JPS5956142A - Measuring method of refractive index distribution - Google Patents

Abstract

PURPOSE:To measure the light intensity only in light guide mode by using a mask which has a sector-type transparent part and removing a leakage mode as much as possible. CONSTITUTION:A lens 1 with focal length f1, photomask 3 having a center angle 2theta and the sector-type transparent part, and lens 2 are arranged coaxially in front of an end surface of an optical fiber to be measured, and the lens 1 and photomask 3 are held at an interval f1. Light projected from the end surface of the fiber 4 is diverged in an elliptic cone shape to enter the lens 1, where it is converted into parallel light whose luminous-flux center line runs in the center 0m of the photomask 3. Only light passing through the transparent part reaches the lens 2. The parallel luminous flux between the lenses 1 and 2 is diffracted by the lens 2 to form an image at a front position f2. In this linear field pattern surface 5, the intensity of light is measured in parallel to the center line of the sector-type transparent part of the photomask 3 to find a refractive index distribution.

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a method for measuring the refractive index profile of optical fibers and preforms.

g) Optical fiber refractive index distribution measurement method There are many known methods for measuring the refractive index of substances.

These methods were homogeneous bulk refractive index measurements.

As research and development in optical communications progresses, it has become necessary to measure the structure of the optical fibers that transmit light.

In particular, there has been a growing demand for measuring the refractive index distribution of optical fibers.

An optical fiber consists of a core and a cladding, but the refractive index varies within a narrow range and is not uniform. It is not possible to measure the refractive index distribution of an optical fiber by using the conventional bulk refractive index measurement method as is.

Even in a multimode optical fiber, the relative refractive index difference between the core center and the cladding is about 0.2 to 0.5%.

For example, refractive index profile measurement using interferometry can be applied to optical fibers.

Using a combination of an interferometer and a microscope, all coherent light is applied to an optical fiber cut into a disk shape to obtain interference fringes, which are then observed using a microscope.

The interferometry technique has already been established and is widely used for measuring the refractive index distribution of multimode optical fibers.

In addition to interferometry, there are scattering diffraction pattern methods, reflection methods, etc.

The near field pattern method is a simple method for measuring refractive index distribution.

(a) Near-field pattern method The near-field pattern method determines the refractive index distribution of an optical fiber from the intensity distribution of light at the output end (afield pattern) when the optical fiber is irradiated with an incoherent light source. .

In order for this method to be applicable, all of the following conditions must be satisfied.

(i) PA refractive index distribution is circularly symmetrical.

(ii) The core diameter is more than 100 times larger than the wavelength, allowing a large number of modes to propagate.

■) The refractive index change within the core is several percent or less.

(iv) The change in refractive index between two points separated by about one wavelength is negligibly small.

(v) All propagation modes are uniformly excited.

Although it is difficult to satisfy all five conditions above,
If this condition holds, the near-field intensity distribution P (r) on the fiber cross section is proportional to the local numerical aperture NA.

Here, the numerical aperture NA is 1/NA(r) = Cn2(r)-n2) 2, where r is the distance from the center.
Defined in (1). Here, n(r) is the refractive index at point r, and n(r) is the refractive index of the cladding.

The refractive index of the fiber core is a function of only r when the conditions (i) to (V) are satisfied regarding cylindrical coordinates (r, θ, 2) with the fiber center axis as two axes.

Numerical aperture NA is the maximum angle of incidence that an optical fiber can receive.
When setting it to 0, sin θ. be equivalent to. Therefore, it can be considered that (when the condition of success is satisfied), the light power P(r) at the output end is proportional to the square of the numerical aperture.

In other words, it can be written as. P(0) is the optical power at the center.

If we replace the refractive index n (r) by the difference Δr) from the refractive index n2 of the cladding, we get n(r) = n2 + Δn (r)
, (8), the power P (r)
is P (0) n' (υ no n The intensity distribution of light at the opposite end has an Afield pattern) P (r) ffi If you measure it, you can know the local refractive index distribution Δn(r) .

However, in reality, it is difficult for all conditions (i) to (V) to hold true. In addition to the propagation mode, there are leakage modes.

