WO2025191746A1 - Interposer circuit - Google Patents

Abstract

An interposer circuit (12), which is connected between a silicon waveguide chip (11) having high refractive index optical waveguides (111) and a fiber block (13) having optical fibers (131), comprises a plurality of connecting waveguides (121) each having one end connected to a high refractive index optical waveguide (111) and the other end connected to an optical fiber (131), wherein the connecting waveguides (121) each: include a height change region (Td) where the height changes proceeding from the optical fiber (131) to the high refractive index optical waveguide (111), an expanding-diameter taper section (121a) that expands in diameter toward the optical fiber (131), a contracting-diameter taper section (121c) that contracts in diameter toward the high refractive index optical waveguide (111), and a pitch change section (121b) where the pitch changes using a curved waveguide; and are configured such that the expanding-diameter taper section (121a), the contracting-diameter taper section (121c), and the pitch change section (121b) are located within the height change region (Td).

Description

Interposer Circuit

This disclosure relates to an interposer circuit that connects an optical waveguide and an optical fiber, and in particular to an interposer circuit that has a spot size conversion function.

High-refractive-index waveguide devices using silicon waveguides or silicon nitride waveguides have a waveguide core with a high refractive index and a waveguide cladding with a large difference in refractive index from the waveguide core. The refractive index of the waveguide core needs to be higher than the refractive index of the waveguide cladding. High-refractive-index waveguide devices allow for high-density integration and are highly compatible with CMOS (Complementary Metal Oxide Semiconductor) devices, so they are being increasingly applied to optical communications transceivers, high-speed data transfer within microchips, sensing devices, and more. In many cases, the optical signals propagating through these waveguides use communication wavelength bands, and waveguide devices for optical communications in particular often connect optical fibers to waveguides.

While the mode-field diameter (MFD) of single-mode fibers used in optical communications is approximately 10 μm, the MFD of silicon waveguides that satisfy the single-mode conditions differs significantly, measuring several hundred nanometers. For this reason, when connecting optical fiber to high-refractive-index optical waveguides, such as silicon waveguides and silicon nitride waveguides, it is common to use small-diameter fibers (MFD approximately 4 μm) designed with a higher refractive index difference between the core and cladding than single-mode fibers. Because small-diameter fibers have high transmission loss, small-core optical fibers are spliced to single-mode fibers with an MFD of approximately 10 μm using methods such as fusion splicing using core diffusion. Because the mechanical strength of the fusion splice point is low, it is common to protect the fusion splice point with a protective sleeve approximately 10 mm in length. Therefore, connecting a silicon waveguide to optical fiber requires the preparation and modularization of numerous connection structures and components, and improvements were needed from the perspective of module size and cost.

To solve the above-mentioned problems, there is a technology that inserts an interposer circuit between a silicon waveguide and an optical fiber. However, there is a large difference between the effective refractive index of a silicon waveguide and that of an optical fiber. When connecting waveguides made of different materials with a large difference in effective refractive index, high connection loss becomes an issue. For this reason, Patent Document 1 describes using a waveguide with an effective refractive index intermediate between that of a silicon waveguide and an optical fiber as an interposer circuit.

Other known technologies include those that use planar lightwave circuits as interposer circuits, or mode conversion components with modified in-plane waveguide patterns. Structures that adjust MFD through mode conversion include widthwise tapers that change the waveguide width, and finely segmenting the waveguide to reduce the effective refractive index. Furthermore, since there is a limit to how much MFD can be increased by changing structural parameters within a plane, it is desirable to provide flexibility in the film thickness direction within the interposer circuit and achieve mode conversion by adjusting the film thickness. Film thickness adjustment can be achieved by, for example, isotropic etching or local etching. Isotropic etching is described, for example, in Patent Document 2. Local etching is described, for example, in Patent Document 3.

