JP2016153850A - Manufacturing method of taper optical fiber - Google Patents

Abstract

A method of manufacturing a tapered optical fiber having a reduced overall length while suppressing loss of light passing through a TOF is provided. A TOF manufacturing apparatus is stretched by pulling in a longitudinal direction of an optical fiber while performing a heating scan for moving a heating position in the longitudinal direction of the optical fiber. The scanning length of the torch 28 is controlled by the controller 21. The calculation unit 25 performs each heating for minimizing the total length of the tapered optical fiber under the constraint that the optimization upper limit angle obtained by multiplying the insulation reference angle by the optimization coefficient is less than the taper angle with respect to the local fiber radius. The scanning length of scanning is obtained. [Selection] Figure 2

Description

  The present invention relates to a method for manufacturing a tapered optical fiber.

  A tapered optical fiber (hereinafter referred to as TOF) has a tapered waist portion whose fiber radius is thinner than the wavelength of light, and a taper which is provided at both ends of the tapered waist portion and the fiber radius gradually decreases toward the tapered waist portion. And a transition part. Since TOF has a strong light confinement effect and a large evanescent field, it is used in fields such as optical engineering and quantum optics.

  Although TOF depends on the field in which it is used, high transmittance is often required because it generally handles weak light. One of the causes for reducing the transmittance of the TOF is a loss due to coupling between a fundamental mode and a higher-order mode due to the shape of the tapered transition portion. This loss can be reduced by adjusting the local taper angle of the taper transition portion according to the fiber radius, and the condition under which this loss can be regarded as sufficiently small is known as an adiabatic condition (for example, Non-Patent Document 1). reference). The upper limit of the taper angle satisfying the heat insulation condition is known as the heat insulation reference angle, and the heat insulation reference angle can be expressed as a function depending on the fiber radius.

  A TOF having an exponential function shape in which a taper angle exponentially increases from a taper transition portion toward a taper waist portion is known (see, for example, Non-Patent Document 2). In this non-patent document 2, the attenuation constant is 10 mm. Further, a TOF having a shape in which the taper angle of the taper transition portion is constant at 2 mrad is known (for example, see Non-Patent Document 3). These TOFs suppress loss and ensure high transmittance by setting the taper angle of the taper transition portion to be equal to or less than the heat insulation reference angle. For example, the transmittance of TOF described in Non-Patent Document 2 has reached 99.4%, and the transmittance of TOF in Non-Patent Document 3 has reached 99.95%.

  As one of such TOF manufacturing methods, a frame brush method is known (see Patent Document 1). In the frame brush method, a heated softening optical fiber is pulled and stretched in the longitudinal direction while performing a heating scan that reciprocates a heating means such as a torch in the longitudinal direction of the optical fiber to move the heating position relative to the optical fiber. To do. For example, the TOF having an exponential function shape can be produced by pulling the optical fiber at a constant speed while keeping the movement width of the heating position constant. Further, by pulling the optical fiber at a constant speed while controlling the movement width of the heating position, it is possible to produce a TOF in which the taper angle of the taper transition portion is constant at 2 mrad.

  A manufacturing method is also known in which an optical fiber is heated while reciprocating in the longitudinal direction instead of moving the heating means (see Patent Document 2). In the manufacturing method of Patent Document 2, various parameters such as the width and speed of the reciprocation of the optical fiber, and the pulling amount (expansion width) of the optical fiber are controlled, so that the TOF (thinned light with various shapes) is controlled. Fiber).

JP 2008-003605 A JP 2013-246329 A

JD Love, WM Henry, WJ Stewart, RJ Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibers and devices. Part 1: Adiabaticity criteria,” IEE Proc. Vol.138, Issue 5, 343−354 (1991). T. Aoki, “Fabrication of Ultralow-Loss Tapered Optical Fibers and Microtoroidal Resonators,” Jpn. J. Appl. Phys. 49, 118001 (2010). J. E. Hoffman, S. Ravets, J. A. Grover, P. Solano, P. R. Kordell, J. D. Wong-Campos, L. A. Orozco, and S. L. Rolston, “Ultrahigh transmission optical nanofibers,” AIP Adv. 4, 067124 (2014).

  By the way, when the TOF is coupled to the minimal resonator, it is desired that the total length is shorter in consideration of mechanical stability. In addition, for example, in the case of being housed in a narrow vacuum chamber of a cryostat, the length of the TOF is limited. From such a background, a TOF having a shorter overall length while suppressing loss of light transmitted through the TOF is desired. However, as in the TOF described in Non-Patent Document 2, in order to suppress the loss, if the taper angle is constant while keeping the angle less than the adiabatic reference angle for any fiber radius, the loss is considerably reduced. While it can be made smaller, the total length of the TOF becomes considerably longer. In addition, in the TOF having an exponential function shape described in Non-Patent Document 1, the total length of the TOF can be shortened as compared with the case where the taper angle is constant, but it cannot be said that the TOF is still sufficiently short. .

  In Patent Document 2, a design method for the shape of a desired TOF including a shape for shortening the total length of the TOF while suppressing loss, and various kinds of devices necessary for producing a TOF having a designed shape are disclosed. The parameter determination method is not described.

  The present invention has been made in view of the above circumstances, and an object of the present invention is to provide a method for manufacturing a tapered optical fiber that can further shorten the overall length while suppressing loss of light transmitted through the TOF.

  In order to solve the above problems, in the present invention, in the method for manufacturing a tapered optical fiber, a pair of tapered transition portions are formed at both ends of the tapered waist portion, and the fiber diameter of the tapered transition portion gradually decreases toward the tapered waist portion. Prior to the stretching process, the stretching process is performed by stretching the heated optical fiber in the longitudinal direction by performing a heating scan that moves the heating position with respect to the optical fiber at a predetermined scanning length along the longitudinal direction of the optical fiber. When the local fiber radius of the tapered optical fiber is r, the taper angle is θ, the adiabatic reference angle for the fiber radius r is Ω (r), and the optimization coefficient F is 0 <F <1 , Θ <F · Ω (r), and obtain the scanning length of each heating scan that minimizes the total length X of the tapered waist portion and the pair of tapered transition portions. Those having a 査長 determining step.

