Optical fiber connector

Abstract

The optical fiber connector of the invention comprises a first optical fiber, a first convex lens that converges light emitted from the first optical fiber, a second convex lens that converges light emitted from the first convex lens, and a second optical fiber that receives a convergent light beam from the second convex lens, wherein, when a core diameter of the first optical fiber is given by E1, a numerical aperture thereof by NA1, a core diameter of the second optical fiber by E2, a numerical aperture thereof by NA2, a focal length of the first convex lens by f1, a focal length of the second convex lens by f2, and (E1/E2)/(f1/f2)=x is introduced, a connection efficiency η of the first and the second optical fibers satisfies the following inequality(E1/E2)2<η≦(1/x)2·NA2/sin(tan−1 E1/E2·NA1/x),in1

Description

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a connection structure of optical fibers, specifically to a connection device that connects optical fibers having different core diameters and made of different materials, such as a plastic fiber and a glass fiber.

2. Description of the Related Art

In connecting optical fibers, the most important technical task is to achieve a low transmission loss of light as far as possible.

As an example, in connecting two optical fibers having the core diameter of 60 μm and the specific refractive index difference of 0.7% with their end faces confronted with each other, it is generally conceived that an adequate transmission of light is difficult to be realized, unless, assuming that there is no crimp in the connecting area, the optical axis displacement is made within 0.2 μm and the connection loss is made within 0.2 dB.

FIG. 17 illustrates a first conventional optical fiber connector 50 that has implemented such a low transmission loss. As illustrated, the first conventional optical fiber connector 50 includes a first optical fiber 51 , a second optical fiber 52 , a cylindrical connecting part 53 that connects the first and second optical fibers 51 , 52 , and a lens 54 contained in this connecting part 53 , in which a light beam emitted from an end face 51 a of the first optical fiber 51 falls on an end face of the second optical fiber 52 through the lens 54 . Thus, the two optical fibers are optically connected.

FIG. 18 illustrates a second conventional optical fiber connector 60 , which includes a first cylindrical connecting part 65 with a flange 65 a and a second cylindrical connecting part 66 with a flange 66 a, and further a first lens 63 contained in the first connecting part 65 and a second lens 64 contained in the second connecting part 66 .

First and second fixing parts 67 , 68 having holes on the centers thereof, are mounted on the ends of the opposite sides to the flanges 65 a , 66 a of the first and second connecting parts 65 , 66 . Opposing ends of the first optical fiber 61 and the second optical fiber 62 are guided in the center holes of the fixing parts 67 , 68 .

The first and second lenses 63 , 64 are fixed inside the first and second connecting parts 65 , 66 , respectively, so that the optical axes coincide with each other; and thereafter, the first and second connecting parts 65 , 66 are attached so that the flanges 65 a , 66 a are engaged with each other. The first and second fixing parts 67 , 68 are fastened to the first and second connecting parts 65 , 66 with screws, etc. The first and second optical fibers 61 , 62 are stripped of the sheathing parts from the front ends thereof, and the stripped ends each are engaged in the center holes of the fixing parts 67 , 68 .

Thus, the first and second optical fibers 61 , 62 are configured so as to form the focuses on the end faces thereof, for example, a light beam emitted from the end face of the first optical fiber 61 is emitted as a parallel beam from the first lens 63 , and the parallel beam falls on the second lens 64 , which transforms the beam into a convergent beam. Thus, the two optical fibers are optically connected.

FIG. 19 illustrates a third conventional optical fiber connector 70 , which includes a first optical fiber 71 , a second optical fiber 72 , two glass spheres 75 in contact with each other. The two glass spheres 75 are disposed between both front ends of the first and second optical fibers 71 , 72 . The connector 70 also includes, liquid substances 78 having a refractive index of approximately 1, which are inserted between the first optical fiber 71 and one glass sphere 75 and between the second optical fiber 72 and the other glass sphere 75 , and a molded resin 80 that sheathes an area including both the front ends of the first and second optical fibers 71 , 72 , the liquid substances 78 , and the two glass spheres 75 thus disposed.

A parallel beam emitted from the first optical fiber 71 falls on the one glass sphere 75 and converges at a point 76 where the two glass spheres come into contact. The convergent beam is transformed into a parallel beam through the other sphere 75 , which falls on the second optical fiber 72 . Thus, the two optical fibers are optically connected with a symmetrical optical path.

However, in such optical fiber connectors 50 , 60 , 70 , a high positioning accuracy in the connection of the two optical fibers is required in order to transmit a stable light beam through the optical fibers connected. Further, it is necessary to enhance the efficiency of optical connection through the optical elements such as the lenses, so that a lower transmission loss of light than that obtained by the optical fibers being directly connected can be achieved.

Furthermore, in the connection of the two optical fibers having different diameters, for example, in the connection of a plastic optical fiber (POF) and a fused quartz fiber (PCF) having different core diameters, a higher positioning accuracy is required than the connection of optical fibers having the same diameter, and a low transmission loss of light has been difficult to be realized.

SUMMARY OF THE INVENTION

The present invention has been made in view of these problems, and it is an object of the invention to provide an optical fiber connector that enhances the efficiency of optical connection and thereby achieves a low transmission loss of light in the connection of optical fibers with different diameters.

