Patent Publication Number: US-7212745-B2

Title: Optical transmission system

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to an optical transmission system, and more particularly to a system for transmitting an optical signal from a transmitter to a receiver through a multi-mode fiber. 
   2. Description of the Background Art 
   The development in technologies in recent years has produced optical fibers which satisfy broadband requirements as well as low loss requirements. As a result, optical fibers are being introduced in the backbone systems for interconnecting exchange systems on a network (e.g., the Internet).Optical fibers are considered promising for future applications in access systems for interconnecting exchanges with households, and also applications in home networks. 
   Optical fibers can be generally classified in two types based on their characteristics: single mode fibers (hereinafter referred to as “SMFs ”) and multi-mode fibers (hereinafter referred to as “MMFs ”).In a SMF, both the core and the cladding are made of silica (SiO 2 ). A SMF has a core diameter as small as about 10 μm. Furthermore, a SMF features a broad transmission bandwidth because it only allows a particular mode to be propagated therethrough. Therefore, SMFs have mainly enjoyed developments for long-distance and broadband transmission purposes in the backbone systems, and have gained wide prevalence there. 
   On the other hand, a MMF has a core diameter of 50μm to 1 mm, which is greater than the core diameter of a SMF. MMFs can be classified in several types based on the materials of the core and cladding. MMFs whose core and cladding are both made of silica are called GOFs (Glass Optical Fibers). MMFs whose core is made of silica, and whose cladding is made of a polymer, are called PCFs (Polymer Clad Fibers). MMFs whose core and cladding are both plastic are called POFs (Plastic Optical Fibers). 
   AMMF has a plurality of propagation modes (i.e., optical paths).  FIG. 12  is a schematic diagram illustrating a plurality of propagation modes. In  FIG. 12 , a MMF  73  has a core  71  and a cladding  72 . The entirety of light travels through the core  71  while being repeatedly reflected at the boundary F bd  between the core  71  and the cladding  72  (TIR: Total Internal Reflection). Therefore, modes which are closer to being parallel to the boundary F bd  will travel longer distances over the fiber axis between one reflection and the next reflection. Such modes (denoted by dot-dash lines) are referred to as lower-order modes (M LO ). On the other hand, modes which travel shorter distances over the fiber axis between one reflection and the next reflection (denoted by double-dot-dash lines) are referred to as higher-order modes (M HI ) A higher-order mode M HI  constitutes a relatively large angle with respect to the fiber axis. Therefore, given a fixed length of the MMF  73 , a higher-order mode M HI  will experience a larger number of reflections at the boundary F bd  than a lower-order mode M LO , thus presenting an optical path which is different from that of the lower-order mode M LO  (“optical path difference”). Due to optical path differences, different modes require different amounts of time to travel from an input plane to an output plane of the MMF  73 . 
   An optical signal is transmitted through an optical fiber in the form of a pulse sequence. Since each mode in the optical signal has its own inherent propagation speed, a pulse sequence which is contained in a lower-order mode M LO  (which has a relatively short propagation time) and the same pulse sequence which is contained in a higher-order mode M HI  (which has a relatively long propagation time) will arrive at the receiving end at different times, although directed to the same information. As a result, the receiving end of the information may not be able to correctly receive the signal. This phenomenon, known as mode dispersion, is a factor which considerably constrains the transmission bandwidth of a MMF as compared to that of a SMF. 
   A transmission bandwidth of an optical fiber is usually represented as a product of a data rate for optical signals transmitted therethrough and a transmission distance (e.g., Mbps×km). The transmission distance must be decreased as the data rate is increased. In order to increase the transmission distance, the data rate must be lowered. The influence of mode dispersion also becomes more significant as the data rate is increased, or as the transmission distance is increased. Therefore, conventional optical transmission systems employing MMFs have a problem in that the transmission distance must be compromised in order to obtain a necessary data rate. 
   However, MMFs are less expensive than SMFs. Therefore, on the bare comparison, an optical transmission system employing MMFs should be able to be constructed inexpensively as compared to a system employing SMFs. Moreover, since the core diameter of a MMF is greater than that of a SMF, it is relatively easy to align the axes of two MMFs with each other. This helps relaxing the mounting precision of a connector for interconnecting MMFs. Thus, MMFs can greatly contribute to the construction of a low-cost optical transmission system. Therefore, MMFs are preferred for optical transmission over a distance which is short enough for the mode dispersion effects to be negligible. 
   In order to take advantage of the aforementioned features of MMFs, a number of techniques for reducing the influence of mode dispersion in MMFs and for improving the transmission bandwidth of an optical transmission system have been proposed. With reference to  FIGS. 13 and 14 , a technique disclosed in Japanese Patent Laid-Open Publication No. 10-227935 will be described.  FIG. 13  is a block diagram illustrating the overall structure of a conventional optical transmission system S cv . As shown in  FIG. 13  , the optical transmission system S cv  includes a light source  82  having a lens  81 , a MMF  83 , a mode separator  84 , and a receiver  85 .  FIG. 14  is a schematic diagram illustrating the optical coupling between the lens  81  and the MMF  83  shown in  FIG. 13 . As shown in  FIG. 14 , the lens  81  and the MMF  83  are disposed so as to attain a maximum coupling efficiency. Specifically, the MMF  83  is affixed in such a manner that an optical axis A lz  (denoted by a dot-dash line) of the lens  81  and a fiber axis A fr  (denoted by a double-dot-dash line) of the MMF  83  are on a single straight line, and that an intersection between an input plane F in  (i.e., one of the end faces of the MMF  83 ) and the fiber axis A fr  coincides with a focal point Z fp  of the lens  81 . 
   In the above-described optical transmission system S cv , an optical signal from the lens  81  is focused on the input plane F in  of the MMF  83 , and therefore efficiently enters the MMF  83  with small coupling losses. Thereafter, the optical signal suffers increasingly more influence of mode dispersion as it is propagated through the core of the MMF  83 . As a result, an optical signal having a plurality of modes associated with different propagation delay amounts goes out at an output plane F out  of the MMF  83  (i.e., the end opposite to the input plane F in ). The optical signal outputted from the MMF  83  enters the mode separator  84 , where only the necessary mode(s) is selected. Thereafter, the receiver  85  receives the optical signal which has been subjected to the selection at the mode separator  84 . Thus, the receiver  85  is allowed to receive an optical signal with a reduced influence of mode dispersion, whereby the transmission bandwidth of MMF  83  is improved. 
