I/O port group to the first I/O port group through the remaining port combinations. 
     {circle around (4)} Among the N port combinations through which optical signals having an equal wavelength are transmitted, the optical signals are transmitted from the first I/O port group to the second I/O port group through the N/2 port combinations, and the optical signals are transmitted from the second I/O port group to the first I/O port group through the remaining port combinations. 
     {circle around (5)} The ports of the second I/O port group to which the optical signals are transmitted from the ports of the first I/O port group connected to any one of the transmitting and receiving apparatuses and the ports of the first I/O port group to which the optical signals are transmitted from the ports of the second I/O port group connected to this transmitting and receiving apparatus are respectively connected to different transmitting and receiving apparatuses. 
     In the above described conditions {circle around (1)} to {circle around (5)}, the number of the port combinations through which the optical signals are transmitted from the first I/O port group to the second I/O port group are made to be equal to that of the port combinations through which the optical signals are transmitted from the second I/O port group to the first I/O port group, that is, N/2. However, both numbers need not to be equal necessarily. Note that if both numbers are made to be equal, the best communication quality can be achieved. 
     Embodiment 2 
     FIG. 5 is a block diagram for explaining a second embodiment of the present invention, which shows a schematic constitution of the full-mesh WDM transmission network device in which the number N is increased to eight from four in the first embodiment. In FIG. 5, reference numerals  91  denotes a transmitting and receiving apparatus;  92  and  93 , transmitters for transmitting a WDM signal (wavelength λ K : K=1 to 8);  94  and  95 , receivers for receiving the WDM signal (wavelength λ K : K=1 to 8);  96  and  97 , 1×8 wavelength multi/demultiplexes for multiplexing four optical signals having different wavelengths onto one optical fiber and demultiplexing a WDM signal wavelength-multiplexed onto one optical fiber, into four optical signals;  98 , an 8×8 wavelength multi/demultiplexer having a first I/O port group (ports  1  to  8  on the left side) composed of eight ports and a second I/O port group (ports  1  to  8  on the right side) composed of eight ports, the 8×8 wavelength multi/demultiplexer showing a periodic wavelength demultiplexing property in input/output combination, and  99  and  100 , optical fibers for optically connecting the transmitting and receiving apparatus  91  and the I/O ports of the 8×8 wavelength multi/demultiplexer  98 . Although the 8×8 wavelength multi/demultiplexer  98  is connected to the eight transmitting and receiving apparatuses, illustrations for the seven transmitting and receiving apparatuses other than the transmitting and receiving apparatus ( 1 )  91  are omitted. In FIG. 5, the wavelength (wavelength λ K : K=1 to 8) of the WDM signals transmitted through the optical fibers  99  and  100 , the WDM signals being wavelength-multiplexed, and the transmission directions of the WDM signals, indicated by the arrow, are illustrated. 
     In this embodiment, a 1×8 AWG was used as the 1×8 wavelength multi/demultiplexes  96  and  97 , and an 8×8 AWG having a periodic wavelength demultiplexing property in input/output combination was used as the 8×8 wavelength multi/demultiplexer  98 . Constituent components including the transmitter, the receiver, the 1×8 AWG, the 8×8 AWG and the optical fiber, which constitute the full-mesh WDM transmission network device of this embodiment, are identical to those of the prior art. Although the 1×8 AWG was conventionally used exclusively for the wavelength multiplexer or the wavelength demultiplexing circuit, this embodiment of the present invention uses the 1×8 AWG for the wavelength multi/demultiplexer that performs the wavelength multiplexing and demultiplexing simultaneously, similarly to the first embodiment. 
     FIG. 6 is a table showing a periodic wavelength demultiplexing property in input/output combination of the 8×8 AWG and a port connection rule between the transmitting and receiving apparatuses and the 8×8 AWG in this embodiment of the present invention. Although the wavelength demultiplexing property of the 8×8 AWG is the same as that of the prior art, the connection relation between the transmitting and receiving apparatuses and the second I/O port group of the 8×8 AWG is different from that of the prior art similarly to the first embodiment. Moreover, the 8×8 AWG performs bi-directional input/output for the optical signals. 
     In this embodiment, the four optical signals among the eight optical signals having the equal wavelength are input from the first I/O port group side to the 8×8 AWG, and other four optical signals are input from the second I/O port group side thereto. Since lightwaves which are traveling in opposite directions are independent from each other, a predetermined WDM wavelength light output from the port of the AWG includes only one optical signal and three coherent crosstalk lights. For example, as shown in FIG. 7, the light having the wavelength λ 3 , which is output from the port  2  of the second I/O port group, includes only the optical signal λ 3  (thick solid line) input from the port  2  of the first I/O port group and the crosswalk lights (thin solid line) of the optical signals λ 3  input from the ports  1 ,  5  and  6  of the first I/O port group, and does not include the crosswalk lights of the optical signals λ 3  input from the ports  1 ,  4 ,  5  and  8  of the second I/O port group. Specifically, the accumulation number of the coherent crosstalk lights is reduced to three from seven that is the accumulation number in the prior art. 