As a first means to solve at least one of the foregoing problems, the optical fiber connector of the invention includes a first optical fiber, a first lens that converges light emitted from the first optical fiber, a second lens that converges light emitted from the first lens, and a second optical fiber that receives convergent light from the second lens. In the optical fiber connector thus configured, provided that the core diameter of the first optical fiber is given by E 1 , the numerical aperture thereof by NA 1 , the core diameter of the second optical fiber by E 2 , the numerical aperture thereof by NA 2 , the focal length of the first lens by f 1 , the focal length of the second lens by f 2 , and (E 1 /E 2 )/(f 1 /f 2 )=x is introduced, the connection efficiency η of the first and the second optical fibers satisfies the following inequality:

( E 1 / E 2 ) 2 <η≦NA 2 /sin(tan −1 E 1 / E 2 ·NA 1 / x ),

in

0 <x ≦1;

( E 1 / E 2 ) 2 <η≦(1 /x ) 2 ·NA 2 /sin(tan −1 E 1 / E 2 · NA 1 / x ),

in

1< x<E 1 / E 2 ·NA 1 /sin(tan −1 NA 2 )

or

( E 1 / E 2 ) 2 <η≦(1/ x ) 2 ,

in

E 1 / E 2 · NA 1 /sin(tan −1 NA 2 )≦ x.

As a second means, provided that the effective aperture of the first lens is given by D 1 and the effective aperture of the second lens is given by D 2 , the connection efficiency η 1 by only the influence of the D 1 is expressed by the equation:

η 1 =D 1 /( E 1 +2 ×f 1 ×tan(sin −1 NA 1 )) 2 ,

and the connection efficiency η 2 by only the influence of the D 2 is expressed by the equation:

η 2 =( D 1 /( D 1 × f 2 / f 1 )) 2 ,

the optical fiber connector has a connection efficiency that is the foregoing η multiplied by η 1 and/or η 2 .

Further, as a third means, the optical fiber connector is comprised of the first lens made by forming the end face of the first optical fiber into a spherical face, and the second lens made by forming the end face of the second optical fiber into a spherical face.

Further, as a fourth means, the optical fiber connector is comprised of either one of the first and the second lenses made by forming the end face of the first or the second optical fiber into a spherical face.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 is a typical sectional view of an optical fiber connector of the invention;

FIG. 2 is a sectional view of a plastic fiber of the connector;

FIG. 3 is a sectional view of a fused quartz fiber of the connector;

FIG. 4 is a typical drawing to explain the expander optical system of the optical fiber connector of the invention;

FIG. 5 is a typical drawing to explain the optical system of the optical fiber connector of the invention;

FIG. 6 is a graph to explain the connection efficiency of the optical fiber connector of the invention;

FIG. 7 is a drawing to explain a state in which the first lens receives a light beam emitted from the first optical fiber of the optical fiber connector of the invention;

FIG. 8 is a drawing to explain a state in which the second lens receives a light beam transmitted through the first lens of the optical fiber connector of the invention;

FIG. 9 is a drawing to explain a state in which the second optical fiber receives a light beam transmitted through the second lens of the optical fiber connector of the invention;

FIG. 10 is a drawing to explain the beam size in the lenses of the optical fiber connector of the invention;

FIG. 11 is a drawing to explain the beam size in the lenses of the optical fiber connector of the invention;

FIG. 12 is a drawing to explain the relation between the beam waist and the numerical aperture of the optical fiber connector of the invention;

FIG. 13 is a drawing to explain the relation between the beam waist and the numerical aperture oil the optical fiber connector of the invention;

FIG. 14 is a drawing to explain the relation between the beam waist and the numerical aperture of the optical fiber connector of the invention;

FIG. 15 is a drawing to explain the relation between the beam waist and the numerical aperture of the optical fiber connector of the invention;

FIG. 16 is a drawing to explain an optical fiber with a radius of curvature in the optical fiber connector of the invention;

FIG. 17 is a sectional view to explain a first conventional optical fiber connector;

FIG. 18 is a sectional view to explain a second conventional optical fiber connector; and

FIG. 19 is a sectional view to explain a third conventional optical fiber connector.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

An optical fiber connector 10 as the first embodiment of this invention is provided with, as shown in FIG. 1 , a cylindrical enclosure 11 made of a synthetic resin or a metal that does not transmit a light, a cylindrical optical guide path 11 a provided inside the enclosure 11 , a first round hole 11 b and a second round hole 11 c provided on both ends of the enclosure 11 , each communicated with the optical guide path 11 a.

A first biconvex lens (not shown) and a second biconvex lens 14 are engaged inside the optical guide path 11 a , and are fixed so that the optical axes y coincide on both the incident and outgoing sides of the biconvex lenses 14 .

A plastic fiber 16 comprises, as shown in FIG. 2 , a core 16 a made of a high purity polymethyl methacrylate (PMMA) and a clad 16 b that sheathes this core 16 a , made of a thin layer of special fluororesin. The diameter of the core 16 a of this plastic fiber 16 is about 1 mm, which is thicker than that of a fused silica fiber 18 described later, and the front end of the plastic fiber 16 is polished to form an accurate spherical face, a convex part 16 c.

The plastic fiber 16 contains the core 16 a whose refractive index n 1 is uniform in the radial direction, and allows long distance propagation of light while absorptions and scatterings attenuate the light gradually, which is the so-called multi-mode type (MMF).