   However, the mode separator  84 , which is essentially an optical system comprising a number of lenses and mirrors, may be expensive. Moreover, the use of such an optical system complicates the overall structure of the optical transmission system S cv . Furthermore, the optical axis alignment between components of the mode separator  84  requires high precision. This presents a problem because it takes considerable cost to construct and maintain the conventional optical transmission system S cv . 
   There is an additional problem in that it is difficult to improve the mode selection efficiency of the mode separator  84 . As used herein, the “mode selection efficiency” is a ratio of the output power to the input power of the mode separator  84  for a given mode. If the mode selection efficiency is poor, the input power for the receiver  85  is diminished, so that it may become necessary to enhance the power of the optical signal originating from the light source  82  and/or the photodetection sensitivity of the receiver  85 , or to provide an optical amplifier subsequent to the mode separator  84 , leading to increased cost for constructing and maintaining the conventional optical transmission system S cv . 
   SUMMARY OF THE INVENTION 
   Therefore, an object of the present invention is to provide a low-cost optical transmission system employing multi-mode fibers which can minimize the influence of mode dispersion. 
   The present invention has the following features to attain the object above. 
   The present invention is directed to an optical transmission system for transmitting an optical signal from a transmitter to a receiver through a multi-mode fiber. The transmitter comprises: a light emission element for generating an optical signal, and at least one lens for converging the optical signal generated by the light emission element to focus at a focal point. The optical signal converged by the at least one lens enters an input plane of the multi-mode fiber to propagate through the multi-mode fiber. The receiver comprises a light receiving element for receiving the optical signal outputted from the multi-mode fiber. The input plane is placed at a position other than the focal point. 
   These and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a block diagram illustrating the overall structure of an optical transmission system S a  according to a first embodiment of the present invention; 
       FIG. 2  is a schematic diagram illustrating optical coupling in the optical transmission system S a  shown in  FIG. 1 ; 
       FIG. 3  is a schematic diagram showing an eye pattern of an optical signal OS out1  shown in  FIG. 1 ; 
       FIG. 4  is a graph showing the eye opening factor R and the output power P of the optical signal Os out1  relative to the distance Z 1  shown in  FIG. 2 ; 
       FIG. 5  is a schematic diagram illustrating a numerical aperture (=sinα) of a transmitter  11  shown in  FIG. 1 ; 
       FIG. 6  is a schematic diagram illustrating an incident light propagation plane F ipr ; 
       FIG. 7  is a block diagram illustrating the overall structure of an optical transmission system S b  according to a second embodiment of the present invention; 
       FIG. 8  is a schematic diagram illustrating optical coupling in the optical transmission system S b  shown in  FIG. 7 ; 
       FIG. 9  is a schematic diagram illustrating a higher-order outgoing angle γ HI  and a lower-order outgoing angle γ LO ; 
       FIG. 10  is a schematic diagram illustrating an output light propagation plane F opr  ; 
       FIG. 11  is a block diagram illustrating the overall structure of an optical transmission system S c  according to a third embodiment of the present invention; 
       FIG. 12  is a schematic diagram illustrating general examples of a higher-order mode M HI  and a lower-order mode M LO ; 
       FIG. 13  is a block diagram illustrating the overall structure of a conventional optical transmission system S cv ; and 
       FIG. 14  is a schematic diagram illustrating optical coupling between a light source  82  and a multi-mode fiber  83  shown in  FIG. 13 . 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   (First Embodiment) 
     FIG. 1  is a block diagram illustrating the overall structure of an optical transmission system S a  according to a first embodiment of the present invention.  FIG. 2  is a schematic diagram illustrating optical coupling in the optical transmission system S a  shown in  FIG. 1 . The optical transmission system S a  includes a transmitter  11 , a multi-mode fiber (MMF)  12 , and a receiver  13 . 
   As shown in  FIG. 1 , the transmitter  11  includes a light emission element  111 , at least one lens  112 , and a receptacle  113 . The light emission element  111 , which typically comprises a laser diode or a light-emitting diode, is driven by an input electrical signal ES in  to generate an optical signal OS in . The lens  112 , whose optical axis is aligned with that of the light emission element  111 , allows the optical signal OS in  generated by the light emission element  111  to pass therethrough. As shown in  FIG. 2 , in the present embodiment, a vertex Z 0  of the lens  112  is defined as the one of the two intersections between the optical axis A lz  and the surface F lz  of the lens  112  which is located farther away from the light emission element  111 . A focal point Z fp  of the lens  112  is defined as a position along the optical axis A lz  where the optical signal OS in , which has passed through the lens  112 , focuses. The receptacle  113  shown in  FIG. 1  will be described later. 
   In  FIG. 1 , the MMF  12  is a glass fiber of a graded index type, a polymer cladding fiber, or a plastic optical fiber. As shown in  FIG. 2 , the MMF  12  includes a core  121  and a cladding  122 . A connector plug  123  is affixed to one end of the MMF  12  around the outer periphery thereof. The connector plug  123  is fitted into the receptacle  113  of the transmitter  11 . As a result, as shown in  FIG. 2 , the fiber axis A fr  of the MMF  12  and the optical axis A lz  of the lens  112  are aligned with each other, and one of the end faces of the core  121  (hereinafter referred to as an “input plane F in ”) is positioned at a predetermined distance Z 1  from the vertex Z 0  of the lens  112  along the fiber axis A fr . The distance Z 1  is set at a value which is not equal to the distance from the vertex Z 0  to the focal point Z fp , and preferably set at a value greater than the distance from the vertex Z 0  to the focal point Z fp . 
   As shown in  FIG. 2 , a connector plug  124  is affixed to the other end of the core  121  around the outer periphery thereof. The optical signal OS in  which has passed through the lens  112  enters the input plane F in  of the MMF  12  having the above-described structure. As described in more detail later, since the input plane F in  is at the distance Z 1  from the vertex Z 0 , the optical signal OS in  entering the input plane F in  is propagated through the core  121  without being substantially affected by the influence of mode dispersion, so as to go out from the other end (hereinafter referred to as the “output plane F out ”) of the core  121  as an optical signal OS out1 . 
