Directional coupler, combiner, and production method for directional coupler

Abstract

Provided is a directional coupler that can achieve greater size reduction and better tolerance with respect to variation in production. This directional coupler is a waveguide-type directional coupler that includes two cores and a cladding. The cladding has a first region that is between adjacent side surfaces of the two cores, respective second regions that are on opposite sides of the two cores from the first region, and a third region that is a portion that is outside the first region and the second regions. When the refractive index of the two cores is ncore, the refractive index of the first region is n1, the refractive index of the second regions is n2, and the refractive index of the third region is n3, ncore>n1≥n3>n2.

Description

Directional coupler, combiner, and method for manufacturing a directional coupler

[0001] The present disclosure relates to a directional coupler, a combiner, and a method for manufacturing a directional coupler.

[0002] A waveguide-type directional coupler is an optical device that realizes optical multiplexing and demultiplexing, and has been widely used in optical communication and devices using visible light. Generally, a directional coupler has a region where light interacts (hereinafter referred to as an interaction region) by arranging two cores of a waveguide in parallel at a narrow interval. The characteristics of a directional coupler change not only depending on the width of the core and the length of the interaction region but also depending on the interval (gap) between the two cores.

[0003] In recent years, research has been underway to use waveguide-type multiplexers and demultiplexers for sensing, and multiplexing over a wider wavelength range than in the past has been demanded. A directional coupler is generally also used as a multiplexer, but several problems may occur when trying to realize multiplexing over a wider wavelength range (for example, not only visible light but also near-infrared light) than in the past. For example, in a directional coupler, the gap between two adjacent cores becomes narrow due to strong confinement of visible light. For this reason, not only high-precision manufacturing technology is required, but the tolerance also becomes low. In addition, it is known that the coupling length of visible light is generally longer than that of light in the near-infrared region. For this reason, in a directional coupler adapted to multiplex near-infrared light, there also occurs a problem that the footprint becomes large.

[0004] As an existing technology for solving such problems, for example, an example has been reported in which an optical branching element with a high tolerance is manufactured by appropriately adjusting parameters such as the refractive index of the cladding and core of a normal directional coupler (see, for example, Patent Document 1). As another example, a technique has been proposed in which the length of a directional coupler is shortened or the loss during optical coupling is suppressed by changing the refractive index of only the cladding located between the cores (see, for example, Patent Document 2).

[0005] However, existing directional couplers have a structure in which only the refractive index of the cladding located between the cores is changed, or the refractive index of the cladding near the core is uniformly changed. With such a structure, there are limitations to miniaturizing the directional coupler or improving tolerance to manufacturing variations by widening the gap. Directional couplers that combine visible light to near-infrared light, as required in recent years, require even greater miniaturization and tolerance than before, especially in the combination of visible light.

[0006] Japanese Patent Publication No. 2011-039286 Japanese Patent Publication No. 2004-118220

[0007] This disclosure has been made in view of the above-mentioned issues, and its purpose is to provide a directional coupler that can be miniaturized and has improved tolerance to manufacturing variations.

[0008] To address the above-mentioned problems, this disclosure provides a waveguide-type directional coupler comprising two cores and a cladding, wherein the cladding comprises a first region between the sides of two adjacent cores, a second region on the side opposite to the first region for each of the two cores, and a third region which is the portion other than the first and second regions, and the refractive index of the two cores is n core The refractive index of the first region is n1, the refractive index of the second region is n2, and the refractive index of the third region is n3, n core We provide a directional coupler configured such that >n1 ≥ n3 > n2.