Originally, the numerical aperture NA is the one that gives the range of incidence angles in which the refractive index of the core is set to a constant value, and the light that enters the center of the core is totally reflected at the interface between the core and cladding and can propagate within the core. It is. The light flux incident on the center of the core is
Even if reflected at the cladding boundary, since they are on the same plane, it can be said that what is defined by equation (1) strictly defines the incident angle range of the propagating light beam.

However, at a point r from the center, the local numerical aperture NA(r)
There is no such clear meaning when defining.

When a ray of light incident on a point far from the center passes on a plane (tentatively called a meridional plane) that includes that point and the fiber central axis, the numerical aperture NA is the critical angle of incidence θ. You can say that you give everything.

There are only a few such meridian rays. If the incident ray is a non-meridional ray, it will be reflected at the interface between the cladding and the core,
It propagates in a spiral inside the core.

FIG. 1 is a schematic illustration of a fiber end face to illustrate such leakage modes.

The origin of the coordinates is set at the boundary between the core and the cladding, with two axes in the axial direction of the fiber and an X-axis in the radial direction of the fiber.

The apex angle θ1 of the cone V connecting the origin O and the shaded part is
This value is defined as sin θ1 being equal to the numerical aperture NA. A light beam whose incident angle is within the cone V and is incident on O is totally reflected at the boundary between the core and the cladding, and can propagate within the fiber.

Not all rays not included in cone V cannot propagate within the fiber core. A ray with an incident angle of 02 (θ2〉
θ, ), some of them propagate within the core.

If it is a non-meridian ray, even if θ2〉θ, the core,
This is because there are cases where the angle of incidence on the boundary surface of the cladding satisfies the total internal reflection condition.

These non-meridional rays travel spirally through the core while being reflected by the boundary surfaces.

This is the leak mode. If there is a leakage mode, equation (2) does not strictly hold. Therefore, as shown in equation (4), the power P (r) is not exactly proportional to the refractive index difference Δn (r).

When all waveguide modes are fully excited, the leakage mode is also excited, so errors caused by the leakage mode must be corrected.

A proposal has been made to measure all P (r) using this method and multiply it by a correction coefficient to find the correct value Δn(r)'e, but it is not very accurate.

Although the near-field pattern method has a simple measurement system, it has these drawbacks.

(1) Explain the electric field E in the leaky mode fiber core, Helmholtz's equation % Formula % (5) Fully satisfied. It is assumed that the axial direction of the core is two axes, and the coordinates are defined by the distance r from the center, the rotation angle θ, and the values of 2.

If the phase constant propagating in two directions is β, and the number of nodes in the rotation angle direction is υ, then the electric field E is E = ・i(β'1
It can be written as ″″′)U (r) (6). (5)
, (6) Yoshi('l). If n (r) is a constant, the solution to (7) becomes a Bessel function. However, since n (r) depends on r, the solution to (7) is not a Bessel function.

It can be said that the value in parentheses in equation (7) generally defines the properties of the solution. When n (r) is unknown, when it is positive in the parentheses, it is close to the oscillation group, and when it is negative, it is close to the reduced representation solution.

Three types of modes can occur in a fiber: guided modes, leaky modes, and radiation modes.

From the condition that the guided mode does not enter the cladding, and that it is attenuated in the cladding, the phase constant β
Is 1 β? ＞kgnj (8)
satisfies the condition.

The leakage mode has a phase constant β2 that allows sound to propagate through the cladding, but this is the case when there is no wave number component in the circumferential direction. That is, /32'〈ko'n2' (Ω). The reason why the leakage mode propagates in the core and does not enter the cladding is because it has a wave number component (0/r) in the circumferential direction. Therefore, υ2 β22 + ) k02n2” (
The inequality 1o)2 holds true. In the end, the phase constant β2 of the leech mode is υ2 ko'n2"<β2"<ko' n2
” (11)2 must be satisfied.

ko is the wave number of light in vacuum, a is the radius of the core, and is a graph showing changes in the n2 value. The horizontal axis is the distance r from the core center, and β1, β2, and β3 are the waveguide mode, leakage mode,
is the phase constant of the radiation mode. Since only the a6 mode will be considered below, β2 will be written as β and #5.