   Referring back to  FIG. 1 , the receiver  13  includes a receptacle  131  and a light receiving element  132 . The connector plug  124  affixed to the MMF  12  is fitted into the receptacle  131 , thereby connecting the receiver  13  to the MMF  12 . The light receiving element  132 , which preferably comprises a Si PIN photodiode (hereinafter referred to as a “Si PIN PD”), has a face (hereinafter referred to as the “light-receiving plane F PD1 ”) at which the optical signal OS out1  outputted from the MMF  12  enters. The light-receiving plane F PD1  has an area nearly equal to or greater than the output plane F out . When the receiver  13  is connected to the MMF  12 , the light-receiving plane F PD1  is positioned so as to oppose the output plane F out  of the MMF  42  in a parallel orientation. The light receiving element  132  having the above-described structure converts the optical signal OS out1  entering the light-receiving plane F PD1  into an electrical signal ES out1  which represents the same information as that represented by the electrical signal ES in . 
   The reason why a Si PIN PD is preferably used as the light receiving element  132  is that a Si PIN PD generally has a large light-receiving plane F PD1 . However, the light receiving element  132  may be composed of a photodiode other than a Si PIN PD because the size of the light-receiving plane F PD1  is not essential to the present embodiment. 
   Next, the distance Z 1 , which is employed in a characteristic manner in the present embodiment, will be described. In order to determine the distance Z 1 , the applicant performed an experiment as follows by using the above-described optical transmission system S a . The experiment was carried out under the following conditions: As the light emission element  111 , a light emission element capable of emitting light having a power of 1.8 mW when a DC current of 30 mA is injected thereto was employed. Two PCFs (Polymer Clad Fibers) having respectively different lengths were prepared as MMFs  12  in order to enable experiments for short-distance transmission and long-distance transmission. More specifically, the MMF  12  for short-distance transmission had a length L fr  of 2.0 m, and the MMF  12  for long-distance transmission had a length L fr  of 100 m. The core  121  of each MMF  12  was composed of silica (SiO 2 ), and had a diameter (hereinafter referred to as the “core diameter”) φ cr  (see  FIG. 2 ) of 200 μm. The cladding  122  was composed of a polymer such as a methacrylic resin (PMMA) with a diameter of 230 μm. 
   Next, an eye opening factor R and an output power P, which were the subjects of measurement under the experiment conducted by the applicant, will be described.  FIG. 3  is a schematic diagram showing an eye pattern of the optical signal OS out1  of the MMF  12 . The eye opening factor R is defined as a ratio of a minimum value V pp1  to a maximum value V pp2  of amplitude of the eye pattern as shown in  FIG. 3 , or V pp1 /V pp2 . From the eye opening factor R as defined above, a transmission bandwidth of the optical transmission system S a  can be determined. The output power P is a light power of the optical signal OS out1  from the MMF  12 . 
   Under the above experimental conditions, the applicant measured the characteristics of the eye opening factor R and the output power P with respect to the position Z 1  of the input plane F in , by means of measurement devices such as a power meter. As a result, measurement results as shown in  FIG. 4  were obtained. In  FIG. 4 , the horizontal axis Z 1 , which is identical to the optical axis A 1z  described above, represents distance to the input plane F in  as taken from the position of the vertex Z 0  of the lens  112 . Herein, the position of the vertex Z 0  of the lens  112  is defined as Z 1 =0. In other words,  FIG. 4  shows the manner in which the eye opening factor R and the output power P change as the input plane F in  of the MMF  12  is gradually pulled away from the vertex Z 0  along the optical axis A lz  (i.e., the “Z 1 ” axis). 
   More specifically,  FIG. 4  shows the eye opening factor R (hereinafter referred to as the “eye opening factor R sd ”; shown by “●” symbols) and the output power P(hereinafter referred to as the “output power P sd ”; shown by “∘” symbols”) of the optical signal OS out1  when the length L fr  of the MMF  12  is 2 m.  FIG. 4  also shows the eye opening factor R(hereinafter referred to as the “eye opening factor R 1d ”; shown by “▴” symbols) and the output power P(hereinafter referred to as the “output power P 1d ”; shown by “Δ” symbols”) of the optical signal OS out1  when the length L fr  is 100 m. 
   Since the maximum values of the output power P sd  and P 1d  are both observed when Z 1  is in the range from 1.0 mm to 1.5 mm, it can be seen that the optical signal OS in  having passed through the lens  112  is focused at a focal point Z fp  which is in this range. In this sense, the range of Z 1  from 1.0 mm to 1.5 mm will be referred to as a “focal range” D fp  (see regions hatched with dots in  FIG. 4 ) Note, however, that the eye opening factor R 1d  is considerably deteriorated in the focal range D fp . The eye pattern ( FIG. 3 ) of the optical signal OS out1  having such a deteriorated eye opening factor R 1d  reveals a significant difference between the minimum value V pp1  and the maximum value V pp2  in amplitude. This indicates that it is difficult to transmit the optical signal OS in  over a long distance (e.g., 100 m) when the input plane F in  of the MMF  12  is set within the focal range D fp . 
   On the other hand, in  FIG. 4 , the eye opening factor R sd  is substantially constant regardless of the value of Z 1 , unlike the eye opening factor R 1d . Such differences in the characteristics of the eye opening factor R indicates the facts that the influence of mode dispersion varies depending on the value of Z 1  and that the influence of mode dispersion becomes more outstanding as the transmission distance of the optical signal OS in  increases. 
   Referring back to  FIG. 14 , in the conventional optical transmission system S cv , the input plane F in  of the MMF  83  is positioned at the focal point Z fp  so as to maximize the coupling efficiency with the MMF  83  (i.e., so as to allow the optical signal to enter the MMF  83  with minimum coupling losses). However, it should now be clear from the characteristic curves shown in  FIG. 4  that, when the input plane F in  is positioned at the focal point Z fp , the optical signal OS in  suffers severer influence of mode dispersion as the MMF  12  becomes longer. This indicates that, in the conventional optical transmission system S cv , the transmission bandwidth is under the constraints imposed by mode dispersion. 
   The above findings can be theorized as follows. Prior to the following explanation, three parameters used therein, i.e., the numerical aperture (hereinafter “NA s ”) of the transmitter  11 , the numerical aperture (hereinafter “NA f ”) of the MMF  12  and the numerical aperture (hereinafter “NA in ”) of the optical signal OS in  entering and propagated through the MMF  12 , will be first described. 
     FIG. 5  is a schematic diagram illustrating the NA s  of the transmitter  11  shown in  FIG. 1 . As shown in  FIG. 5 , the optical signal OS in , which once focuses at the position Z fp , propagates while spreading at an angle of α with respect to the optical axis A lz . The NA s , which is a measure of such spread, can be expressed by equation (1) below:
 NA s =sinα  (1) 
   The value of NA s  increases as the once-focused optical signal OS in  has a greater expanse. The value of NA s  is within the range 0&lt;NA s ≦1. 
   In the light entering the MMF  12 , the only components which propagate to the output plane F out  are those within a certain range of angles (hereinafter referred to as the “propagation angles” of the MMF  12 ). Based on the largest propagation angle of the MMF  12 , named β max , the NA f  can be expressed by equation (2) below:
 