[0009] This figure conceptually shows the structure of the directional coupler 100 according to this disclosure, where (a) is a top view and (b) is a cross-sectional view along the Ib-Ib section. This figure conceptually shows the structure of the directional coupler 200, which is a modified example of the directional coupler 100, where (a) is a top view and (b) is a cross-sectional view along the IIb-IIb section. This figure shows the schematic structure of the directional coupler 300, where (a) is a top view and (b) is a cross-sectional view along the IIIb-IIIb section. The figure shows the optical properties in the interaction region 130 of the directional coupler 300. (a) shows the relationship between wavelength and transmittance in the directional coupler 300 when the first region 121 and the third region 123 have the same refractive index. (b) shows the relationship between the difference in relative refractive index between the first region 121 and the third region 123 and the coupling length of light with a wavelength of 770 nm. (c) shows the relationship between wavelength and transmittance in the directional coupler 300 when the difference in relative refractive index between the first region 121 and the third region 123 is 0.6%. This figure shows the optical properties in the interaction region 130 of the directional coupler 100. (a) shows the relationship between the relative refractive index difference between the third region 123 and the second regions 122a and b and the coupling length of light with a wavelength of 770 nm. (b) shows the relationship between wavelength and transmittance in the directional coupler 200 when the relative refractive index difference between the third region 123 and the second regions 122a and b is 1.1%. This is a schematic top view showing the structure of a combiner 600 in which multiple directional couplers 100 according to this disclosure are connected in stages. The directional couplers according to this disclosure (e.g., directional couplers 100, 200) described above can be extended to combiners that combine light of more wavelengths by connecting them in stages. This is a flowchart of a manufacturing method 700 for the directional coupler 200 according to this disclosure.

[0010] Various embodiments of this disclosure are described below in detail with reference to the drawings. Identical or similar reference numerals indicate identical or similar elements, and redundant descriptions may be omitted. Materials and numerical values ​​are illustrative and are not intended to limit the technical scope of this disclosure. The following description is illustrative and some configurations may be omitted or modified, or implemented with additional configurations, without departing from the gist of one embodiment of this disclosure.

[0011] (Configuration of Directional Coupler) Figure 1 is a conceptual diagram showing the structure of the directional coupler 100 according to this disclosure, where (a) is a top view and (b) is a cross-sectional view along the Ib-Ib cross-sectional line. In Figure 1, it is assumed that light propagates in the x-direction, and in Figure 1(a), the left side is depicted as the input side of the light and the right side as the output side.

[0012] As shown in Figure 1, the directional coupler 100 is a waveguide-type directional coupler comprising two cores 110a and 110b, and a cladding 120 surrounding the cores 110a and 110b. The directional coupler 100 also includes an interaction region 130 in which the gap between the two cores 110a and 110b in the width direction (y direction in Figure 1) is relatively narrow.

[0013] The cladding 120 further includes a first region 121 positioned between cores 110a and 110b in the interaction region 130, second regions 122a and 122b positioned on the sides opposite to the first region 121 for each of the cores 110a and 110b in the interaction region 130, and a third region 123 corresponding to regions other than the first region 121 and the second regions 122a and 122b.

[0014] In one example, the directional coupler 100 may be a silica waveguide. In such a case, silica materials are used for the cores 110a, b and cladding 120. For example, the cores 110a, b may be silica (SiO2) doped with germanium (Ge). On the other hand, the cladding 120 may be, for example, undoped SiO2, or SiO2 doped with boron (B) or phosphorus (P). The cores 110a, b, the first region 121, the second region 122a, b, and the third region 123 are configured to satisfy the magnitude relationship of the refractive indices described later (for example, the doping amount of the added element can be adjusted to satisfy this magnitude relationship).

[0015] In the directional coupler 100, the refractive indices of the cores 110a and 110b are set to n core If the refractive index of the first region 121 is n1, the refractive index of the second region 122a and b is n2, and the refractive index of the third region 123 is n3, then the relative magnitudes of each are n coreIt is configured such that >n1 ≥ n3 > n2. The basis for this relationship of refractive index will be explained later. Note that in the conventional directional coupler described above, n core It is configured such that >n1 >n3 = n2, and its configuration differs from that of the directional coupler 100 according to this disclosure.

[0016] The directional coupler 100 according to this disclosure only needs to be configured such that the above-described relationship of refractive indices is satisfied, and the dimensions of the cores 110a, b, the first region 121, the second region 122a, b, and the third region 123, as well as the length of the interaction region 130 in the direction of light propagation (x direction in Figure 1) and the gap between the cores 110a and 110b in the interaction region 130, may be set to any value according to the design.