  According to the present invention, when the local fiber radius r of the tapered optical fiber, the taper angle θ, the adiabatic reference angle for the fiber radius r is Ω (r), and the optimization coefficient F is 0 <F <1, , Θ <F · Ω (r), the scanning length for each heating scan that minimizes the total length of the tapered optical fiber is obtained, and each heating scan is performed with the obtained scanning length. A tapered optical fiber with a shorter length can be manufactured.

It is a top view which shows the external appearance of a taper optical fiber. It is a block diagram which shows the outline of the TOF manufacturing apparatus which implemented this invention. It is explanatory drawing which shows the formation model of a taper optical fiber. It is explanatory drawing which shows the state after the kth heating scan by a formation model. It is a graph which shows an example of the relationship between a heat insulation reference angle and a fiber radius. It is a graph which shows the profile of scanning length. It is a graph which shows the calculated taper angle with respect to a fiber radius. It is a graph which shows the transmittance | permeability of the taper optical fiber produced in Examples 1-4 and Comparative Examples 1 and 2. FIG. It is a graph which expands and shows the transmittance | permeability of the taper optical fiber produced in Examples 1-3 and the comparative example 1. FIG. 3 is a graph showing the shape of a tapered optical fiber manufactured in Example 2 and Comparative Example 1.

  In FIG. 1, a tapered optical fiber (hereinafter referred to as TOF) 10 includes a tapered waist portion 11 having a diameter smaller than the wavelength of light, and tapered transition portions 12 respectively formed at both ends of the tapered waist portion 11. have. The tapered waist portion 11 and the tapered transition portion 12 have a circular cross section, and the tapered transition portion 12 has a shape in which the diameter gradually decreases toward the tapered waist portion 11. In this example, the TOF 10 is manufactured by a stretching process in which a part of the optical fiber 14 is pulled while being stretched.

  In FIG. 2, the TOF manufacturing apparatus 20 that manufactures the TOF 10 forms the TOF 10 in the optical fiber 14 by performing a calculation process for obtaining a scanning length and a stretching process for stretching the optical fiber 14 as will be described in detail later. The drawing process includes a heating scanning process for moving the heating position with respect to the optical fiber 14 and a pulling process for pulling the optical fiber 14 softened by the heating by the heating scanning in both directions along the longitudinal direction. The TOF is manufactured by the so-called frame brush method. As the optical fiber 14, glass, plastic, or the like can be used. The TOF manufacturing apparatus 20 includes a controller 21, moving units 22 and 23, a heating unit 24, and a calculation unit 25. The controller 21 controls movement of the moving units 22 and 23 and the heating unit 24.

  The moving parts 22 and 23 constitute a pulling means for pulling the optical fiber 14. The moving unit 22 includes a clamp 26 and a moving stage 27 to which the clamp 26 is fixed. The clamp 26 sandwiches and grips one end of the optical fiber 14. The moving stage 27 is a uniaxial moving stage operated by a motor 27a. The moving unit 23 is also the same as the moving unit 22 and includes a clamp 26 and a moving stage 27 operated by a motor 27 a. The clamp 26 holds the other end of the optical fiber 14. Each moving stage 27 is adjusted so as to move in parallel with the longitudinal direction (arrow Z direction) of the optical fiber 14.

When the TOF 10 is manufactured, by driving the motor 27a under the control of the controller 21, the clamps 26 of the moving units 22 and 23 move in directions away from each other. Thereby, the optical fiber 14 is pulled. Each clamp 26 is continuously moved at each constant tensile speed V _1.

  The heating unit 24 includes a torch 28 as a heating unit and a moving stage 29. The torch 28 heats the optical fiber 14 with, for example, a flame burned using hydrogen gas as fuel. As the torch 28, one having a sufficiently small flame width in the longitudinal direction of the optical fiber 14 is used. The torch 28 is attached to the moving stage 29. The moving stage 29 is a uniaxial moving stage operated by a motor 29a, and is adjusted so as to reciprocate the torch 28 along the longitudinal direction of the optical fiber 14 held by the moving units 22 and 23. The heating means is not limited to the torch 28.

During manufacture of TOF10, by driving the motor 29a under the control of the controller 21 moves the torch 28 at a constant scan speed _{V 2.} Thereby, the heating scanning which moves the heating position by the torch 28 along the longitudinal direction of the optical fiber 14 is performed a plurality of times. One heating scan is a movement of the heating position in either the right direction or the left direction in the figure, and the heating position is moved in the opposite direction in the next one heating scan. The moving direction of the heating position and the scanning length by the heating scanning are controlled by the controller 21. The number of heating scans will be described later.

As the ratio (V ₁ / V ₂ ) between the pulling speed V ₁ and the scanning speed V ₂ is decreased, the number of heating scans n is increased, but the change in the fiber radius of the TOF 10 particularly in the tapered transition portion 12 is smoother. A tapered shape can be obtained. The pulling speed V ₁ is set to be smaller than the scanning speed V ₂ (V ₁ <V ₂ ).

The computing unit 25 obtains the scanning lengths L _{1 to} L _n in the first to n-th heating scans (calculation process), and sets the obtained scanning lengths L _{1 to} L _n in the controller 21. When the TOF 10 is manufactured under the same conditions as the TOF 10 that has already been manufactured, the scanning lengths L _{1 to} L _n previously obtained under the same conditions may be set in the controller 21. The calculation unit 25 obtains scanning lengths L _{1 to} L _n for manufacturing the TOF 10 in which the total length X of the TOF 10 is shortened while suppressing loss. The total length X of the TOF 10 is the total length of the tapered waist portion 11 and the pair of tapered transition portions 12. Details of the calculation of the scanning lengths L _{1 to} L _n will be described later.

  The formation process of the TOF 10 using the TOF manufacturing apparatus 20 will be described with reference to the formation model of FIG. In FIG. 3, illustration of members such as the clamp 26 that holds both ends of the optical fiber 14 is omitted. Further, in the formation model, the width of the flame of the torch 28 is sufficiently small to be negligible with respect to the length of the optical fiber 14.