NA f =sinβ max   (2)
 
   Usually, the above-defined NA f  is determined by the refractive indices of the core  121  and the cladding  122 , and is a parameter which is independent of the aforementioned NA s . If light having a numerical aperture greater than the NA f  enters the input plane F in , any components which spread outside the aforementioned range of propagation angles of the MMF  12  will be transmitted through to the exterior of the MMF  12 . On the other hand, if the optical signal OS in  has a numerical aperture smaller than the NA f , then all components of the light will propagate through the core  121  as explained above. Moreover, since the optical signal OS in  has a smaller numerical aperture than the NA f  in this case, the higher-order modes in the optical signal OS in  are decreased, so that the mode dispersion can be reduced. 
   Moreover, in the optical transmission system S a , once the position Z 1  of the input plane F in  is determined, only those components of the optical signal OS in  having the NA s  which are within a predetermined range of angles (which in the present embodiment are referred to as the “reachable angles”, i.e. angles reachable to the MMF  12 ) can actually enter the input plane F in . Any light components which lie outside the range of reachable angles, which do not enter the input plane F in , will not be propagated through the core  121 . Furthermore, due to the NA f  of the MMF  12 , all components of the optical signal OS in  may not always be propagated to the output plane F out  even if it enters the input plane F in . Assuming that the components of the optical signal OS in  which enter the input plane F in  and which are propagated through the MMF  12  to the output plane F out  have a largest incident angle of β th , the aforementioned NA in  can be expressed by equation (3) below:
 