One end of the plastic fiber 16 is made to be detachably fit in the first round hole 11 b of the enclosure 11 .

The fused silica fiber 18 comprises, as shown in FIG. 3 , a core 18 a made of a quartz, whose diameter is about 0.05˜0.2 mm, a cladding 18 b made of the same quartz that sheathes this core 18 a , and a fiber coating 18 c made of a nylon resin that sheathes the cladding 18 b. One end face 18 d of the fiber 18 has a mirror finish applied.

The fused silica fiber 18 contains the core 18 a whose refractive index n 2 is uniform in the radial direction, and allows long distance propagation of light while absorptions and scatterings attenuate the light gradually, which is the so-called multi-mode type, the same as the plastic fiber 16 .

One end of the fused silica fiber 18 is made to be detachably fit in the second round hole 11 c of the enclosure 11 . The inner diameters of the first and second 11 b , 11 c are made different in size to the fibers 16 , 18 that have different outer diameters.

In this optical fiber connector 10 , as shown in FIG. 1 , a light beam fallen on one end face of the core 16 a of the plastic fiber 16 propagates through the core 16 a , and reaches the convex part 16 c being the other end face. An outgoing beam from the convex part 16 c diverges toward the second lens 14 in the optical guide path 11 a , and after passing through the second lens 14 , converges on the one end face 18 d of the core 18 a of the fused silica fiber 18 . The light beam converged on the one end face 18 d propagates through the core 18 a and emits from the other end face of the core 18 a.

In reverse to this, a light beam fallen on the other end face of the core 18 a of the fused silica fiber 18 propagates through the core 18 a , the one end face 18 d , and the second convex lens 14 , reaches the convex part 16 c of the plastic fiber 16 , propagates through the core 16 a , and emits from the one end face.

In this manner, bidirectional communication of information is made between a transmitting end and a receiving end which are remotely located, and the receiving end converts a light signal into an electrical signal, thus receiving the information.

Next, in the optical fiber connector 10 , the optimization condition for connecting optical fibers having different core diameters will be discussed with the following models.

In the model A, the plastic fiber 16 is handled as follows. As shown in FIG. 4 , the plastic fiber 16 is equivalently divided into a first optical fiber, namely, a plastic fiber (hereunder, POF) 16 S having a core diameter D 1 and an end face 16 d of a vertical section with the convex part 16 c cut off, and a first lens, namely, a first convex lens 13 having a spherical shape and the same focal length as the convex part 16 c. The second optical fiber, namely, the fused silica fiber (hereunder, PCF) 18 and the second lens, namely, the second convex lens 14 are exactly the same as shown in FIG. 1 .

When light propagating through the POF 16 S is ideal, the light emitted from the end face 16 d is a parallel light beam, which falls on the first convex lens 13 . Then, the first convex lens 13 converges the light at the focus (focal length f 1 ), and the convergent light is expanded into a parallel light of the same size as a core diameter E 2 of the ECF 18 by the second convex lens 14 having a different focal length (focal length f 2 ), and the parallel light advances toward the end face 18 d of the PCF 18 .

Thus, to diminish the diameter of a parallel light beam or to expand it in reverse, the so-called beam expander theory is employed.

The beam expander optical system in this case can be expressed by the following expression.

E 1 / E 2 =γ= f 1 / f 2   (1)

Here, E 1 represents the core diameter of the POF 16 S, which is the same size as the diameter (beam size) of the bundle of rays of the parallel light beam,

E 2 represents the core diameter of the PCF 18 , which is the same size as the diameter (beam size) of the bundle of rays of the parallel light beam,

f 1 represents the focal length of the first convex lens 13 , and

f 2 represents the focal length of the second convex lens 14 .

E 1 can be regarded as the outer diameter of the core 16 a of the plastic fiber 16 S, and E 2 can be regarded as the outer diameter of the core 18 a of the fused silica fiber 18 . Therefore, assuming that the core diameter of the POF 16 S is 1 mm and the core diameter of the PCF 18 is 0.2 mm, for example, the optical system will be the beam expander of the reduction ratio 1/5 (=γ).

As mentioned above, the beam expander optical system premises the parallel light beam in the treatment.

However, in multi-mode propagation through the POF 16 S, PCF 18 , generally, the propagation speed of light becomes high when the light comes, in with a shallow angle from multiple point light sources, and it becomes low when the light comes in with a deep angle. Accordingly, when light (light pulse of a specially thin beam) is brought into incidence on the one end of the core 16 a of the POF 16 S, as shown in FIG. 5 , the light reaching the other end face 16 d of the core 16 a of the POF 16 becomes not a parallel light beam but a divergent light.

Therefore, considering this divergent light, the optical fiber connector 10 recipes to add, as the factors for the optimization condition, the numerical apertures NA 1 , NA 2 by the divergent luminous fluxes of the POF 16 S, PCF 18 , and the effective apertures D 1 , D 2 of the first and second convex lenses 13 , 14 to the beam sizes E 1 , E 2 and focal lengths f 1 , f 2 being the factors for the expander optical system.