[0017] Figure 2 is a conceptual diagram showing the structure of a directional coupler 200, which is a modified example of the directional coupler 100, where (a) is a top view and (b) is a cross-sectional view along the IIb-IIb section. As shown in Figure 2, the directional coupler 200 has a configuration in which the first region 121 and the second regions 122a,b of the directional coupler 100 are replaced by the first region 221 and the second regions 222a,b. Unlike the first region 121 and the second regions 122a,b, the first region 221 and the second regions 222a,b are configured to have a greater thickness than the core 110, and Figure 4 illustrates a configuration in which the upper end in the thickness direction (z direction in Figure 2) coincides with the upper end in the thickness direction of the third region. Even with such a configuration, the same effects as the directional coupler 100 can be achieved.

[0018] Furthermore, in the above example, the cores 110a, b, the first region 121, the second region 122a, b, and the third region 123 were described as being made of silica-based materials, but other material systems may be used. For example, the cores 110a, b, the first region 121, the second region 122a, b, and the third region 123 may be oxides such as silicon (Si), silicon nitride (SiN), or tantalum oxide, or polymers. The cores 110a, b and the cladding 120 (first region 121, second region 122a, b, and third region 123) may be made of the same material system, or different material systems may be used, as long as the above-mentioned relationship of refractive index magnitudes is satisfied. For example, as mentioned above, the cores 110a and 110b and the cladding 120 may both be made of quartz-based materials, and the cores 110a and 110b may be Si and the cladding 120 may be SiN.

[0019] (Setting the refractive index of the core and cladding) The basis for the relative refractive indices described above in the directional coupler 100 will be explained in detail below. For the sake of explanation, we will first consider the case where a directional coupler 300 that does not include the second region as shown in Figure 3 combines and outputs light with a wavelength of 500 nm and light with a wavelength of 770 nm.

[0020] Figure 3 shows the schematic structure of the directional coupler 300, where (a) is a top view of the directional coupler 300 and (b) is a cross-sectional view along the IIIb-IIIb cross-sectional line. As shown in Figure 3, the directional coupler 300 has a configuration in which the second regions 122a and b are replaced by a third region 123 compared to the directional coupler 100 shown in Figure 1. In other words, in the directional coupler 300, the cladding 120 consists only of the first region 121 and the third region 123. Here, as an example, n coreThe relative refractive index difference between and n3 was assumed to be 1.1%, the width of cores 110a and b was 3 μm, the thickness of cores 110a and b was 4 μm, and the gap between core 110a and core 110b in the interaction region 130 was 3 μm. This is a structure that can be manufactured in the mass production process of a typical planar optical circuit (PLC). In addition, in a PLC as shown in Figure 3, the width of cores 110a and b, the thickness of cores 110a and b, and the gap between core 110a and core 110b in the interaction region 130 are preferably 1 μm to 10 μm.

[0021] Consider the case where a directional coupler 300 having such a structure is input with 500 nm light from input terminal 110aI and 770 nm light from input terminal 110bI, and after the respective lights are combined in the interaction region 130, the output is output from output terminal 110aO.

[0022] Figure 4 shows the optical properties in the interaction region 130 of the directional coupler 300, where (a) shows the relationship between wavelength and transmittance in the directional coupler 300 when the first region 121 and the third region 123 have the same refractive index, (b) shows the relationship between the difference in relative refractive index between the first region 121 and the third region 123 and the coupling length of light with a wavelength of 770 nm, and (c) shows the relationship between wavelength and transmittance in the directional coupler 300 when the difference in relative refractive index between the first region 121 and the third region 123 is 0.6%. In this document, "coupling length" refers to the shortest length in the interaction region (interaction region 130 in Figure 3) at which the coupling ratio of light propagating through one core (for example, 770 nm light propagating through core 110b in Figure 3) to the other core (for example, core 110a in Figure 3) is highest.

[0023] Assuming that the refractive indices of the first region 121 and the third region 123 are equal, the coupling length of cores 110a and 110b is calculated to be approximately 15,000 μm (this corresponds to the case where the horizontal axis in Figure 4(b) is 0.0%). The relationship between wavelength and transmittance in the directional coupler 300 in this case is shown in Figure 4(a). In Figure 4(a), the transmittance from the input terminal 110aI to the output terminal 110aO is shown by a solid line, and the transmittance from the input terminal 110bI to the output terminal 110aO is shown by a dashed line. As shown in Figure 4(a), in the directional coupler 300, when the coupling length is 15,000 μm, the 500 nm light input from the input terminal 110aI and the 770 nm light input from the input terminal 110bI are combined in the interaction region 130 and output from the output terminal 110aO.

