JP2003035833A - Quartz type optical waveguide circuit and method for manufacturing the same - Google Patents

Abstract

PROBLEM TO BE SOLVED: To shorten the manufacturing time for a quartz type optical waveguide circuit while sufficiently keeping the spot size conversion function. SOLUTION: In the quartz type optical waveguide circuit which is provided with a lower clad layer 12 mounted on a substrate 11, a core 13a for guiding light formed from a core layer 13 mounted on the lower clad layer 12 and an upper clad layer 14 which covers the lower clad layer 12 and the core 13a, a core 13b of input/output part of which the thickness is formed larger than that D of the inner core and a tapered part which connects the core 13b of the input/output part and the inner core 13a, a core layer of the input/output part is formed at the side face of the core 13b of the input/output part and the thickness T of the layer of the input/output part which comes into contact with the side face of the core 13b of the input/output part of the core layer of the input/output part is smaller than the thickness H of the core 13b of the input/output part.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a silica-based optical waveguide circuit and a method for manufacturing the same, and more particularly, a silica-based optical waveguide circuit capable of reducing coupling loss with other optical waveguides or optical fibers and a method for manufacturing the same. Regarding the method.

[0002]

2. Description of the Related Art With the rapid progress of optical communication, as in the case of semiconductor optical waveguides, quartz optical waveguides have become larger and more highly integrated.
There are increasing demands for cost reduction and mass productivity improvement. For large scale and high integration, the confinement of light in the core must be strengthened. As a result, the distance between adjacent optical waveguides can be reduced, the bending radius of the optical waveguides can be reduced, and more optical waveguides can be arranged in a limited area.

Increasing the confinement of light in the silica-based waveguide increases the coupling loss with the optical fiber and other optical components. There are several known methods for reducing this coupling loss. For example, a method of expanding the core size in the input / output unit to match the spot size of the fiber is practical in terms of manufacturing tolerance and tolerance when connecting fibers. As an example,
Japanese Patent Publication No. 001-56415 discloses a spot size conversion structure using vertical and horizontal tapered waveguides.

FIG. 7 shows a conventional spot size conversion structure. In the spot size conversion structure, the lower clad layer 52 is formed on the substrate 51, and the core 5 is formed on the lower clad layer 52.
3a is formed. The core 53a is further covered with the upper cladding layer 54. Such a spot size conversion structure has a simple structure and has a large effect of reducing the coupling loss. For example, in a core specification in which a coupling loss of about 2 dB occurs due to a difference between the fiber and the spot size, it is possible to reduce the coupling loss to 0.2 dB or less by performing spot expansion using a vertical and horizontal taper.

[0005]

However, an optical waveguide having such a spot size conversion structure has a larger core thickness at the input / output portion as compared with a normal optical waveguide, so that it has a high reactivity. There is a problem that the time spent for processing the core by ion etching becomes long. That is, the mass productivity is lower than that in the normal process.

The present invention has been made in view of the above problems, and an object of the present invention is to make a silica-based waveguide circuit capable of shortening the manufacturing time while sufficiently operating the spot size conversion function. And a method for manufacturing the same.

[0007]

In order to achieve such an object, the present invention provides a lower clad layer placed on a substrate and an upper clad layer on the lower clad layer. A core for guiding light formed from a placed core layer, and an upper clad layer covering the lower clad layer and the core are provided, and are formed thicker than the thickness of the inner core. In a silica-based optical waveguide circuit having a core of the input / output section and a taper section connecting the core of the input / output section and the core of the inside, an input / output section formed on a side surface of the core of the input / output section It is characterized in that it has a core layer, and a layer thickness T of the core layer of the input / output unit in contact with a side surface of the core of the input / output unit is less than a thickness H of the core of the input / output unit.

According to this structure, the core layer having a thickness less than the thickness H of the core of the input / output section is formed on the side surface of the core of the input / output section, so that the silica-based material is made to function sufficiently while the spot size conversion function is sufficiently functioning. The manufacturing time of the waveguide circuit can be shortened.

The invention according to claim 2 is characterized in that the material of the substrate according to claim 1 is silicon or quartz.