FIG. 6 illustrates a graph, in which the horizontal axis plots the values based on the four factors (E 1 , E 2 , f 1 , f 2 ) that characterize FIG. 5 , and the vertical axis plots the connection efficiency η of the optical fibers connected through the two lenses. As described later, the graph shows the influence to the connection efficiency η by the numerical aperture NA (NA 1 , NA 2 ) and the two factors of the beam sizes.

In FIG. 6 , the horizontal axis of the graph plots x, wherein, when the core diameter of the POF 16 S is given by E 1 , the core diameter of the PCF l 8 by E 2 , the focal length of the first convex lens 13 by f 1 , and the focal length of the second convex lens 14 by f 2 , x is given by the following expression.

( E 1 / E 2 )/( f 1 / f 2 )= x   (2)

Although the effective apertures (D 1 , D 2 ) of the lenses are other factors, regarding these sizes as ∞, the influence of these effective apertures D 1 , D 2 is assumed to be ignorable.

In FIG. 6 , the curve A shows the influence of the numerical aperture NA, namely, the lowering of the connection efficiency η resulting from a loss from the numerical aperture NA.

Further, the curve B shows the influence of the beam size, the lowering of the connection efficiency resulting from a loss from the beam size.

Considering that the connection efficiency does not exceed 100%, the connection efficiency retains the following three ranges.

That is, the connection efficiency is divided into a range influenced only by the numerical aperture NA, a range influenced by the numerical aperture NA and the beam size, and a range influenced only by the beam size.

Further, the connection efficiency is required to be better than that when the POF 16 S and PCF 18 are connected directly on the end faces with each other, and the following expression is deduced from the area ratio of each cores.

η>( E 1 / E 2 ) 2   (3)

Therefore, in the optical connector, the connection efficiency is required to be higher than that when the two optical fibers are directly connected, and preferably the connection efficiency η of the POF 16 S and PCF 18 exceeds 0.5 (50%)˜0.6 (60%) in the consideration of the transmission losses by the optical fibers themselves.

Next, based on FIG. 6 , the influences of each factors will be discussed in the foregoing three ranges.

First, the curve A is given by the following expression.

η= NA 2 /sin(tan −1 E 1 / E 2 ·NA 1 / x 0 )  (4)

Further, the curve B is given by the following expression.

η=(1/ x ) 2   (5)

In the drawing, under the influence only of the numerical aperture NA (0<x≦1), the connection efficiency η is better than that of the direct connection of the optical fibers, within the range enclosed by the expression (4) and the expression (3).

Further, under the influence only of the beam size E 1 /E 2 ·NA 1 /sin(tan −1 NA 2 )≦x, the connection efficiency is specified within the range enclosed by the expression (5) and the expression (3).

Under the influence of both the numerical aperture NA and the beam size

1 <x<E 1 / E 2 ·NA 1 /sin(tan −1 NA 2 ),

the curve C showing both the influences is obtained by multiplying the expression (4) and the expression (5), which is given by the following expression.

η=(1/ x ) 2 ·NA 2 /sin(tan −1 E 1 / E 2 · NA 1 / x )  (6)

Thus, the connection efficiency is specified within the range enclosed by the expression (6) and the expression (3).

From FIG. 6 , under the influence only of the numerical aperture NA, or under the influence of the numerical aperture NA and the beam size, when the ratio of the core diameter E 1 of the POF 16 S against the core diameter E 2 of the PCF 18 is equal to the ratio of the focal length f 1 of the first convex lens 13 against the focal length f 2 of the second convex lens 14 , namely, x becomes equal to 1, the connection efficiency of the optical fiber connector 10 becomes a maximum (ηa).

Under the influence only of the beam size, the connection efficiency of the optical fiber connector 10 becomes a maximum (ηb), in x=E 1 /E 2 ·NA 1 /(sin(tan −1 NA 2 )).

From the comparison of the connection efficiency ηa and ηb, the beam size rather than the numerical aperature NA is found to he the stronger factor to reduce the connection efficiency.

Therefore, in the optical fiber connector 10 , the setting of the ratio of the focal length f 1 against f 2 to be equal to the ratio of the core diameter E 1 against E 2 (x=1), aiming at the maximization (ηa) of the connection efficiency, will reduce the influence to the connection efficiency of the numerical aperture NA and the beam size.

Next, the optical fiber connector 10 will be discussed from the view point of the light beam passing through the optical components, with reference to FIG. 7 through FIG. 15 . Here, the effective apertures D 1 , D 2 of the first and second convex lenses 13 , 14 will be taken in as the factors for the optimization condition.

1) at receiving an outgoing light from the POF 16 S by the first convex lens 13

As shown in FIG. 7 , the core diameter E 1 and numerical aperture NA 1 of the POF 16 S specifies a beam size E 1 s at the focal length f 1 . Using this beam size E 1 s, a take-in efficiency η 1 by the effective aperture D 1 of the first convex lens 13 is expressed as follows.

E 1 s=E 1 +2× f×tan(sin −1 NA 1 )  (7)

η 1 =( D 1 / E 1 s ) 2   (8)

Here, if the effective aperture D 1 of the first convex lens 13 is sufficiently large, the whole light beam is transmitted through the lens, and the take-in efficiency η 1 becomes 1.00 (100%).

FIG. 7 illustrates a case of the effective aperture D 1 of the first convex lens 13 being sufficiently large, as an example.