     In this embodiment, since the four optical signals having the equal wavelength, which are input from the first I/O port group side, are input from the ports  1 ,  2 ,  5  and  6  or the ports  3 ,  4 ,  7  and  8  and the four optical signals having the equal wavelength, which are input from the second I/O port group side, are input from the ports  1 ,  4 ,  5  and  8  or the ports  2 ,  3 ,  6  and  7 , respectively, three coherent crosstalk lights included in the output WDM wavelength fight are one adjacent crosstalk light and two non-adjacent crosstalk lights. Accordingly, in the full-mesh WDM transmission network device of this embodiment, the S/N of the WDM wavelength light received is expressed as follows. 
     
       
         S/N= P   Signal   /[P   AdjCT +2 P   OthCT ]  (3) 
       
     
     The S/N is equal to 29 dB when P AdjCT /P Signal  is assumed to be −30 dB and P OthCT /P Signal  is assumed to be −40 dB, respectively, and the S/N is improved by 3 dB compared to 26 dB in the prior art. 
     FIG. 8 is a diagram for explaining wavelength addressing in this embodiment. In FIG. 8, reference numerals  101  to  108  denote eight transmitting and receiving apparatuses, and reference numeral  109  denotes an 8×8 AWG. The wavelength demultiplexing property of the 8×8 AWG and the connection relation between the transmitting and receiving apparatuses and the 8×8 AWG are explained in FIG.  6 . For example, the optical signal having the wavelength λ 6 , transmitted from the transmitting and receiving apparatus ( 1 )  101 , is guided to the port  5  of the second I/O port group in the 8×8 AWG, and switched within the 8×8 AWG  109 . This optical signal is then sent to the transmitting and receiving apparatus ( 2 )  102  from the port  2  of the first I/O port group. Similarly, the return signal λ 4  transmitted from the transmitting and receiving apparatus ( 2 )  102  is guided to the port  4  of the second I/O port group in the 8×8 AWG  109 , and then sent to the transmitting and receiving apparatus ( 1 )  101  from the port  1  of the first I/O port group. Moreover, the optical signals having the wavelengths λ 5  andλ 7 , transmitted from the transmitting and receiving apparatus ( 1 )  101 , for example, are automatically delivered to the transmitting and receiving apparatus ( 5 )  105  and the transmitting and receiving apparatus ( 3 )  103 , respectively. 
     As described above, the full-mesh WDM transmission network device in this embodiment uses the constituent components similar to those of the prior art, and keeps the similar wavelength addressing function, while reducing the accumulation number of the coherent crosstalk lights included in each WDM wavelength light to three from seven, thus realizing higher quality communication. Specifically, the S/N of the received light is improved by 3 dB. 
     Embodiment 3 
     FIG. 9 is a block diagram for explaining a third embodiment of the present invention, which shows a schematic constitution of the full-mesh WDM transmission network device in which the number N is increased to  16  compared to the first and the second embodiments. In FIG. 9, reference numeral  111  denotes a transmitting and receiving apparatus;  112  and  113 , transmitters for transmitting a WDM signal (wavelength λ K : K=1 to 16);  114  and  115  , receivers for receiving the WDM signal (wavelength λ K : K=1 to 16);  116  and  117 , 1×16 wavelength multi/demultiplexes for multiplexing eight optical signals having different wavelengths onto one optical fiber and demultiplexing a WDM signal wavelength-multiplexed onto one optical fiber, into eight optical signals;  118 , a 16×16 wavelength multi/demultiplexer having a first I/O port group (ports  1  to  16  on the left side) composed of sixteen ports and a second I/O port group (ports  1  to  16  on the right side) composed of sixteen ports, the 16×16 wavelength multi/demultiplexer showing a periodic wavelength demultiplexing property in input/output combination; and  119  and  120 , optical fibers for optically connecting the transmitting and receiving apparatus  111  and the I/O ports of the 16×16 wavelength multi/demultiplexer  118 . Although the 16×16 wavelength multi/demultiplexer  118  is connected to the sixteen transmitting and receiving apparatuses, illustrations for the fifteen transmitting and receiving apparatuses other than the transmitting and receiving apparatus ( 1 )  111  are omitted. In FIG. 9, illustrated are the wavelength λ K : K=1 to 16) of the WDM signals transmitted through the optical fibers  119  and  120 , the WDM signals being wavelength-multiplexed, and the transmission directions of the WDM signals, indicated by the arrow. 
     In this embodiment, a 1×16 AWG was used as the 1×16 wavelength multi/demultiplexes  116  and  117 , and a 16×16 AWG having a periodic wavelength demultiplexing property in input/output combination was used as the 16×16 wavelength multi/demultiplexer  118 . Constituent components including the transmitter the receiver, the 1×16 AWG, the 16×16 AWG and the optical fiber, which constitute the full-mesh WDM transmission network device of this embodiment, are identical to those of the prior art. Although the 1×16AWG was conventionally used exclusively for the wavelength multiplexer or the wavelength demultiplexing circuit, this embodiment of the present invention uses the 1×16 AWG for the wavelength multi/demultiplexer that performs the wavelength multiplexing and demultiplexing simultaneously, similarly to the first and second embodiments. 