FIG. 3 is a perspective view showing the wave number vector of the emitted light beam at the end face of the fiber core.

The center of the core is the origin O, and zII is in the axial direction of the fiber.
Take LIII. The XSy axis corresponds to the end face of the fiber core.

Consider light emitted from point A on the X-axis.

The wave number vector of the emitted light is represented by AB. The length is ko.

Point B, xz plane
Let it be F.

Let H be the foot of the perpendicular line drawn from point B to the y-axis.

Let D be the intersection of a straight line that passes through point A and is parallel to the two axes and a plane that passes through point B and is parallel to the xy plane. A rectangle including the three points B and C1D2 is represented by IBEDC, and a rectangle including the three points A and H1F is represented by AHFG.

The angle that the emitted light makes with the normal line AD is set to 0. The output light AB is
Let the angle between it and the straight line AG parallel to the y-axis be a. Let φ be the angle that the line segment DB makes with the straight line DF:.

The length of the orthogonal projection AG of the emitted light in the y-axis direction is I'/r. This is because it is a wave number vector component in the circumferential direction.

The following formula holds true regarding ΔABG. If the emission angle in vacuum is θ, the refraction angle in the core is θ, and the refractive index of the core at point A k n (r), sin θ == n (r) sin θ
The formula (β3) holds true.

In △EDB, ED is k. cosa, DB is k. sin
Since θ, it comes out.

The phase constant β of the light emitted at point A is 2 of the wave number within the core.
Since it is defined as the value of the component, β = k, H(r
) cosa (15).

Substituting these values into the inequality (11) gives the following equation.

From here, by eliminating υ and θ, we get 2 n22−-Co52φ51n2θ(β2(r) −5i
We obtain the inequality n2θ(β2'' (17)2).

If the maximum value of the output angle θ is θmax, then the following equation is obtained. This is obtained from both sides of the inequality sign before inequality (17).

From the latter inequality sign, the minimum value θurnk of the exit angle can be determined.

The minimum exit angle θ control of the leakage mode is 8. f) sin = (β2(r) −n223”
(19) is given by. The leaky mode indicates the condition that it is emitted just outside the guided mode.

The maximum exit angle θmax of the leakage mode depends on the angle φ.

In this example, when φ=-4, θmax ”θmin
(!: Yes. In other words, there is no leakage mode in the ±πZ direction.

When φ=0 and π, θmax takes the maximum value. This means that the leakage mode emitted in this direction is the largest.

The angle φ corresponds to the magnitude of the angular component of the exit vector. This is because the angular direction component of the orthogonal projection of the output vector AB onto the core end surface (xy plane) is expressed by the angle φ.

The leakage mode rarely occurs in the radial direction, but
This means that more light is emitted in the angular direction.

FIG. 4 is a schematic diagram showing the emission direction of the leakage mode of light emitted from the core end face. Point A1 on the x-axis and point A on the y-axis
The leakage mode emitted from 2 is indicated by the dot area. The dot area is an ellipse with a major axis in the angular direction (circumferential direction) and a minor axis in the radial direction.

The circular area surrounded by the dot area corresponds to the emission angle of the waveguide mode.

In this way, light emitted from a point other than the origin 0 always includes a leakage mode.

The leaky mode is emitted to the outside of the guided mode, but it is not emitted uniformly, and there are few in the radial direction.

Mostly in the angular direction.

If such leakage mode anisotropy is utilized, it should be possible to measure the refractive index distribution of a fiber core, etc., with high accuracy even by the near-field pattern method.

(Refractive index distribution measurement method according to the present invention) In the present invention, a mask of an appropriate shape is used to eliminate all leaky modes to the extent possible and measure only the light intensity of the guided mode.

FIG. 5 is a perspective view of a measurement system used in the refractive index distribution measurement method of the present invention.

The measurement system includes a first lens 1, a second lens 2, an optical mask 3 interposed between them, and an end face of a core ino (4) and a near field pattern (5).

