Measuring method of hole diameter, hole position, hole surface roughness, or bending loss of holey optical fiber, manufacturing method of holey optical fiber, and test method of optical line of holey optical fiber

A manufacturing method of a holey optical fiber, comprising:

• manufacturing a holey optical fiber by melting and drawing an optical fiber preform formed with holes;
• and
• measuring a hole position of the holey optical fiber by using a hole position-measuring method,
• the hole position-measuring method comprising:
• preparing a second holey optical fiber;
• calculating an arithmetical mean value I(x) from two backscattering light intensities at a position x of two backscattering light waveforms of the holey optical fiber, in which the two backscattering light waveforms are obtained by OTDR measurement;
• obtaining a mode field diameter 2W(x) using the arithmetical mean value I(x) and formula (3) or formula (4);
• 2W(x)=2W(x0)·10(·(I(x)·I(x0))+k)/20) (3)
• 2W(x0):
• a mode field diameter at a position x0 of an optical fiber for reference or a first terminal point of each of the holey optical fibers;
• I(x0):
• an arithmetical mean value at the position x0 of the optical fiber for reference or the first terminal point of each of the holey optical fibers;
• k:
• a constant expressed by the following formula;
• k
• =
• 10
• ·
• log
• [
• {
• 1
• +
• 0.62
• ⁢
• Δ
• ⁢
• ⁢
• (
• x
• )
• 1
• +
• 0.62
• ⁢
• Δ
• ⁡
• (
• x
• 0
• )
• }
• ⁢
• {
• 50
• -
• Δ
• ⁡
• (
• x
• )
• 50
• -
• Δ
• ⁡
• (
• x
• 0
• )
• }
• ]
• 2W(x)=2W(x0)·[2W(x1)/2W(x0)]((I(x)·I(x0))/(I(x1)·I(x0))) (4)
• 2W(x0):
• a mode field diameter at the position x0 of the optical fiber for reference or the first terminal point of each of the holey optical fibers;
• 2W(x1):
• a mode field diameter at a position x1 of the optical fiber for reference or a second terminal point of each of the holey optical fibers;
• I(x0):
• an arithmetical mean value at the position x0 of the optical fiber for reference or the first terminal point of each of the holey optical fibers;
• I(x1):
• an arithmetical mean value at the position x1 of the optical fiber for reference or the second terminal point of each of the holey optical fibers;
• and
• obtaining a hole position 2R (x) at the position x, based on the relational expression (12) and the obtained mode field diameter 2W(x):
• Δ
• ⁢
• ⁢
• I
• ⁡
• (
• x
• )
• ≅
• 20
• ⁢
• log
• [
• ω
• ⁡
• (
• R
• ⁡
• (
• x
• 0
• )
• ,
• d
• ⁡
• (
• x
• 0
• )
• )
• ω
• ⁡
• (
• R
• ⁡
• (
• x
• )
• ,
• d
• ⁡
• (
• x
• )
• )
• ]
• +
• 10
• ⁢
• log
• [
• Γ
• ⁡
• (
• x
• )
• Γ
• ⁡
• (
• x
• 0
• )
• ]
• (
• 12
• )
• R(x0):
• a radius of a virtual circle that is supposed to be inscribed to an outer peripheries of all holes of the holey optical fiber at the position x0;
• d(x0):
• an internal hole diameter at the position x0;
• d(x):
• an internal hole diameter at the position x;
• Γ(x0):
• a hole surface roughness of the holey optical fiber at the position x0;
• Γ(x):
• a hole surface roughness of the holey optical fiber at the position x;
• ω(R(x0), d(x0)):
• a mode field radius of the holey optical fiber at the position x0;
• ω(R(x), d(x):
• a mode field radius of the holey optical fiber at the position x.

A manufacturing method of a holey optical fiber, comprising:

