Abstract:
An optical transmission line relayed with multistage optical amplifiers wherein the plurality of optical amplifiers inserted in the optical transmission line include at least two types mixed together: first optical amplifiers including broad band optical filters and second optical amplifiers including narrow band optical filters, whereby the amount of amplified spontaneous emission (ASE) from the optical amplifiers is reduced overall without applying any major frequency band limitation to the signal light spectrum.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to an optical transmission line wherein signal light is relayed by optical amplifiers linked together. 
     In the past, for long distance optical communications, the general practice was to perform optical-electrical conversion at predetermined intervals so as to process the signals as electrical signals to reproduce them, then perform electrical-optical conversion and once again send the converted signals on to the next regenerative repeater. 
     In recent years, however, optical amplifiers have been able to be realized at low cost, so development is being made of commercial optical transmission lines with multistage optical AMP&#39;s connected in cascade instead of the regenerative repeaters. Optical amplifiers are simple in circuit construction compared with the conventional regenerative repeaters, so are higher in reliability and further are lower in costs, so are particularly suitable when used for long distance ocean optical transmission lines. 
     2. Description of the Related Art 
     In general, optical transmission lines relayed with multistage optical amplifiers, as explained in detail later, are comprised of an optical transmission line (optical fiber) and a plurality of optical amplifiers connected in cascade along the optical transmission line. Signal light is transmitted from the input end of the optical transmission line and is relayed successively by the optical amplifiers until it reaches the output terminal of the optical transmission line. The input end is provided with an optical transmitter, while the output terminal side is provided with an optical receiver. 
     In such an optical transmission line relayed with optical amplifiers linked together, each time light is relayed and amplified by the different stages of the optical amplifiers, the amplified spontaneous emission (ASE) increases monotonously. Along with this monotonous increase in the amount of ASE, the nonlinear effects of phase noise, which is caused by the Kerr effect, increase. The nonlinear effects are proportional to the optical power of the amount of ASE of the output signal light from the output terminal of the optical transmission line, so the nonlinear effects increase proportionally with the integral value of the amount of ASE along with distance. 
     The easiest way to reduce the integral value of the amount of ASE along with distance is to reduce the bandwidths of the optical filters provided in the different stages of optical amplifiers. However, if the bandwidths of the optical filters are reduced across the board, there is the new problem that wave distortion occurs in the output signal light. This is because if the bandwidths of the optical filters are reduced across the board, there is a large frequency band limitation in the signal light spectrum. 
     SUMMARY OF THE INVENTION 
     Therefore, the present invention was made in consideration of the above problems and has as its object the provision of an optical transmission line relayed with multistage optical amplifiers which can reduce the amount of ASE. 
     To achieve the above-mentioned object, the present invention provides an optical transmission line relayed with multistage optical amplifiers which are comprised of a combination of both a plurality of optical filters including the center frequency of the signal light and having a bandwidth sufficient for the transmission and a plurality of other optical filters including the center frequency of the signal light and having a variety of types of bandwidths narrower than the above bandwidths. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The above object and features of the present invention will be more apparent from the following description of the preferred embodiments with reference to the accompanying drawings, wherein: 
     FIG. 1 is a view showing a general optical transmission line relayed with multistage optical amplifiers; 
     FIG. 2 is a level diagram showing the changes in the level along the transmission line 10 in FIG. 1; 
     FIG. 3 is a view of the construction of an optical amplifier; 
     FIG. 4 is a graph of the relationship between the ASE and an optical amplifier using the bandwidth of the optical filter as a parameter; 
     FIG. 5 is a view of the basic constitution according to the present invention; 
     FIG. 6 is a view of an embodiment of an optical transmission line according to the present invention; 
     FIG. 7 is a view for explaining the ASE reduction effect in FIG. 6; 
     FIG. 8 is a view of the relationship between the value b and an evaluation function using the value a as a parameter; 
     FIG. 9 is a view of the relationship between the value a and the evaluation function; 
     FIG. 10 is a view of the relationship between the value b and the evaluation function using the value a as a parameter; 
     FIG. 11 is a view of the relationship between the value a and the evaluation function; 
     FIG. 12 is a view of the results of simulation using the optimal value obtained in FIG. 8; 
     FIG. 13 is a view showing the results of simulation using the optimal value obtained in FIG. 10; 
     FIG. 14 is a view of another embodiment of an optical transmission line according to the present invention; 
     FIG. 15 is a view of the changes in the ASE power in FIG. 14; and 
     FIG. 16 is a view of an example wherein a similar change is obtained as with the change of the ASE power shown in FIG. 15 by gradually making narrower the bandwidths of the narrow band optical filters. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Before describing the embodiments of the present invention, the prior art and the problems therein will be first described with reference to the related figures. 
     FIG. 1 is a view of a general optical transmission line relayed with multistage optical amplifiers. In the figure, 10 is an optical transmission line relayed with multistage optical amplifiers and is comprised of an optical transmission line (optical fiber) 12 and a plurality of optical amplifiers 11 connected in cascade along the optical transmission line 12. Signal light is sent from an input end IN of the optical transmission line 12 and is relayed by the optical amplifiers 11 to reach the output terminal OUT of the optical transmission line 12. Note that the input end IN side is provided with the optical transmitter (TX), while the output terminal OUT side is provided with the optical receiver (RX). Reference numeral 13 in the figure is an optical filter which is usually provided just before the receiver (RX). 
     FIG. 2 is a level diagram showing the changes in level along the optical transmission line 10 in FIG. 1. The light amplifying gain (G) of the optical amplifiers 11 and the optical loss (L) at the optical transmission line 12 is considered to be equal (G=L). These values are, for example, G=20 dB and L=20 dB. Further, the noise figure (NF) of the optical amplifiers 11 is considered 8 dB. 
     In the optical transmission line relayed by multistage multistage optical amplifiers shown in FIG. 1, however, the ASE generated at the optical amplifiers 11 becomes noise, so there is the problem that the S/N ratio of the signal light deteriorates. 
     Due to the self phase modulation caused by the so-called Kerr effect and other nonlinear effects of the optical transmission line (optical fiber) 12, an expansion of the spectrum of the signal light occurs. This expansion of the spectrum causes deterioation of the receiving sensitivity of the optical receiver (RX). 
     FIG. 3 shows the constitution of the optical amplifiers. The optical amplifiers 11 are each comprised of an optical amplification unit 15 for amplifying the input signal light OS in  and an optical filter 16 which has as its main object to produce an output signal light OS out  reduced in the amount of ASE. 
     FIG. 4 is a graph showing the relationship of the ASE and an optical amplifier using as a parameter the bandwidth of the optical filter. The graph of the figure will now be explained with reference to the optical transmission line of FIG. 1. For simplicity, as mentioned before, the optical amplifying gain G and the optical loss L are considered both constant and the ASE is also considered constant. Here, the bandwith of the optical fiber at the n-th (n=1, 2, 3 ... ) optical amplifier 11 counted from the input end IN is set as Δf n . This being so, the effective bandwidth Δf eff  of all the optical filters 16 used until the n-th optical amplifier 11 is reached is generally known to be expressed as: 
     