According to a third aspect of the present invention, a quartz substrate is used as a lower cladding layer, a core for guiding light formed from a core layer placed on the lower cladding layer, and the lower cladding layer. And an upper clad layer covering the core, the core of the input / output section formed thicker than the thickness of the internal core, and the tapered section connecting the core of the input / output section and the internal core. And a core layer of the input / output section formed on the side surface of the core of the input / output section, and in contact with the side surface of the core of the input / output section of the core layer of the input / output section. The layer thickness T is less than the thickness H of the core of the input / output unit.

The invention according to claim 4 is characterized in that the layer thickness T in contact with the side surface of the core of the input / output part according to claim 1, 2 or 3 is T≤H / 2.

According to a fifth aspect of the present invention, the core thickness H of the input / output unit and the internal core thickness D of the fourth aspect are in contact with the side surface of the core of the input / output unit. It is characterized in that 0 <T <HD (when D> H / 2) and 0 <T ≦ H / 2 (when D ≦ H / 2) with respect to the layer thickness T.

The invention according to claim 6 is characterized in that the length of the taper portion according to any one of claims 1 to 5 is 100 μm or more in the light guiding direction.

According to a seventh aspect of the present invention, the core of the input / output section according to any one of the first to sixth aspects has a thickness of 100 μm or more in a direction in which light is guided from an end face of the input / output section. Is constant over the length of.

According to an eighth aspect of the present invention, in the silica-based optical waveguide circuit according to any one of the first to seventh aspects, the core of the input / output section and the core layer of the input / output section provide the input. The output part is characterized by having a convex cross-sectional shape.

According to a ninth aspect of the present invention, a lower clad layer placed on the substrate, a core for guiding light formed from the core layer placed on the lower clad layer, The core of the input / output unit, which comprises the lower clad layer and the upper clad layer covering the core, and is formed thicker than the thickness of the inner core, and the core of the I / O unit and the inner core. In a method of manufacturing a silica-based optical waveguide circuit having a connecting taper portion, a deposition step of depositing the core layer having the same thickness as the core thickness of the input / output portion on the lower cladding layer, By etching a part of the core of the input / output unit and the core of the inside to have different thicknesses,
A layer thickness change forming step of forming a change in layer thickness of the core layer; and a core forming step of etching the core layer to form a core of the input / output unit and the internal core,
In the core forming step, a core layer of the input / output unit whose layer thickness T in contact with the side face of the core of the input / output unit is less than a thickness H of the core of the input / output unit It is characterized in that it is formed.

According to a tenth aspect of the present invention, a lower clad layer placed on the substrate, a core for guiding light formed from the core layer placed on the lower clad layer,
The core of the input / output unit, which comprises the lower clad layer and the upper clad layer covering the core, and is formed thicker than the thickness of the inner core, and the core of the I / O unit and the inner core. In a method for manufacturing a silica-based optical waveguide circuit having a connecting taper portion, a deposition step of depositing the core layer having the same thickness as the thickness of the inner core on the lower cladding layer, and further depositing the core layer. Then, a layer thickness change forming step of forming the input / output unit core and the internal core to have different thicknesses, and etching the core layer to form the input / output unit core and the internal core. And a core forming step of forming a core layer in which a layer thickness T in contact with a side surface of the core of the input / output unit is less than a thickness H of the core of the input / output unit. It is formed on the side surface of the core of the input / output unit, That.

According to an eleventh aspect of the present invention, in the step of forming the layer thickness change according to the ninth or tenth aspect, a mask arranged above the core layer is used to change the layer thickness of the core layer. It is characterized by forming.

The invention described in claim 12 is characterized in that the mask according to claim 11 is separated from the core layer by 100 μm or more.

According to a thirteenth aspect of the present invention, the mask according to the eleventh or twelfth aspect has a marker forming portion for alignment in the core forming step.

According to a fourteenth aspect of the present invention, the marker forming portion according to the thirteenth aspect is formed so as to be in contact with the core layer.

[0022]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described in detail below with reference to the drawings. In the following embodiments, description will be made on the case where the silica-based glass film to be the core layer, the lower clad layer and the upper clad layer is formed by using the flame deposition method, but the present invention is not limited to the method for producing the glass film. Alternatively, a part or all of the glass layer can be formed by a glass film forming method such as a sputtering method or a CVD (Chemical Vapor Deposition) method. Further, the present embodiment will be described on the premise of an optical communication wavelength in the 1.55 μm band and a single mode optical fiber.

