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A METHOD OF FABRICATING A FIBER COUPLER
FIELD OF INVENTION
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The present invention relates to a method of fabricating a fiber coupler.
BACKGROUND OF INVENTION
Electric field propagation in fiber couplers still faces the problem of polarization. The
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effects of these polarizations are that there are still losses experienced during
propagation which could have been redirected to improve efficiency.
There is therefore a need for improvements on reducing polarization in fiber couplers.
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SUMMARY OF INVENTION
Accordingly there is provided a method of fabricating a fiber coupler, the method
includes the steps of positioning 3 single mode fibers on a plurality of stages,
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connecting the fibers to a diode laser and displaying to a photodiode, wherein the two
fibers are twistable and held by vacuum means, fusing and pulling of the fibers, heating
of the coupling regions and stopping the heating and pulling upon reaching a preset
coupling ratio.
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The present invention consists of several novel features and a combination of parts
hereinafter fully described and illustrated in the accompanying description and
drawings, it being understood that various changes in the details may be made without
departing from the scope of the invention or sacrificing any of the advantages of the
present invention.
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BRIEF DESCRIPTION OF THE DRAWINGS
The present invention will be fully understood from the detailed description given
herein below and the accompanying drawings which are given by way of illustration
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only, and thus are not limitative of the present invention, wherein:
Figure 1 shows a block diagram for an experimental set up for a method of fabricating
a fiber coupler in a preferred embodiment of the invention;
Figure 2 shows a block diagram of Measurement of Polarization at the output ports
3X3 SMF coupler in the preferred embodiment of the invention;
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Figure 3 illustrates a graphical representation of power transfer between the three
waveguides with variable coupling coefficient;
Figure 4 illustrates a graphical representation of power input being distributed
symmetrically to the two outer waveguide (WG 1 and WG 3); and
Figure 5 illustrates a graphical representation of decreasing output powers versus
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different angles of polarization.
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DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
The present invention relates to a method of fabricating a fiber coupler. A detailed
description of a preferred embodiment of the invention is disclosed herein. It should be
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understood, however, that the disclosed preferred embodiment is merely exemplary of
the invention, which may be embodied in various forms. Therefore, the details
disclosed herein are not to be interpreted as limiting, but merely as the basis for the
claims and for teaching one skilled in the art of the invention.
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The following detailed description of the preferred embodiment will now be described in
accordance with the attached drawings, either individually or in combination.
Figure 1 shows an experimental set up for a method of fabricating a fiber coupler. The
method includes the steps of positioning 3 single mode fibers on a plurality of stages,
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connecting the fibers to a diode laser and displaying to a photodiode, wherein the two
fibers are twistable and held by vacuum means, fusing and pulling of the fibers, heating
of the coupling regions and stopping the heating and pulling upon reaching a preset
coupling ratio. The method is carried out by placing three single mode fibers (SMF) on
the stages. Corning fiber with diameter of core and cladding 125 and 8.2 micrometer
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respectively, is connected to the diode laser and displayed to the photodiode. The two
fibers are twisted and held by a vacuum system with both ends.
All parameters are recorded by data acquisition card installed to the computer system.
The initial step is to pre-set parameters such as coupling ratio, maximum pulling
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length, x-y-z position of torch flame, and flowing of H2 gas. 1 mW laser launched to the
one of input ports is detected by photo detector and kept for calibration, while the
fusion and pulling process are started. During the step of the torch flame heating the
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coupling region, the fibers are elongated by pulling stages with suitable pulling speed
of 100µm/s. Heating and pulling process will be automatically stopped when the preset coupling ratio is reached. For safety reason, the coupling region is saved and
packaged. The mechanical operation is motorized in micrometers scale.
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A next set up of fused 3X3 Single Mode Fiber (SMF) coupler is designed to investigate
polarization characteristics as shown in Figure 2. Continuous Wave (CW) laser as an
optical source is launched to an outer fiber (fiber 3) with wavelength operation of 1550
nm. A laser beam is polarized by different angle of polarizer before moving at one of
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outer fiber (Waveguide 3). Optical Spectrum Analyzer (OSA) and Optical Power Meter
(OPM) are set to detect the power at three output ports of 3X3 fiber coupler.
Propagation of optical power in silica-fiber waveguide coupler described by coupled
mode theory shows the strength of the coupling coefficient to transfer power from a
waveguide to other waveguide. The propagation of optical power significantly depends
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on separation between fibers axis at coupled region. Since a 3X3 SMF coupler
successfully fabricated with waveguides are weakly coupled, the fiber cross section
and separation are nearly identical, powers detected at output ports will be normalized.
However, the transfer power between the waveguides is different for not only every
configuration or arrangement of that three fibers joined, but also which input port fed by
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power. With this method, linear arrangements of three waveguides at coupling region
are purposed.
Power is launched to outer waveguide (WG 1 or WG 3), the power transfer between
three waveguides can be determined from matrix transform which is given by (4) in two
conditions. The first condition, power is launched in to waveguide 1 or waveguide 3 as
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a linear order. By substituting 
A1 (0)  1, and A2 (0)  A3 (0)  0 
in (4) as shown in Figure 3
yields as follow.
(6a)
(6b)
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(6c)
The propagation of optical power in silica-fiber waveguide coupler described by
coupled mode theory shows the strength of the coupling coefficient to transfer power
from a waveguide to other waveguide. It significantly depends on separation between
fibers axis at coupled region. Since a 3X3 SMF coupler successfully fabricated with
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waveguides are weakly coupled, the fiber cross section and separation are nearly
identical, powers detected at output ports will be normalized. However, the transfer
power between the waveguides is different for not only every configuration or
arrangement of that three fibers joined, but also which input port fed by power. In this
paper, linear arrangements of three waveguides at coupling region are purposed.
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Power P1 propagates gradually from initial waveguide (WG 1) to the center waveguide
(WG 2). Power P2 affected by the coupling coefficient  23 , will optimize it at waveguide
3 (fiber 3). The second condition, input power is fed in the center of the three
waveguides .Similarly by substituting
 A2 (0)  1, and A1 (0)  A3 (0)  0 in (4), will yield as
follow:
A1  z   A3  z    j
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sin
2
1