2) at receiving a light transmitted through the first convex lens 13 by the second convex lens 14

As shown in FIG. 8 , the beam size (E 1 s or D 1 ) at transmitting through the first lens 13 and a beam size E 1 t at reaching the second lens 14 are specified by the ratio of the focal length f 1 against f 2 of the first and second convex lenses 13 , 14 . Using this E 1 t, a take-in efficiency η 2 by the effective aperture D 2 of the second convex lens 14 is expressed as follows.

E 1 t=D 1 × f 2 / f 1 (here, E 1 s>D 1 )  (9)

E 1 t=E 1 s×f 2 / f 1 (here, E 1 s≦D 1 )  (10)

η 2 =( D 2 / E 1 t ) 2   (11)

Here, provided that the effective aperture D 2 of the second convex lens 14 is sufficiently large, the light beam of the beam size E 1 t transmitted entirely through the lens, and the take-in efficiency η 2 becomes 1.0 (100%).

FIG. 8 illustrates a case that the light beam sufficiently taken in by the first convex lens 13 overflows from the effective aperture D 2 of the second convex lens 14 .

3) at receiving a light transmitted through the second convex lens 14 by the PCF 18

As shown in FIG. 9 , a take-in efficiency η 3 of the PCF 18 is specified by the numerical aperture (NAu) of the convergent light and the numerical aperture (NA 2 ) of the PCF 18 in addition to the beam size E 1 t.

Assuming that a take-in efficiency by the beam size E 1 t is η 31 , and a take-in efficiency by the numerical aperture (NAu) of the convergent light and the numerical aperture (NA 2 ) of the PCF 18 is η 32 , the take-in efficiency η 3 , namely, the connection efficiency η is the multiplication of the two take-in efficiencies η 31 , η 32 , which is given by the following expressions.

η 31 =( E 2 / E 2 s ) 2 (here, E 2 s>E 2 )  (12)

η 31 =1.0 (here, E 2 s≦E 2 )  (13)

Here, E 2 s represents the beam size on the PCF 18 . Provided that the core diameter E 2 of the PCF 18 is larger than E 2 s, the light beam of the beam size entirely falls on the PCF 18 , and the take-in efficiency η 31 becomes 1.0 (100%).

And, the take-in efficiency η 32 is given by the following expressions.

η 32 = NA 2 / NAu (here, NAu>NA 2 )  (14)

 η 32 =1.0 (here, NAu≦NA 2 )  (15)

Therefore, the take-in efficiency η 3 is expressed as follows.

η 3 =η 31 ×η 32   (16)

Thus, the take-in efficiency η 3 is the total connection efficiency η of the optical fiber connector 10 , and as shown by the expression (6) and FIG. 6 , and is the connection efficiency η in the range where it is influenced by both of the numerical aperture NA and the beam size.

Next, the take-in efficiency η 31 will be explained with reference to FIG. 10 and FIG. 11 .

FIG. 10 illustrates an optical system in which the beam size E 1 t falling on the second convex lens 14 is larger than the effective aperture D 2 of the second convex lens 14 . And, the beam size E 2 s on the PCF 18 is acquired from the proportional relation between the bean size E 1 s at the first convex lens 13 and the effective aperture D 2 of the second convex lens 14 , which is expressed as follows.

E 1 : E 2 s=E 1 s:D 2   (17)

Reducing (17),

E 2 s=E 1 × D 2 / E 1 s   (18)

FIG. 11 illustrates an optical system in which the beam size E 1 t falling on the second convex lens 14 does not exceed the effective aperture D 2 of the second convex lens 14 , which is opposite to the case in FIG. 10 . The beam size E 2 s on the PCF 18 is acquired from the proportional relation between the beam size at the first convex lens 13 and the beam size E 1 t at the second convex lens 14 , which is expressed as follows.

E 1 : E 2 s=E 1 s:E 1 t   (19)

Reducing (19),

E 2 s=E 1 × E 1 t/E 1 s   (20)

Next, the take-in efficiency η 32 will be explained with reference to FIG. 12 through FIG. 15 .

As shown in FIG. 12 through FIG. 15 , provided that W represents the beam waist where the beam becomes the thinnest at a midpoint between the two lenses, the first convex lens 13 and the second convex lens 14 in this case, W is given by the following expression.

W =2× f 1 × NA 1   (21)

As shown in FIG. 12 , in case that the effective apertures D 1 , D 2 of the first and second convex lenses 13 , 14 each are sufficiently large, the numerical aperture NAu of the foregoing convergent light is expressed as follows.

NAu= sin(tan −1 W /2 ·f 2 )  (22)

Next, in FIG. 13 , in case that the effective apertures D 2 of the second convex lenses 14 is smaller than a specific size, the numerical aperture NAu of the convergent light is expressed as follows.

NAu =sin(tan −1 ( D 2/2)· f 2 )  (23)

Next, in FIG. 14 , in case that the affective apertures D 1 of the first convex lenses 13 is smaller than the specific size, the numerical aperture NAu of the convergent light is expressed as follows.

NAu =sin(tan −1 ( D 1/2)· f 2   (24)

Next, in FIG. 15 , in case that the effective apertures D 1 , D 2 of the first and second convex lenses 13 , 14 both are smaller than the specific size, the numerical aperture NAu of the convergent light is given by the same expression as (22).