NA in =sinβ th   (3)
 
   In general, mode dispersion is more reduced as the NA in  expressed by equation (3) decreases. 
     FIG. 6  is a schematic diagram illustrating an incident light propagation plane F ipr  (defined below), which helps detailed explanation of the NA in . In the following description, it is assumed that the input plane F in  (shown hatched with oblique lines in  FIG. 6 ) has an area S f ; the input plane F in  has a diameter (i.e., core diameter) φ cr  as shown in  FIG. 2 ; and the incident light propagation plane F ipr  (shown hatched with dots in  FIG. 6 ) has an area S (Z 1 ). First, a geometric definition of the incident light propagation plane F ipr  will be given. The optical signal OS in  which has passed through the lens  112  (not shown) converges until reaching the focal point Z fp , and thereafter diverges in a conical shape. When one draws an imaginary plane at a distance of Z 1  from the vertex Z 0 , such that the imaginary plane is perpendicular to the optical axis A lz , the incident light propagation plane F ipr  is defined as a cross-section of the optical signal OS in  taken at the imaginary plane. As will be clear from  FIG. 6 , the ratio of the area S(Z 1 ) to the area S f  changes depending on the position Z 1  of the input plane F in . Thus, it is possible to adjust the NA in  by changing the position Z 1  of the input plane F in ; in other words, the NA in  is a function of Z 1 , and can be expressed as NA in  (Z 1 ). Thus, by changing the position Z 1  of the input plane F in , it is possible to control the mode dispersion, which affects the transmission distance and the data rate of the optical signal OS in . 
   First, the case in which the NA s  is equal to or less than the NA f  will be considered. In this case, all of the components of the optical signal OS in  which have passed through the lens  112  and which enters the core  121  are propagated to the output plane F out . If S(Z 1 ) is equal to or greater than S f , NA in  (Z 1 ) decreases as Z 1  increases, as expressed by equation (4) below: 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           NA 
                           in 
                         
                         ⁡ 
                         
                           ( 
                           
                             Z 
                             1 
                           
                           ) 
                         
                       
                       = 
                       
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           β 
                           th 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         = 
                         
                           sin 
                           ⁡ 
                           
                             ( 
                             
                               ( 
                               
                                 arctan 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       ϕ 
                                       cr 
                                     
                                     
                                       
                                         2 
                                         · 
                                       
                                       | 
                                       
                                         
                                           Z 
                                           1 
                                         
                                         - 
                                         
                                           Z 
                                           fp 
                                         
                                       
                                       | 
                                     
                                   
                                   ) 
                                 
                               
                               ) 
                             
                             ) 
                           
                         
                       
                       ; 
                       
                         
                           S 
                           ⁡ 
                           
                             ( 
                             
                               Z 
                               1 
                             
                             ) 
                           
                         
                         ≥ 
                         
                           S 
                           f 
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 4 
                 ) 
               
             
           
         
       
     
   
   On the other hand, if S(Z 1 ) is smaller than S f , all of the optical signal OS in  which has passed through the lens  112  enters the input plane F in , and is propagated to the output plane F out . In this case, the NA in  can be expressed by equation (5) below.
 
 NA   in ( Z   1 )=sinβ th   =NA   s   ; S ( Z   1 )&lt; S   f   (5)
 
   Next, the case in which NA s  is greater than NA f  will be considered. In this case, even if all of the optical signal OS in  which has passed through the lens  112  enters the input plane F in , any components (modes) thereof which fall outside the NA f  cannot be propagated through the core  121 . Therefore, NA in  (Z 1 ) is fixed such that NA in  (Z 1 )=NA f . However, as Z 1  increases therefrom so that NA in  (Z 1 )&lt;NA f  is satisfied, thereafter NA in (Z 1 ) decreases with an increase in Z 1 , as can be expressed by equation (6) below: 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           NA 
                           in 
                         
                         ⁡ 
                         
                           ( 
                           
                             Z 
                             1 
                           
                           ) 
                         
                       
                       = 
                       
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           β 
                           th 
                         
                       
                     
                   
                 