Japanese Patent Application Laid-Open No. 2020-126128 Patent No. 3602514 Japanese Patent Application Laid-Open No. 2021-124646

Y. Sakamaki et al., JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 25, NO. 11, pp.3511-3518, NOVEMBER 2007.

In particular, local etching using local plasma allows for high film thickness control and is useful as a method for adjusting waveguide height. However, when using local etching to process the waveguide height, the processing range is determined by the reactive gas material and its flow rate and pressure, and is generally 1 mm to 10 mm in diameter, which poses the challenge of making it difficult to miniaturize the interposer circuit.

This disclosure has been made in consideration of the above points, and relates to an interposer circuit that is advantageous for miniaturization by performing mode conversion by adjusting the effective refractive index by adjusting the width and height in the film thickness direction of the waveguide, and at the same time performing pitch conversion using a curved waveguide whose radius of curvature changes in accordance with the change in effective refractive index.

In order to achieve the above object, one embodiment of the interposer circuit disclosed herein is an interposer circuit connected between an optical circuit having input/output waveguides and a fiber block having input/output fibers. The interposer circuit has a plurality of connection waveguides, one end of which connects to the input/output waveguides and the other end of which connects to the input/output fibers. The connection waveguides include a height change region whose height changes from the input/output fibers toward the input/output waveguides, a first width tapered portion whose width changes toward the input/output waveguides, a second width tapered portion whose width changes toward the input/output fibers, and a pitch change portion located between the first width tapered portion and the second width tapered portion and which changes the pitch using a curved waveguide. The first width tapered portion, the second width tapered portion, and the pitch change portion are arranged within the height change region.

The above configuration allows for the MFD to be adjusted by adjusting the width of the waveguide and its height in the film thickness direction, and provides an interposer circuit that is advantageous for miniaturization.

FIG. 2 is a top view illustrating an interposer circuit according to an embodiment of the present disclosure. 2 is a more detailed top view of the silicon waveguide chip, interposer circuit, and fiber block shown in FIG. 1. FIG. 1A is a diagram illustrating a known two-dimensional taper, and FIG. 1B is a diagram illustrating a known three-dimensional taper. FIG. 2 is a top view of an interposer circuit according to the present embodiment. FIG. 5 is a cross-sectional view taken along the arrow in the top view shown in FIG. 4. FIG. 10 is a diagram for explaining the effect of the present embodiment. 10 is a diagram showing the relationship between the effective refractive index and film thickness of a curved waveguide used in the interposer circuit of the present embodiment. FIG. 10 is a diagram showing the relationship between the radius of curvature and the effective refractive index of a curved waveguide used in the interposer circuit of the present embodiment. FIG. 10 is a diagram showing the relationship between the relaxation curve of the curvature radius of a curved waveguide used in the interposer circuit of the present embodiment and the propagation length normalized by the total propagation length. FIG.

Below, one embodiment of the present disclosure will be described using the drawings. The drawings used in this embodiment are intended to illustrate the configuration, arrangement, action, effects, and technical concepts of the present disclosure, and are not intended to limit the specific shape or aspect ratio of the present disclosure.

Figure 1 is a top view illustrating an interposer circuit according to an embodiment of the present disclosure. Figure 1, which illustrates this embodiment, is a schematic diagram of a configuration in which a silicon waveguide chip 11 and a fiber block 13 are connected using an interposer circuit 12 according to an embodiment of the present invention. The integrated configuration of the silicon waveguide chip 11, interposer circuit 12, and fiber block 13 constitutes an optical component. An optical fiber 14 is connected to the optical component. The silicon (Si) waveguide chip corresponds to the optical circuit of this embodiment. The figure shows x, y, and z coordinates, and in the following description of this embodiment, the direction of the z axis is assumed to be "up." Furthermore, the direction of light propagation in the interposer circuit 12 and fiber block 13 is along the x axis, and the y axis is perpendicular to the x axis.