Thus, as shown in FIG. 12 , when the effective apertures D 1 , D 2 of the first and second convex lenses 13 , 14 both are sufficiently large, the take-in efficiency η 31 of the beam size E 1 t is given by the curve B in FIG. 6 ; and the substitution of the expression (20) for E 2 s in the expression (12), and the substitution of the expression (10) for E 1 t in the expression (20) will induce the foregoing expression (5).

Similarly, the take-in efficiency η 32 is given by the curve A in FIG. 6 ; and the substitution of the expression (22) for NAu in the expression (14), and the substitution of the expression (21) for W in the expression (22) will induce the foregoing expression (4).

From the above expressions (4), (5), and (16), the expression (6) which gives the curve C in FIG. 6 can be acquired.

Next, the effective aperture D 1 of the first convex lens 13 and the effective aperture D 2 of the second convex lens 14 will be discussed as factors that influence the optical fiber connector.

1) For the Case of only the Effective Aperture D 1 of the First Convex Lens 13 having Influence

For the case that the effective aperture D 1 of the first convex lens 13 is smaller than a specific size, the light emitted from the PCF 16 S is restrained by the effective aperture D 1 of the first convex lens 13 , and the beam to the second convex lens 14 and the POF 18 is limited.

Therefore, since the connection efficiency η at the POF 18 is affected by η 1 of the expression (8), it becomes the expression (16) multiplied by the expression (8), which is expressed as follows. $$ η =   ⁢ η ⁢   ⁢ 1 × η ⁢   ⁢ 3 = η ⁢   ⁢ 1 × η ⁢   ⁢ 31 × η ⁢   ⁢ 32 =   ⁢ ( D1 / E1s ) 2 × ( E2 / E2s ) 2 × NA2 / NAu =   ⁢ ( D1 / ( E1 + 2 × f × tan ⁢   ⁢ ( sin - 1 ⁢   ⁢ NA1 ) ) ) 2 ×   ⁢ ( 1 / x ) 2 · NA2 / sin ⁢   ⁢ ( tan - 1 ⁢ E1 / E2 · NA1 / x ) ( 25 )

2) For the Case of only the Effective Aperture D 2 of the Second Convex Lens 14 having Influence

For the case that the effective aperture D 2 of the second convex lens 14 is smaller than a specific size, the light emitted from the first convex lens 13 is restrained by the effective aperture D 2 of the second convex lens 14 , and the beam to the POF 18 is limited.

Therefore, since the connection efficiency η is affected by η 2 of the expression (11), it becomes the expression (16) multiplied by the expression (11) , which is expressed as follows. $$ η =   ⁢ η ⁢   ⁢ 2 × η ⁢   ⁢ 3 = η ⁢   ⁢ 2 × η ⁢   ⁢ 31 × η ⁢   ⁢ 32 =   ⁢ ( D1 / E1t ) 2 × ( E2 / E2s ) 2 × NA2 / NAu =   ⁢ ( D1 / ( D1 × f2 / f1 ) ) 2 ×   ⁢ ( 1 / x ) 2 · NA2 / sin ⁢   ⁢ ( tan - 1 ⁢   ⁢ E1 / E2 · NA1 / x ) =   ⁢ ( f1 / f2 · 1 / x ) 2 · NA2 / sin ⁢   ⁢ ( tan - 1 ⁢   ⁢ E1 / E2 · NA1 / x ) ( 26 )

3) For the Case of both the Effective Apertures D 1 , D 2 of the First and Second Convex Lenses 13 , 14 having Influence

For the case that the effective apertures D 1 , D 2 of the first and second convex lenses 13 , 14 are both smaller than a specific size, since the connection efficiency η is affected by these effective apertures D 1 , D 2 , it becomes the expression (16) multiplied by the expression (8) and the expression (11), which is expressed as follows. $$ η =   ⁢ η ⁢   ⁢ 1 × η ⁢   ⁢ 2 × η ⁢   ⁢ 3 =   ⁢ η ⁢   ⁢ 1 × η ⁢   ⁢ 2 × η ⁢   ⁢ 31 × η ⁢   ⁢ 32 =   ⁢ ( D1 / ( E1 + 2 × f × tan ⁡ ( sin - 1 ⁢   ⁢ NA1 ) ) ) 2 ×   ⁢ ( f1 / f2 · 1 / x ) 2 × NA2 / sin ⁢   ⁢ ( tan - 1 ⁢   ⁢ E1 / E2 · NA1 / x ) ( 27 )

The following table 1 presents the contents explained above, in which the influence of only the numerical aperture NA and the influence of only the beam size correspond to a case of η 31 =1.0 and η 32 =1.0 in the expressions (25), (26), (27).

	TABLE 1
		influence by
	influence by	NA & influence	influence by
	NA	by beam size	beam size
influence by
D1: null
influence by	η32	η31 × η32	η31
D2: null
(D1, D2:∞)
influence by	η1 × η32	η1 × η31 × η32	η1 × η31
D1
influence by	η2 × η32	η2 × η31 × η32	η2 × η31
D2
influence by
D1
influence by	η1 × η2 × η32	η1 × η2 × η31 × η32	η1 × η2 × η31
D2

Next, a concrete example of this type of optical fiber connector 10 will now be explained.