2 z e  j  z
(7a)
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

A2  z   cos 2 z e j z
(7b)
Figure 4 shows that power input will be distributed symmetrically to the two outer
waveguide (WG 1 and WG 3). Power P2 is minimum.
Polarization is a factor that affects the sensitivity and stability of the optical network
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system, especially for the passive device of fiber optics systems, polarization may
cause losses in that device. It is possible to a fiber coupler to have significant losses
caused by polarization effects. determined from the coupled-mode theory. By rewriting
the differential matrix for MXN fiber coupler as (8), where
electric field for the
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ith
Ai ( z ) , and Ai (0) are the
output powers and input powers respectively.
. . .
 A1 ( z ) 
 B C1 0
 A ( z) 
C B C 0 . .
1
 2

 1
 A3 ( z ) 
 0 C1 B C1 0 .
d 


.   j .
.
.
. . .
dz 


.
.
.
.
. . .



.
.
. . .
 . 
.
 A (Z )
0
.
.
. 0 C1
 M


0   A1 (0) 
.   A2 (0) 
.   A3 (0) 


.  . 
.  . 


0 . 
B   AN (0) 
(8)
Every amplitudes has two component vector polarization, they are x and y component.
 x
B
  xy
Defining
 xy 
 y 
  ixjx
C1  
  ixjy
is matrix of coupling for single fiber, and
matrix of coupling between two adjacent fibers. Where
 ixjy 
 iyjy 
is the
 ixjx  iyjy

,
and ixjy are the
two x polarization modes, and two y -polarization modes, and x and y polarized modes
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of two adjacent fibers of coupling coefficients respectively.
Consider all fibers, which are identically isolated and weakly coupled, have different
polarization, and the coupling coefficient of this mode
 ixjy
is assumed zero. The
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coupling
coefficients
 ixjx  xx  iyjy  yy
assumed
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  x
 A1x ( z ) 



   xy
 A1 y ( z ) 
 
 A ( z) 
 ixjx
 2x 
 0
 A2 y ( z ) 



A3 x ( z ) 

d 
A3 y ( z )    j 

dz 

 . 




 . 

 . 




 AMx ( z ) 

 A ( z)
 My 

between
and
 xy 
 y 
two
identical
modes
of
polarization
are
 xx =  yy =  . Eq. 1 can be given as,
  ixjx

 0
  A1x (0) 


  A1 y (0) 



0    x  xy    ixjx
0 
  A2 x (0) 
0
.
.
.
 
 

  A2 y (0) 
 iyjy    xy  y   0  iyjy 


0    x  xy    ixjx
0 
  A3 x (0) 
  ixjx
0
.
.

 
 
 0
  A (0) 
 0  iyjy    xy  y   0  iyjy 
  3y 
 . 
.
.
.
.
.
.
.


.
.
.
.
.
.
.
 . 

