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Coherently Coupled Optical Waveguide
報 告 者 ：陳 嘉 怜
指導教授：王 維 新 博 士
Outline
 Introduction
 Paper Review
 Principle of Operation
 Experiences and Results
 Summery
 References
2
Introduction
Motivation:
Optical bending waveguide are used to change the direction of light propagation
in many integrated optical devices such as MZ and directional couplers. In order
to reduce the device area and increase the packing density, we must to find bend
structures with large bend angles and low loss.
Structure:
Curved optical waveguide; Conventional bend waveguide;
Etched-wall bend waveguide; Coupler bend waveguide; Prism waveguide.
Principle of coupler bend waveguide:
Coupled-bend transmission can be an oscillatory function of the interconnection length L
due to interference between the guided and radiation modes.
Material:
Ti ; Ni ; Zn and Ni
3
 Introduction
 Paper Review
 Principle of Operation
 Experiences and Results
 Summery
 References
4
Conventional Bend Waveguide
P0
x
n1
n2
n1
Pi
P0  Pi T
 < 2º
z
2
exp   0 L 0 
P0: output power
Pi: input power
0: radiation and absorb parameter
Lo: distance of optical beam propagating in waveguide
T: power combine parameter(
T
2

  
 exp   2 x0 sin 2  
 4 

)
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Etched-wall Bend Waveguide
Wave front in the part is speeded up to
make bending easier and reduce the power
loss.
n1
P0

n2
n1
Advantage: power loss
Pi
x
z
/2
is lower than convention bend
waveguide.
Disadvantage: As  larger than 20,
power loss will be
higher and make this bending waveguide
not to have the ability of light propagation.
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Coupler Bend Waveguide
speeded
down
Wave front
front ininthe
thepart
partis is
speeded
up to
make bending easier and reduce the power
loss.
n1
P0
n2
n1
Pi
x

d
z
/2
Advantage:
power loss is lower with
suitable coherent length.
7
 Introduction
 Paper Review
 Principle of Operation
 Experiences and Results
 Summery
 References
8
Principle of Coherent Coupler I
X2
3
1
W

Z2

2
L
Electric field:
Guided mode
Radiation mode


Ei ( xi , z i )  Gi u g ( xi ) exp( j g z i )   Rms ,i u ms ( xi )  Rma ,i u ma ( xi ) exp( j m z i )
m
Propagation constant:
 2n
b
 m  
 0



2

2
2
 m  

1
2
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Principle of Coherent Coupler II
1
Electric field:
2
3
L


Ei ( xi , z i )  Gi u g ( xi ) exp( j g z i )   Rms ,i u ms ( xi )  Rma ,i u ma ( xi ) exp( j m z i )
m
Electric Field parameter:
Waveguide 1:
Rms ,1  Rma .1  0;
Waveguide 2:
Rms ,1  c gs ,m ;
G1  1
Rma .1  c ga,m ;
G2  c gg
Waveguide 3:
G3  c gg 
2


2
2
s
a


   c g ,m  c g ,m  exp i g   m L 



m 
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Principle of Coherent Coupler III
1
Electric field:


2
3
L
Ei ( xi , z i )  Gi u g ( xi ) exp( j g z i )   R u ( xi )  R u ( xi ) exp( j m z i )
s
m ,i
s
m
a
m ,i
a
m
m
Guided mode
Radiation mode
Guided-mode transmission equation:
G3
2


2
a

 s

 c gg    
 c g ,m  c g ,m  exp i g   m L 


m 
2
2
2
The equation shows that the coupled-bend transmission can be an
oscillatory function of the interconnection length L due to interference
between the guided and radiation modes.
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Principle of Coherent Coupler V
1
Interconnection Length L:
L
2m  1 
m  0, 1, 2......
2n

n  N eff  N effR

2
3
L
(m  0, 1, 2......)
Neff: guided-mode effective index
NeffR:weighted-average effective index of the radiation modes excited after the first bend.
If the phase difference between the modes shifts is:
2m  1 rad
m  0, 1, 2......
light coupled from the guided mode into an unguided
mode at a bend can be completely coupled back into the
guided mode at a succeeding bend.
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Principle of Coherent Coupler VI
1
2
3
L
L=180m
2m  1 
2n
m  0, 1, 2......
GUIDE-MODE TRANSMISSION
L
PHASE FRONTS
L=380m
INTERCONNECTING-SEGMENT LENGTH. L(um)
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 Introduction
 Paper Review
 Principle of Operation
 Experiences and Results
 Summery
 References
14
Coherently Coupler Bend
L
L
2Θ
(Relative Transmission)
1/2
Θ
SECTION LENGTH, L( m )
15
Coherently Coupler Bend
N=2
L
L
3Θ
2Θ
(Relative Transmission)
1/2
Θ
NUMBER OF SECTIONS ( N )
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Coherently Coupler Bend
Phase rocking region
4Θ
3Θ
2Θ
Θ
(a)standard structure
Phase rocking region
4Θ
3Θ
Θ
(b)new structure
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Transmitted Power with Total
Bending Angle
18
Transmitted Power with Launching
Wavelength
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Summery
The transmission function of the coupler bend waveguide depends
on the interference of guided mode and radiation mode in the
interconnection length L.
We study the principle of coupler bend waveguide which is better
than conventional bend and etched-wall bend waveguide in being
a suitable bending structure with large bend angles and low loss.
Other new structures include prism and new structure couple bend
waveguide.
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References
L. M. Johnson and F. J. Leonberger, “Low-loss LiNbO3 waveguide bends
with coherent coupling,” Optics Letters, Vol. 8, No. 2, Feb. 1983.”
L. M. Johnson and D. Yap, “Theoretical analysis of coherently coupled
optical waveguide bends,” Applied Optics, Vol. 23, No.17, 1 Sep.1984.
張文清, “An Investigation of integrated optical waveguide bends, ”
蘇 振 嘉 , “Coherent-coupling-based wide-angle bending optical
waveguide design and fabrication, ”
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