                 
                   
                     
                       = 
                       
                         
                           sin 
                           ⁡ 
                           
                             ( 
                             
                               ( 
                               
                                 arctan 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       ϕ 
                                       cr 
                                     
                                     
                                       
                                         2 
                                         · 
                                       
                                       | 
                                       
                                         
                                           Z 
                                           1 
                                         
                                         - 
                                         
                                           Z 
                                           fp 
                                         
                                       
                                       | 
                                     
                                   
                                   ) 
                                 
                               
                               ) 
                             
                             ) 
                           
                         
                         ≤ 
                         
                           NA 
                           f 
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 6 
                 ) 
               
             
           
         
       
     
   
   As described above, by adjusting the position Z 1 , it is possible to reduce the NA in  (i.e., NA in  (Z 1 )). Thus, the influence of mode dispersion, which is a problem associated with a long-distance transmission of the optical signal OS in , can be minimized. 
   In an actual implementation of the optical transmission system S a , the determination of the position Z 1  must be made while considering both the output power P from the MMF  12  and the eye opening factor R as design requirements. The reason is that, as the influence of mode dispersion is reduced by increasing the value of Z 1 , the coupling losses between the transmitter  11  and the MMF  12  increase, making it difficult to obtain the required output power P. 
   For example, let us assume that the three following design requirements are given in the optical transmission system S a  shown in  FIG. 1 : MMF  12  has a length L fr  of 100 m; the output power P is equal to greater than 0.1 mW; and the eye opening factor R is equal to greater than 50%. Under this assumption, it can be seen from the eye opening factor R 1d  characteristics (represented by ▴) and the output power P 1d  characteristics (represented by Δ) shown in  FIG. 4  that the value of Z 1  is preferably in the range from 2.0 mm to 2.5 mm (see the region hatched with oblique lines in  FIG. 4 ). Note that a Z 1  value of at least 2.0 mm or more can be employed in order to simply reduce the influence of mode dispersion without considering any other design requirements. Thus, the present optical transmission system S a  allows the influence of mode dispersion in the MMF  12  to be reduced based on the adjustment of the position Z 1 , whereby the transmission bandwidth of the MMF  12  can be broadened. This eliminates the need for a mode separator  84  (see  FIG. 13 ) in the optical transmission system S a , unlike in the conventional optical transmission system S cv . Thus, a low-cost optical transmission system S a  can be provided according to the present embodiment of the invention. 
   Note that the value of Z 1  is not always limited to 2.0 mm or above, but may vary depending on design requirements such as the length L fr  of the MMF  12 , the output power P, and the eye opening factor R . In general, the influence of mode dispersion becomes more outstanding as the transmission distance (length L fr ) increases. Stated otherwise, the value of Z 1  decreases as the transmission distance decreases. 
   (Second Embodiment) 
     FIG. 7  is a block diagram illustrating the overall structure of an optical transmission system S b  according to a second embodiment of the present invention.  FIG. 8  is a schematic diagram illustrating how optical coupling occurs in the optical transmission system S b  shown in  FIG. 7 . The optical transmission system S b  is identical to the optical transmission system S a  except that the transmitter  11  and the receiver  13  are replaced by a transmitter  21  and a receiver  22 . Accordingly, any component elements in the optical transmission system S b  which find their counterparts in the optical transmission system S a  will be denoted by the same reference numerals as those used in  FIGS. 1 and 2 , and the descriptions thereof are omitted. 
   With reference to  FIG. 7 , the transmitter  21 is identical to the transmitter  11  shown in  FIG. 1  except that the receptacle  113  is replaced by a receptacle  211 . Accordingly, any component elements in the transmitter  21  which find their counterparts in the transmitter  11  will be denoted by the same reference numerals as those used in  FIG. 1 , and the descriptions thereof are omitted. The connector plug  123  which is affixed to the input plane F in  of the MMF  12  is fitted into the receptacle  211 . As a result, as shown in  FIG. 8 , the fiber axis A fr  of the MMF  12  and the optical axis A lz  of the lens  112  are aligned with each other, and the input plane F in  is positioned substantially at the focal point Z fp  so as to maximize the coupling efficiency between the lens  112  and the MMF  12 . In this aspect, the transmitter  21  is clearly distinct from the transmitter  11  shown in  FIG. 1 . Therefore, an optical signal OS in  entering the input plane F in  is propagated trough the core  121  while being affected by mode dispersion, so as to be outputted from the output plane F out  as an optical signal OS out2 . 
   As shown in  FIG. 7 , the receiver  22  includes a receptacle  221  and a light receiving element  222 . The connector plug  124  which is affixed to the MMF  12  is fitted into the receptacle  221 . The light receiving element  222  which preferably comprises a Si PIN PD, has a face (hereinafter referred to as the “light-receiving plane F PD2 ”) at which the optical signal OS out2  outputted from the MMF  12  enters. In the present embodiment, it is assumed that the light-receiving plane F PD2 has a circular shape for the sake of explanation. As shown in  FIG. 8 , when the receiver  22  is connected to the MMF  12 , the light-receiving plane F PD2  having the above-described structure opposes the output plane F out  of the MMF  12  in a parallel orientation, with a distance Z 2  therebetween. Furthermore, a central axis A PD  of the light-receiving plane F PD2  is aligned with the fiber axis A fr . Thus, as shown in  FIG. 7 , the light receiving element  222  converts the optical signal OS out2  entering the light-receiving plane F PD2  into an electrical signal ES out2  which represents the same information as that represented by the electrical signal ES in . 
   As described above, according to the present embodiment, the input plane F in  is positioned at the focal point Z fp , so that the optical signal OS in  entering the input plane F in  suffers severer influence of mode dispersion than in the first embodiment. As a result, the respective modes in the optical signal OS in  which simultaneously enter the input plane F in  arrive at the output plane F out  at respectively different times. Therefore, the outputted optical signal OS out2  has a relatively “closed” eye pattern. When all modes in the outputted optical signal OS out2  enter the light-receiving plane F PD2 , the receiver  22  cannot correctly receive the information which is represented by the electrical signal ES in . 
     FIG. 9  is a schematic diagram illustrating a higher-order outgoing angle γ HI  of a higher-order mode M HI  and a lower-order outgoing angle γ LO  of a lower-order mode M LO , both contained in the optical signal OS out2  shown in  FIG. 8 . As shown in  FIG. 9 , the higher-order mode M HI  and the lower-order mode M LO go out at respectively different angles, i.e., the higher-order outgoing angle γ HI  and the lower-order outgoing angle γ LO , with respect to the fiber axis A fr . The lower-order outgoing angle γ LO  is smaller than the higher-order outgoing angle γ HI . Therefore, the higher-order mode M HI  will travel farther away from the fiber axis A fr  as the value of Z 2  increases. Accordingly, the value of Z 2  can be adjusted to prevent the higher-order mode M HI  from entering the light-receiving plane F PD , so that the light receiving element  222  will selectively receive only the lower-order mode M LO . 
   The aforementioned selective reception can be explained as follows. First, the parameters employed in the following explanation, i.e., the outgoing numerical aperture (hereinafter referred to as “NA out  ”) of the MMF  12  and the numerical aperture (hereinafter referred to as “NA PD ”) of the light-receiving plane F PD2 , will be described. 
   As seen above, modes with various outgoing angles go out from the output plane F out  of the MMF  12 . Based on the largest angle among such outgoing angles, named γ max , the NA out  can be expressed by equation (7) below:
 
