Method and apparatus for fabricating microstructured optical fibers

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[zƒ(z,τ)+g(z,τ)],
• in which z is a position within the fiber, ƒ(z)□ƒiz+□(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 zn(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, Zn (τ) is a centroid position of the nth pore, an,−1(τ) and an,k(τ) are time varying parameters that describe the shape of the pore, and N is an integer greater than 2, and wherein Re{zn(ζτ)}≡xn(ζ,τ) denotes the x-coordinate of the pore boundary and Im{zn(ζ,τ)}≡yn(ζ,τ) denotes the y-coordinate of the pore boundary;
• for each pore of the plurality of pores, determining first values an,−1(τ0), an,k, (τ0) and Zn (τ0) from the user-selected properties of the microstructured optical fiber to be fabricated, where τ0 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 an,−1(τ1), an,k(τ1) and Zn (τ1) corresponding to a second value of the time variable τ1, where τ1 is a time at which the drawing process begins, and where the boundary of the nth 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 zn(ζ,τ1) of the pores in the preform and may be used to fabricate the preform.