         Δf.sub.eff =[Σ(Δf.sub.k).sup.-2]-1/2 (where Σ is k=1 to k=n) 
    
     This being the case, when the bandwidth of one of the optical filters 16 is constant (Δf n  =Δf c , Δf c  being the constant bandwith), the amount of ASE of the output signal OS out  from the n-th optical amplifier 11 and the effective bandwidth Δf eff  may be expressed by: 
     
         ASE=2n(G-1)N.sub.sp Δf.sub.eff =Δf.sub.c /n.sup.1/2 
    
     However, 2×N sp  shows the ASE per optical amplifier stage. Further, n is the number of the optical amplifiers 11, whose gains G are generally G&gt;&gt;1. 
     Referring to FIG. 4, the graph shows that the amount of ASE increases monotonously with each successively relaying and amplification by the optical amplifiers 11. As already mentioned, along with the monotonous increase in the amount of ASE, the nonlinear effects, such as the Kerr effect, increase. In general, the nonlinear effects are proportional to the optical power of the amount of ASE of the output signal light OS out , so the nonlinear effects increase in proportion to the area of the triangular surface enclosed by the characteristic lines and the horizontal axis in the figure. 
     The triangular area, that is, the integral value of the amount of ASE along with distance, must be reduced. The easiest way to reduce the integral value along with distance is to reduce the bandwidths (Δf nr ) of the optical filters 16 in the optical amplifiers 11 across the board, as mentioned earlier. The characteristic line shown by the dotted line in FIG. 4 shows the amount of ASE when reducing the bandwidths (Δf br ) of the optical filters in the prior art across the board to Δf nr . The triangular area defined by the solid characteristic line under this Δf br  is considerably reduced. That is, the nonlinear effects are suppressed. Note that the &#34;br&#34; in Afar means &#34;broad&#34;, while the &#34;nr&#34; in Δf nr  means &#34;narrow&#34;. 
     According to the above easy method of reducing the bandwidths (Δf n ) of the optical filters 16 across the board, however, a new problem is created. This new problem is that wave distortion ends up occurring in the output signal light OS out . This is because if the bandwidths of the optical filters 16 are reduced too much, it is no longer possible to secure the bandwidth necessary for the transmission of the signal light. That is, since the bandwidths of the optical filters 16 are reduced across the board, the result is that a frequency band limitation is applied to the signal light spectrum. That is, even from the viewpoint of the stability of the optical frequency of the light source in the optical transmitter (TX), there is a limit to the reduction of the bandwidths. 
     A detailed explanation will now be made of the optical transmission line relayed with multistage optical amplifiers of the present invention, which resolves the above problems. 
     FIG. 5 shows the basic constitution according to the present invention. According to the optical transmission line 10 relayed with multistage optical amplifiers of the present invention, a plurality of optical amplifiers 11 are provided comprised of a plurality of optical filters 16-1 having bandwidths (Δf br ) required for transmission of signal light and a plurality of optical filters 16-2, 16-3, 16-4 ... including the central frequency of the signal light and having various types of bandwidths (Δf nr1 , Δf nr2 , Δf nr3 , ... ) narrower than the above-mentioned required bandwidth mixed in with the same. 
     By interposing narrow bandwidths (Δf nr1 , Δf nr2 , Δf nr3 , ... ) here and there among the group of optical filters 16-1 having the usual bandwidth (Δf br ), it is possible to easily optimize the effective combined bandwidth and the amount of ASE compared with the case of making all the optical amplifiers a single type of optical amplifier and therefore it is possible to reduce the amount of ASE without applying that much of a frequency band limitation to the signal light spectrum. 
     FIG. 6 shows an embodiment of an optical transmission line according to the present invention. In the figure, 11 is the above-mentioned first optical amplifier and 21 is the second optical amplifier introduced according to the present invention. That is, the optical transmission line 10 relayed with multistage optical amplifiers according to this embodiment is comprised of a plurality of first optical amplifiers 11 each provided with a broad band optical filter 16-1 including the center frequency f 0  of the signal light and having a desired bandwidth Δf br , a plurality of second optical amplifiers (shown by hatching) 21 each provided with a narrow band optical filter 16-2 including the central frequency f 0  of the signal light and having a bandwidth Δf nr  smaller than the bandwidth of the broad-band optical filters, and an optical transmission line 12 connecting these optical amplifiers 11 and 21. 
     FIG. 7 is a view for explaining the effect of reduction of the amount of ASE in FIG. 6 and shows the output light of the n-th stage optical amplifier. The horizontal axis shows the optical frequency, while the vertical axis direction shows the optical power level. In parallel with the axis of the optical frequency, the bandwidth Δf br  of the broad band optical filters and the bandwidths Δf nr  of the narrow band optical filters are shown at the top of the figure. The hatched areas in the figure show the state of accumulation of the ASE by the optical amplifiers 11 with the built-in broad band optical filters from the first stage optical amplifier 11 (including broad band optical filter 16-1) to the ninth stage optical amplifier 11 (including broad band optical filter 16-1). The number of stages (9) is only an example. 
     At the 10th stage second optical amplifier 21 (among the three second optical amplifiers 21 in FIG. 6, corresponding to the optical amplifier at the side nearest the input end IN), the accumulated ASE is cut off by the narrow band optical filter (bandwidth Δf nr ) included within it. However, the signal light having as the central frequency the frequency f 0  positioned at the center of the bandwidth Δf nr  or near the same passes through as it is. Here, it is possible to reduce the amount of ASE without applying that much of a frequency band limitation on the signal light spectrum. In this case, it is not possible to provide narrow band optical filters with the bandwidths Δf nr  for all of the first to the 10th optical amplifiers. The reason is that if all are made narrow band optical filters, the signal light will be transmitted with a band narrower than the desired bandwidth (Δf br ) required for the transmission of the signal light. In the end, the amount of ASE would be reduced, but the basic signal light spectrum would also be reduced and this would invite wave distortion. Therefore, in the conventional optical transmission line (FIG. 1), all the optical amplifiers 11 had to be provided with broad band optical filters. 
     The phenomenon of FIG. 7 will be explained in more detail using numeral equations. As mentioned earlier, if the bandwidth of the broad band optical filter 16-1 in the first optical amplifier 11 is set as Δf br  and the bandwith of the narrow band optical filter 16-2 in the second optical amplifier 21 is set as Δf nr , then Δf br  &gt;Δf nr  stands. Here, the ratio (a) between the value of the bandwidth Δf nr  of the narrow band optical filter 16-2 and the value of the bandwidth Δf br  of the broad band optical filter 16-1 will be defined. That is, 
     
