JPH087069B2 - Closed curve optical waveguide - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a closed-curve optical waveguide which is applied to, for example, a ring resonator of a ring resonant laser gyro, is composed of an optical waveguide, and is coupled to a linear optical waveguide for input and output.

[0002]

2. Description of the Related Art A conventional closed curve optical waveguide is shown in FIG. 2A.
A closed curve optical waveguide 12 is coupled to an input / output linear optical waveguide 11. A part of the closed curve optical waveguide 12 is a straight line portion 1
2a, and the linear portion 12a is provided in parallel with and in close proximity to the linear optical waveguide 11, and the directional coupler 13 is constituted by both. The other part of the closed curve optical waveguide 12 is an arc part 12
It is assumed to be b.

The light 14 incident on one end of the linear optical waveguide 11 travels in the closed curved optical waveguide 12 along the traveling direction of the closed curved optical waveguide 12 by the directional coupler 13.
Move to join. The light that has moved to the closed curve optical waveguide 12 travels in the closed curve optical waveguide 12, and when passing through the directional coupler 13, a part of the light moves to the linear optical waveguide 11 and is emitted as light 15 from the other end.

By the light orbiting the closed curve optical waveguide 12 a plurality of times, the light becomes multiple interference light, the strengthened portion is further strengthened, the weakened portion is further weakened, and the light emitted from the linear optical waveguide 11 is 15 Is pulsed. When the angular velocity around the axis of the closed curve optical waveguide 12 is applied, the phase of the light advances due to the Sagnac effect if the angular velocity matches the direction of light circulation in the closed curve optical waveguide 12, and the emitted light 15 When the pulse frequency is high and the applied angular velocity is in the direction opposite to the circulating direction of the light, the phase of the light is delayed and the pulse frequency of the emitted light 15 becomes low. Therefore, the applied angular velocity can be measured by measuring the pulse frequency of the emitted light 15. This is the principle of the ring resonance laser gyro.

[0005]

The coupling portion of the closed curve optical waveguide 12 with the linear optical waveguide 11 is the directional coupler 1 thereof.
From the easiness of the design of No. 3, it was made into the straight line part 12a and the other part was made into the circular arc part 12b. Therefore, the straight part 1
At the connecting portion 16 between the 2a and the arc portion 12b, due to the difference in the radius of curvature between the straight portion 12a and the arc portion 12b, mismatch of the field distribution occurs and mode conversion loss occurs. Such an increase in loss causes a decrease in finesse (the larger the index, the better the sensitivity), which is an index indicating the sensitivity of the resonator, and the performance of the gyro deteriorates when used in a ring resonance laser gyro, for example.

If the closed curve optical waveguide 12 is made to be a perfect circle, mode conversion will be eliminated, but at present, it is difficult to make light enter and output light to the closed curve optical waveguide 12. Therefore, the straight line portion 12a must be provided in the closed curve optical waveguide 12.
In need.

[0007]

According to the present invention, there are provided a first straight line portion which is in close proximity to and parallel to a linear optical waveguide, and a second straight line portion which is parallel to and apart from the first straight line portion.
The respective ends of the first and second curved portions having a four-half arc shape are connected to the respective ends on the same side of the linear portion, and the respective other ends of the first and second curved portions are connected to each other. The other ends of the first and second straight line portions are connected to the respective one ends of the fourth semicircular arc-shaped third and fourth curved portions, and the third and fourth
The other ends of the curved portions are connected to each other. Each of the first to fourth curved line portions, when the curved line is displayed in polar coordinates,
The second derivative with respect to the angle is continuous, and at each connecting point, the second derivatives of both sides thereof are continuous with each other.

[0008]

FIG. 1 shows an embodiment of the present invention. The input / output linear optical waveguide 11 has a closed curved optical waveguide 2 according to the present invention.
1 is supplied. The closed curve optical waveguide 21 has a first straight line portion 21a that is close to and parallel to the straight line optical waveguide 11, and the directional coupler 1 is formed by the first straight line portion 21a and the straight line optical waveguide 11.
3 are configured. The closed curve optical waveguide 21 includes a first straight line portion 21a and a second straight line portion 21 that is opposed to and parallel to the first straight line portion 21a.
b, and each of the first and second straight line portions 21a and 21b has four semi-circular arc-shaped first and second curved portions 21 at one end on the same side.
One ends of the c and 21d are connected, and the other ends of the first and second curved portions 21c and 21d are connected to each other. Further, the other ends of the first and second straight line portions 21a and 21b are respectively connected to the respective one ends of the fourth semicircular arc-shaped third and fourth curved portions 21e and 21f, and the third and fourth curved portions 21e and 21f are connected. The other ends of each are connected to each other. In this way, the closed curve optical waveguide 21
Is composed of first and second linear portions 21a and 21b and first to fourth curved portions 21c to 21f.