Near field pattern ti5KX, Y*41,
The intensity of the emitted light is measured along the y-axis. Detection g?
r consists of a microscope, a vidicon, etc., and the one used in the conventional near-field patterning method can be used as is.

7 The centers of the fiber 4, the first and second lenses 1.2, and the optical mask 3 are on the same straight line, and this is taken as the kz axis.

It is assumed that the focal lengths of the first lens 1 and the second lens 2 are kf+ and f2.

Fiber end face and second lens 1 First lens 1 and optical mask 3
The interval between is fl. The distance between the optical mask 3 and the lens 2 is f2.

Light emitted from an arbitrary point on the end face of the fiber 4 expands into an elliptical cone shape and enters the lens 1. This light is converted into parallel light by the lens 1.

Since the distance between the optical mask 3 and the first lens 1 is fI, the center line of the parallel light beam always passes through the center Om of the optical mask 3.

This is because the center line of the parallel light beam corresponds to the light ray emitted from the fiber end face along the normal line (parallel to the y-axis).

The xy section of the parallel light beam between the first lens 1 and the optical mask 3 has an elliptical shape, and its center passes through the center Om of the mask.
It will be projected onto the mask so that it is always symmetrical.

This property is common to all elliptical cone-shaped light beams emitted from any point on the fiber end face.

The optical mask 3 is arranged along the ±X axis from the disk, with a central angle of 2θ.
It is shaped like a fan-shaped cutout. It can also be said that fan shapes having a central angle of (π-2θ) are arranged symmetrically with respect to the y-axis along the ±y-axis.

It is important that the transparent portion 5 has a fan shape with a central angle of 2θ centered on X@. In the figure, parts that block light are shaded.

Only the light that has passed through the transparent part of the optical mask 3 reaches the lens 2. In the figure, out of the ellipse drawn on the soil of lens 2,
The white part corresponds to light passing through the transparent part. The shaded area indicates the portion blocked by the original mask 3.

The distance between the optical mask 3 and the lens 2 is equal to the focal length f2 of the lens 2, so when the light ray that passes through the center Om of the optical mask passes through the lens 2, it is 6f (folded and parallel to the y-axis). It becomes a light.

The parallel light beam existing between the first lens 1 and the second lens 2 is
It is refracted by the lens 2, and an image is formed at a position f2 in front of the lens 2. Near field pattern 5 is set here.

The figure shows the mode of propagation of light emitted from the center A of the end face of the fiber 4, a point B on the x-axis, and a point C on the y-axis.

The light emitted from the center A expands into a circular area on the first lens 1, passes through the optical manure 3, and converges from the lens 2 onto the center A of the near-field pattern surface 5.

This light travels along the y-axis. No leakage mode occurs.

If attenuation by the lens is ignored, only the proportion (LED,) of the amount of light that leaves point A that passes through the optical manufacturer reaches point A.

The light emitted from the point B on the y-axis expands into an elliptical cone shape and enters the elliptical area B1 on the first lens 1. In B1, the white background corresponds to the guided mode, and the blacked out area corresponds to the leakage mode. It becomes a parallel light beam at the second lens 1, passes through the center Om of the optical mask, and reaches the elliptical region B2 on the opposite side on the X-axis of the second lens 2. In B2, only the fan-shaped area represented by a narrow white background is the area where light exists. The light leaving B2 is
An image is formed at point B' on the near field pattern surface.

Comparing the elliptical area BI B2 on lens 1.2,
It can be seen that almost all of the lingering mode is blocked by the optical mask. Since the optical mask has fan-shaped transparent parts on the ±X axis, it is possible to effectively remove the leakage mode of light emitted from the fiber end face on the X axis.

The opposite is true for light emitted from the y-axis. Light emitted from the 0 point on the y-axis creates elliptical areas C1 and C2 north of the first lens 1 and second lens 2. .

Most leakage modes occur in the xm direction. Since the transparent part of Manuk is along the y-axis, it cannot block almost all leakage modes.

On the near-field pattern surface 5, when the detection point is on the y-axis, the proportion of leakage mode is the lowest. When the detection point is on the y-axis, the percentage of leakage modes included is highest.