As shown in FIG. 3 (A), the in the first heating scan, the torch 28 is moved to the right in FIG scanning length L ₁ in the scanning speed V _2. In the movement of the torch 28, heating position on the optical fiber 14 between the pair of clamp 26 is moved by the scanning length L ₁ in the scanning speed V _2. Simultaneously with the start of the heating scan, the optical fiber 14 as both ends of the optical fiber 14 is moved at a speed V ₁ tensile each is pulled by the moving section 22, 23. As a result, the heating region H ₁ of the optical fiber 14 heated by the torch 28 is stretched, and as shown in FIG. 3B, a cylindrical shape having a fiber radius r ₂ smaller than the initial fiber radius r ₁ of the optical fiber 14. the stretching region E ₂ is formed.

Here, although not constitute a TOF10, for convenience, a virtual micro area _{S 0} to the optical fiber 14 in the left drawing region _{E 2} is also on the right side of the optical fiber 14 in the stretching region _{E 2} is small region _{S 1} respectively It is assumed that it is formed. Further, the fiber radii of the micro regions S ₀ and S ₁ are the same as the fiber radius R of the optical fiber 14 used for manufacturing the TOF ₁₀ , but are r ₀ and r ₁ , respectively.

After the first heating scan, the torch 28 reverses the moving direction and the second heating scan is started. In the second heat scan a heating position of the optical fiber 14 is moved leftward in the drawing by the scanning length L ₂ by the movement of the torch 28. Also in this second and subsequent heating scan, scan speed is V _2. Both ends of the optical fiber 14 are continuously pulled. Therefore, the heating region of H ₂ length L ₂ starting from the right end of the stretching region E ₂ is heated. Then, the heating region H ₂ is stretched, as shown in FIG. 3 (C), the stretching region E ₃ cylindrical small fiber radius r ₃ is formed than stretch zone E _2. Further, on the left side of the drawing area E ₃ are micro-region S ₂ of the cylindrical shape is formed. The micro region S ₂ is a region that remains without being heated and stretched in the second heating scan in the stretching region E ₂ . Therefore, the fiber radius of the minute region S ₂ is the same fiber radius r _{2 as} that of the stretched region E ₂ .

After the second heating scan, the torch 28 reverses the moving direction and the third heating scan is started. The heating scans the third, the heating region H ₃ starting from the left end of the stretching region E ₃ is heated, this heating region H ₃ is stretched. Length of the heating region H ₃ is the same as L ₃ and the scanning length of the third heat scan. Thus, as shown in FIG. 3 (D), the stretched area E ₄ is formed of a cylindrical shape of a small fiber radius r ₄ than stretching region E _3, a minute area S ₃ of the cylindrical on the left side of the drawing area E ₄ It is formed. Minute domains S ₃ is a remaining region without being heated and stretched in the third heat scan of the stretching region E _3, the same r ₃ and the stretching region E _3.

After the third heating scan, the torch 28 reverses the moving direction and the fourth heating scan is started. The heating scans the fourth, the heating region H ₄ starting from the right end of the stretching region E ₄ is heated. Length of the heating region H ₄ is the same as L ₄ and the scanning length of the fourth heating scan. Then, the heated region H ₄ is stretched, as shown in FIG. 3 (E), the the stretching region E ₅ formed of cylindrical shape of smaller fiber radius r ₅ than stretching region E _4, further left stretching region E ₅ Is formed with a cylindrical minute region S ₄ having a fiber radius r ₄ . Similarly, the processes up to the nth heating scan are sequentially performed.

In the formation model, the micro regions S ₂ , S ₃ ,... _Sn are formed for each second and subsequent heating scans. For each heating scan, minute regions S ₃ , S ₅ ,... Where the fiber radius gradually decreases are formed sequentially on the end side of the heating scan, for example, on the right side in the drawing for each heating scan in the right direction. In addition, minute regions S ₂ , S ₄ ,... Where the fiber radius gradually decreases are sequentially formed on the left side in the drawing for each heating scan in the left direction. As a result, a pair of tapered transition portions 12 are formed. In the formation model, the taper waist portion 11 is an extension region En _{+ 1} formed by the nth heating scan. As will be described later, when a heating scan is added, it is a stretched region formed by the last heating added.

In the formation model, the micro area _Sk is a cylindrical shape with the scanning number indicating the order of the heating scanning being k (= 1, 2,..., N), but actually the width of the flame of the torch 28 is The fiber radius is gradually reduced due to the finiteness or the viscosity of the softened optical fiber 14 and has a taper angle. The minute region S _k in this formation model is the local area of the TOF 10, the fiber radius r _k is the local fiber radius, and the taper angle θ _k is the local taper angle. Further, in the formation model, the stretched region E _k has a cylindrical shape, but the actual stretched region E _k has an exponential function shape in which the fiber radius decreases exponentially toward the center in the longitudinal direction. Therefore, the tapered waist portion 11 has the same shape.

The arithmetic unit 25 performs optimization using the following equation (1) as an objective function. That is, the scanning lengths L _{1 to} L _n that minimize the total length X are obtained. The calculation unit 25 performs calculation processing using the downhill simplex method for optimization. In this optimization, the first constraint condition expressed by the equation (2) is given in order to suppress the loss of light transmitted through the TOF 10. The optimization algorithm is not limited to the downhill simplex method. Incidentally, F in the formula (2) is an optimization factor to be described later, Omega (r _k) is a thermal insulation reference angle for the fiber radius r _k.

以下、式（１），式（２）について図４を参照して説明する。図４は、形成モデルにおいて、ｋ回目の加熱走査後の光ファイバ１４の一部の状態を示している。なお、図４では、ｋ回目の加熱走査開始時の加熱位置を原点とし、ｋ回目の加熱走査においてトーチ２８が移動する方向を正としたＺ軸を記し、各部の位置（Ｚ座標）を示してある。

Hereinafter, the expressions (1) and (2) will be described with reference to FIG. FIG. 4 shows a state of a part of the optical fiber 14 after the k-th heating scan in the formation model. In FIG. 4, the Z-axis is shown with the heating position at the start of the k-th heating scan as the origin, and the direction in which the torch 28 moves in the k-th heating scan is positive, and the position (Z coordinate) of each part is shown. It is.