FIG. 1 is a structural diagram showing a spot size conversion structure according to an embodiment of the present invention. In the spot size conversion structure, the lower clad layer 12 is formed on the substrate 11, and the waveguide core 13a (inner core) for guiding the light formed from the core layer 13 deposited on the lower clad layer 12 is used. And the input / output unit core 13b and the input / output unit core 1
The core layer 13 left with a constant layer thickness in the portions other than 3b is further covered with the upper clad layer 14.

Here, the input / output core 13b has a taper structure on the upper surface and both side surfaces to perform spot enlargement and connect the waveguide core 13a and the input / output core 13b. In FIG. 1, the cross-sectional shape of the input / output unit core 13b is shown as a rectangle, but it may be trapezoidal or may have a shape in which the upper edge is chamfered with a straight line or an arc. Further, although the core layer 13 left with a constant layer thickness is also shown as a rectangle, it does not have to have a constant layer thickness and may be a trapezoid. The length of the tapered portion in the tapered structure is preferably 100 μm or more in the light guiding direction in order to suppress the loss and enlarge the spot. In addition, in order to stabilize the enlarged spot size, 10
It is desirable that the thickness and width of the input / output core 13b be constant over the length of 0 μm or more.

FIG. 2 is a diagram showing a method of manufacturing the spot size conversion structure according to the first embodiment of the present invention.
First, on a substrate 11 made of silicon or quartz, by flame hydrolysis _deposition, depositing a lower cladding layer 12 composed mainly of S i _{O 2} (see FIG. 2 (a).), _{Then, G} e O
After ₂ was deposited core layer 13 consisting primarily of S _i O ₂ was added with dopant (see FIG. 2 (b).), Vitrification is performed in an electric furnace. The thickness of the lower clad layer 12 is 20μ
m, and the layer thickness of the core layer 13 is 11 μm.

A shadow mask 15 is set in a state of being separated by 1 mm from the substrate 11 on which the lower clad layer 12 and the core layer 13 are formed (see FIG. 2C). In this state, the reactive ion etching method is used to remove a certain amount of the core layer other than the input / output portion (see FIG. 2D). In the first embodiment, 6 μm is removed and the thickness of the waveguide core 13a is set to 5 μm. At this time, at the boundary of the shadow mask 15, the plasma wraps under the shadow mask 15, and etching also slightly progresses in this part, so that a gentle taper structure in the vertical direction is formed. In this way, the input / output core and the waveguide core have different thicknesses, and an optical waveguide circuit in which the input / output core and the waveguide core are connected in a smooth tapered shape is formed.

Then, the core for guiding the light is patterned by using photolithography and reactive ion etching (see FIG. 2E). At this time, the etching is finished while leaving a constant layer thickness without removing all the layer thickness 11 μm of the core layer 13 of the input / output section. Therefore, the cross-sectional shape of the core of the input / output section, that is, X shown in FIG.
The cross section has a convex cross-sectional shape. The constant layer thickness T in the first embodiment is 2.5 μm and 5 μm.
The etching time is 23% and 45% respectively.
Could be reduced.

Finally, the upper clad layer 14 was deposited and made into a transparent glass to manufacture the spot size conversion structure shown in FIG. 1 (see FIG. 2F). The specifications of the optical waveguide used in the first embodiment are as follows: the relative refractive index difference between the core and the clad is 1.5%, and the width of the waveguide core 13a is 5 μm.
m, the thickness D of the waveguide core 13a is 5 μm, the width of the input / output core 13b is 11 μm, and the thickness H of the input / output core 13b is 11 μm.

FIG. 3 is a diagram showing the coupling loss of the spot size conversion structure according to one embodiment of the present invention. Figure 2
FIG. 6 is a diagram showing coupling loss between a silica-based optical waveguide circuit and a single mode optical fiber manufactured by the method shown in FIG. When the constant layer thickness T of the core layer in the input / output section is 0 μm, the coupling loss is 0.21 dB / point. The constant layer thickness T is 2.
When the thickness is 5 μm, the coupling loss is 0.22 dB / point, and when the constant layer thickness T is 5 μm, the coupling loss is 0.25 dB / point. That is, in the input / output unit, even if the core layer other than the core of the input / output unit is left with a thickness of 5 μm, the coupling loss only increases by 0.04 dB.