Figure 2 is a top view of the silicon waveguide chip 11, interposer circuit 12, and fiber block 13 shown in Figure 1, showing a more detailed state. The silicon waveguide chip 11 uses silicon (Si) as the substrate, and three high-refractive-index optical waveguides 111 (input/output waveguides) are fixed to the substrate using known photolithography and etching techniques at a predetermined pitch and angle in the x-y plane. The fiber block 13 is composed of three optical fibers 131 (input/output fibers).

As shown in Figure 2, the interposer circuit 12 has three connection waveguides 121, 122, and 123. One end of each of the connection waveguides 121, 122, and 123 faces the silicon waveguide chip 11 and is connected to a high-refractive-index optical waveguide 111 such as the silicon waveguide chip 11 or a silicon nitride waveguide chip. The other ends of the connection waveguides 121, 122, and 123 face the fiber block 13 and are connected to an optical fiber 131.

Connection waveguides 121, 122, and 123 include expanding tapers 121a, 122a, and 123a that change so that the mode field diameter of light propagating through the interposer waveguide toward the optical fiber 131 becomes wider, and contracting tapers 121c, 122c, and 123c that change so that the mode field diameter of light propagating through the interposer waveguide toward the high-refractive-index optical waveguide 111 becomes smaller. Furthermore, connection waveguide 121 includes a pitch change section 121b between expanding taper 121a and contracting taper 121c that changes the pitch using a bent waveguide. Connection waveguide 122 also includes a pitch change section 122b between expanding taper 122a and contracting taper 122c. Connection waveguide 123 includes a pitch change section 123b between expanding taper 123a and contracting taper 123c that uses a bent waveguide.

In other words, the width of the optical fiber 131 is sufficiently wider than the width of the pitch change sections 121b, 122b, and 123b, and the height of the optical fiber 13 is sufficiently higher than the height of the pitch change sections 121b, 122b, and 123b. Therefore, the connecting waveguides 121, 122, and 123 have expanding tapers 121a, 122a, and 123a that increase in width and increase in height to match the mode field diameter (MFD) of the optical fiber 131, thereby matching the MFD with that of the optical fiber 131. Furthermore, because the MFD of the pitch change sections 121b, 122b, and 123b of the interposer circuit 12 is wider than the MFD of the high-refractive-index optical waveguide 111, the connecting waveguides 121, 122, and 123 have contracting tapers 121c, 122c, and 123c that decrease in width and height to match the high-refractive-index optical waveguide 111. In Figure 2, the region where the expanding tapers 121a, 122a, and 123a are formed is referred to as taper region Tw1, the region where the contracting tapers 121c, 122c, and 123c are formed is referred to as taper region Tw2, and the region where the pitch change portions 121b, 122b, and 123b are formed is referred to as pitch change region Cp. The expanding tapers 121a, 122a, and 123a correspond to the first taper portion of this embodiment, and the contracting tapers 121c, 122c, and 123c correspond to the second taper portion of this embodiment.

Furthermore, in addition to the above-mentioned expanding and contracting tapers, the connecting waveguides 121, 122, and 123 have a height change region (Figure 5) where the height changes from the optical fiber 131 to the high-refractive-index optical waveguide 111. The height of the connecting waveguides 121, 122, and 123 is determined by the thickness of the core layer that forms the optical waveguide. The height change regions of the connecting waveguides 121, 122, and 123 will be described in detail later.

Figures 3(a) and 3(b) are perspective views illustrating a known tapered structure that converts the mode of an optical waveguide. Note that the "mode" of the optical waveguide in this embodiment refers to the behavior and distribution pattern of light propagating within the optical waveguide. Figure 3(a) shows a tapered structure (two-dimensional taper) that expands in the width direction. As shown in Figure 3(a), in a two-dimensional taper, the width of the optical waveguide expands from W2 to W1, while its thickness H remains constant throughout.