In the k-th heating scan, the heating region H _k of the optical fiber 14 is heated and stretched to form a stretching region E _{k + 1} . The length of the heating region H _k is obtained by using the scanning length L _k , the scanning speed V ₂ , and the pulling speed V ₁ of the k-th heating scanning, “{(V ₂ −V ₁ ) / V ₂ } · L _k. Is required. The heating region H _k, it is because it is part of the stretching region E _k formed of (k-1) -th heating scan, the same fiber radius r _k and the stretching region E _k. The length of the stretching region E _k is determined as “{(V ₂ + V ₁ ) / V ₂ } · L _k ”.

Total length X of TOF10 can be obtained and the length of the stretching region E ₂ by first heating scan, as the sum of the lengths of increments per second or subsequent heating scan. Length _{X 2} of the drawing region _{E 2} is represented by the following equation (3). Further, the increment ΔX in length for each heating scan after the second time is the difference between the heating region H _k-1 and the stretching region E _k, and therefore can be expressed by Expression (4). Equation (1) is obtained from these equations (3) and (4).

ＴＯＦ１０の任意の位置における局所的なファイバ半径ｒについて、その位置の局所的なテーパ角θが断熱基準角Ω（ｒ）以下であれば、その局所において基本モードと高次モードの光の結合による損失の影響が十分に小さくなり、断熱条件が満たされることになる。断熱基準角Ω（ｒ）は、ＨＥ_１１モード（基本モード）の伝搬定数をβ_１，高次モードの１つであるＨＥ_１２モードの伝搬定数をβ_２としたときに、次の式（５）で求められる。式（５）は、ＨＥ_１１モードとＨＥ_１２モードとの結合の損失に着目したものであり、その他の高次モードとの結合の損失は無視できる程度に十分に小さいものと想定している。

For a local fiber radius r at an arbitrary position of the TOF 10, if the local taper angle θ at the position is equal to or smaller than the adiabatic reference angle Ω (r), the local mode is caused by the coupling of light of the fundamental mode and higher order mode. The influence of the loss is sufficiently reduced and the heat insulation condition is satisfied. The adiabatic reference angle Ω (r) is expressed by the following equation (5) when the propagation constant of the HE ₁₁ mode (fundamental mode) is β ₁ and the propagation constant of the HE ₁₂ mode, which is one of the higher order modes, is β _2. ). Expression (5) focuses on the coupling loss between the HE ₁₁ mode and the HE ₁₂ mode, and assumes that the coupling loss with other higher-order modes is sufficiently small to be negligible.

ｋ回目の加熱走査で形成される微小領域Ｓ_ｋのファイバ半径ｒ_ｋは、次の式（６）のように表すことができる。微小領域Ｓ_ｋのファイバ半径ｒ_ｋは、ｋ−１回目の加熱走査で形成される延伸領域Ｅ_ｋのものと同じであり、その延伸領域Ｅ_ｋは、加熱領域Ｈ_ｋ−１を延伸したものであるから、延伸領域Ｅ_ｋと加熱領域Ｈ_ｋ−１との体積が同じになることに基づいて式（６）が導き出される。

Fiber radius r _k of the minute regions S _k which is formed by the k-th heat scan can be represented as the following equation (6). The fiber radius r _k of the minute region S _k is the same as that of the stretching region E _k formed by the (k−1) th heating scan, and the stretching region E _k is a stretching of the heating region H _k−1. Therefore, Formula (6) is derived based on the fact that the volume of the stretching region E _k and the heating region H _k-1 are the same.

ｋ回目の加熱走査で形成される微小領域Ｓ_ｋのテーパは、図４に示されるように、微小領域Ｓ_ｋと微小領域Ｓ_ｋ−２との段差部分により形成される斜面として近似できる。このため、ｋ回目の加熱走査で形成されるテーパ角θ_ｋは、式（６）に基づいて得られるファイバ半径ｒ_ｋ−２，ｒ_ｋを用いて、次の式（７）に基づいて求めることができる。なお、１回目の加熱走査では、微小領域が形成されないのでテーパ角を求める必要はないので、２回目以降の加熱走査で形成されるテーパ角θ_ｋ、すなわちｋ≧２の場合についてのテーパ角θ_ｋを求めればよい。

taper of microscopic regions S _k which is formed by the k-th heating scan, as shown in FIG. 4 can be approximated as the slope formed by the micro-regions S _k and the step portion between the small regions S _k-2. Therefore, the taper angle theta _k formed in the k-th heating scan, using a fiber radius r _k-2, r _k obtained based on the equation (6), determined on the basis of the following equation (7) be able to. In the first heating scan, there is no need to obtain the taper angle because no micro-region is formed, so the taper angle θ _k formed in the second and subsequent heating scans, that is, the taper angle θ for k ≧ 2. _What is necessary is just to obtain | require _k .

最適化係数Ｆは、ファイバ半径ｒの増減に対して断熱基準角度Ω（ｒ）が変化することに着目し、この断熱基準角度Ω（ｒ）の変化に沿った新たなテーパ角の上限（以下、最適化上限角という）である「Ｆ・Ω（ｒ）」を設定するために導入している。最適化上限角でテーパ角θを制限して、式（１）を最適化することにより、損失を抑えながら、短い全長ＸのＴＯＦ１０を製造するための走査長Ｌ_１〜Ｌ_ｎを決定することができる。

The optimization factor F focuses on the fact that the adiabatic reference angle Ω (r) changes as the fiber radius r increases and decreases, and a new upper limit of the taper angle along the change of the adiabatic reference angle Ω (r) (below) This is introduced to set “F · Ω (r)” which is an optimization upper limit angle). By limiting the taper angle θ with the optimization upper limit angle and optimizing the expression (1), the scanning lengths L _{1 to} L _n for manufacturing the TOF 10 having the short full length X are determined while suppressing the loss. Can do.