As shown in Table 2, the model A is made up with the following data: the core diameter E 1 of the POF 16 S being 1 mm, the numerical aperture NA 1 of the POF 16 S being 0.15, the effective aperture D 1 of the first convex lens 13 being sufficiently large, the focal length f 1 being 5 mm, the effective aperture D 2 of the second convex lens 14 being sufficiently large, the focal length f 2 being 1 mm, the core diameter E 2 of the PCF 18 being 0.2 mm, and the numerical aperture NA 2 of the PCF 18 being 0.33. These data induce x=1, which implies the maximum efficiency ηa shown in FIG. 6 . Substituting x=1 and the relevant data from the above for the expression (6), ηa=0.55 is acquired, and the loss ηLOS in this fiber connection can be expressed as follows.

η LOS =−10·log (η a (=0.55)) ≈2.6 dB

TABLE 2
Model A
	numerica		numerica
core	1	core	1		focal	focal
diameter	aperture	diameter	aperture		length	length
E1	NA1	E2	NA2	x	f1	f2
1	0.15	0.2	0.33	1	5	1
mm		mm			mm	mm

Next, as shown in table 3, the model B is made up with the following data: the core diameter E 1 of the POF 16 S being 0.75 mm, the numerical aperture NA 1 of the POF 16 S being 0.2, the effective aperture D 1 of the first convex lens 13 being sufficiently large, the focal length f 1 being 3.75 mm, the effective aperture D 2 of the second convex lens 14 being sufficiently large, the focal length f 2 being 1 mm, the core diameter E 2 of the PCF 18 being 0.2 mm, and the numerical aperture NA 2 of the PCF 18 being 0.33. From the same calculation as the model A, the loss ηLOS=2.6 dB is acquired.

Therefore, the connection efficiency η of the fibers is satisfied with a desirable value of approximately 0.5 (50%).

TABLE 3
Model B
	numerica		numerica
core	1	core	1		focal	focal
diameter	aperture	diameter	aperture		length	length
E1	NA1	E2	NA2	x	f1	f2
0.75	0.2	0.2	0.33	1	3.75	1
mm		mm			mm	mm

Thus, the optical fiber connector 10 of the invention has been described by using the model cases. And here, the POF 16 is an integration of the POF 16 S and the convex lens 16 , as shown in FIG. 1 , which is equivalent to one formed by polishing the front end of the POF 16 S into a convex lens-shape. This convex part 16 c being the front end of the POF 16 will be explained on the basis of FIG. 16 .

In the POF 16 , provided that the radius of curvature of the convex part 16 c of the core 16 a is, given by r 1 , and the refractive index of the core 16 a is given by n 1 , the relation by the following expression is deduced.

Focal length: f 1 = r 1 /( n 1 −1)  (28)

Therefore, by substituting the expression (28) for the expression (2), the POF 16 can be applied to the optical fiber connector 10 shown in FIG. 16 as it is.

Next, concrete examples as this type of the optical fiber connector 10 will be discussed. As shown in Table 4, the model C is constructed having the following data: the core diameter E 1 of the POF 16 being 1 mm, the numerical aperture NA 1 of the POF 16 being 0.15, the refractive index n 1 being 1.5, the lens-shaped radius r 1 of the front end of the core 16 a being 2.5 mm, the core diameter E 2 of the PCF 18 being 0.2 mm, and the numerical aperture NA 2 of the PCF 18 being 0.33. Thereby, without using the first convex lens 13 , the model C will be the same optical fiber connector as the model A.

Further, the model D is constructed having the following data: the core diameter E 1 of the POF 16 being 0.75 mm, the numerical aperture NA 1 of the POF 16 being 0.2, the refractive index n 1 being 1.5, the lens-shaped radius r 1 of the front end of the core 16 a being 1.875 mm, the core diameter E 2 of the PCF 18 being 0.2 mm, and the numerical aperture NA 2 of the PCF 18 being 0.33. Thereby, without using the first convex lens 13 , the model D will be the same optical fiber' connector as the model B.

Thus, in the optical fiber connector, the connection of a plastic optical fiber (POF 16 ) and a fused quartz fiber (PCF 18 ) has been described, however it is not limited to this combination.

For example, it may be a combination of two plastic fibers each having different diameters. In this case, without using lenses, it is only needed to use the plastic fibers by polishing both the front ends thereof into spherical shaped-lenses.

For example, by setting the radius of curvature r 2 of the plastic fiber core on the light receiving side to 0.5 mm and setting the focal length f 2 to 1 mm, an optical fiber connector with a high efficiency of the optical connection will be achieved without using the first and the second convex lenses 13 , 14 .

	TABLE 4
	POF
	core	numerical	refractive	focal	radius of
	diameter	aperture	index	length	curvature
	E1	NA1	n1	f1	r1
model C	1	0.15	1.5	5	2.5
model D	0.75	0.2	1.5	3.75	1.875
	mm			mm	mm
	2nd convex
	lens	PCF
	focal	core	numerical	focal	radius of
	length	diameter	aperture	length	curvature
	f2	E2	NA2	f2	r2
model C	1	0.2	0.33	1	0.5
model D	1	0.2	0.33	1	0.5
	mm	mm		mm	mm

As described above, the optical fiber connector of this invention exhibits a high connection efficiency of the fibers in the region shown by the slant lines in FIG. 6 . Therefore, to set the values of the factors that enter the region will achieve the apparatus of a predetermined connection efficiency.