         a=Δf.sub.br /Δf.sub.nr 
    
     Further, the total number of the optical amplifiers (11, 21) is set as n and the number of the second optical amplifiers 21 having the narrow band optical filters is set as b. 
     Here, the effective bandwidth Δf eff  of all the optical amplifiers is 
     
         Δf.sub.eff =[(n-b)Δf.sub.br.sup.-2 +bΔf.sub.nr.sup.-2]-1/2 
    
     If the above-mentioned a=Δf br  /Δf nr  is substituted for the Δf br  in the equation, then it is possible to express it as: 
     
         Δf.sub.eff =Δf.sub.nr /[(n-b)/a.sup.2 +b].sup.1/2 
    
     On the other hand, when the bandwidth is a single type such as in FIG. 4, the integral value of the amount of ASE along with distance, that is, the area corresponding to the triangle in FIG. 4, is set as S 1 , then S 1  is expressed as follows using the above-mentioned effective bandwith Δf eff  : 
     
         S.sub.1 =1/2-Δf.sub.eff ·n.sup.1/2 ·n.sup.2 
    
     As opposed to this, as shown in FIG. 6, when assembling two different types of filters, that is, the broad band and narrow band filters, and, as shown in FIG. 6, when inserting and disposing the second optical amplifiers 21 in the plurality of first optical amplifiers 11 at substantially equal intervals, the integral value S 2  of the amount of ASE along with distance can be expressed as 
     
         S.sub.2 =1/2·Δf.sub.eff [(n-b)/a.sup.2 +b].sup.1/2 ]1+(a-1)/b]·n.sup.2 
    
     Further, if the ratio of the S 1  and S 2  is used as an evaluation function, the evaluation function S 2  /S 1  can be expressed as: 
     