Therefore, the light intensity will be detected along the y-axis.

Regarding the refractive index distribution of the fiber core, m1 rotation symmetry n
Since this is a near-field pattern method that assumes (r), generality is not lost even if the detection position is along the MkX axis.

The refractive index difference Δn(r) can be easily determined from the light intensity distribution P (r) measured along the y-axis.

(2) Shape of the optical mask The optical mask 3 must pass the guided mode and block the leakage mode of the parallel light beam between the first lens 1 and the second lens 2.

The intestinal fluid mode is located in the circular area, and the leakage mode is located in the crescent-shaped area (surrounded by an oval and a circle) outside of the reed.

It seems best for the transparent part of the optical manuk to be a simple circle in order to pass the waveguide mode.

However, rather than simply passing the guided mode, it is necessary to pass a certain percentage of the light intensity of the guided mode.

Although it also depends on the refractive index distribution n (r), the local aperture @
N A (r) varies depending on r. The numerical aperture is
The areas of the light irradiation areas Ai, B1, and C1 on the lens 1 are defined. The light irradiation area is generally elliptical in shape, but its area, major axis, and minor axis vary significantly depending on the emission point. The part containing the waveguide mode is always a circular region, but the emission point (
The area differs depending on r).

The light intensity of the guided mode is proportional to the area of this circle.

No matter how the radius of the circle changes, a light manuk that allows only a certain percentage to pass through must have the following limitations.

The distance from the center of Manuku is fr, and the coordinate in the circumferential direction is θ
shall be. The characteristic function X(r, θ) at (r, θ) is
It is defined as 0 when non-transparent and 1 when transparent.

In order to pass only a certain proportion m of the parallel light from a circle of arbitrary area, 0 must hold.

When divided by R, Rf X (r, θ) dθ= 2 yr Rm
@) 0. The left side is a value obtained by integrating the transparent portion along a constant radius H. The meaning of this equation is that the area of the transparent portion of the mask is proportional to the distance H from the center.

Therefore, the above-mentioned mask having a simple circular transparent portion is inappropriate.

Furthermore, the observation point is placed along the X plane, and a condition is imposed that the leakage mode is minimized. This means that it is most desirable for the transparent part of the optical mask to be fan-shaped with its center line on the ±X axis.

(to) Spacing of optical system In FIG. 5, the spacing between the fiber end face, second lens 2, optical mask 3, lens 2, and near field pattern 5 is fl.
, F7, F2, F2.

The light emitted from the end face of the fiber spreads in a conical shape around the normal line to that point. 2nd lens, 2nd lens 2
It is not necessarily required that the light beam be parallel between the two.

However, the center of the light beam must communicate with the center Omm of the mask 3.

The observation point on the near field pattern surface 5 will now be considered. The light flux is 2 on the near field pattern plane (xy plane).
In order for the light to enter as a beam parallel to the axis, the distance between the optical mask 3 and the lens 2 must be F2.

However, if the direction of the detector can be changed, the condition that the light beam must be incident at right angles to the near-field pattern surface 5 can be removed.

In the end, f+51 (M kFl,
Assuming F2, F3, and F4, only F2=f2 is always required. However, for the others, Fi=fi(i=1
．． 3.4) is not necessarily required.

It is sufficient that the image of the fiber end face is formed on the near field pattern surface 5. Generally, (f+”10F3fl F3F+)(F2 F4)=
F2F4 (Fl '4) (Thank you) is fine.

(g) Derivation of the ratio of the four-wave mode and the leakage mode The present invention is characterized in that it attempts to remove the leakage mode as much as possible by using a fan-shaped optical mask.

So, how much leakage mode can be removed with a fan-shaped mask? Let's evaluate.

FIG. 6 is a schematic diagram for evaluating how the light emitted from the fiber end face is enlarged and projected onto the xy plane in front.

Consider an elliptical cone beam emitted from the center of the fiber core end face to a point r.

Let the major axis of the ellipse projected onto the xy plane be q, and the minor axis wop. Maximum output angle lx in short axis direction, maximum output angle 2 in long axis direction
Let it be Y. 8, which gives the fiber end face and the maximum value θmax of the output angle in the xy plane. ” =
(n2(r), 22, '/2(5).