  The optimization coefficient F is set within the range of “0 <F <1”. The smaller the optimization factor F, the lower the loss and the higher the transmittance. As the optimization factor F is reduced, the extrinsic loss influenced by the adhesion of dust or the like becomes more dominant than the loss due to the coupling between the fundamental mode and the higher order mode, and the transmittance is remarkable. There may be no difference. In such a case, if the optimization factor F is excessively reduced, the total length X increases in a state where there is almost no effect of improving the transmittance. Therefore, the optimization factor F including the manufacturing environment is selected. Is good.

Formation model TOF10 underlying the calculation such as the fiber radius r _k, the taper angle theta _k are assumed to form minute domains S _k of finite length by k-th heating scan. That is, it is premised that the heating position does not reach the minute region _Sk-2 in the _k- th heating scan. Since the distance D _k−2 from the origin O to the minute region S _k−2 when the k-th heating scan is completed is expressed by the following expression (8), the expression (9) is the second expression regarding the scanning length L _k . It is given as a constraint when optimizing.

式（１）の最適化の際の自由度を抑え、演算処理数を減らして演算時間の短縮を図るために、走査長Ｌ_ｋが走査番号ｋについての関数であり、その関数が走査番号ｋの増減に対して滑らかな変化を示すものとして、走査長Ｌ_ｋに関する第３の制約条件を加えている。これは、連続的に変化するファイバ半径ｒに対して断熱基準角Ω（ｒ）がなめらかな変化を示す関数となることに基づいている。

The scanning length L _k is a function for the scanning number k in order to reduce the number of arithmetic processing steps and shorten the arithmetic time by suppressing the degree of freedom in optimization of the expression (1), and that function is the scanning number k. as indicating a smooth change with respect to an increase or decrease, it is added a third constraint on the scanning length L _k. This is based on the fact that the adiabatic reference angle Ω (r) becomes a function showing a smooth change with respect to the continuously changing fiber radius r.

That is, the scanning length L _k is a function represented by a high-order polynomial with k as a variable, and the scanning length L _k corresponding to a plurality of specific _k is minimized (optimization of Expression (1)). The scanning length L _k corresponding to the remaining _k is a function value determined based on the combination of the specific k and the corresponding scanning length L _k .

Specifically, m is a natural number of 3 or more smaller than n, and the scanning length L _k is expressed by a (m−1) -dimensional polynomial function (hereinafter referred to as a scanning length function) with the scanning number k as a variable. Suppose that The scan length L _k corresponding to m specific scan numbers k out of the n scan lengths L _k is treated as a variable when optimizing the equation (1). Further, using the m-number of combinations of the scan length L _k corresponding thereto and specific scan number k, by interpolation, obtaining the respective scanning length L _k corresponding to the remaining (n-m) pieces of scan number k . That is, a scan length function satisfying m combinations of a specific scan number k and the corresponding scan length L _k is obtained, but each scan length L corresponding to the remaining (nm) scan numbers k. _k is obtained as a value of the scanning length function, and is used as the scanning length L _k when the expression (1) is optimized. Since the scan length L _k corresponding to the specific scan number k is treated as a variable, the scan length function changes according to the scan length L _k that is a variable.

  In this example, a Lagrange interpolation method is used as the interpolation method, and 9 (= m) scan numbers k are set at equal intervals between 1 and n as specific scan numbers k. Although the value of m can be set as appropriate, the downhill simplex method used in this example is generally effective when the number of variables is relatively small, for example, about 10 or less. Nine. The value of m is preferably set to a number suitable for the algorithm for optimizing equation (1).

For the scanning length L _k , an upper limit value Lupper and a lower limit value Llower are further given as the fourth constraint condition. The upper limit value Lupper is set as a mechanical limit of heating scanning by the TOF manufacturing apparatus 20. The lower limit Llower takes into account the finite width of the flame of the torch 28. In this example, the upper limit Lupper is 40000 μm and the lower limit Llower is 400 μm.

断熱基準角Ω（ｒ）が急激に増大する特定ファイバ半径以下になるファイバ半径ｒ_ｋに対応する加熱走査については、その走査長Ｌ_ｋをＬlowerに固定する第５の制約条件を加えることも好ましい。走査長関数として（ｍ−１）次元の多項式の関数を使うことで最適化の自由度を制限しているが、この第５の制約条件により、この制約を加えずに全ての走査長Ｌ_ｋを最適化した場合に比べて、断熱基準角Ω（ｒ）が急激に増大する領域を除かれることによって、より真の最適解に近い解（走査長）が得られる。延伸領域（または加熱領域）のファイバ半径が特定ファイバ半径以下となる加熱走査の回数は、上記式（６）に示されるｒ_ｋとｒ_ｋ−１の関係と、光ファイバ１４の初期のファイバ半径（Ｒ）とを用いて導き出すことができる。

For heating scan adiabatic reference angle Omega (r) corresponds to the rapidly increasing specific fiber radius below made fiber radius r _k, it is also preferable to add a fifth constraint to fix the scanning length L _k in Llower . Although the degree of freedom of optimization is limited by using a (m−1) -dimensional polynomial function as the scan length function, all the scan lengths L _k are added without adding this constraint due to the fifth constraint condition. Compared to the case where is optimized, by removing the region where the adiabatic reference angle Ω (r) increases rapidly, a solution (scanning length) closer to the true optimum solution can be obtained. Number of heating scan the fiber radius is below a certain fiber radius stretching region (or heated region), the above equation and relation r _k and r _k-1 as shown in (6), the optical fiber 14 initial fiber radius (R) and can be derived.

The number of times of heating n can be obtained based on the following equation (12). The value r _w in the equation (12) is the target fiber radius of the tapered waist portion 11 to be finally produced, and the value r ₀ is the fiber radius of the virtual minute region S ₀ described above. It is the same as the fiber radius R of the optical fiber 14 used for manufacturing. Equation (12) can be derived based on the relationship of Equation (6) above.