 . 
.
.
.
.
.
.
0


0    x  xy    ANx (0) 
  ixjx
0
.
.
.
0 
 
   A (0) 
 0  iyjy    xy  y    Ny 
0 
 iyjy 
0
.
.
.
0
(9)
or, it can be simplified in term of transpose matrix describing the matrix transmission of
the MXN fiber coupler including the two polarized modes.
E
1x
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E1 y
E2 x
T  E1x
E2 y
E1 y
E3 x
E2 x
E3 y
E2 y
. . . EMx
E3 x
EMy  z 
t
E3 y . . . EMx
EMy 
t
(10)
The polarization characteristics of single mode fiber coupler can be investigated by
applying matrix (1), then inserting the boundary condition to the calculation. In this
research, the polarization characteristic of 3X3 are purposed to be investigated. To
examine the polarization behavior of 3X3 SMF coupler, it is simplified three fibers are
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in linear arrangement.
Consider the coupling coefficient given by (5) is held to be constant along the fiber, and
the coupling region is very short, it can be simplified
 x2  2 x  y   y2  4 xy2   2
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2  1 ,    x   y , and
. Using matrix equation of polarization of multiport fiber
coupler given by (9), Eq. 5 becomes.
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T e
i
x   y
2
L
 M1
M
 2
 M 3
M3 
M 2 
M1 
M2
M4
M2
1

 L 
 L
sin 2 
  cos 1 L  1  cos 2  i
2
2
2 

2
M1  
i xy
 L

sin 2  cos 1 L  1

2
2

(11)
i xy



*
1

 2 L 
 2 L   

i
sin
  cos 1 L  1  cos
 
2
2
2 


2
 
2
sin
2 L
2
 cos 1L  1
 2

2 xy
 
 L
 L
 L


sin 1 L  
sin 2  i cos 2 

sin 1 L sin 2
2
2 
2
2
 2

 2
M2  
*

2 xy

 
2 L
2 L
 2 L   
 2

sin 1 L sin
sin 1 L  
sin
 i cos

  

2
2
2
2 
 2
 
 2


1

 L 
 L
sin 2 
  cos 1 L  1  cos 2  i
2
2
2 

2
M3  
i xy
 L

sin 2  cos 1 L  1

2
2

i xy



*
1

 2 L 
 2 L   

i
sin
  cos 1 L  1  cos
 
2
2
2 


2
 
2
sin
2 L
2
 cos 1L  1
 2

2 xy
 
 L
 L
 L


sin 1 L  
sin 2  i cos 2 

sin 1 L sin 2
2
2 
2
2
 2

 2
M4  
*

2 xy

 
2 L
2 L
 2 L   
 2

sin 1 L sin
sin 1 L  
sin
 i cos

  

2
2
2
2 
 2
 
 2


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The Eq. 11 depends on where the input power is launched. For example, if the input
power to the center (fiber 2), the output power at fiber 1 and fiber 3 given by following
equation.
  2  4 xy
 L
 L 
1 2
sin 1 L 
sin 2 2  cos 2  

2
2
2
2  


2 xy

2
2 2 L
S2 
sin

L
sin

1
2
 22


2 xy

L

L
2
2 2
2

S3 
sin

L
sin
cos
1
2
2
 22

 (12)
S1 
Figure 5 shows a good agreement among output power in both three output ports
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decreases exponentially by increasing the angle of polarization in (12). However, Initial
power at P1 is slightly higher than power at P2 and P3. This is a weakness of 3X3 as a
power splitter since the coupled region is linear arrangement. P2 and P3 are held
identical and similar power.
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A directional fiber coupler is fabricated with the method as described above. The fiber
coupler which has an identical-output ratio is successfully fabricated by heating the
coupling region with fusion temperature of 800-1350 °C. The coupled-mode theory has
been used to model power transfer between the waveguides based on transfer matrix
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method. By launching 1mW input power to one of three input ports, it shows that power
propagation among three coupled fibers is always normalized if the waveguides are
nearly identical and have same separation between them. This constructed matrix 3x3
also has been used to determine the polarization behavior of directional fiber coupler. It
is found that incident beam polarized at different angle causes power output at both
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three output ports decrease exponentially.
It is to be understood that the embodiments of the invention described are
exchangeable for other variations of the same in order to be used in various
applications. The present embodiment of the invention is intended for, but not
restricted to, use as a passive device that can be used as power splitter and routers.
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