Fig. 7 shows that for an ellipse with short mp and long axis q, x! 11+
This shows a straight line that makes an angle θ with and passes through the origin.

A portion S1 surrounded by a straight line and a circle corresponds to the light intensity of the guided mode. A portion S2 surrounded by a straight line and an ellipse corresponds to the light intensity of all modes. The straight line m corresponds to the radial direction of the sector-shaped transparent part of the mask.

S+ = -p20 (27) It is.

The equation of the straight line m is z = ycotθ (28), and the equation of the ellipse is. The y-coordinate of the intersection of both is y. Write.

It is. This can be integrated, get. however It is.

Of the total light intensity, the proportion of light intensity due to the deflection mode is 52 (3
8) Rewriting this becomes η. However, in order to evaluate the mode where η, ξ are omitted, the refractive index distribution n (r)
(z must be known. n (r) is the object of measurement, but since evaluation is the issue here, α, which is commonly used as the refractive index distribution of an optical fiber,
We decided to assume a power-law distribution.

That is, n (r) is r (when a, (inside the core) r a l/ n (r) = n□ [1-2Δ(-)] 2 (37) r
> a (cladding).

(23) to (26) and (37), (38) and (35)
From the formula, cotξ can be found.

It is. Δ is approximately equal to the difference in refractive index between the core and the cladding, but this is small at about 1%. nl is an amount of 1-2.

After all, approximately ξ is It is.

It is important when the central angle θ of the mask is small.

Assuming that O is small, according to equation (36), η is a very small amount. Equation (36) allows approximation of η.

The well-known approximate formula % formula % (41) (42) is used. (36), (41), (42)
) (43) can be written.

By substituting this into the equation k (34,), the ratio R including the curl mode can be determined.

θ2 R kan-(1-cot2ξ) (dll
) to obtain a simple expression. This only uses the condition that O is small, and does not depend on n (r). When θ is small, the leakage mode is 0 squared.
Assuming that K, the refractive index distribution equations (37) and (88) k, and using equation (40) regarding ξ, the ratio of the drowning mode can be expressed by an extremely simple approximation equation.

This approximation actually does not include the refractive index distribution n(r) at all. This is an approximate expression that holds true as long as θ is small, no matter what the refractive index distribution n (r) is.

When θ is small, the ratio R of the deflection mode is proportional to the square of θ and proportional to the square of the distance r from the core center. In particular, it should be noted that the property that R is proportional to r2 does not depend on the distribution of n (r).

For example, when O=2°, 6°, 10', the leakage mode R is 0.04% at the core and cladding boundaries (r=a).
, 0.36%, and 1%.

In Figures 8 and 9, the horizontal axis is r//13-, and the leakage mode R
This is a graph that shows how R changes depending on r, with (to) as the vertical axis. no=1.46.621%
And so. The half O of the central angle of the fan shape was set to 2°, 6°, and 10'. In FIG. 8, α=2.0, and in FIG. 9, α=(a).

In other words, FIG. 8 corresponds to a case where the refractive index distribution of the core changes by the square of r. FIG. 9 corresponds to the case where the refractive index of the core is constant. It is a Nutep type fiber.

Either way, they show similar changes.

This was calculated numerically using a computer, but it can be seen that it almost agrees with the near <p equation (45).

A small center angle 2θ of the optical mask is effective in the present invention. Now, let's examine how the leakage mode increases as e increases. This is to know the desirable range of O.

The condition for approximation is that (r/a　> is small.

Equation (40) giving cos ξ is used.

(86) From equation (40), it can be written as. (84), (40), (46) formulas,
It can be written as It can be seen that equation (45) gives an approximation to the limit of θ→0. Equation (47) is a good approximation within a small range of (r/a) or l.

Figures 10 and 11 show 0=20°, 40°, 60°,
The ratio of leakage mode H in the case of 80° was determined by all numerical calculations. No=1.46.621%.

In FIG. 10, α=2. The refractive index has a square distribution. FIG. 11 shows an example in which α=(2) and the refractive index of the core is uniform.