     FIG. 10 is a table showing a periodic wavelength demultiplexing property in input/output combination of the 16×16 AWG and a port connection rule between the transmitting and receiving apparatuses and the 16×16 AWG in this embodiment of the present invention. Although the wavelength demultiplexing property of the 16×16 AWG is the same as that of the prior art, the port connection rule between the transmitting and receiving apparatuses and the second I/O port group of the 16×16 AWG is different from that of the prior art, similarly to the first and second embodiments. Moreover, the 16×16 AWG performs bi-directional input/output for the optical signals. 
     In this embodiment, the eight optical signals among the sixteen optical signals having the equal wavelength are input from the first I/O port group side to the 16×16 AWG, and other eight optical signals are input from the second I/O port group side thereto. Since lightwaves which are traveling in opposite directions are independent from each other, a predestined WDM wavelength light output from the port of the AWG includes only one optical signal and seven coherent crosstalk lights. For example, as shown in FIG. 11, the light having the wavelength λ 3 , which is output from the port  2  of the second I/O port group, includes only the optical signal λ 3  (thick solid line) input from the port  2  of the first I/O port group and the crosstalk lights (thin solid line) of the optical signals  3  input from the ports  1 ,  5 ,  6 ,  9 ,  10 ,  13 , and  14  of the first I/O port group, and does not include the crosstalk lights of the optical signal  13  input from the ports  1 ,  4 ,  5 ,  8 ,  9 ,  12 ,  13 , and  16  of the second I/O port group. Specifically, the accumulation number of the coherent crosstalk lights is reduced to seven from fifteen that is the accumulation number in the prior art. 
     In this embodiment since the eight optical signals having the equal wavelength, which are input from the first I/O port group side, are input from the ports  1 ,  2 ,  5 ,  6 ,  9 ,  10 ,  13 , and  14  or the ports  3 ,  4 ,  7 ,  8 ,  11 ,  12 ,  15 , and  16  and the eight optical signals having the equal wavelength, which are input from the second I/O port group side, are input from the ports  1 ,  4 ,  5 ,  8 ,  9 ,  12 ,  13 , and  16  or the ports  2 ,  3 ,  6 ,  7 ,  10 ,  11 ,  14 , and  15 , seven coherent crosstalk lights included in the output WDM wavelength light are one adjacent crosstalk light and six non-adjacent crosstalk lights. Accordingly, in the full-mesh WDM transmission network device of this embodiment, the S/N of the WDM wavelength light received is expressed as follows: 
     
       
         S/N= P   Signal   /[P   AdjCT +6 P   OthCT ]  (4) 
       
     
     The S/N is equal to 28 dB when P AdjCT /P Signal  is assumed to be −30 dB and P OthCT /P Signal  is assumed to be −40 dB, respectively, and the S/N is improved by 3 dB compared to 25 dB in the prior art. 
     FIG. 12 is a diagram for explaining wavelength addressing in this embodiment. In FIG. 12, reference numerals  121  to  136  denote sixteen transmitting and receiving apparatuses, and reference numeral  137  denotes a 16×16 AWG. The wavelength demultiplexing property of the 16×16 AWG and the connection relation between the transmitting and receiving apparatuses and the 16×16 AWG are explained in FIG.  10 . For example, the optical signal having the wavelength λ 10 , transmitted from the transmitting and receiving apparatus ( 1 )  121 , is guided to the port  9  of the second I/O port group in the 16×16AWG  137 , and switched within the 16×16 AWG  137 . This optical signal is then sent to the transmitting and receiving apparatus ( 2 )  122  from the port  2  of the first I/O port group. Similarly, the return signal λ 8  transmitted from the transmitting and receiving apparatus ( 2 )  122  is guided to the port  8  of the second I/O port group in the 16×16 AWG  137 , and then sent to the transmitting and receiving apparatus ( 1 )  121  from the port  1  of the first I/O port group. Moreover, the optical signals having the wavelengths λ 6 and λ 9 , transmitted from the transmitting and receiving apparats ( 1 )  121 , for example, are automatically delivered to the transmitting and receiving apparatus ( 6 )  126  and the transmitting and receiving apparatus ( 9 )  129 , respectively. 
     As described above, the full-mesh WDM transmission network device in this embodiment uses the constituent components similar to those of the prior art, and keeps the similar wavelength addressing function, while reducing the accumulation number of the coherent crosstalk lights included in each WDM wavelength light to seven from fifteen, thus realizing higher quality communication. Specifically, the S/N of the received light is improved by 3 dB. 