Figure 3(b) shows a tapered structure (three-dimensional taper) that expands in both the width and thickness directions. As shown in Figure 3(b), in a three-dimensional taper, the width of the optical waveguide expands from W2 to W1, and the thickness also expands from H2 to H1. This type of three-dimensional taper allows for a high degree of design freedom when expanding the diameter of the optical waveguide, making it a structure that makes it easy to adjust the MFD. Therefore, a three-dimensional taper can achieve a configuration with less optical loss when connecting optical waveguides than a two-dimensional taper.

Note that this embodiment shows an example in which the two-dimensional taper expands at a constant gradient, as shown in Figure 3(a). However, this embodiment is not limited to a configuration in which the width of the optical waveguide changes at a constant rate of change. For example, it may be a structure in which the average value of the width of the connecting waveguide per unit propagation length (1 μm in this embodiment) changes continuously along the propagation axis of the light wave, and the MFD is adjusted to change adiabatically. In such a case, the tapered structure may be a complex structure in which the optical waveguide width does not change continuously, but which generates periodic and quasi-periodic unevenness. Note that such a configuration is publicly known, for example, from Non-Patent Document 1.

Figures 4 and 5 are diagrams for explaining the interposer circuit 12 of this embodiment in more detail. Figure 4 is a top view of the interposer circuit 12, and Figure 5 is a cross-sectional view taken along the arrow V-V in the top view shown in Figure 4. As shown in Figure 4, the connection waveguides 121, 122, and 123 are each composed of expanding tapers 121a, 122a, and 123a, pitch change sections 121b, 122b, and 123b, and contracting tapers 121c, 122c, and 123c. The pitch change sections 121b and 123b are S-shaped bent waveguides, which enable the wiring density of the connection waveguides 121, 122, and 123 to be set high, thereby reducing the area of the spot size conversion configuration of the interposer circuit 12.

Figure 5 shows a longitudinal cross section of the connection waveguide 122 shown in Figure 4. As shown in Figure 5, the connection waveguide 122 includes, for example, a quartz substrate 51, a lower cladding 52 formed on the substrate 51, a connection waveguide 122 (core), and an upper cladding 54. The connection waveguide 122 has a height that increases in the order of tapered region Tw1, pitch change region Cp, and tapered region Tw2. The region where the height changes is shown in the figure as height change region Td. In this embodiment, in which the core height gradually decreases from the fiber block 13 to the silicon waveguide chip 11, the height of the connection waveguide 122 connected to the fiber block 13 and the optical waveguide chip 11 is gradually decreased, and the MFD is ultimately adjusted to match the small-diameter, high-refractive-index optical waveguide 111.

In this embodiment, the distance from the silicon waveguide chip 11 toward the fiber block 13 in the height change region Td is preferably 10 mm or less. Setting this distance to 10 mm or less enables a more compact implementation than when using a thin-core optical fiber. Furthermore, the tapered region Tw1, pitch change region Cp, and tapered region Tw2 are all located within the height change region Td. Note that such height adjustment of the connection waveguide 122 can be achieved, for example, by a local etching process using local plasma.

However, it is known that the processing range of a local etching process using local plasma is approximately 1 to 10 mm. This relatively large processing range makes it undesirable to create three-dimensional tapers toward both the silicon waveguide chip 11 and the fiber block 13 in terms of miniaturizing the interposer circuit. This embodiment focuses on this point and forms the expanding tapers 121a, 122a, 123a, the pitch change portions 121b, 122b, 123b, and the narrowing tapers 121c, 122c, 123c all within the height change region Td formed by a single local etching process. This configuration places the expanding tapers 121a, 122a, 123a, the pitch change portions 121b, 122b, 123b, and the narrowing tapers 121c, 122c, 123c all within the processing range of the local etching process, enabling the interposer circuit 12 to be miniaturized.