Equation (47) is a good approximation for these graphs when (r/a) is small.

Conversely, if we consider the limit where r/a is close to 1, we obtain -〇-〇Rkan (48) Peng θ from equations (36) and (34) as the limit of cotξ→0.

In equation (48), θ=20°, 4o0.60', 80
', then R is calculated as 4%, 17%, 40%, and 75%. It can be seen that a fairly reasonable approximation value is given as the value of H at r/a'=1.

Next, we will discuss the dependence of α. If a=2, the refractive index of the core takes a maximum value at the center and decreases at r2.

This is an example of continuous change.

α=■ means that the core refractive index is constant at nl, and corresponds to a Nutep type optical fiber.

Let's examine how R differs between when α=2 and when using a sword.

FIG. 12 is a graph of R showing the difference between a=2 and ■. n
o=1.46.621%, e=lO'. The upper part of the two graphs corresponds to α=father, and the lower part corresponds to the example of α=2. In any case, equation (45) is appropriate as an approximate equation.

Pain mode ratio k when α = 2, ■ R (2), R)
When abbreviated as, Equation (39) becomes. The difference appears when (r/a) is close to 1, but
Very little.

The same thing can be said even when θ is large.

FIG. 13 is a graph obtained by numerically calculating the leakage mode ratio R2 when α=2 and ■ when no=1.46, Δ=1%, and θ=600. The approximate expression (49) is similarly valid.

Through the above numerical calculations and approximate calculations from exact solutions, the following can be found.

(i) When r/a and θ are small, R can be approximated by equation (45).

It hardly depends on the refractive index difference Δ, the power of the distribution, or the Cuturad refractive index n2.

(ii) When r/a = 1, R at the core and cladding boundary can be approximated by equation (48). Δ, n2,
It hardly depends on α.

R is maximum when r/a = 1. For example, if we try to suppress the maximum value of R to 1%, O is lO° from equation (48).
It turns out that the following is good.

Measurement results according to the present invention FIGS. 14 and 15 are graphs showing the results of measuring the refractive index distribution of a certain optical fiber using the near-field pattern method (solid line) and the interferometry method (dashed line).

The horizontal axis indicates a position r along a certain diameter direction of the fiber end face. The unit is μm.

The vertical axis is the difference between the refractive index of the core and the refractive index of the cladding (n+
”2) ff: 100 times L fc 1ili k
.

FIG. 14C shows a pattern using a normal near-field pattern method without using a mask. There is a large discrepancy with the interferometry data.

FIG. 15 shows the measurement results of the near field pattern method of the present invention. The central angle 2θ of the transparent part of the mask is 20° (e = ioo). It shows good agreement with the data obtained by interferometry (dashed line).

Since FIG. 14 shows the 1lIJ constant without using a mask, as r becomes larger, the proportion of the leakage mode becomes thicker and the apparent amount of light becomes excessive. For this reason, R is underestimated when r=Q, and overestimated when r-) a.

(g) Effects of the present invention (i) The refractive index distribution of optical fibers, preforms, etc. can be easily and accurately measured.

(n) It is a non-destructive measurement method.

(iii) A mask having a fan-shaped transparent part eliminates the leakage mode, allowing more accurate measurements than the conventional near-field pattern method.

(iv) Optical masks can be easily and accurately produced using photographic techniques. First, a light mask pattern is drawn at a magnification of 20 to 100 times, then it is scaled down and photographed on a dry plate.

[Brief explanation of drawings]