     Embodiment 4 
     FIG. 13 is a block diagram for explaining a fourth embodiment of the present invention, which shows a schematic constitution of a full-mesh WDM transmission network device having a different connection constitution from that of the first embodiment, in which the number N is four. Referring to FIG. 13, reference numerals  141  to  144  denote a transmitting and receiving apparatus;  145  to  152 , a transmitter for sending a WDM signal (wavelength λ K : K=1, 2, 3, 4);  153  to  160 , a receiver for receiving a WDM signal (wavelength λ K : K=1, 2, 3, 4);  161  to  168 , a 1×4 wavelength multi/demultiplexer which multiplexes two optical signals of different wavelengths onto one optical fiber and demultiplexes a WDM signal wavelength-multiplexed on one optical fiber, into two optical signals of different wavelengths;  169 , a 4×4 wavelength multi/demultiplexer having a first I/O port group ( 1  to  4  on the left side) composed off our ports and a second I/O port group ( 1  to  4  on the right side) composed of four ports, the 4×4 wavelength multi/demultiplexer having a periodic wavelength demultiplexing property in input/output combination; and  170  to  177 , an optical fiber for optically connecting each of the transmitting and receiving apparatuses  141  to  144  and the I/O port of each of the 4×4 wavelength multi/demultiplexer  169 . In FIG. 13, shown are the wavelengths (λ K : K=1, 2, 3, 4) of the WDM signals transmitted on the corresponding optical fibers  170  to  177 , the WDM signals being wavelength-multiplexed, and the transmission directions (arrow) thereof. 
     In this embodiment, as the 1×4 wavelength multi/demultiplexes  161  to  168 , a 1×4 AWG was used, and as the 4×4 wavelength multi/demultiplexer  169 , a 4×4 AWG having a periodic wavelength demultiplexing property in input/output combination was used. Constituent components including the transmitter, the receiver, the 1×4 AWG, the 4×4 AWG and the optical fiber, which constitute the full-mesh WDM transmission network device of this embodiment, are the same as those of the prior art. Note that although the 1×4 AWG was conventionally used exclusively for the wavelength multiplexer or the wavelength demultiplexing circuit, in this embodiment of the present invention the 1×4 AWG is used for the wavelength multi/demultiplexer which performs the wavelength multiplexing and demultiplexing simultaneously, similarly to the first to third embodiments. 
     FIG. 14 is a table showing a periodic wavelength demultiplexing property in input/output combination of the 4×4 AWG and a port connection rule between the transmitting and receiving apparatuses and the 4×4 AWG in this embodiment. The wavelength demultiplexing property of the 4×4 AWG has the same periodicity as that of the prior art. However the connection relation between the transmitting and receiving apparatuses and the second I/O port group of the 4×4 AWG is different from that of the prior art similarly to the first to third embodiments. A bi-directional input/output of the optical signal is performed. 
     In this embodiment, two optical signals among the four optical signals having an equal wavelength are input from the first I/O port group side to the 4×4 AWG, and other two optical signals are input from the second I/O port group side thereto. Since lightwaves which are traveling in opposite directions are independent from each other, a predetermined WDM wavelength light output from the port of the 4×4 AWG includes only one optical signal and one coherent crosstalk light. For example, as shown in FIG. 15, the light having the wavelength λ 3 , which is output from the port  2  of the second I/O port group, includes only the optical signal λ 3  (thick solid line) input from the port  2  of the first I/O port group and the crosstalk light (thin solid line) of the optical signal λ 3  input from the port  4  of the first I/O port group, and does not include the crosstalk lights of the optical signals λ 3  input from the ports  1  and  3  of the second I/O port group. Specifically, the accumulation number of the coherent crosstalk lights is reduced to one from three, which is the accumulation number in the prior art. 
     In this embodiment, since the two optical signals having the equal wavelength, which are input from the same port group side, are input from the ports which are not adjacent to each other, for example, the ports  1  and  3  or the ports  2  and  4 , one coherent crosstalk light included in the output WDM wavelength light from the 4×4 AWG is a nonadjacent crosstalk light. Accordingly, in the full-mesh WDM transmission network device of this embodiment, the S/N of the WDM wavelength light received is expressed as follows. 
     
       
         S/N= P   Signal   /P   OthCT   (5) 
       
     
     The S/N is equal to 40 dB when P othCT /P signal  is assumed to be −40 dB, and the S/N is improved by 13 dB compared to 27 dB of the prior art. 
     FIG. 16 is a diagram for explaining wavelength addressing in this embodiment. In FIG. 16, reference numerals  181  to  184  denote four transmitting and receiving apparatuses, and reference numeral  185  denotes 4×4 AWG. The wavelength demultiplexing property of the 4×4 AWG and the connection relation between the transmitting and receiving apparatuses and the 4×4 AWG are explained in FIG.  14 . For example, one optical signal having the wavelength λ 1  transmitted from the transmitting and receiving apparatus ( 1 )  181  is guided to the port  4  of the second I/O port group in the 4×4AWG  185 , and switched within the 4×4 AWG  185 . This optical signal is then sent to the transmitting and receiving apparatus ( 2 )  182  from the port  2  of the first I/O port group. Similarly, the return signal λ 2  returned from the transmitting and receiving apparatus ( 2 )  182  is guided to the port  3  of the second I/O port group in the 4×4 AWG  185 , and then sent to the transmitting and receiving apparatus ( 1 )  181  from the port  1  of the first I/O port group. Furthermore, the other optical signal having the wavelength λ 1 , and one optical signal having the wavelength λ 2 , which are transmitted from the transmitting and receiving apparatus ( 1 )  181 , are automatically delivered to the transmitting and receiving apparatuses ( 4 )  184  and ( 3 )  183 , respectively. 
