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A METHOD OF DETERMINING POWER PROPAGATION
FIELD OF INVENTION
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The present invention relates to a method of determining power propagation between a
plurality of power input coupling means and a plurality of optical fibers.
BACKGROUND OF INVENTION
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Fiber couplers are main devices in optical communication system. It is used to split, to
combine, and to switch the optical signal. The fiber coupler is commonly fabricated by
fusion process. The analysis and fabrication of 2X2 SMF-28 fiber couplers has been
clearly investigated in Amir Hosseini, David N. Kwong, Yang Zhang, Yazhao Liu, and
Ray T. Chen, “On the Optimum Design for 1xN Multimode Interference Coupler based
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Beam Splitters.” Microelectronics Research Center, Electrical and Computer
Engineering Department, University of Texas at Austin, Austin, TX, 78758, USA. 2010.
It describes how the light intensity is transferred from fiber one to fiber two. It was
found that the coupling coefficient is a parameter that affected by refractive index,
separation between fibers, and radius of fibers. During fusion process, coupling
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coefficient is experimentally controlled by pulling the end of fibers as to elongate it to
get desired coupling ratio.
The fabrication of MXN fiber couplers will be benefit for optical circuits. This is a new
and interesting phenomena where multi fibers with many junction fibers have not been
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investigated much, especially in experiments due to difficulties in controlling fiber
coupling parameters as seen in US 5,355,426. Therefore, M input ports and N output
ports are introduced to show how the power propagates along multi fiber coupling.
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Assuming M-parallel fibers, having same cross section, propagation constant,
refractive indices and separation between the fibers, are twisted together before fusion.
The properties of M- channel linear fiber couplers depend on where the input power is
launched. By launching input power to the different input ports gives different coupling
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velocity profile. Certainly, it results different coupling ratio. Based on the input and
output ports, MXN fiber couplers can be differed to be star and tree couplers.
There is therefore a need for a solution to determine propagation of power between
optical fibers in relation to the above identified parameters.
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SUMMARY OF INVENTION
Accordingly there is provided a method of determining power propagation between a
plurality of power input coupling means and a plurality of optical fibers, the method
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includes launching identically powered input into input ports simultaneously, detecting
output from the plurality of optical fibers from output ports and adjusting a coupling
coefficient in order to measure coupling velocity.
The present invention consists of several novel features and a combination of parts
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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 DRAWING
The present invention will be fully understood from the detailed description given
herein below and the accompanying drawing 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 of a cross section and coupling velocity of linear 1X7
fiber coupler in a preferred embodiment of the invention;
Figure 2 shows a block diagram of an experimental set up for 7 input ports of fiber
coupler in a preferred embodiment of the invention;
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Figure 3 shows a graphical representation of coupling power propagation on 1X7
monolithic fiber coupler in a preferred embodiment of the invention; and
Figure 4 shows a graphical representation of coupling power propagation on 7X1
optical fiber combiner in a preferred embodiment of the invention.
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DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
The present invention relates to a method of determining power propagation between a
plurality of power input coupling means and a plurality of optical fibers. A detailed
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description of a preferred embodiment of the invention is disclosed herein. It should be
understood, however, that the disclosed preferred embodiment are 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.
The preferred embodiment of a method of determining power propagation between a
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plurality of power input coupling means and a plurality of optical fibers is described
herein as seen in Figure 1. The method includes launching identically powered input
into input ports simultaneously, detecting output from the plurality of optical fibers from
output ports and adjusting a coupling coefficient in order to measure coupling velocity.
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The plurality of optical fibers is positioned parallel to each other and the input power is
launched into a proximally positioned optical fiber. The method includes the step of
transferring optical power which depends on length of interaction region or phase.
A plurality of M X N fiber couplers are investigated for an embodiment of seven fibers
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joined in linear array. An example of this is a 1X7 monolithic fiber coupler and 7X1
optical fiber combiner. The method is developed by using a matrix transfer to calculate
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power propagation of M X N fiber couplers. The measurement will be done on the
output power of 7X1 optical power combiner and compared with simulation results.
The M X N fiber coupler is arranged from N fibers. First, a linear array of 1X7 is used.
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The seven identical fibers are in parallel arrangement having the same separations of
fiber between them as shown in Figure 1. By launching input power to the fiber 1, the
coupling velocity will vary for each fiber. The coupling velocity describes how fast the
power can be transferred to others fiber. It is expected to decrease gradually to the
outer fiber.
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Light propagation theory was described by Maxwell equation that was applied in fiber
optic and especially for the fiber couplers. The transfer of light in fiber couplers was
determined by coupling-mode theory, where it much depend on coupling coefficient
and propagation constant of the fibers. Coupled mode theory is based on a
perturbation approach which assumes that the optical fibers are electromagnetically
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isolated. This theory is determined mathematically to be a general case that a fiber
coupler consists of M fibers.
dAm ( z )
  j  m Am ( z )  j m ( m 1) Am 1 ( z )  j m ( m 1) Am 1 ( z )
dz
dAn ( z )
  j  n An ( z )  j n ( n 1) An 1 ( z )
dz
(1a)
(1b)
Where the z-axis in Cartesian coordinate is taken to be parallel to the fiber axes, n and
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m refer to the mth fiber and nth fiber respectively. Then value of 
denotes
propagation constants, and  is the coupling coefficient. In this paper, the interaction
of photon inside the fibers ignores between the nearest fibers only.
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Rewriting Equation 1 in term of the model of differential transfer-matrix we obtain as
follows.
 1 12
 A1 ( z ) 

 A ( z) 
 21  2
 2

 0  32
 A3 ( z ) 

d 

.
.   j .

dz 


.
.
.



