Method and apparatus for fabricating microstructured optical fibers
Prior to fabrication of an optical fiber with desired optical properties, a preform geometry is determined dependent upon a fiber geometry that possesses the desired optical properties. The desired geometry may contain a large number of channels. The processor determines the preform geometry by tracking backwards in time the parameters of a set of conformal mappings that describe the cross section of the fiber. Some of the drawing process parameters may be specified, while other parameters may be determined along with the preform geometry. The determined preform geometry may be used to fabricate the required preform. Using this preform, the determined drawing process parameters may be used to draw the desired fiber.
1. A non-transient computer readable medium containing processor instructions that, when executed by a hardware processor, perform a method for determining fabrication parameters for a microstructured optical fiber fabrication process that draws a microstructured optical fiber from a heated preform, where the microstructured optical fiber contains a plurality of pores, the method comprising:
providing a user interface;
receiving, via the user interface, one or more user-selected properties of the microstructured optical fiber to be fabricated, where, for each pore n of the plurality of pores, the user-selected properties comprise values that specify a boundary of the pore in the fabricated microstructured optical fiber;
executing an inverse model of the fiber draw process that accounts for the outer boundary of the fiber and for interaction between pores of the plurality of pores;
determining the fabrication parameters dependent upon the one or more user-selected properties, where the one or more fabrication parameters specify a geometric configuration for the preform; and
outputting the fabrication parameters for use in the microstructured optical fiber fabrication process,
where executing the inverse model comprises:
representing flow in the heated preform by a stream function of the form:
ψ= Im [ z ƒ(z,τ)+g(z,τ)],
in which z is a position within the fiber, ƒ(z)□ƒ i z+□(1/z),
g
′
(
z
)
=
∑
k
=
1
N
-
1
g
k
z
k
+
•
(
1
/
z
)
and the function fi is related to the far-field pressure p and vorticity w, as follows from the relation
4
f
′
(
z
,
τ
)
=
p
μ
-
i
ω
;
for each pore of the plurality of pores, representing a time varying boundary z n (ζτ) of the pore as a conformal mapping of a unit disc |ζ|<1, where ζ is a complex parameter and the conformal mapping given by:
z
n
(
ζ
,
τ
)
=
Z
n
(
τ
)
+
a
n
,
-
1
(
τ
)
ζ
+
∑
k
=
1
N
-
1
a
n
,
k
(
τ
)
ζ
k
,
in which τ is a time variable, n is an index of the pore, Z n (τ) is a centroid position of the n th pore, a n,−1 (τ) and a n,k (τ) are time varying parameters that describe the shape of the pore, and N is an integer greater than 2, and wherein Re{z n (ζτ)}≡x n (ζ,τ) denotes the x-coordinate of the pore boundary and Im{z n (ζ,τ)}≡y n (ζ,τ) denotes the y-coordinate of the pore boundary;
for each pore of the plurality of pores, determining first values a n,−1 (τ 0 ), a n,k , (τ 0 ) and Z n (τ 0 ) from the user-selected properties of the microstructured optical fiber to be fabricated, where τ 0 is a time at which the drawing process ends;
dependent upon the first values for the plurality of pores, determining, in the hardware processor, second values a n,−1 (τ 1 ), a n,k (τ 1 ) and Z n (τ 1 ) corresponding to a second value of the time variable τ 1 , where τ 1 is a time at which the drawing process begins, and where the boundary of the n th pore in the preform is given by:
z
n
(
ζ
,
τ
1
)
=
Z
n
(
τ
1
)
+
a
n
,
-
1
(
τ
1
)
ζ
+
∑
k
=
1
N
-
1
a
n
,
k
(
τ
1
)
ζ
k
;
and outputting the fabrication parameters, where the fabrication parameters describe the boundaries z n (ζ,τ 1 ) of the pores in the preform and may be used to fabricate the preform.
2. The non-transient computer readable medium of claim 1 , wherein, in the inverse model, τ 1 <τ 0 such that the n th pore in fabricated fiber has a boundary given by
z
n
(
ζ
,
τ
0
)
=
Z
n
(
τ
0
)
+
a
n
,
-
1
(
τ
0
)
ζ
+
∑
k
=
1
N
-
1
a
n
,
k
(
τ
0
)
ζ
k
,
and a boundary of a corresponding pore in the preform is determined to be
z
n
(
ζ
,
τ
1
)
=
Z
n
(
τ
1
)
+
a
n
,
-
1
(
τ
1
)
ζ
+
∑
k
=
1
N
-
1
a
n
,
k
(
τ
1
)
ζ
k
.
3. The non-transient computer readable medium of claim 1 , wherein the fabrication parameters further comprise one or more draw parameters of the fiber draw process.
4. The non-transient computer readable medium of claim 1 , containing further processor instruction that, when executed on the hardware processor, output system controller set points for provision to a system controller that controls the fiber draw process.
5. The non-transient computer readable medium of claim 1 , wherein the fiber draw process is characterized by a set of draw parameters consisting of a first subset of draw parameters and second subset of draw parameters, and wherein the method further comprises:
retrieving the first subset of draw parameters; and
the hardware processor executing the inverse model to determine the second subset of draw parameters.
6. The non-transient computer readable medium of claim 1 , wherein, in the inverse model, flow in the preform is characterized by a stream function of the form
ψ= Im [ z ƒ(z,τ)+g(z,τ)],
in which ƒ(z) □ 1 z+□(1/z),
g
′
(
z
)
=
∑
k
=
1
N
-
1
g
k
z
k
+
•
(
1
/
z
)
and the function ƒ 1 is related to the far-field pressure p and vorticity ω, as follows from the relation
4
f
′
(
z
,
τ
)
=
p
μ
-
i
ω
.