     As described above, the full-mesh WDM transmission network device in this embodiment uses the constituent components similar to those of the prior art, and maintains the same wavelength addressing function, while reducing the accumulation number of the coherent crosstalk lights included in each WDM wavelength light to one from three, thus realizing higher quality communication. Specifically, the S/N of the received light is improved by 13 dB. 
     Note that the table shown in FIG. 14 is strictly an example, and another examples applicable to this embodiment exist. The way to prepare such tables will be explained below. 
     (1) Connection of the First I/O Port 
     The port  1  of the first I/O port group is connected to the transmitting and receiving apparatus ( 1 ), and the port  2  is connected to the transmitting and receiving apparatus ( 2 ). The port  3  is connected to the transmitting and receiving apparatus ( 3 ), and the port  4  is connected to the transmitting and receiving apparatus ( 4 ). 
     (2) Determination of Directions of the Optical Signals 
     Direction of the optical signal in each column of the table (direction of the arrows) will be any one of the following cases 1 to 4. 
     Case 1. . . . The following optical signals will be directed to the right, and the remaining will be directed to the left. 
     the optical signal between the port  1  of the first I/O port group and the port  1  of the second I/O port group 
     the optical signal between the port  1  of the first I/O port group and the port  2  of the second I/O port group 
     the optical signal between the port  2  of the first I/O port group and the port  2  of the second I/O port group 
     the optical signal between the port  2  of the first I/O port group and the port  3  of the second I/O port group 
     the optical signal between the port  3  of the first I/O port group and the port  3  of the second I/O port group 
     the optical signal between the port  3  of the first I/O port group and the port  4  of the second I/O port group 
     the optical signal between the port  4  of the first I/O port group and the port  4  of the second I/O port group 
     the optical signal between the port  4  of the first I/O port group and the port  1  of the second I/O port group 
     Case 2. . . . The following optical signals will be directed to the right, and the remaining will be directed to the left. 
     the optical signal between the port  1  of the first I/O port group and the port  4  of the second I/O port group 
     the optical signal between the port  1  of the first I/O port group and the port  1  of the second I/O port group 
     the optical signal between the port  2  of the first I/O port group and the port  1  of the second I/O port group 
     the optical signal between the port  2  of the first I/O port group and the port  2  of the second I/O port group 
     the optical signal between the port  3  of the first I/O port group and the port  2  of the second I/O port group 
     the optical signal between the port  3  of the first I/O port group and the port  3  of the second I/O port group 
     the optical signal between the port  4  of the first I/O port group and the port  3  of the second I/O port group 
     the optical signal between the port  4  of the first I/O port group and the port  4  of the second I/O port group 
     Case 3. . . . The following optical signals will be directed to the fight and the remaining will be directed to the left. 
     the optical signal between the port  1  of the first I/O port group and the port  3  of the second I/O port group 
     the optical signal between the port  1  of the first I/O port group and the port  4  of the second I/O port group 
     the optical signal between the port  2  of the first I/O port group and the port  4  of the second I/O port group 
     the optical signal between the port  2  of the first I/O port group and the port  1  of the second I/O port group 
     the optical signal between the port  3  of the first I/O port group and the port  1  of the second I/O port group 
     the optical signal between the port  3  of the first I/O port group and the port  2  of the second I/O port group 
     the optical signal between the port  4  of the first I/O port group and the port  2  of the second I/O port group 
     the optical signal between the port  4  of the first I/O port group and the port  3  of the second I/O port group 
     Case 4. . . . The following optical signals will be directed to the right, and the remaining will be directed to the left. 
     the optical signal between the port  1  of the first I/O port group and the port  2  of the second I/O port group 
     the optical signal between the port  1  of the first I/O port group and the port  3  of the second I/O port group 
     the optical signal between the port  2  of the first I/O port group and the port  3  of the second I/O port group 
     the optical signal between the port  2  of the first I/O port group and the port  4  of the second I/O port group 
     the optical signal between the port  3  of the first I/O port group and the port  4  of the second I/O port group 
     the optical signal between the port  3  of the first I/O port group and the port  1  of the second I/O port group 
     the optical signal between the port  4  of the first I/O port group and the port  1  of the second I/O port group 
     the optical signal between the port  4  of the first I/O port group and the port  2  of the second I/O port group 
     (3) Connection of the second I/O port group 
     The ports of the second I/O port group and the transmitting and receiving apparatuses ( 1 ) to ( 4 ) are connected in any one of the following manners. 
     The port  1  of the second I/O port group is connected to transmitting and receiving apparatus ( 4 ), and the port  2  is connected to the transmitting and receiving apparatus ( 3 ). The port  3  is connected to the transmitting and receiving apparatus ( 2 ) and the port  4  is connected to the transmitting and receiving apparatus ( 1 ). 