光ファイバ１４の長手方向についてのトーチ２８の炎の幅、すなわち加熱位置で光ファイバ１４が加熱される幅が走査長Ｌ_ｋの下限値Ｌlowerに比べて無視できない場合ある。この場合には、実際に作製されるテーパウエスト部１１のファイバ半径が、形成モデルから求められるファイバ半径よりも太くなる。このような場合には、上述の各種制約条件下で求められる走査長Ｌ_ｋのプロファイルを修正する。この修正では、ｎ回の加熱走査の後に加熱走査を追加して、テーパウエスト部１１を必要とするファイバ半径にする。追加する加熱走査の回数は、例えば計算によりあるいは実験的に決めることができる。また、シングルモードで導波するのに必要なファイバ半径のテーパウエスト部１１のファイバ半径を得る場合では、ｎ回の加熱走査後に、製造中のＴＯＦ１０の透過光強度の測定結果に基づいてテーパウエスト部１１によるシングルモードでの導波が確認されるまで加熱走査を追加してもよい。製造中のＴＯＦ１０の透過光強度を測定するには、例えばレーザダイオード等の光源からの光を、ＴＯＦ製造装置２０にセットされている光ファイバ１４の一端に入射させ、その光ファイバ１４の他端から射出される光をフォトディテクタ（光強度測定装置）で検出することで測定できる。シングルモードで導波になった否かは、透過光強度の振動が消失することで確認できる。これは高次モードと基本モードの干渉状態が延伸によって変化し、透過光強度の振動が生じることを利用している。なお、追加する加熱走査の走査長Ｌ_ｋは、下限値Ｌlowerとすればよい。

The width of the flame of the torch 28 in the longitudinal direction of the optical fiber 14, i.e. when the width of the optical fiber 14 is heated is not negligible as compared with the lower limit value Llower scan length L _k in the heating position. In this case, the fiber radius of the taper waist part 11 actually produced becomes thicker than the fiber radius calculated | required from a formation model. In such a case, modifying the profile of the scan length L _k required by various constraints under the conditions described above. In this modification, a heating scan is added after n heating scans to make the tapered waist 11 a required fiber radius. The number of heating scans to be added can be determined, for example, by calculation or experimentally. Further, in the case of obtaining the fiber radius of the taper waist portion 11 having the fiber radius necessary for guiding in the single mode, the taper waist is determined based on the measurement result of the transmitted light intensity of the TOF 10 being manufactured after n heating scans. Heating scanning may be added until waveguide in the single mode by the part 11 is confirmed. In order to measure the transmitted light intensity of the TOF 10 being manufactured, for example, light from a light source such as a laser diode is incident on one end of the optical fiber 14 set in the TOF manufacturing apparatus 20 and the other end of the optical fiber 14 is entered. It can measure by detecting the light inject | emitted from a photo detector (light intensity measuring device). Whether or not the light is guided in the single mode can be confirmed by the disappearance of the vibration of the transmitted light intensity. This utilizes the fact that the interference state between the higher-order mode and the fundamental mode changes due to stretching and vibration of the transmitted light intensity occurs. The scanning length L _k of the heat scan to be added may be the lower limit Llower.

Next, the operation of the TOF manufacturing apparatus 20 will be described. When manufacturing the TOF 10, both ends of the optical fiber 14 used for manufacturing are held by a pair of clamps 26. Subsequently, the fiber radius R of the optical fiber 14, propagation constants β 1 and β 2, the target fiber radius r _{w of} the tapered waist portion 11, and the optimization coefficient F are set in the computing unit 25 as parameters. The fiber radius r _w of the target of the tapered waist portions 11, enter the fiber radius required, for example, to waveguide in a single mode. Relationship between TOF10 full length X and transmittance (loss), since that is determined by the optimum factor F entered, there is no need to enter detailed information profile concerning fiber radius r _k and the taper angle theta _k. When the tapered waist portion 11 is guided in a single mode, the fiber radius r _w is set to be equal to or less than the radius of the fiber that satisfies the cutoff condition and guides in the single mode.

When the parameter setting is completed, the calculation unit 25 calculates the parameter from the set parameter, the fiber radius r ₀ (= R) of the optical fiber 14, and the fiber radius r _w of the tapered waist portion 11 based on Expression (12). The number of scans n is determined. An operation for optimizing equation (1) is performed by the downhill simplex method. Scanning for the first to nth heating scans is performed by optimizing the expression (1) under the first constraint condition into which the set optimization coefficient F is substituted and the second to fifth constraint conditions. The lengths L _{1 to} L _n are determined. Since the addition of the first constraint, the freedom of the scanning length L _k has sufficiently suppressed, operation of the operation portion 25 is short. In applying the downhill simplex method to Equation (1), different scanning lengths L _{1 to} L _n may be obtained depending on the scanning length L _k corresponding to the specific nine scanning numbers k given as initial values. A plurality of sets of initial values are given, and an optimal set of scan lengths L _{1 to} L _n is selected from the scan lengths L _{1 to} L _n obtained by optimizing equation (1) for each initial value. You may choose.

The calculation unit 25 sets the obtained scanning lengths L _{1 to} L _n in the controller 21. The controller 21, after ignition of the torch 28, and starts to move the torch 28 in the longitudinal direction to the speed V ₂ of the optical fiber 14, performs first heating scan. In this first heating scan, the scan length L ₁ by the torch 28 is moved. Simultaneously with the start of the first heating scan, movement of the pair of clamps 26 in the longitudinal direction of the optical fiber 14 starts at a speed V ₁ in a direction away from each other. Thereafter, as described using the formation model shown in FIG. 3, the second to nth heating scans are sequentially performed.

During the 1st to nth heating scans, the optical fiber 14 softened by heating is pulled by the movement of the pair of clamps 26. For this reason, at one downstream end in the scanning direction of the torch 28, the taper transition portion 12 is formed so that the minute regions S ₂ , S ₄ ,. . Further, another tapered transition portion 12 is also formed at the other downstream end in the scanning direction so that minute regions S ₃ , S ₅ . A tapered waist portion 11 is formed between the pair of tapered transition portions 12. In case the width of the flame of the torch 28 is of a size not negligible as compared with the lower limit Llower scan length L _k is the optical fiber 14 extends by adding heat scan as described above, the radius of the desired fiber A tapered waist portion 11 is formed.