(effect)
FIG. 6 is a graph illustrating the effects of this embodiment in comparison with known optical devices. The horizontal axis of FIG. 6 represents the propagation length of light, and the vertical axis represents the thickness of the core that serves as the connecting waveguide. The propagation length refers to the shortest distance light propagates through the connecting waveguide. In FIG. 6 , the dots (●) represent the results of an optical device using the interposer circuit of this embodiment, and the dots (×) represent the results of an interposer circuit of a comparative example. The interposer circuit of the comparative example is disposed between the silicon waveguide chip 11 and the fiber block 13 shown in FIG. 2 . The interposer circuit of the comparative example includes a three-dimensional taper that expands in diameter toward the fiber block 13 and a three-dimensional taper that contracts in diameter toward the silicon waveguide chip 11. Furthermore, as shown in FIG. 6 , the interposer circuit of the comparative example includes a pitch-changing portion (CP2) with a constant film thickness (height) located between the two three-dimensional tapers.

As is clear from Fig. 6, this embodiment, in which a pitch change region C _P (shown as CP1 in Fig. 6) is formed within the height change region Td, can reduce the area within the interposer circuit to 60% of that of the comparative example. However, this embodiment is not limited to this range, and the inventors have confirmed that by adjusting the design, the area of the interposer circuit can be reduced to 50% of that of the comparative example.

To reduce the area of the interposer circuit, it is necessary to bend the optical waveguide within a single height change region Td, rather than fabricating a curved waveguide under a constant film thickness condition as in the comparative interposer circuit. The change in film thickness ΔT per minute propagation length ΔL defined within the height change region Td, the change in effective refractive index ΔN _eff per film thickness change ΔT, and the change in radius of curvature ΔR per effective refractive index change ΔN _eff can be calculated. Using this relationship, the minimum radius of curvature R _min of the curved waveguide in the height change region Td can be expressed by the following equation (1). Figure 7 shows the relationship between the effective refractive index N _eff and film thickness T, as expressed in equation (1). Figure 8 shows the relationship between the radius of curvature R _min and the effective refractive index N _eff .

...Formula (1)

In the above formula (1), R _min0 is the minimum radius of curvature immediately before the light wave enters the height change region Td, and can be derived using numerical analysis such as the finite-difference time-domain method or the beam propagation method. For pitch conversion of the interposer circuit of this embodiment, it is desirable to use a curved waveguide that conforms to the above formula. This curved waveguide is not simply a design feature; the curve of the waveguide that conforms to the above formula is an optically optimized transition curve, which is complex to draw and is not available commercially. For example, in typical transition curves such as a clothoid curve and a sine half-wavelength attenuation curve, the curvature (the reciprocal of the radius of curvature R) has a specific relationship with the propagation length L, such as a linear or sinusoidal waveform, but the curve used in the present invention is not limited to this.

Specifically, when deriving the minimum radius of curvature of a curved waveguide, the correlations in Figures 6, 7, and 8 must be derived by numerical analysis or experiment. When the minimum radius of curvature of a curved waveguide derived in this way is applied, the relationship between the relaxation curve of the radius of curvature R and the propagation length Lnorm normalized by the total propagation length for a single curved waveguide at a pitch change is shown in Figure 9. In this embodiment, the relationship between the radius of curvature and the propagation length in the height change region shown in Figure 9 is asymmetrical with respect to half the total propagation length. This relationship is expressed by the following equation (2):

...Formula (2)

In equation (2), R _i is the radius of curvature of the i-th (1 ≥ i ≥ M) transition curve when the transition curve is divided into M parts, and ΔR _j /ΔL indicates the rate of change of the radius of curvature such that R _i becomes a transition curve that asymptotically approaches R _min from infinity according to the propagation length.