         S.sub.2 /S.sub.1 =[(n-b)/a.sup.2 +b].sup.1/2 ·[1+(a-1)/b]/n.sup.1/2 
    
     If the bandwidths (Δf br  and Δf nr ) of the broad band optical filters 16-1 and the narrow band optical filters 16-2 are set and the number (b) of the narrow-band optical filters is set in accordance with the optimal value a 0  of the above value a obtained based on this evaluation function (S 2  /S 1 ) and the optimal value b 0  of the above-mentioned value b, the amount of ASE can be reduced without applying too large a frequency band limitation to the spectrum of the signal light. In the above case, the above-mentioned values a and b when the S 2  /S 1  is made minimum form the optimal values a 0  and b 0 , respectively. 
     The invention will be explained below using specific examples. 
     FIG. 8 is a view of the relationship of the value b and the evaluation function using the value a as a parameter. As the ratio a (=Δf br  /Δf nr ), three types which may be selected (a=2, a=3, a=6) are shown. The total number n of the optical amplifiers, however, is made 50 and the effective bandwidth Δf eff  is made constant. According to what is shown by the calculation data of this figure, the values a and b giving the smallest value of the evaluation function are a=3 and b=6, it is learned. That is, it is most suitable when the ratio a of the bandwidth (Δf nr ) of the narrow-band optical filter 16-2 and the bandwidth (Δf br ) of the broad-band optical filter 16-1 is 3 and of the total 50 optical amplifiers, the number of of narrow band optical filters is six. 
     FIG. 9 shows the relationship between the value a and the evaluation function. This shows the changes in the value of the evaluation function when the value b obtained in FIG. 8 is 6 and the ratio a is made variable. The conditions that n=50 and Δf eff  is constant are the same as in the case of FIG. 8. According to what is shown by the calculation data of the figure, the value a giving the smallest value of the evaluation function is found to be a=3. That is, it was confirmed that it is most suitable when the ratio a (=Δf br  /Δf nr ) of the bandwidth (Δf nr ) of the narrow band optical filter 16-2 and the bandwidth (Δf br ) of the broad band optical filter 16-1 is 3. 
     FIG. 10 shows the relationship between the value b and the evaluation function using the value a as a parameter. As the ratio a (=Δf br  /Δf nr ), three types which may be selected (a=2, a=4, a=10) are shown. The total number n of the optical amplifiers, however, is made 100 and the effective bandwidth Δf eff  is made constant. According to what is shown by the calculation data of this figure, the values a and b giving the smallest value of the evaluation function are a=4 and b=8, it is learned. That is, it is most suitable when the ratio a of the bandwidth (Δf nr ) of the narrow band optical filter 16-2 and the bandwidth (Δf br ) of the broad band optical filter 16-1 is 4 and of the total 100 optical amplifiers, the number of of narrow band optical filters is eight. 
     FIG. 11 shows the relationship between the value a and the evaluation function. This shows the changes in the value of the evaluation function when the value b obtained in FIG. 8 is eight and the ratio a is made variable. The conditions that n=100 and Δf eff  is constant are the same as in the case of FIG. 10. According to what is shown by the calculation data of the figure, the value a giving the smallest value of the evaluation function is found to be a=4. That is, it was confirmed that it is most suitable when the ratio a (=Δf br  /Δf nr ) of the bandwidth (Δf nr ) of the narrow band optical filter 16-2 and the bandwidth (Δf br ) of the broad band optical filter 16-1 is 4. 