As described above, the optical fiber connector of the invention includes a first optical fiber, a first lens that converges light emitted from the first optical fiber, a second lens that converges light emitted from the first lens, and a second optical fiber that receives convergent light from the second lens. In the optical fiber connector thus configured, provided that the ore diameter of the first optical fiber is given by E 1 , the numerical aperture thereof by NA 1 , the core diameter of the second optical fiber by E 2 , the numerical aperture thereof by NA 2 , the focal length of the first lens by f 1 , and the focal length of the second lens by f 2 , and (E 1 /E 2 )/(f 1 /f 2 )=x is introduced, the connection efficiency η of the first and the second optical fibers satisfies the following inequality:

( E 1 / E 2 ) 2 <η≦NA 2 /sin (tan −1 E 1 / E 2 · NA 1 / x ),

in

0 <x ≦1;

( E 1 / E 2 ) 2 <η≦(1/ x ) 2 ·NA 2 /sin(tan −1 E 1 / E 2 · NA 1 / x ),

in

−1 <x<E 1/ E 2· NA 1/sin(tan) −1 NA 2 )

or

( E 1 / E 2 ) 2 <η≦(1/ x ) 2 ,

in

E 1 / E 2 · NA 1 /sin (tan −1 NA 2 )≦ x

From the relation given by the above inequity, The optical fiber connector of the invention can significantly enhance the connection efficiency compared with the direct connection of the fist and second optical fibers, and can transmit light between remotely located places under an optimized condition, since it is designed to make the diameter of the first optical fiber differ from the diameter of the second optical fiber, and to adjust either one of the numerical apertures and the beam sizes of the fist and second optical fibers, or variable factors of the numerical apertures and the beam sizes.

Further, provided that the effective aperture of the first lens is given by D 1 , the effective aperture of the second lens is given by D 2 , the connection efficiency η 1 is influenced by only D 1 and is expressed by the equation:

η 1 = D 1 /( E 1 +2× f 1 ×tan(sin −1 NA 1 )) 2 ,

and the connection efficiency η 2 is influenced by only D 2 and is expressed by the equation:

η 2 =( D 1 /( D 1 × f 2 / f 1 )) 2 ,

the connection efficiency is the foregoing η multiplied by η 1 and/or η 2 .

Thereby, the invention can achieve a connection efficiency between the divergent light and the convergent light by taking into consideration either one or both of the effective apertures of the first and second lenses.

Further, the first lens is made by forming the end face of the first optical fiber into a spherical face, and the second lens is made by forming the end face of the second optical fiber into a spherical face. Thereby, the invention can form an optical fiber connector without a separately provided lens member, reducing the number of the components, and increasing the connection efficiency of the optical fibers, since alignment of the lenses is not needed.

Further, either one of the first and the second lenses is made by forming the end face of the first or the second optical fiber into a spherical face.

Thereby, the invention can form an optical fiber connector with a reduced number of lens members, thus reducing the number of the components, and allowing assembly with a high accuracy, since the alignment work of the lenses is reduced, and increasing the connection efficiency of the optical fibers.

Claims

1. An optical fiber connector comprising a first optical fiber, a first lens that converges light emitted from the first optical fiber, a second lens that converges light emitted from the first lens, and a second optical fiber that receives a convergent light beam from tine second lens, wherein, when a core diameter of the first optical fiber is given by E1, a numerical aperture thereof by NA1, a core diameter of the second optical fiber by E2, a numerical aperture thereof by NA2, a focal length of the first lens by f1, a focal length of the second lens by f2, and (E1/E2)/(f1/f2)=x is given, a connection efficiency η of the first and the second optical fibers satisfies the following inequalities:(E1/E2)2<η≦NA2/sin(tan−1E1/E2·NA1/x), for0<x≦1; (E1/E2)2<η≦(1/x)2·NA2/sin(tan−1E1/E2·NA1/x), for1<x≦E1/E2·NA1/sin(tan−1NA2); or(E1/E2)2<η≦(1/x)2, forE1/E2·NA1/sin(tan−1NA2)≦x.

2. An optical fiber connector according to claim 1, wherein, when an effective aperture of the first lens is given by D1 and an effective aperture of the second lens is given by D2, a connection efficiency 01 is influenced by only D1 and is expressed by the equation:η1=D1/(E1+2×f1×tan(sin−1NA1))2, and a connection efficiency 02 is influenced by only D2 and is expressed by the equation:η2=(D1/(D1×f2/f1))2, the connection efficiency is the η multiplied by η1 and/or η2.

3. An optical fiber connector according to claim 1, wherein the first lens is made by forming an end face of the first optical fiber into a spherical face, and the second lens is made by forming an end face of the second optical fiber into a spherical face.

4. An optical fiber connector according to claim 1, wherein only one of the first and the second lenses is made by forming an end face of the eslective optical fiber into a spherical face.

5. An optical fiber connector according to claim 2, wherein the first lens is made by forming an end face of the first optical fiber into a spherical face, and the second lens is made by forming an end face of the second optical fiber into a spherical face.

6. An optical fiber connector according to claim 2 wherein only one of the first and the second lenses is made by forming an end face of the respective optical fiber into a spherical face.