This result is in good agreement with the result of numerical calculation performed using the finite difference method. FIG. 3 also shows a waveguide in which the relative refractive index difference is 3% and 5%, the width of the input / output core is 11 μm, and the thickness H of the input / output core is 11 μm.
As in the case where the relative refractive index difference is 1.5%, it can be seen that the coupling loss increases when the constant layer thickness T exceeds 5 μm. That is, regardless of the relative refractive index difference, it can be seen that the coupling loss does not increase excessively if the constant layer thickness T in the core layer other than the input / output core is less than half the thickness H of the input / output core. .

Although the layer thickness of the portion other than the input / output portion core is constant in this embodiment, as described above, the cross-sectional shape need not be rectangular. The layer thickness of the portion other than the input / output unit core may be such that the layer thickness T in contact with the side surface of the input / output unit core is less than the thickness H of the core of the input / output unit. Further, in order that the light propagating through the input / output unit core does not seep out to the portion other than the input / output unit core and the coupling loss does not increase, the layer thickness T in contact with the side surface of the input / output unit core is The thickness may be half or less than the thickness H of the above.

FIG. 4 is a diagram showing a method for manufacturing the spot size conversion structure according to the second embodiment of the present invention.
First, on a substrate 11 made of silicon or quartz, by flame hydrolysis _deposition, depositing a lower cladding layer 12 composed mainly of S i _{O 2} (see FIG. 4 (a).), _{Then, G} e O
_After depositing the core layer 13 whose main component is S _i O ₂ to which ₂ is added as a dopant (see FIG. 4B), it is made into transparent glass by an electric furnace. Here, the layer thickness of the core layer 13 is the same as the thickness D of the waveguide core.

1 m at a place other than the input / output section on the substrate 11
The shadow mask 17 is installed in a state of being separated by a distance of m (see FIG. 4C). In this state, the core layer 13 having a layer thickness of HD is additionally deposited (see FIG. 4D). Hereinafter, formation of the core is the same as the method shown in FIG. (See FIGS. 4 (e) and 4 (f).).

The method of depositing the core layer 13 having a layer thickness of HD by setting the shadow mask 17 is a flame deposition method, and it is possible to form a gentle layer thickness change portion in the vertical direction. Since it is difficult, a vapor phase film forming method such as a sputtering method or a plasma CVD method is suitable.

The shadow mask described above will be described in detail. In the manufacturing methods according to the first and second embodiments, the taper formed using the shadow mask and the waveguide core pattern formed by photolithography and reactive ion etching must be accurately aligned. .

FIG. 5A and FIG. 5B show the first embodiment of the present invention.
7 shows a shadow mask used in the manufacturing method according to the embodiment. The shadow mask 15 is for providing a taper on the input / output portion 16b of the circuit pattern 16a formed by the photomask 16 shown in FIG. 5C. The shadow mask 15 includes an opening 15a provided in a central portion where the circuit pattern 16a is formed, a mask 15b corresponding to the input / output unit 16b, and a marker forming unit 1 for alignment.
5c and. In addition, the thickness of the shadow mask 15 in the portion where the marker forming portion 15c is formed is thicker than the thickness of the central portion.

Such a shadow mask 15 is shown in FIG.
As shown in (d), the marker forming portion 15c has the core layer 1
Place it so that it touches 3. By performing shadow etching in this state, a gentle taper structure is formed in the input / output portion, and a steep concave structure 13c is formed in the marker forming portion 15c (see FIG. 5 (e)). The steep concave structure 13c formed by the marker forming portion 15c can facilitate alignment with the marker portion 16c of the photomask 16 used for photolithography.

FIGS. 6A and 6B show the second embodiment of the present invention.
7 shows a shadow mask used in the manufacturing method according to the embodiment. The shadow mask 17 is for providing a taper to the input / output portion 16b of the circuit pattern 16a formed by the photomask 16 shown in FIG. 6C. The shadow mask 17 has a mask 17a at the center where the circuit pattern 16a is formed, an opening 17b provided in a portion corresponding to the input / output section 16b, and a marker forming section 17c for alignment. There is. The marker forming unit 17c
The thickness of the shadow mask 17 in the portion where is formed is
Thicker than the central part.