     FIG. 12 shows the results of a simulation using the optimum values obtained in FIG. 8. That is, when the total number n of optical amplifiers 11 is 50, the number b of the narrow band optical filters is six, and the value a of the ratio of the bandwidth of the broad band optical filter and the narrow band optical filter is 3, the results of the simulation were that it is possible to reduce the ASE without applying that large a limitation to the frequency band of the signal light spectrum. The horizontal axis in the figure shows the number of stages of the optical amplifiers 11 and 21 from the input end IN to the output terminal OUT along the optical transmission line 12. The vertical axis shows the accumulated value of the amount of the ASE. Here, S 3  shows the integral value of the amount of ASE along with distance in the case of using only broad band optical filters, S 0  shows the integral value of the amount of ASE along with distance in the case of using only narrow band optical filters, and S 2  shows the area defined with the horizontal axis when mixing the two types of broad and narrow band optical filters. The latter is the integral value S 2  of the amount of ASE along with distance mentioned earlier. Further, S 1  is the (prior art) integral value of amount of ASE along with distance in the case of using only one type of optical filter corresponding to an effective bandwith Δf eff . From this figure, it is understood that the effect of reduction of the amount of ASE by the present invention is great. 
     Calculated more specifically, the evaluation function S 2  /S 1  is 0.62 and the amount of ASE is reduced as much as 38 percent. 
     FIG. 13 shows the results of a simulation using the optimum values obtained in FIG. 10. That is, when the total number n of optical amplifiers is 100, the number b of the narrow band optical filters is eight, and the value a of the ratio of the bandwidths of the broad band optical filter and the narrow band optical filter is 4, the results of the simulation were that it is possible to reduce the ASE without applying that large a limitation to the frequency band of the signal light spectrum. The horizontal axis and the vertical axis in the figure and the symbols S 1 , S 2 , and S 3  has the same meanings as in FIG. 12. As clear from the S 2  in the results of the simulation, when two types of broad and narrow band optical filters are mixed, the area defined with the horizontal axis, that is, the integral value of the amount of ASE along with distance, mentioned earlier, becomes minimum. 
     According to a more specific calculation, the evaluation function S 2  /S 1  becomes 0.51 and it is possible to reduce the amount of ASE 49 percent as well. 
     Note that experimental findings on the state of the art of long distance optical communication were reported in the 17th European Conference on Optical Communication ECOC&#39;91, Post-Deadline Papers; Page 68, S. Saito et al. According to this report, success was achieved in optical communication at a transmission distance of 4500 km at a transmission speed of 2.5 Gb/s by connecting multistages of optical amplifiers in cascade in an intensity-modulation direct detection (IM/DD) system. Further, success was achieved with optical communication at a transmission distance of 2500 km at a transmission speed of 2.5 Gb/s by connecting multistages of optical amplifiers in cascade in a coherent optical communication (heterodyne detection) system. 
     According to the above-mentioned experimental report, the effective bandwith Δf eff  when relaying in n stages using a uniform bandwidth of 3 nm (373 GHz) becomes: 
     [1]When n=50, Δf eff  =52.8 GHz 
     [2]When n=100, Δf eff  =37.3 GHz 
     On the other hand, if the required frequency band of the optical receiver (RX) is made about 3 GHz, the effective bandwidth Δf eff  required of the optical filter 16 has to be about 6 GHz, double that amount. Therefore, if the bandwidths of the optical filters 16-1 and 16-2 giving a Δf eff  of 6 GHz are sought, 
     [1]When n=50, Δf br  =59.4 GHz and Δf nr  =19.8 GHz 
     [2]When n=100, Δf br  =89.0 GHz and Δf nr  =22.3 GHz 
     According to the present invention, if use is made of the above numeral example, first the effect of reduction of the ASE by reducing the bandwidths of the optical filters by using one type of optical filter is 6/52.8 when n=50 and 6/37.3 when n=100. Further, the effect of reduction of the ASE by using two types of optical filters is 0.62 when n=50 and 0.51 when n=100. Due to this multiplier effect, the integral value of the amount of ASE along with distance is reduced as follows: 
     [1]When n=50, (6/52.8)×0.62=0.070 
     [2]When n=100, (6/37.3)×0.51=0.082 
     Giving another numerical example, in the case of fixing the broad bandwidth Δf br  =373 GHz (3 nm), if use is made of 25 (b=25) narrow band optical filters with narrow bandwidths of Δf nr  =31.1 GHz, the value of the evaluation function (S 2  /S 1 ) becomes 
     