.
.

 . 
0
 A (Z )
.
 M


0
.
.
 23 0 .
 3  34 0
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
0  N ( N 1)
0   A1 (0) 
.   A2 (0) 


.   A3 (0) 


.  . 
.  . 


0  . 
 N   AN (0) 
(2)
The solution of inner matrix on Equation 2 is determined by eigenvalue and
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eigenvector that describes transformation of power between the fibers as follow,
 A1 (0) 
 A1 ( z ) 
 A (0) 
 A ( z) 
 2 
 2

 A3 (0) 
 A3 ( z ) 






 .    j  M pq   . 
 . 
 . 




 . 
 . 
 A (0) 
 A (Z )
 M

 N 
M pq 
Where
n
 pm 
(3)
 qm 
 sin  n  1  sin  n  1  e
p , q 1
mz
is the transfer matrix. It has been shown that
the power transfers between the fibers are the case where the coupling coefficient is
much smaller than the propagation constant. The Propagation constant and the
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coupling coefficient are given by Equation 4 and 5 respectively [6].
1/ 2
 2 n1  2 U 2 
  
  2 
  


(4)
 U 2 K 0 W  d /   
V 3 K12 (W )
(5)
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where  is the wavelength of light in vacuum, K ‘s are modified Hankel function, the
2
value
n 
  1  2 
 n1  ,
of
U  2.405e

 1
2
V
V
2 n1 

 U 2 W 2
is
a
normalized
frequency,
is the progression of phase, and W is the transverse decay of
amplitude.
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The solution of Equation 3 consists of coupling coefficient and propagation constant.
Assuming the cross section, separation of the fibers, and propagation constant held to
be constant, the power PN in each output port can be written as follows.
n
n
n
n
2
 is   ms   it   qt   s  c  z
PN ( z )   AN ( z )    sin 
Pq (0) Pm (0)
 sin 
 sin 
 sin 
e
 n 1   n 1   n 1  n 1
m 1 q 1 s 1 t 1
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(6)
Where
 m 
  , m, q, s, t  1, 2,3,....n
 n 1 
m  2 jK cos 
are
eigenvalue
of
coupled-mode
differential matrix. The MXN fiber coupler represents as a star coupler where the
source wavelength any input ports and output detector can be used as optical logic
system.
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The 7X1 fiber coupler is simply examined by launching identical 1mW from the input
ports, and a photo detector is put at the end of output port connecting to the
oscilloscope as shown in Figure 2.
All input power is launched in to seven input ports simultaneoulsy, and power at the
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end of output port is measured.
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Result and Discussion
The simulation of power propagation on fiber coupler using Equation 3 and 4 with
single input power such as 1X7 shows that power in initial fiber is gradually transferred
to the other fibers as a function of length of the interaction region or phase. Power of
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each fiber oscillates in the propagation period. Firstly, the input power is transferred to
fiber two, three until fiber seven. As can be seen, the initial peak of fiber one is equal to
1 mW, and the 2st peak decreases rapidly due to propagation to other fibers. This
condition occurs for 1XN or NX1 with N>3, which means the fiber cannot return all
power to the initial fiber as 1X2 and 1X3 fiber couplers.
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In Figure 3, power is transferred with different coupling velocity. The coupling velocity
follows the profile given in Figure 1, where it is slower for the outer fiber. If power is
launched to fiber 1, the fiber 7 has the slower coupling velocity, and has the higher
transferred power. For the case of input power is not launched to fiber 1, i.e. fiber 2, or
fiber 3, or fiber 4, the coupling velocity will be different for every those conditions. To
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control coupling ratio in output ports the appropriate coupling coefficient is required.
For example the identical output characteristics of 1X7 monolithic fiber coupler can be
designed by launching input power to the center (fiber 4), and the coupling coefficient
is adjusted until reach all power in output ports are identical.
The coupling power propagation on 7X7 fiber coupler with seven input power and
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single output ports such as 7X1 fiber combiner is also calculated using Equation 3 and
6. Comparison of power propagation for coupling power model to experiment can be
seen in Figure 4.
Generally, the model calculation result shows good agreement with the experimental
curve. When all input powers are launched to the input ports, the output power is
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maximum or equal to 7 milli Watt (mw) (with very small losses). Firstly, simulation
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result decreases sharply from 7mW to 6mW at distance around 20 nanometers (nm).
It then decreases rapidly until 60nm. Power is absorbed by the silicon dioxide fiber
structure, and some energy is transferred to them in term of mechanical heating and
radiation. As the distance increases, power increases gradually with the small
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decrease at around 0.9. Therefore, the experimental result remains not too many
changes in power amplitude in the range of  0-10nm, the simulation result follows the
experiment with the small discrepancy. These differences occur due to the fiber
geometry, where the coupling velocity no longer transfers all power to the center of
fiber. It can be seen clearly for distance longer than 10 nm, power could not increase
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as high as simulation results. In summary, the experiment curve describes there are
power losses along fibers due to absorption, radiation where it is not assumed in
simulation as power is held lossless.
Therefore, power is transferred to other fibers with different coupling velocity. The test
for linear 1X7 fiber, the fiber 7 has the slowest coupling velocity and has the higher
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transferred power for input of fiber 1. Comparison between simulation and
experimental results has shown good agreement with small discrepancy due to no
assumption of power losses in model. There is different normalized power by factor
fiber geometry where the coupling velocity no longer transfers to all power to others
fiber.
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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, measuring power transferred between optical fibers.