NA out =sinγ max   (7)
 
   Note that, since the input plane F in  is positioned at the focal point Z fp  in the present embodiment, the NA out  is substantially the same value as the NA in  (Z fp ) obtained from equations (4) to (6) above. 
   Moreover, in accordance with the optical transmission system S b , once the position Z 2  is determined, only those modes in the outputted optical signal OS out2  having the NA out  which are within a predetermined range of angles (which in the present embodiment are referred to as the “reachable angles”, i.e. , angles reachable to the light-receiving plane F PD2 ) can actually reach the light-receiving plane F PD2 . Assuming that the modes in the optical signal OS out2  outputted from the output plane F out  which enter the light-receiving plane F PD2  have a largest outgoing angle of γ th , the aforementioned NA PD  can be expressed by equation (8) below:
 
NA PD =sinγ th   (8)
 
     FIG. 10  is a schematic diagram illustrating an output light propagation plane F opr  (defined below), which helps detailed explanation of the NA PD . In the following description, it is assumed that the output plane F out  (shown cross-hatched in  FIG. 10 ) has an area S f ; the output plane F out  has a diameter (i.e., core diameter) φ cr ; and the light-receiving plane F PD2  (shown hatched with oblique lines in  FIG. 10 ) has an area S PD . The light-receiving plane F PD2  is assumed to have a circular shape in the present embodiment. Under this assumption, it is further assumed that the light-receiving plane F PD2  has a diameter φ PD . It is also assumed that the output light propagation plane F opr  (shown hatched with dots in  FIG. 10 ) has an area S(Z 2 ). First, a geometric definition of the output light propagation plane F opr  will be given. The optical signal OS out2  outputted from the MMF  12  diverges in a radial manner. When one draws an imaginary plane at a distance of Z 2  from the output plane F out , such that the imaginary plane is perpendicular to the optical axis A lz , the output light propagation plane F opr  is defined as a cross-section of the aforementioned outputted optical signal OS out2  taken at the imaginary plane. It is possible to adjust the largest outgoing angle γ th , and hence the NA PD , by changing the position Z 2  of the output plane F out ; in other words, the NA PD  is a function of Z 2 , and can be expressed as NA PD  (Z 2 ) Thus, by changing the distance Z 2  of the light-receiving plane F PD  from the output plane F out , it can be ensured that the light receiving element  222  selectively receives only the lower-order mode M LO  (shown in  FIG. 9 ) while avoiding the higher-order mode M HI , which would cause the outgoing optical signal OS out2  to have a relatively closed eye pattern. As a result, the light receiving element  222  can generate the electrical signal ES out2  representing the same information as that represented by the electrical signal ES in . 
   The NA PD  (Z 2 ) will be described in more detail. First, the case where S(Z 2 ) is greater than SPD will be considered. In this case, NA PD  (Z 2 ) decreases as the value of Z 2  increases, as expressed by equation (9) below:
 