         S.sub.2 /S.sub.1 =0.73 
    
     and the integral value of the amount of ASE along with distance is reduced to 
     
         (6/37.3)×0.73=0.117 
    
     In the embodiment explained above, the effect of the reduction of the ASE was evaluated by the value of the ratio of the integral values of the amount of ASE along with distance as S 1  and S 2 . In this case, in general, the saturation output of the optical amplifiers is expressed by the sum of the ASE and the signal light power, so if the ASE increases to an extent where it can no longer be ignored compared with the signal light power, the signal light power ends up being decreased by that amount. Therefore, to prevent a reduction of the signal light power in this way, it is necessary to keep the ASE from exceeding a certain threshold. 
     FIG. 14 shows another embodiment of an optical transmission line according to the present invention and corresponds to FIG. 6. According to the embodiment shown here, to prevent the reduction of the signal light power, the distance for arrangement of the narrow band optical filters 16-2 is made smaller as the proximity to the output terminal OUT of the optical transmission line 12 is reduced. This keeps the ASE power from exceeding a certain threshold. By way of reference, in FIG. 6, the second optical amplifiers 21 are disposed at the same pitch in the group of first optical amplifiers (11). 
     FIG. 15 is a view of the changes in the ASE power in FIG. 14. The horizontal axis shows the number of stages of the optical amplifiers. The distance for insertion of the second optical amplifiers 21 becomes gradually smaller toward the right end. This prevents the ASE power from exceeding a certain threshold. 
     A similar effect to that shown in FIG. 15 can be obtained by gradually decreasing the bandwidths (Δf nr ) of the narrow band optical filters 16-2, 16-3 ... (FIG. 5) toward the right end of FIG. 15 while holding the distance of the insertion position of the second optical amplifiers 21 constant. FIG. 16 shows this. The area S 0  in the case of use of the narrow band optical filter shown in FIG. 13 gradually becomes smaller, such as the area S 4  and the area S 5  ..., by gradually reducing the bandwidths (Δf nr ) toward the right side. As a result, the ASE power is kept from exceeding a certain threshold TH. 
     As explained above, according to the present invention, it is possible to reduce the amount of ASE without applying any major frequency band limitation to the signal light spectrum. For example, in the abovementioned experimental report, there is the possibility that the optical communication distance of 4500 km reached in the above-mentioned experimental report can be extended to about 10,000 km.