Such a shadow mask 17 is shown in FIG.
As shown in (d), the marker forming portion 17c has the core layer 1
Place it so that it touches 3. In this state, by further depositing a core layer, a gentle taper structure is formed in the input / output portion and a steep convex structure 13d is formed in the marker forming portion 17c (see FIG. 6 (e)). The steep convex structure 13d formed by the marker forming portion 17c can facilitate alignment with the marker portion 16c of the photomask 16 used for photolithography.

Although the shadow mask and the photomask have the same marker for alignment, they may have different shapes as long as they do not interfere with the alignment. Further, in the present embodiment, the distance between the central portions of the shadow masks 15 and 17 and the core layer 13 is set to 1 mm, but it is possible to set an arbitrary distance of 100 μm or more depending on the specifications of the core, the circuit pattern, the manufacturing conditions and the like. Good. Furthermore, shadow mask 1
5 and 17, the marker forming portions 15c and 17c are arranged in the core layer 13
Although they are arranged so as to be in contact with each other, they may be arranged apart from each other as long as sufficient irregularities can be formed for performing alignment.

The first and second embodiments described above are
Needless to say, when used for an optical communication wavelength in the 1.3 μm band or used for connection with a dispersion shift fiber, it can be applied by changing specifications of the optical waveguide.

In this embodiment, the thickness H of the core of the input / output portion and the thickness D of the inner core are 0 <T <H− with respect to the layer thickness T in contact with the side surface of the core of the input / output portion. D (when D> H / 2) 0 <T ≦ H / 2 (when D ≦ H / 2) The range is arbitrary considering the process burden and the specifications of the optical waveguide to be used. It may be set to.

Further, it is clear that the same effect can be obtained even if the substrate is quartz or the structure in which the core is directly formed on the quartz substrate. The present invention can be applied to all silica-based optical waveguide circuits that require a spot size conversion structure.

Furthermore, in the spot size conversion structure according to the present invention, if the core of the input / output portion is formed thicker than the thickness of the internal core and the connection is made by a gentle taper structure, the silica-based optical waveguide is used. It can be applied regardless of the glass composition of the circuit or the manufacturing method thereof.

[0045]

As described above, according to the present invention,
By forming a core layer that is less than the thickness of the core of the input / output section on the side surface of the core of the input / output section, it is possible to fully function the spot size conversion function and reduce the fabrication time of the silica-based waveguide circuit. Is possible.

[Brief description of drawings]

FIG. 1 is a structural diagram showing a spot size conversion structure according to an embodiment of the present invention.

FIG. 2 is a diagram showing a method for manufacturing the spot size conversion structure according to the first embodiment of the present invention.

FIG. 3 is a diagram showing a coupling loss of the spot size conversion structure according to the embodiment of the present invention.

FIG. 4 is a diagram showing a method for manufacturing the spot size conversion structure according to the second embodiment of the present invention.

FIG. 5 is a diagram showing a shadow mask used in the manufacturing method according to the first embodiment of the present invention.

FIG. 6 is a view showing a shadow mask used in the manufacturing method according to the second embodiment of the present invention.

FIG. 7 is a structural diagram showing a conventional spot size conversion structure.

[Explanation of symbols]

11,51 substrate 12,52 Lower clad layer 13 core layer 13a Waveguide core 13b I / O core 14,54 Upper clad layer 15,17 Shadow mask 16 Photomask 53a core

   ─────────────────────────────────────────────────── ─── Continued front page    (72) Inventor Yasuhiro Hida             2-3-1, Otemachi, Chiyoda-ku, Tokyo             Inside Telegraph and Telephone Corporation (72) Inventor Yasuyuki Inoue             2-3-1, Otemachi, Chiyoda-ku, Tokyo             Inside Telegraph and Telephone Corporation F term (reference) 2H047 KA03 PA05 PA24 TA32

Claims (14)