• manufacturing a holey optical fiber by melting and drawing an optical fiber preform with holes;
• and
• measuring a hole surface roughness of the holey optical fiber by using a hole surface roughness-measuring method,
• the hole surface roughness-measuring method comprising:
• preparing a holey optical fiber;
• calculating an arithmetical mean value I(x) from two backscattering light intensities at a position x of two backscattering light waveforms of the holey optical fiber, in which the two backscattering light waveforms are obtained by OTDR measurement;
• obtaining a mode field diameter 2W(x) using the arithmetical mean value I(x) and formula (3) or formula (4):
• 2W(X)=2W(x0)·10(·(I(x)·I(x0))+k)/20) (3)
• 2W(x0):
• a mode field diameter at a position x0 of an optical fiber for reference or a first terminal point of each of the holey optical fibers;
• I(x0):
• an arithmetical mean value at the position x0 of the optical fiber for reference or the first terminal point of each of the holey optical fibers;
• k:
• a constant expressed by the following formula;
• k
• =
• 10
• ·
• log
• [
• {
• 1
• +
• 0.62
• ⁢
• Δ
• ⁢
• ⁢
• (
• x
• )
• 1
• +
• 0.62
• ⁢
• Δ
• ⁡
• (
• x
• 0
• )
• }
• ⁢
• {
• 50
• -
• Δ
• ⁡
• (
• x
• )
• 50
• -
• Δ
• ⁡
• (
• x
• 0
• )
• }
• ]
• 2W(x)=2W(x0)·[2W(x1)/2W(x0)((I(x)·I(x0))/(I(x1)·I(x0))) (4)
• 2W(x0):
• a mode field diameter at the position x0 of the optical fiber for reference or the first terminal point of each of the holey optical fibers;
• 2W(x1):
• a mode field diameter at a position x1 of the optical fiber for reference or a second terminal point of each of the holey optical fibers;
• I(x0):
• an arithmetical mean value at the position x0 of the optical fiber for reference or the first terminal point of each of the holey optical fibers;
• I(x1):
• an arithmetical mean value at the position x1 of the optical fiber for reference or the second terminal point of each of the holey optical fibers;
• and
• obtaining a surface roughness Γ(x) of the holes at the position x, based on the relational expression (12) and the obtained mode field diameter 2W(x):
• Δ
• ⁢
• ⁢
• I
• ⁡
• (
• x
• )
• ≅
• 20
• ⁢
• log
• [
• ω
• ⁡
• (
• R
• ⁡
• (
• x
• 0
• )
• ,
• d
• ⁡
• (
• x
• 0
• )
• )
• ω
• ⁡
• (
• R
• ⁡
• (
• x
• )
• ,
• d
• ⁡
• (
• x
• )
• )
• ]
• +
• 10
• ⁢
• log
• [
• Γ
• ⁡
• (
• x
• )
• Γ
• ⁡
• (
• x
• 0
• )
• ]
• (
• 12
• )
• R(x0):
• a radius of a virtual circle that is supposed to be inscribed to an outer peripheries of all holes of the holey optical fiber at the position x0;
• R(x):
• a radius of a virtual circle that is supposed to be inscribed to an outer peripheries of the all holes of the holey optical fiber at the position x;
• d(x0):
• an internal hole diameter at the position x0;
• d(x):
• an internal hole diameter at the position x;
• Γ(x0):
• a hole surface roughness of the holey optical fiber at the position x0;
• ω(R(x0), d(x0)):
• a mode field radius of the holey optical fiber at the position x0;
• ω(R(x), d(x)):
• a mode field radius of the holey optical fiber at the position x.

A manufacturing method of a holey optical fiber, comprising:

• manufacturing a holey optical fiber by melting and drawing an optical fiber preform formed with holes;
• and
• measuring a hole diameter of the holey optical fiber by using a hole diameter-measuring method,
• the hole diameter-measuring method comprising:
• preparing first holey optical fibers with different first hole diameters;
• obtaining first arithmetical mean values as a result of calculating a first arithmetical mean value I(x1) from two backscattering light intensities at a position x1 of two backscattering light waveforms of each of the first holey optical fibers, in which the two backscattering light waveforms are obtained by OTDR measurement;
• obtaining the first hole diameters of the first holey optical fibers, the first hole diameters being actually measured using an offline measurement method;
• drawing a graph by obtaining datapoints, each of which is defined by each of the first arithmetical mean values and each of the obtained first hole diameters;
• acquiring a relational expression (1) between the obtained first arithmetical mean values and the obtained first hole diameters as a results of approximating the datapoints by a linear function;
• d=A+B×I(x) (1)
• d:
• a hole diameter;
• A:
• a first constant value obtained by approximating the datapoints by the linear function;
• B:
• a second constant value obtained by approximating the datapoints by the linear function;
• preparing a second holey optical fiber which is different from the first holey optical fibers;
• calculating a second arithmetical mean value I(x2) from two backscattering light intensities at a position x2 of two backscattering light waveforms of the second holey optical fiber, in which the two backscattering light waveforms are obtained by OTDR measurement,
• calculating a second arithmetical mean value I(x2) from two backscattering light intensities at a position x2 of two backscattering light waveforms of the second holey optical fiber, in which the two backscattering light waveforms are obtained by OTDR measurement;
• and
• obtaining a second hole diameter at the position x2, based on the calculated second arithmetical mean value I(x2) and the relational expression (1).

A manufacturing method of a holey optical fiber, comprising:

• manufacturing a holey optical fiber by melting and drawing an optical fiber preform formed with holes;
• and
• measuring a bending loss of the holey optical fiber by using a bending loss-measuring method,
• the bending loss-measuring method comprising:
• preparing first holey optical fibers with different first bending losses;
• obtaining first arithmetical mean values as a result of calculating a first arithmetical mean value I(x1) from two backscattering light intensities at a position x1 of two backscattering light waveforms of each of the first holey optical fibers, in which the two backscattering light waveforms are obtained by OTDR measurement;
• obtaining the first bending losses of the first holey optical fibers, the first bending losses being actually measured using an offline measurement method;
• drawing a graph by obtaining datapoints, each of which is defined by each of the calculated first arithmetical mean values and each of the obtained first bending losses;
• acquiring a relational expression (1) between the first arithmetical mean values and the obtained first bending losses as a result of approximating the datapoints by an exponential function;
• αb=A×exp(B×I(x)) (1)
• αb:
• a bending loss;
• A:
• a first constant value obtained by approximating the datapoints by the exponential function;
• B:
• a second constant value obtained by approximating the datapoints by the exponential function;
• preparing a second holey optical fiber which is different from the first holey optical fibers;
• calculating a second arithmetical mean value I(x2) from two backscattering light intensities at a position x2 of two backscattering light waveforms of the second holey optical fiber, in which the two backscattering light waveforms are obtained by OTDR measurement;
• and
• obtaining a second bending loss at the position x2, based on the calculated second arithmetical mean value I(x2) and the relational expression (1).