Multi-mode multiplexing using staged coupling and quasi-phase-matching
A mode-selective add/drop unit for a mode division de/multiplexing device includes an optical ADU waveguide adapted for coupling to an input optical waveguide. The optical ADU waveguide includes at least one region providing optical signal coupling between the ADU waveguide and a multi-mode waveguide; and, one or more phase matching regions for controlling a relative or absolute phase difference between an electromagnetic wave (EMW) carried in the ADU waveguide and the multi-mode waveguide. The mode-selective add/drop unit may further include a transition region connecting the coupling region and a phase matching region, wherein a shape of a transition region is governed by a polynomial function, exponential function, logarithmic function, trigonometric function or, any combination of these functions.
1. A method of designing a mode-selective add-drop (MSADU) unit having an optical ADU waveguide for coupling signals from an input optical waveguide to a multi-mode waveguide, the optical ADU waveguide having a region for coupling said input optical waveguide, said method comprising:
specifying a gap value d κ between said optical ADU waveguide and said multi-mode waveguide, a wavelength value λ l and, an allowable optical ADU waveguide width ω a x ;
calculating one or more transfer matrices and propagation constants for modes in a coupling regions and quasi phase matching region between said optical ADU waveguide and said multi-mode waveguide;
forming a representation of an output width of said ADU waveguide as a function of said calculated one or more transfer matrices and propagation constants for modes in coupling regions and quasi phase matching regions;
minimizing a value of said representation such that a difference between a desired modal power distribution and an actual modal power distribution is minimized;
calculating an optimum ADU waveguide width based on said minimized value; and,
optimizing a profile of said coupling region of said ADU waveguide to preserve continuity in the width and at least a first derivative of said profile to minimize power loss,
wherein a program using a processor unit executes one or more of said calculating one or more transfer matrices and propagation constants, forming, minimizing, calculating ADU waveguide width, and optimizing.
2. The method as claimed in claim 1 , wherein said output width representation is a function governed according to:
w
~
a
x
(
d
k
,
λ
l
)
=
arg
min
w
a
x
∈
[
w
min
,
w
max
]
{
∑
i
∈
I
(
∑
k
=
1
,
l
=
1
n
c
[
T
1
,
k
-
1
T
k
,
i
T
1
,
l
-
1
T
l
,
i
∫
θ
2
π
/
β
_
c
[
B
c
k
(
z
)
B
c
l
(
z
)
*
]
ⅆ
z
]
)
}
where T is the transfer matrix and the scalars β c l . . . β c n c are functions of width ω a x and a gap d κ between ADU and multi-mode waveguide, and λ l the wavelength of the optical signal waveguide mode being transferred.
3. The method as claimed in claim 2 , wherein said optimum ADU width is calculated according to:
w
a
*
=
1
N
1
N
2
∑
n
=
1
N
1
∑
l
=
1
N
2
w
~
a
(
d
k
,
λ
l
)
where N 1 is the number of different gap values under consideration and N 2 is the number of different wavelength values under consideration.
4. A method of designing a mode-selective add-drop (MSADU) unit having an optical ADU waveguide for coupling signals from an input optical waveguide to a multi-mode waveguide, said method comprising:
specifying a gap value d κ between said optical ADU waveguide and said multi-mode waveguide, a wavelength value λ l and, an allowable optical ADU waveguide width ω a x ;
calculating one or more transfer matrices and propagation constants for modes in coupling regions and quasi phase matching regions between said optical ADU waveguide and said multi-mode waveguide;
forming a representation of a length L c of a staged coupling region and a length of a phase matching region L t of said optical ADU waveguide as a function of said calculated one or more transfer matrices and propagation constants for modes in coupling regions and quasi phase matching regions, said staged coupling and phase matching region of said optical ADU waveguide for coupling an optical signal to said multi-mode waveguide at a desired mode to said multi-mode waveguide; and,
calculating an optimum value of the staged coupling length L c and the phase matching length L t based on a maximized power value to said desired mode of said multi-mode waveguide,
wherein a program using a processor unit executes one or more of said calculating one or more transfer matrices and propagation constants, forming, and calculating lengths L c and L t .