In this example, the first and second straight portions 21a, 2
1b has the same length, and the first to fourth curved portions 21c
21 f have the same size as each other. The curve of the first curved portion 21c has an origin 23a on a line (x-axis) that passes through the connection point 22a between the first linear portion 21a and the first curved portion 21c and is orthogonal to the first linear portion 21a. In polar coordinates where the angle with respect to the axis is θ and the distance from the origin 23a is r, it can be expressed by the following equation.

R = a (1-cos θ) / 2 (1) This is called a Limason curve, and a is an arbitrary constant. At the connection point 22b of the first and second curved portions 21c and 21d, the first curved portion 21c is the first straight portion 21a.
It is made to be orthogonal to the extension line of. That is, the origin 23a
Is used as a common origin, and the equation (1) is expressed by the Cartesian coordinate system having the y-axis parallel to the first straight line portion 21a, and the change rate of the y-axis component with respect to the angle θ is zero at the connecting point 22b. It

On the other hand, the radius of curvature ρ is given by the following equation. ρ (r ² + r ′ ² ) ^3/2 / (r ² + 2r ′ ² −rr ″) (2) r ′: first-order derivative of θ, r ″: second-order derivative of θ (1) Equation (2) Substituting into the equation, the relationship between ρ and θ is shown in Fig. 2.
As shown in B. When θ = 0, ρ becomes ∞, that is, x
The straight line is parallel to the first straight line portion 21a having a change rate of 0 with respect to θ in the axial direction. ρ decreases as θ increases, and θ
_{At e} = 111.47 °, θ = a. This θ = a is where the rate of change of the y-axis component with respect to θ is zero.
Further, the expression (2) can be expressed by the 0th to the 2nd derivative with respect to θ, while the expression (1) is continuous up to the 2nd derivative with respect to the θ, the curvature radius of the first curve portion 21c continuously changes. The fact that the second derivative with respect to θ is continuous means that the 0th derivative and the first derivative with respect to θ are also continuous.

As described above, in this example, the second to fourth curved portions 21d, 21e, and 21f have the same size and shape as the first curved portion 21c, but have different directions. Therefore, the connection point 2 of the second curved portion 21d and the first curved portion 21c
In 2b, the direction is perpendicular to the first straight line portion 21a, and the connecting point 22b of the first and second curved line portions 21c and 21d has a smoothly continuous curvature. Further, at the connection point 22c of the second curved portion 21d with the second straight portion 21b, the second straight portion 2
1b is parallel to the second curved portion 21d and the second curved portion 21d.
The respective second-order differentials with the straight line portion 21b are continuous with each other, and the connecting point 22c also has a smooth continuous curvature.

Similarly, the connection points 22d, 2 of the first curved portion 21a and the fourth curved portion 21f of the third curved portion 21e are connected.
2e has a smoothly continuous curvature, and the fourth curved portion 2
The connecting point 22f between the 1f and the second straight portion 21b also has a smoothly continuous radius of curvature. As described above, in the closed curve optical waveguide 21, the inclinations and the curvatures are continuous at the respective connection points 22a to 22f, and the field distribution is not inconsistent.
~ Since no discontinuity of the radius of curvature occurs in the fourth curved portions 21c to 21f, mode conversion loss does not occur. Moreover, since the linear optical waveguide 11 and the first linear portion 21a are coupled,
The connection can be easily made as designed.

In the above description, the first to fourth curved portions 21c-
Although the Limasson curve is used as the curve of 21f, other curves may be used as long as they are second-order differentials with respect to θ in polar coordinate display, that is, the curvature level satisfies continuity.

[0015]

As described above, according to the present invention, a curve having continuity up to the second derivative with respect to θ is used as the curve portion, and the connecting portion is in the same direction as the other party, and at the connecting point, Since the second-order differentials on both sides are continuous, the slope and curvature are continuous at all points, mode conversion loss due to field distribution mismatch is eliminated, and a ring resonator with low finesse and high finesse can be obtained. Moreover, since the coupling with the input / output linear optical waveguide is performed at the linear portion, the coupling can be easily performed as designed.

[Brief description of drawings]

FIG. 1 is a plan view showing an embodiment of the present invention.

2A is a plan view showing a conventional closed curve optical waveguide, and FIG. 2B is a view showing the relationship between θ and ρ of the curved portion in FIG.

Claims (1)

[Claims] 1. A closed-curve optical waveguide coupled to an input / output linear optical waveguide, the first linear portion being in parallel with and adjoining the input / output linear optical waveguide, and being parallel to the first linear portion, A second straight line portion which is provided separately from the first straight line portion, and first and second curved line portions in which one end of each of the first and second straight line portions on the same side is connected to each other and the other ends thereof are connected to each other. The first and second curved portions are respectively connected to the other ends of the first and second curved portions, and the other ends of the first and second curved portions are connected to each other. A closed-curve optical waveguide, characterized in that, when the curve is displayed in polar coordinates, the second derivative with respect to the angle is continuous, and the second differentials on both sides of the curve are continuous with each other at each connecting point.