The TOF 10 manufactured as described above is removed from the clamp 26. Since the manufactured TOF 10 is manufactured by the first to n-th heating scans with the scanning lengths L _{1 to} L _n determined based on the equations (1) and (2), the loss is suppressed, and The total length X is shortened.

  In this example, the torch 28 is moved for heating scanning, but the torch 28 may be fixed and the moving parts 22 and 23 may be moved integrally in the longitudinal direction of the optical fiber 14. When pulling the optical fiber 14, one of the moving parts 22 and 23 may be fixed and only the other may be moved. Furthermore, although the example which performs a heating scanning process and a tension | pulling process simultaneously as an extending | stretching process was demonstrated, for example, a tension | pulling process is performed for every heating scanning process which consists of 1 time or multiple times of heating scanning, and an optical fiber is extended | stretched. Also good. In this case, what is necessary is just to derive | lead-out the formula which calculates | requires the full length of TOF10 produced based on the formation model of TOF10 in such a procedure.

[Examples 1 to 4]
In Examples 1 to 4, the TOF 10 was manufactured by the TOF manufacturing apparatus 20. In Examples 1 to 4, TOF 10 was produced under the same conditions except that the optimization coefficient F was different. In Example 1, the optimization coefficient F was set to 0.2. In the second embodiment, the optimization coefficient F is set to 0.4, 0.6 in the third embodiment, and 0.8 in the fourth embodiment.

  As the optical fiber 14, a commercially available step index type single mode (manufactured by Thorlabs, SM800) was used. The optical fiber 14 has a core refractive index of 1.4574 and a cladding refractive index of 1.4525 for a wavelength of 852 nm. The core radius is 2.4 μm, and the cladding radius (= R) is 62.5 μm.

In the calculation of the scanning length L _k , a plurality of sets of initial values were given, and Equation (1) was optimized by the downhill simplex method for each initial value. Then, from among the 10 sets of scanning length L ₁ ~L _n obtained, was used to select the optimal set.

In the first constraint, a heat insulation reference angle Ω (r) calculated for a wavelength of 852 nm was used in consideration of a three-layer structure including a core, a clad, and air. A graph of the calculated adiabatic reference angle Ω (r) is shown in FIG. In the fourth constraint condition, the upper limit value Lupper was set to 40000 μm, and the lower limit value Llower was set to 400 μm. With respect to the fifth constraint condition, the specific fiber radius was set to 4 μm based on the adiabatic reference angle Ω (r) calculated as described above. Under such constraint, it shows the profile of a scanning length L _k of the four types of optimization factor F obtained by the calculation in FIG.

  Further, in order to obtain a fiber radius (≦ 300 nm) necessary for the tapered waist portion 11 to be guided in a single mode, the number of times of heating scanning is increased. Specifically, the number of scans n used in the initial optimization calculation for Examples 1 to 4 is 288 times, but in order to make the tapered waist portion 11 a necessary fiber radius, 288 times. A heating scan was added after the heating scan. The added heating scan was repeated until it was confirmed that the taper waist 11 was guided in the single mode by the disappearance of the vibration of the transmitted light intensity of the light transmitted through the optical fiber 14. The measurement of the transmitted light intensity of the optical fiber 14 will be described later.

The TOF manufacturing apparatus 20 was installed in a class 100000 clean hood to produce the TOF 10. The moving parts 22 and 23 were obtained by attaching a fiber clamp (manufactured by Thorlabs, T711 / M250) on a linear motion stage (manufactured by Suruga Seiki Co., Ltd., KX1250) driven by a stepper motor. Both ends of the optical fiber 14 were held with these fiber clamps. Pulling speed _{V 1} was set to 15μm / sec.

The torch 28 is made of stainless steel and has a single hole with a nozzle inner diameter of 135 μm. Pure hydrogen gas (without premixed oxygen) was supplied to the torch 28, and the gas flow rate was adjusted to 10 mL / min. For the adjustment of the gas flow rate, a flow meter with a precision needle valve (Koflock Co., Ltd., RK1250) was used. Further, the torch 28 is mounted on a linear stage which is driven by a stepper motor, a scanning speed V ₂ was 750 [mu] m / sec.

  FIG. 7 shows the calculational relationship between the taper angle θ of the TOF 10 manufactured for Examples 1 to 4 and the fiber radius r. In FIG. 7, the calculational relationship between the taper angle θ and the fiber radius r is indicated by a solid line, and a corresponding optimization coefficient F is attached thereto. In addition, the curve shown with a broken line is the optimization upper limit angle (0.2Ω, 0.4Ω, 0.6Ω, 0) obtained by multiplying the insulation reference angle Ω (r) and the insulation reference angle Ω (r) by the optimization coefficient F. .8Ω).

  In Examples 1 to 4, five TOF10 samples were prepared, and the transmittance of each sample was measured. In order to measure the transmittance, light from a laser diode having an output wavelength of 852 nm was split by a beam splitter, and a 99% output port of the beam splitter was melt-connected to one end of the optical fiber 14 held by the clamp 26. . Further, the output of the laser diode was feedback-controlled based on the laser output from the 1% output port of the beam splitter, and the output was stabilized within ± 0.1%. The other end of the optical fiber 14 was connected to a photodetector device (self-made), and the transmitted light intensity (transmittance) of the TOF 10 was continuously measured from the manufacturing stage until completion.

  The transmittance of each sample of the completed TOF 10 is shown in FIG. About the transmittance | permeability of each sample of Examples 1-3 (F = 0.2, 0.4, 0.6), it expands and shows in FIG. Note that the relative error in transmittance is ± 0.1%, which depends on the stability of the laser output used for the measurement. There is no significant difference in transmittance between the TOF10 sample with an optimization factor F of 0.2 and the TOF10 sample with an optimization factor F of 0.4. This is considered because the loss due to coupling between the fundamental mode and the higher order mode is sufficiently suppressed in the TOFs 10 of the first and second embodiments. In these samples, exogenous losses are considered to be dominant.