In the embodiment described above, it is desirable to use a material with a refractive index intermediate between that of silicon and optical fiber, such as a quartz waveguide, aluminum oxide, or silicon nitride waveguide, for the interposer circuit 12. This is to reduce connection loss between the silicon waveguide chip 11 and the fiber block 13. Furthermore, when a quartz waveguide is used for the interposer circuit 12, the difference in refractive index between it and optical fiber, which is also made of quartz, is small, so no special anti-reflection configuration is required. However, because the difference in refractive index between the interposer circuit 12 and the silicon waveguide chip 11 is relatively large, it is desirable to tilt the quartz waveguide and silicon waveguide on the interposer circuit 12 side so that they form an angle in the x-y plane. This is to prevent reflection at the boundary between the quartz waveguide and the silicon waveguide, which would result in significant optical loss. In other words, when light travels from a material with a high refractive index to a material with a low refractive index, all light incident at an angle less than the total reflection angle is reflected by refraction at the boundary surface. In such cases, this embodiment angles the optical waveguide at the boundary to adjust the angle of incidence of light and reduce light reflection.

Furthermore, in this embodiment, both the expanding tapers 121a, 122a, 123a and the contracting tapers 121c, 122c, 123c can be formed under single-mode conditions. However, to achieve an interposer circuit with lower loss and more stable characteristics, it is preferable to fabricate the expanding tapers 121a, 122a, 123a under multi-mode conditions, and the pitch-changing sections 121b, 122b, 123b and the contracting tapers 121c, 122c, 123c under single-mode conditions.

In the interposer circuit 12 of this embodiment, it is preferable that the following be arranged in order from the fiber block 13 toward the silicon waveguide chip 11: expanding tapers 121a, 122a, 123a, pitch change sections 121b, 122b, 123b, and narrowing tapers 121c, 122c, 123c. If the arrangement of expanding tapers 121a, 122a, 123a and pitch change sections 121b, 122b, 123b is interchanged, the width of the curved waveguide increases, resulting in increased insertion loss due to inter-modal interference in the curved waveguides of pitch change sections 121b, 122b, 123b. Furthermore, if the diameter-converging tapers 121c, 122c, and 123c are interchanged with the pitch-changing sections 121b, 122b, and 123b, light waves propagate through the curved waveguide under conditions that allow low-loss connection to the silicon waveguide. The narrower the width of the curved waveguide, the weaker the confinement of light waves, resulting in radiation loss and increased insertion loss. To suppress this insertion loss, in this embodiment, as shown in Figures 2 and 4, the pitch-changing sections 121b, 122b, and 123b are positioned between the diameter-expanding tapers 121a, 122a, and 123a and the diameter-converging tapers 121c, 122c, and 123c. However, if a higher insertion loss is acceptable, the positions of the pitch-changing sections 121b, 122b, and 123b may be changed.

The interface between the tapered tapers 121c, 122c, and 123c and the silicon waveguide often has a high reflectance, and when using quartz-made connection waveguides 121, 122, and 123 in the interposer circuit 12, it is desirable to tilt the angle in the xy plane between the connection waveguides 121, 122, and 123 and the high-refractive-index optical waveguide 111 of the silicon waveguide chip 11 by a few degrees to 20 degrees. On the other hand, because the reflectance is low at the interface between the fiber block 13 and the quartz waveguide, there is little need to tilt the connection waveguides 121, 122, and 123 and the optical fiber to create an angle.

The fiber block 13, interposer circuit 12, and silicon waveguide chip 11 are connected using adhesives made from resin or other materials, or by fusion bonding. When using a UV-curing adhesive, using a quartz substrate for the interposer circuit 12 has a higher UV light transmittance than silicon, a common wafer material, making it possible to efficiently connect the silicon waveguide chip 11 and interposer circuit 12, and the interposer circuit 12 and fiber block 13. Even when using a thermosetting resin or fusion bonding, the large difference in thermal conductivity between quartz and silicon creates a thermal gradient, making it difficult to effectively heat the area near the connecting waveguide (core). Therefore, if the interposer circuit is formed on a silicon wafer, the adhesive strength of the core portion is likely to be weak. For these reasons, it is desirable to fabricate the interposer circuit 12 on a quartz substrate.