 NA   PD ( Z   2 )=sinγ th  
                 

   
     
       
         
           
             
               
                 
                   
                     
                       
                         
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                         = 
                         
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                                   ( 
                                   
                                     
                                       
                                         ϕ 
                                         PD 
                                       
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                             ) 
                           
                         
                       
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                           S 
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   The smaller the outgoing angle of a given mode in the optical signal OS out2  outputted from the MMF  12 , the lower the order of the mode. Therefore, by setting the light-receiving plane F PD2  at the distance Z 2  from the output plane F out  along the fiber axis A fr , the light receiving element  222  can selectively receive the lower-order mode M LO  while avoiding the higher-order mode M HI . Thus, according to the present embodiment, without requiring a mode separator  84  as shown in  FIG. 13 , the influence of mode dispersion in the MMF  12  can be reduced by simply adjusting the position Z 2 , and the transmission bandwidth of the MMF  12  can be broadened. As a result, a low-cost optical transmission system S b  with a broad transmission bandwidth can be provided. 
   On the other hand, in the case where S(Z 2 ) is smaller than S PD , all of the modes contained in the optical signal OS out2  outputted from the MMF  12  will enter the light-receiving plane FDP 2 . In other words, NA PD  (Z 2 ) takes the same value as NA out , as expressed by equation (10) below:
 
 NA   PD ( Z   2 )=sinγ th   =NA   out   ; S ( Z   2 )&lt;S PD   (10)
 
   Note that S (Z 2 ) being smaller than S PD  means that φ cr  is greater than φ PD  and that the light-receiving plane F PD2  is in proximity of the output plane F out . Moreover, in this case, the light receiving element  222  cannot selectively receive only the lower-order mode M LO . This fact also rationalizes the need for setting the light-receiving plane F PD2  away from the output plane F out . 
   In an actual implementation of the optical transmission system S b , the determination of the distance Z 2  described above must be made while considering both the input power to the light-receiving plane F PD2  and the eye opening factor of the optical signal F out  entering the light-receiving plane F PD2  as design requirements. The reason is that, as the influence of mode dispersion is reduced by increasing the value of Z 2 , the coupling losses between the transmitter  11  and the MMF  12  increase, making it difficult to obtain the required input power P. Furthermore, the determination of the distance Z 2  described above must be made while considering the length L fr  of the MMF  12  and the data rate of the optical signal OS in , which are design requirements of the optical transmission system S b . In other words, as the length L fr  and the data rate become greater, the influence of mode dispersion becomes more outstanding, therefore requiring a greater Z 2  value. 
   (Third Embodiment) 
     FIG. 11  is a block diagram illustrating the overall structure of the optical transmission system S c  according to a third embodiment of the present invention. In short, the optical transmission system S c  shown in  FIG. 11  combines the features of the first and second embodiments, and comprises the transmitter  11 , the MMF  12 , and the receiver  22 . Accordingly, any component elements in  FIG. 11  which find their counterparts in  FIGS. 1  or  7  will be denoted by the same reference numerals as those used therein, in order to simplify description. 
   As shown in  FIG. 11 , the connector plug  123  is fitted into the receptacle  113  of the transmitter  11 . As a result, as described with reference to  FIG. 2 , the fiber axis A fr  of the MMF  12  and the optical axis A lz  of the lens  112  are aligned, and the input plane F in  of the core  121  is positioned at a predetermined distance Z 1  from the vertex Z 0  of the lens  112 . The distance Z 1  is set at a value which is not equal to the distance from the vertex Z 0  to the focal point Z fp , and preferably set at a value greater than the distance from the vertex Z 0  to the focal point Z fp . 
   The connector plug  124  which is affixed to the MMF  12  is fitted into the receptacle  221 . As a result, as described with reference to  FIG. 8 , the light-receiving plane F PD2  opposes the output plane F out  of the MMF  12  with a distance Z 2  therefrom. Furthermore, the central axis A PD  of the light-receiving plane F PD2  is aligned with the fiber axis A fr . 
   In the optical transmission system S c  as described above, the optical signal OS out2  from the MMF  12  is substantially free from the influence of mode dispersion because the input plane F in  is positioned at the distance Z 1  from the vertex Z 0 . Even if there is any influence of mode dispersion, only the lower-order mode M LO  of the optical signal OS out2  is selectively received because the light-receiving plane F PD2  is positioned at the distance Z 2  from the output plane F out . Therefore, the optical transmission system S c  is capable of further reducing mode dispersion in the MMF  12  as compared to the optical transmission systems S a  and S b , while eliminating the need for a mode separator  84  (see  FIG. 13 ). Thus, a lower-cost and more broadband-oriented optical transmission system S c  can be provided. 
   While the invention has been described in detail, the foregoing description is in all aspects illustrative and not restrictive. It is understood that numerous other modifications and variations can be devised without departing from the scope of the invention.