[Claims] 1. A lower cladding layer mounted on a substrate,
A core for guiding light, which is formed from a core layer placed on the lower clad layer, and an upper clad layer covering the lower clad layer and the core. In a silica optical waveguide circuit having a core of an input / output section formed thicker than the core and a taper section connecting the core of the input / output section and the internal core, the silica-based optical waveguide circuit is formed on a side surface of the core of the input / output section. And a layer thickness T of the core layer of the input / output unit in contact with the side surface of the core of the input / output unit is less than the thickness H of the core of the input / output unit. Characteristic quartz optical waveguide circuit. 2. The silica-based optical waveguide circuit according to claim 1, wherein the material of the substrate is silicon or quartz. 3. A quartz substrate serving as a lower clad layer, and a core for guiding light formed from a core layer mounted on the lower clad layer, the lower clad layer and the core are mounted. A silica-based optical waveguide having an input / output section core formed thicker than the internal core and a taper section connecting the input / output section core and the internal core. In the circuit, the core layer of the input / output unit is formed on the side surface of the core of the input / output unit, and the layer thickness T of the core layer of the input / output unit in contact with the side surface of the core of the input / output unit is A silica-based optical waveguide circuit, wherein the core thickness of the output portion is less than H. 4. The silica-based optical waveguide circuit according to claim 1, wherein a layer thickness T in contact with the side surface of the core of the input / output unit is T ≦ H / 2. 5. The thickness H of the core of the input / output unit and the thickness D of the inner core are 0 <T <H− with respect to the layer thickness T in contact with the side surface of the core of the input / output unit. The silica-based optical waveguide circuit according to claim 4, wherein D (when D> H / 2) 0 <T ≦ H / 2 (when D ≦ H / 2). 6. The silica-based optical waveguide circuit according to claim 1, wherein a length of the tapered portion is 100 μm or more in a light guiding direction. 7. The thickness of the core of the input / output unit is constant over a length of 100 μm or more from the end face of the input / output unit in the light guiding direction. The silica-based optical waveguide circuit according to any one of claims. 8. The input / output part has a convex cross-sectional shape by the core of the input / output part and the core layer of the input / output part. The silica-based optical waveguide circuit described. 9. A lower cladding layer mounted on the substrate,
A core for guiding light, which is formed from a core layer placed on the lower clad layer, and an upper clad layer covering the lower clad layer and the core. In a method of manufacturing a silica-based optical waveguide circuit having a core of an input / output section formed thicker than a core and a taper section connecting the core of the input / output section and the internal core, A deposition step of depositing the core layer having the same thickness as the core of the writing / outputting section; and etching a part of the core layer so that the core of the input / output section and the core of the inside have different thicknesses. As described above, a layer thickness change forming step of forming a change in the layer thickness of the core layer, and a core forming step of etching the core layer to form the core of the input / output unit and the inner core are included. In the core forming step, the core of the input / output unit is A silica-based optical waveguide circuit, characterized in that a core layer of the input / output portion having a layer thickness T in contact with the side surface is less than the thickness H of the core of the input / output portion is formed on the side surface of the core of the input / output portion. Of manufacturing. 10. A lower clad layer mounted on a substrate, a core for guiding light formed from a core layer mounted on the lower clad layer, the lower clad layer and the core. And an upper clad layer for covering the core of the input / output portion formed thicker than the thickness of the internal core, and a taper portion connecting the core of the input / output portion and the internal core. In the method for manufacturing a silica-based optical waveguide circuit, a depositing step of depositing the core layer having the same thickness as the inner core on the lower cladding layer, further depositing the core layer, and the input / output unit Layer thickness change forming step of forming the core and the inner core to have different thicknesses; and a core forming step of etching the core layer to form the core of the input / output unit and the inner core. And the core forming step, A silica-based optical waveguide, characterized in that a core layer having a layer thickness T in contact with the side surface of the core of the output section is less than the thickness H of the core of the input / output section is formed on the side surface of the core of the input / output section. How to make a circuit. 11. The layer thickness change forming step according to claim 9, wherein the layer thickness change of the core layer is formed by using a mask arranged above the core layer. Manufacturing method of silica-based optical waveguide circuit. 12. The mask comprises 100 from the core layer.
The method for manufacturing a silica-based optical waveguide circuit according to claim 11, wherein the optical waveguide circuits are separated by at least μm. 13. The method for manufacturing a silica-based optical waveguide circuit according to claim 11, wherein the mask has a marker forming portion for alignment in the core forming step. 14. The marker forming portion is formed so as to be in contact with the core layer.
7. A method for manufacturing a silica-based optical waveguide circuit according to.