As explained above, in this embodiment, the connecting waveguide of the interposer circuit is configured with an expanding taper, a contracting taper, and a pitch change section, all of which are positioned within the range of the height change section to adjust the MFD. This configuration eliminates the need to separate the expanding taper and the contracting taper with a pitch change section or to provide a separate pitch change section, and allows the length of the silicon waveguide chip and fiber block of the interposer circuit in the alignment direction to be shortened. Furthermore, by ensuring a sufficient length of the height change section, the degree of freedom in the rate (slope) of height change and length can be increased, allowing for optimal adjustment of the MFD. Note that, although the number of connecting waveguides in this embodiment is three, the number of connecting waveguides in the interposer circuit can be two, four, or more, without departing from the spirit of this disclosure.

11 Silicon waveguide chip 12 Interposer circuit 13 Fiber block 14 Optical fiber 51 Substrate 52 Lower cladding 54 Upper cladding 111 High refractive index optical waveguides 121, 122, 123 Connection waveguides 121a, 122a, 123a Diameter-expanding tapers 121b, 122b, 123b Pitch-changing portions 121c, 122c, 123c Diameter-contracting tapers 131 Optical fiber Td Height-changing region

Claims (8)

An interposer circuit connected between an optical circuit having input and output waveguides and a fiber block having input and output fibers,
The interposer circuit comprises:
a plurality of connection waveguides, one end of which is connected to the input/output waveguide and the other end of which is connected to the input/output fiber;
the connection waveguide includes a height changing region whose height changes from the input/output fiber toward the input/output waveguide, a first width tapered section whose width changes toward the input/output waveguide, a second width tapered section whose width changes toward the input/output fiber, and a pitch changing section that is located between the first width tapered section and the second width tapered section and whose pitch changes using a bent waveguide;
the first width tapered portion, the second width tapered portion, and the pitch change portion are disposed within the height change region.
Interposer circuit. the first width tapered portion is formed of a multi-mode waveguide, and the pitch changing portion and the second width tapered portion are formed of a single-mode waveguide;
The interposer circuit of claim 1 . The interposer circuit of claim 1, wherein the shortest distance from the optical circuit to the fiber block in the height change region is 1 mm or more and 10 mm or less. The interposer circuit of claim 1, wherein the angle formed by the connection waveguide with the input/output waveguide within the plane of the boundary with the optical circuit is different from the angle formed by the input/output fiber within the plane of the boundary with the fiber block. The interposer circuit of claim 1, wherein the connection waveguide is formed on a quartz substrate. The interposer circuit of claim 1, wherein the first width tapered portion, the pitch change portion, and the second width tapered portion are arranged in this order from the fiber block toward the optical circuit: the first width tapered portion, the pitch change portion, and the second width tapered portion. The interposer circuit of claim 1 , wherein a minimum radius of curvature R _min of the curved waveguide in the height transition region is given by the following formula:
In the above equation, R _min0 is the minimum radius of curvature immediately before the light wave is input to the height change region, ΔL is the infinitesimal propagation length in the height change region, ΔR _min is the minimum value of the amount of change in radius of curvature ΔR per infinitesimal propagation length ΔL, ΔN _eff is the amount of change in effective refractive index in the curved waveguide, and ΔT is the amount of change in film thickness per infinitesimal propagation length ΔL. 2. The interposer circuit of claim 1, wherein the relationship between the radius of curvature of the curved waveguide and the propagation length in the height transition region is asymmetrical about half the total propagation length and is expressed by the following equation:
In the above equation, R _i is the i-th (1 ≥ i ≥ M) radius of curvature when the transition curve with radius of curvature R is divided into M parts, and ΔR _j /ΔL is the rate of change of the radius of curvature such that R _i becomes a transition curve that asymptotically approaches R _min from infinity according to the propagation length.