     The port  1  of the second I/O port group is connected to the transmitting and receiving apparatus ( 3 ), and the port  2  is connected to the transmitting and receiving apparatus ( 2 ). The port  3  is connected to the transmitting and receiving apparatus ( 1 ) and the port  4  is connected to the transmitting and receiving apparatus ( 4 ). 
     The port  1  of the second I/O port group is connected to the transmitting and receiving apparatus ( 2 ), and the port  2  is connected to the transmitting and receiving apparatus ( 1 ). The port  3  is connected to the transmitting and receiving apparatus ( 4 ) and the port  4  is connected to the transmitting and receiving apparatus ( 3 ). 
     The port  1  of the second I/O port group is connected to the transmitting and receiving apparatus ( 1 ), and the port  2  is connected to the transmitting and receiving apparatus ( 4 ). The port  3  is connected to the transmitting and receiving apparatus ( 3 ) and the port  4  is connected to the transmitting and receiving apparatus ( 2 ). 
     The table is completed by the above-described ways (1) to (3). The table completed in such ways satisfies the following condition {circle around (6)} in addition to the conditions {circle around (1)} to {circle around (5)} described in the first embodiment. Note that in this embodiment N is four. 
     {circle around (6)} The wavelengths of all the optical signals transmitted from any one of the ports of one I/O port group to the other I/O port group, are different from a wavelength of any optical signal transmitted from a port adjacent to the said one port toward the other I/O port group. 
     Embodiment 5 
     FIG. 17 is a block diagram for explaining a fifth embodiment of the present invention, which shows a schematic constitution of a full-mesh WDM transmission network device in which the number N is increased to eight compared to the fourth embodiment. Referring to FIG. 17, reference numerals  191  denotes a transmitting and receiving apparatus;  192  and  193 , a transmitter for sending a WDM signal (wavelength λ K : K=1, 2, 3, . . . , 8);  194  and  195 ,a receiver for receiving a WDM signal (wavelength λ K : K=1, 2, 3, . . . , 8);  196  and  197 , a 1×8 wavelength multi/demultiplexer which multiplexes four optical signals of different wavelengths onto one optical fiber and demultiplexes a WDM signal, wavelength-multiplexed onto one optical fiber, into four optical signals;  198 , an 8×8 wavelength multi/demultiplexer having a first I/O port group ( 1  to  8  on the left side) composed of eight ports and a second I/O port group ( 1  to  8  on the right side) composed of eight ports, the 8×8 wavelength multi/demultiplexer having a periodic wavelength demultiplexing property in input/output combination; and  199  and  200 , an optical fiber for optically connecting each of the transmitting and receiving apparatus  191  and the I/O port of the 8×8 wavelength multi/demultiplexer  198 . Although the 8×8 wavelength multi/demultiplexer  198  is connected to the eight transmitting and receiving apparatuses, illustrations for the seven transmitting and receiving apparatuses other than the transmitting and receiving apparatus ( 1 )  191  are omitted. In FIG. 17, shown are the wavelengths (λ K : K=1, 2, 3, . . . , 8) of the WDM signals transmitted on the corresponding optical fibers  199  and  200 , the WDM signals being wavelength-multiplexed, and the transmission directions (arrow) thereof. 
     In this embodiment, as the 1×8 wavelength multi/demultiplexes  196  and  197 , a 1×8 AWG was used, and as the 8×8 wavelength multi/demultiplexer  198 , an 8×8 AWG having a periodic wavelength demultiplexing property in input/output combination was used. Constituent components including the transmitter, the receiver, the 1×8 AWG, the 8×8 AWG and the optical fiber, which constitute the full-mesh WDM transmission network device of this embodiment, are the same as those of the prior art. Note that although the 1×8 AWG was conventionally used exclusively for the wavelength multiplexer or the wavelength demultiplexing circuit, in this embodiment the 1×8 AWG is used as the wavelength multi/demultiplexer which performs the wavelength multiplexing and demultiplexing simultaneously, similarly to the first to fourth embodiments. 
     FIG. 18 is a table showing a periodic wavelength demultiplexing property in input/output combination of the 8×8 AWG and a port connection rule between the transmitting and receiving apparatuses and the 8×8 AWG in this embodiment. The wavelength demultiplexing property of the 8×8 AWG has the same periodicity as that of the prior art. However the connection relation between the transmitting and receiving apparatuses and the second I/O port group of the 4×4 AWG is different from that of the prior art, similarly to the first to third embodiments. A bi-directional input/output of the optical signal is performed. 
     In this embodiment, the four optical signals among the eight optical signals having the equal wavelength are input from the first I/O port group side to the 8×8 AWG, and other four optical signals are input from the second I/O port group side thereto. Since lightwaves which are traveling in opposite directions are independent from each other, a predetermined WDM wavelength light output from the port of the 8×8 AWG includes only one optical signal and thee coherent crosstalk lights. For example, as shown in FIG. 19, the light having the wavelength λ 3 , which is output from the port  2  of the second I/O port group, includes only the optical signal λ 3  (thick solid line) input from the port  2  of the first I/O port group and the crosstalk lights (thin solid line) of the optical signals λ 3  input from the ports  4 ,  6 , and  8  of the first I/O port group, and does not include the crosstalk lights of the optical signals λ 3 input from the ports  1 ,  3 ,  5 , and  7  of the second I/O port group. Specifically, the accumulation number of the coherent crosstalk lights is reduced to three from seven that is the accumulation number in the prior art. 