FIG. 1 is a perspective view of an end face of an optical fiber schematically showing light rays in a waveguide mode and a leaky mode that are incident on the end face. Figure 2 shows (ko2n2(r)) in the core and cladding.
- FIG. 3 is an explanatory perspective view showing components of the wave number vector of light emitted to the end face of the core. FIG. 4 is a schematic view of the expansion of light emitted from the end face of the fiber core, viewed from the axial direction. The dotted area corresponds to the wave mode, and the white area within it corresponds to the waveguide mode. FIG. 5 is a perspective view showing the arrangement of an optical system for a refractive index profile measurement method according to an embodiment of the present invention. FIG. 6 is a schematic perspective view showing the waveguide mode and leakage mode when light emitted from the end face of the fiber core illuminates a plane parallel to the front end face. FIG. 7 is a schematic projection diagram schematically showing a region S1 for the waveguide mode and a region S2 including all modes when a fan-shaped mask is used. p is the short axis and q is the long axis. 20 is the central angle of the transparent part of the fan-shaped mask. Figure 8 shows the distance 1iflf (r/a) from the center of the core.
A graph showing the results of numerical calculations of how the ratio of swamp mode changes depending on the situation. no=1.46,
The figures are illustrated for the cases where Δ-1%, α=2, and θ=2°, 6°, and lOo. FIG. 9 is a graph similar to FIG. 8, showing the swamp mode ratio Ri for the example of α=(3). FIG. 10 is a graph obtained by numerical calculation of how the bending mode ratio R changes depending on the distance (r/a) from the core center. -= 1.46, Δ=1%, α=
2, the amount θ of 1/2 of the central angle of the sector is 20°, 40',
It is illustrated as 60° and 80°. FIG. 11 is a graph similar to FIG. 10, showing the distortion mode ratio R1 for the example of a=■. Figure 12 is a similar graph, but no = 1.46,
Δ=1%, θ=10°, H for α=father and α=2
This is a graph showing that the difference is slight. Figure 13 shows H in the case of α=■ and α=2 as in Figure 12.
Graph showing that the difference between is small. θ=60°. FIG. 14 is a graph showing an example of measuring the refractive index distribution of an optical fiber. The horizontal axis represents the distance Mr (μm) from the center, and the vertical axis represents the refractive index difference (n, −n2) x 100=. The solid line is the measurement data using the conventional near-field pattern method, and the broken line is the measurement data using the interferometry method? show. FIG. 15 is a graph showing an example of measuring the refractive index distribution of an optical fiber. The solid line represents the measurement data according to the present invention, and the dashed line represents the measurement data according to the interferometry method. The central angle 2θ of the transparent part of the mask is 200 ((El=10'). 1...... Second Rennes 2... Second Rennes 3... ...... Optical mask 4 ... ... ... Fiber 5 ...... Near field pattern surface f1 ...... Focus of "th runne" Distance f2 ...... Focal length F1 of the second lens ...... Distance between the fiber end face and the first lens F2 ...... Distance between the second lens and the optical mask Spacing F3 ...... Distance between optical mask and second lens 2 axes ... Main axis X taken in the longitudinal direction of the fiber core ...... X axis Maximum output angle in the direction Y ・・・・・・・・・ Maximum output angle q in the y-axis direction ・・・・・・ Length θ of similar light in the long axis direction ・・・・・・・・・... 1/2 of the central angle 2θ of the transparent part of the optical mask Fig. 3 y Fig. 7 Fig. 10 Fig. 11 Fig. 8 Fig. 14 Fig. 40 30 20 10 0 10 20 30 4
0 (l1m) Figure 15 n,''n2 40 30 20 10 0 10 20 30 4
0(l)m)

Claims (3)

[Claims] (1) In front of the end face of the optical fiber consisting of the core and cladding whose refractive index distribution is to be measured, an optical mask 3 having a lens 1 with a focal length f1 and a sector-shaped transparent part with a central angle of 2θ.
, and the second lens 2 are arranged on the same axis, and the second lens 1
The distance between the lens and the optical manuk 3 is made equal to the focal length f1 of the first lens, and the light emitted from the fiber end face is directed to the second lens 2.
At the near-field pattern surface 5 that is imaged in front of
A refractive index distribution measuring method in which the refractive index distribution is determined by measuring the intensity of light in a direction parallel to the center line of the fan-shaped transparent part of the optical mask 3. (2) Claim (1) in which the distance between the fiber end face and the first lunion is equal to the focal length f1 of the first lunion.
The refractive index distribution measurement method described in Section 1. (3) Half θ of the central angle 2θ of the fan-shaped transparent part of the light manuk is 1
The refractive index distribution measuring method according to claim (1), wherein the angle is 0° or less.