5. The method as claimed in claim 4 , wherein said representation of a length L c of a coupling region and a length of the phase matching region L t of said ADU waveguide is a summation governed according to:
[
L
~
c
n
(
λ
l
)
,
L
~
t
n
(
λ
l
)
]
=
argmin
L
c
n
∈
[
L
c
min
,
L
c
max
]
,
L
t
n
∈
[
0
,
L
t
max
]
{
min
z
′
∈
[
0
,
2
L
c
max
]
[
Φ
s
′
(
z
′
)
·
Φ
s
′
(
z
′
)
*
-
ϕ
s
′
n
a
+
m
(
z
′
)
ϕ
s
′
n
a
+
m
(
z
′
)
*
]
}
where L c min and L c max are minimum and maximum allowable values for L c based on geometrical limitation due to fabrication, size, etc., and, L t max is a maximum allowable value for L t based on geometrical limitation due to fabrication, size, etc. and Φ represents modal coefficients depending upon the electric field distribution among various modes, and z′ is a distance along the direction of wave propagation.
6. The method as claimed in claim 5 , calculating said optimum values of the output staged coupling and phase matching region according to:
[
L
c
n
,
L
t
n
]
*
=
1
N
2
∑
l
=
1
N
2
[
L
~
c
n
(
λ
l
)
,
L
~
t
n
(
λ
l
)
]
where N 2 is the number of different wavelength values under consideration.
7. The method as claimed in claim 6 , wherein calculating said optimum values comprises:
setting index n=1;
calculating an optimum staged coupling length L c and the optimum quasi change length L t for the n th stage;
checking a power transfer to said an m th mode of said multi-mode waveguide;
determining if said power transfer to said m th mode is not optimized, and,
if said power transfer is not optimized, setting n=n+1 and returning to said calculating L c and L t ; and, otherwise, if said power transfer to said m th mode is optimized, terminating the calculating.
8. The method as claimed in claim 7 , wherein calculating said optimum values comprises:
calculating an optimum staged coupling length for the last stage according to
L
~
c
n
(
λ
l
)
=
argmin
L
c
n
∈
[
L
c
min
,
L
c
max
]
{
Φ
s
(
L
c
n
)
·
Φ
s
(
L
c
n
)
*
-
ϕ
c
n
a
+
m
(
L
c
n
)
ϕ
s
n
a
+
m
(
L
c
n
)
*
}
.
9. The method as claimed in claim 7 , wherein calculating said optimum values comprises:
calculating an optimum staged coupling length for the last stage according to:
[
L
c
n
]
*
=
1
N
2
∑
l
=
1
N
2
L
~
c
n
(
λ
l
)
.
10. A non-transitory computer program product for designing a mode-selective add-drop unit (MSADU) having an optical ADU waveguide for coupling signals from an input optical waveguide to a multi-mode waveguide, the computer program product comprising:
a storage medium readable by a processing circuit and storing instructions for execution by the processing circuit for performing a method comprising:
specifying a gap value d κ between said optical ADU waveguide and said multi-mode waveguide, a wavelength value λ l and, an allowable optical ADU waveguide width ω a x ;
calculating one or more transfer matrices and propagation constants for modes in coupling regions and quasi phase matching regions between said optical ADU waveguide and said multi-mode waveguide;
forming a representation of a length L c of a staged coupling region and a length of a phase matching region L t of said optical ADU waveguide as a function of said calculated one or more transfer matrices and propagation constants for modes in coupling regions and quasi phase matching regions, said staged coupling and phase matching region of said optical ADU waveguide for coupling an optical signal to said multi-mode waveguide at a desired mode to said multi-mode waveguide; and,
calculating an optimum value of the staged coupling length L c and the phase matching length L t based on a maximized power value to said desired mode of said multi-mode waveguide.
11. A non-transitory computer program product for designing a mode-selective add-drop unit (MSADU) having an optical ADU waveguide for coupling signals from an input optical waveguide to a multi-mode waveguide, the optical ADU waveguide having a region for coupling said input optical waveguide, the computer program product comprising:
a storage medium readable by a processing circuit and storing instructions for execution by the processing circuit for performing a method as claimed in claim 1 .