     In this embodiment since the four optical signals having the equal wavelength which are input from the same port group side, are input from either the ports  1 ,  3 ,  5 , and  7  or the ports  2 ,  4 ,  6 , and  8 , which are not adjacent to each other, three coherent crosstalk lights included in the output WDM wavelength light from the 8×8 AWG are non-adjacent crosstalk lights. Accordingly, in the full-mesh WDM transmission network device of this embodiment the S/N of the WDM wavelength light received is expressed as follows. 
     
       
         S/N= P   Signal /3 P   OthCT   (6) 
       
     
     The S/N is equal to 35 dB when P othCT /P signal  is assumed to be −40 dB, and the S/N is improved by 9 dB compared to 26 dB in the prior art. 
     FIG. 20 is a diagram for explaining wavelength addressing in this embodiment. In FIG. 20, reference numerals  201  to  208  denote eight transmitting and receiving apparatuses, and reference numeral  209  denotes an 8×8 AWG. The wavelength demultiplexing property of the 8×8 AWG and the connection relation between the transmitting and receiving apparatuses and the ports of the 8×8 AWG are explained in FIG.  18 . For example, one optical signal having the wavelength λ 1  transmitted from the transmitting and receiving apparatus ( 1 )  201  is guided to port  8  of the second I/O port group of the 8×8 AWG  209 , and switched within the 8×8 AWG  209 . This optical signal is then sent to the transmitting and receiving apparatus ( 2 )  202  from the port  2  of the first I/O port group. Similarly, the return signal λ 7  returned from the transmitting and receiving apparatus ( 2 )  202  is guided to the port  7  of the second I/O port group in the 8×8 AWG  209 , and then sent to the transmitting and receiving apparatus ( 1 )  201  from the port  1  of the first I/O port group. Furthermore, the optical signals having the wavelengths λ 4  and λ 6 , which are transmitted from the transmitting and receiving apparatus ( 1 )  201 , for example, are automatically delivered to the transmitting and receiving apparatuses ( 5 )  205  and ( 3 )  203 , respectively. 
     As described above, the full-mesh WDM transmission network device in this embodiment uses the constituent components similar to those of the prior art, and keeps the similar wavelength addressing function, while reducing the accumulation number of the coherent crosstalk lights included in each WDM wavelength light to three from seven, thus realizing higher quality communication. Specifically, the S/N of the received light is improved by 9 dB. 
     Embodiment 6 
     FIG. 21 is a block diagram for explaining a sixth embodiment of the present invention, which shows a schematic constitution of a full-mesh WDM transmission network device in which the number N is increased to sixteen compared to the fourth and fifth embodiments. Referring to FIG. 21, reference numerals  211  denotes a transmitting and receiving apparatus;  212  and  213 , a transmitter for sending a WDM signal (wavelength λ K : K=1, 2, 3, . . . , 16);  214  and  215 , a receiver for receiving a WDM signal (wavelength λ K : K=1, 2, 3, . . . , 16);  216  and  217 , a 1×16 wavelength multi/demultiplexer which multiplexes eight optical signals of different wavelengths onto one optical fiber and demultiplexes a WDM signal wavelength-multiplexed on one optical fiber, into eight optical signals of different wavelengths;  218 , a 16×16 wavelength multi/demultiplexer having a first I/O port group ( 1  to  16  on the left side) composed of sixteen ports and a second I/O port group ( 1  to  16  on the right side) composed of sixteen ports, the 16×16 wavelength multi/demultiplexer having a periodic wavelength demultiplexing property in input output combination; and  219  and  220 , an optical fiber for optically connecting each of the transmitting and receiving apparatus  211  and the I/O port of the 16×16 wavelength multi/demultiplexer  218 . Although the 16×16 wavelength multi/demultiplexer  218  is connected to the sixteen transmitting and receiving apparatuses, illustrations for the fifteen transmitting and receiving apparatuses other than the transmitting and receiving apparatus ( 1 )  211  are omitted. In FIG. 21, shown are the wavelengths (λ K : K 1, 2, 3, . . . , 16) of the WDM signals transmitted on the corresponding optical fibers  219  and  220 , the WDM signals being wavelength-multiplexed, and the transmission directions (arrow) thereof. 
     In this embodiment, as the 1×16 wavelength multi/demultiplexes  216  and  217 , a 1×16 AWG was used, and as the 16×16 wavelength multi/demultiplexer  218 , a 16×16 AWG having a periodic wavelength demultiplexing property in input/output combination was used. Constituent components including the transmitter, the receiver, the 1×16 AWG, the 16×16 AWG and the optical fiber, which constitute the fir-mesh WDM transmission network device of this embodiment, are the same as those of the port art. Note that although the 1×16 AWG was conventionally used exclusively for the wavelength multiplexer or the wavelength demultiplexing circuit, in this embodiment the 1×16 AWG is used as the wavelength multi/demultiplexer which performs the wavelength multiplexing and demultiplexing simultaneously, similarly to the first to fifth embodiments. 