  Table 1 shows the total length and transmittance of Example 2. The total length of the TOF 10 was the average value of the total lengths of the five samples measured by SEM (Scanning Electron Microscope). Further, the transmittance was also an average value of the transmittance of five samples. In Table 1, predicted values of the total length of TOF 10 for Examples 1, 3, and 4 are shown in parentheses. The expected value of the total length of the TOF 10 was a value obtained by adding the predicted value of the increase in the length of the TOF 10 stretched by the added heating scan to the total length of the TOF 10 calculated from the formation model. The expected value of the increase in length is the difference between the total length (19 mm) calculated from the formation model when F = 0.4 and the measured value (23) mm of the TOF 10 produced in Example 2. Using.

  Moreover, the shape of one sample of Example 2 (F = 0.4) among each sample of TOF10 was measured using SEM. The shape of the measured sample of TOF10 is shown in FIG. In FIG. 10, the horizontal axis represents the distance in the longitudinal direction (stretching direction) of the TOF 10, and the vertical axis represents the fiber radius. The distance shown on the horizontal axis is the distance from the center of the TOF 10 in the longitudinal direction. In FIG. 10, the calculated shape of the TOF 10 to be produced is shown by a solid line. Further, the relationship between the measured fiber radius and the taper angle for one sample of Example 2 (F = 0.4) is indicated by ● in FIG.

[Comparative Examples 1 and 2]
As Comparative Example 1, a TOF with a constant taper angle at the taper transition portion was produced, and as Comparative Example 2, a TOF with an exponential change in fiber radius was produced. For Comparative Examples 1 and 2, five samples of TOF were prepared. In Comparative Example 1 and Comparative Example 2, except that the TOF manufacturing apparatus 20 was used to adjust the scanning length, the pulling speed V ₁ , the scanning speed V _{2 and the} like of the torch 28 in order to form the shape of each TOF, It is the same as Examples 1-4.

  In Comparative Example 1, the taper angle of the taper transition portion was set to 2 mrad, and the change in the fiber radius was an exponential function shape for the taper waist portion. In addition, the length of the taper waist part is 400 μm. In Comparative Example 2, the taper waist portion has an exponential function shape in which the change in fiber radius is an attenuation constant of 3 mm. The calculational relationship between the taper angle θ of the TOF produced for Comparative Examples 1 and 2 and the fiber radius r is shown in FIG. 7 by a two-dot chain line and a one-dot chain line. “2 mrad” is attached to the TOF graph of Comparative Example 1, and “exp” is attached to the TOF of Comparative Example 2. Further, the relationship between the fiber radius and the taper angle measured for one TOF sample of Comparative Example 1 is indicated by □ in FIG.

  The transmittance measured for each sample of Comparative Examples 1 and 2 is shown in FIG. 8, and the transmittance of the sample of Comparative Example 1 is also shown in FIG. Moreover, the result of having measured the shape of the sample of TOF of the comparative example 1 with SEM is shown in FIG. Further, the total length and transmittance of the TOFs of Comparative Examples 1 and 2 are shown in Table 1 above. The total length of the TOF of Comparative Example 2 is an expected value as in Example 1 and the like.

  Although the TOF 10 of Examples 1 and 2 has extremely high transmittance, that is, the loss is extremely small, its total length X is considerably shorter than that of the TOF of Comparative Example 1 having substantially the same transmittance. ing. In addition, although the TOF 10 of Example 3 has a total length X that is less than 1/3 of the total length of the TOF of Comparative Example 1, the transmittance is only slightly lower than that of Comparative Example 1. Although the transmittance of the TOF 10 of Examples 1 to 3 is considerably higher than that of the comparative example 2, the total length X is equal to the comparative example 2 or sufficiently shorter than the comparative example 2. The TOF 10 of Example 4 has a total length X that is considerably shorter than the TOFs of Comparative Examples 1 and 2, for example. However, since the loss is still suppressed, the TOF 10 has a transmittance of 80% or more.

10 tapered optical fiber 11 taper waist portion 12 tapered transition portion 14 optical fiber 21 controller 25 operation unit 28 torch L _k scanning length r _k fiber radius theta _k taper angle

Claims (4)

In the method for manufacturing a tapered optical fiber, a pair of tapered transition portions are formed at both ends of the tapered waist portion, and the fiber diameter of the tapered transition portion gradually decreases toward the tapered waist portion.
A stretching step of stretching the optical fiber heated in the longitudinal direction by performing a heating scan that moves the heating position with respect to the optical fiber at a predetermined scanning length along the longitudinal direction of the optical fiber;
Prior to the drawing step, the local fiber radius of the tapered optical fiber is r, the taper angle is θ, the adiabatic reference angle for the fiber radius r is Ω (r), and the optimization factor F is 0 <. When F <1, the scanning length of each heating scan satisfies θ <F · Ω (r) and minimizes the total length X of the tapered waist portion and the pair of tapered transition portions. A method of manufacturing a tapered optical fiber, comprising: a scanning length determining step for obtaining each of The stretching step includes a heating scan that moves the heating position in a first scanning direction along a longitudinal direction of the optical fiber, and a heating scan that moves in a second scanning direction opposite to the first scanning direction. Are alternately performed, and both ends of the optical fiber are moved away from each other during the heating by the heating scanning, and the optical fiber is pulled. Moving at a speed V ₁ and moving the heating position at a constant speed V ₂ in the heating scan,
The scanning length determining step, a k as 1 to n, the scanning length of the k-th heat scan and L _k, also 2 or more tapered optical fiber which is formed by the k-th heat scan for k local fiber When the radius r is r _k and the taper angle θ is θ _k , the total length X is obtained from the equation (I), and the taper angle θ _k is obtained based on the equation (II). Item 2. A method for manufacturing a tapered optical fiber according to Item 1.

In the scanning length determination step, the scanning length L _k is a function represented by a high-order polynomial with k as a variable,
The scan length L _k corresponding to a plurality of specific k is used as a variable when minimizing, and the scan length L _k corresponding to the remaining _k is a plurality of scan lengths L _k corresponding to the specific k. The method of manufacturing a tapered optical fiber according to claim 2, wherein the value of the function determined based on a combination is used.   The method for manufacturing a tapered optical fiber according to claim 1, wherein the optimization coefficient F is 0.4.

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