     FIG. 22 is a table showing a periodic wavelength demultiplexing property in input/output combination of the 16×16 AWG and a port connection rule between the transmitting and receiving apparatuses and the 16×16 AWG in this embodiment. The wavelength demultiplexing property of the 16×16 AWG has the same periodicity as that of the prior art. However the connection relation between the transmitting and receiving apparatuses and the second I/O port group of the 16×16 AWG is different from that of the prior art, similarly to the first to fifth embodiments. A bi-directional input/output of the optical signal is performed. 
     In this embodiment eight optical signals among the sixteen optical signals having the equal wavelength are input from the first I/O port group side to the 16×16 AWG, and other eight optical signals are input from the second I/O port group side thereto. Since lightwaves which are traveling in opposite directions are independent from each other, a predetermined WDM wavelength light output from the port of the 16×16 AWG includes only one optical signal and seven coherent crosstalk lights. For example, as shown in FIG. 23, the light having the wavelength λ 3 , which is output from the port  2  of the second I/O port group, includes only the optical signal λ 3  (thick solid line) input from the port  2  of the first I/O port group and the crosstalk lights (thin solid line) of the optical signals λ 3  input from the ports  4 ,  6 ,  8 ,  10 ,  12 ,  14 , and  16  of the first I/O port group, and does not include the crosstalk lights of the optical signals λ 3  input from the ports  1 ,  3 ,  5 ,  7 ,  9 ,  11 ,  13 , and  15  of the second I/O port group. Specifically, the accumulation number of the coherent crosstalk lights is reduced to seven from fifteen hat is the accumulation number in the prior art. 
     In this embodiment, since the eight optical signals having the equal wavelength, which are input from the same port group side, are input from either the ports  1 ,  3 ,  5 ,  7 ,  9 ,  11 ,  13 , and  15  or the ports  2 ,  4 ,  6 ,  8 ,  10 ,  12 ,  14 , and  16  which are not adjacent to each other, seven coherent crosstalk lights included in the output WDM wavelength light from the 16×16 AWG are non-adjacent crosstalk lights. Accordingly, in the full-mesh WDM transmission network device of this embodiment, the S/N of the WDM wavelength light received is expressed as follows: 
     
       
         S/N= P   Signal /7 P   OthCT   (7) 
       
     
     The S/N is equal to 32 dB when P otheCT /P signal  is assumed to be −40 dB, and the S/N is improved by 7 dB compared to 25 dB in the prior art. 
     FIG. 24 is a diagram for explaining wavelength addressing in this embodiment. In FIG. 24, reference numerals  221  to  236  denote sixteen transmitting and receiving apparatuses, and reference numeral  237  denotes a 16×16 AWG. The wavelength demultiplexing property of the 16×16 AWG and the connection relation between the transmitting and receiving apparatuses and the ports of the 16×16 AWG are explained in FIG.  22 . For example, one optical signal having the wavelength λ 1  transmitted from the transmitting and receiving apparatus ( 1 )  221  is guided to the port  16  of second I/O port group of the 16×16 AWG  237 , and switched within the 16×16 AWG  237 . This optical signal is then sent to the transmitting and receiving apparatus ( 2 )  222  from the port  2  of the first I/O port group. Similarly, the return signal λ 15  returned from the transmitting and receiving apparatus ( 2 )  222  is guided to the port  15  of the second I/O port group in the 16×16 AWG  237 , and then sent to the transmitting and receiving apparatus ( 1 )  221  from the port  1  of the first I/O port group. Furthermore, the optical signals having the wavelengths λ 8  and λ 11 , which are transmitted from the transmitting and receiving apparatus ( 1 )  221 , for example, are automatically delivered to the transmitting and receiving apparatuses ( 9 )  229  and ( 6 )  226 , respectively. 
     As described above, the full-mesh WDM transmission network device in this embodiment uses the constituent components similar to those of the prior art and maintains the same wavelength addressing function, while reducing the accumulation number of the coherent crosstalk lights included in each WDM wavelength light to seven from fifteen, thus realizing higher quality communication. Specifically, the S/N of the received light is improved by 7 dB. 
     Although the full-mesh optical wavelength division multiplexing transmission network device of the present invention in which N is 4, 8 and 16 in six embodiments, was described, as a matter of course, it is possible to constitute the full-mesh optical wavelength division multiplexing transmission network device of the present invention even when N takes any value. Moreover, the connection relation between the transmitting and receiving apparatuses and the ports of the N×N AWG and the combinations of the transmitting directions of the optical signals between I/O ports in the N×N AWG are not limited to those illustrated in FIGS. 2,  6 ,  10 ,  14 ,  18  and  22 . It is apparent that other connection relations and other combinations, by which the operations similar to those of the embodiments can be realized, are within the spirit and scope of the present invention.