[0024] Next, consider the case where the refractive index n1 of the first region 121 is varied as a parameter in the directional coupler 300. Here, as an example, the thickness of the first region 121 is assumed to be 4.0 μm. The relationship between the relative refractive index difference between the first region 121 and the third region 123 and the coupling length of 770 nm light is shown in Figure 4(b). As shown in Figure 4(b), a tendency was observed for the coupling length of 770 nm light to decrease as the relative refractive index difference between the first region 121 and the third region 123 increased. That is, it can be seen that the coupling length of 770 nm light can be shortened as n1 becomes larger than n3. However, this relationship is a trade-off with the coupling ratio of 550 nm light. Therefore, when actually manufacturing the directional coupler according to this disclosure, an appropriate n1 should be set according to the design. Here, as an example, the relative refractive index difference between the first region 121 and the third region 123 was set to 0.6%. The bond length at this time corresponds to approximately 2300 μm, as can be seen from Figure 4(b).

[0025] Furthermore, the relationship between wavelength and transmittance in the directional coupler 300 at this time is shown in Figure 4(c). In Figure 4(c), as in Figure 4(a), the transmittance from the input terminal 110aI to the output terminal 110aO is shown by a solid line, and the transmittance from the input terminal 110bI to the output terminal 110aO is shown by a dashed line. As shown in Figure 4(c), when the relative refractive index difference between the first region 121 and the third region 123 is 0.6% and the coupling length is approximately 2300 μm, it can be seen that, as in the case shown in Figure 4(a), the combined light of the 500 nm light input from the input terminal 110aI and the 770 nm light input from the input terminal 110bI is output from the output terminal 110aO. In other words, by placing the first region 121 and setting its refractive index n1 to a value higher than the refractive index n3 of the third region 123, it becomes possible to achieve multiplexing of light of the same wavelength with a shorter coupling length compared to when the first region 121 is not placed.

[0026] Furthermore, let's consider the case where the directional coupler 300 includes a second region. Since this is essentially equivalent to assuming the configuration of the directional coupler 100 described above, the following explanation will refer to the configuration of the directional coupler 100 shown in Figure 1.

[0027] Figure 5 shows the optical properties in the interaction region 130 of the directional coupler 100. (a) shows the relationship between the relative refractive index difference between the third region 123 and the second regions 122a and b and the coupling length of light with a wavelength of 770 nm. (b) shows the relationship between wavelength and transmittance in the directional coupler 200 when the relative refractive index difference between the third region 123 and the second regions 122a and b is 1.1%. However, as mentioned above, it is assumed that the relative refractive index difference between the first region 121 and the third region 123 is set to 0.6%. Also, as an example, the width of the second regions 122a and b is set to 10.0 μm and the thickness of the second regions 122a and b is set to 4.0 μm. However, this is intended as an example, and as mentioned above, the dimensions of the second regions 122a and b can be set to any value according to the design. In the case of a PLC such as the directional coupler 100, the width of each of the second regions 122a and 122b is preferably 2.0 μm to 10.0 μm, and the thickness of each is preferably 1.0 μm to 40.0 μm.

[0028] As shown in Figure 5(a), a tendency was observed for the coupling length of 770 nm light to shorten as the difference in relative refractive index between the third region 123 and the second regions 122a and 122b increased. In other words, it can be seen that the coupling length of 770 nm light can be shortened as n3 becomes larger than n2. Here, as an example, the difference in relative refractive index between the third region 123 and the second regions 122a and 122b was set to 1.1%. The coupling length at this time corresponds to approximately 1900 μm, as can be seen from Figure 5(a).

[0029] Furthermore, the relationship between wavelength and transmittance in the directional coupler 100 at this time is shown in Figure 5(b). In Figure 5(b), as with Figures 4(a) and 4(c), the transmittance from the input terminal 110aI to the output terminal 110aO is shown by a solid line, and the transmittance from the input terminal 110bI to the output terminal 110aO is shown by a dashed line. As shown in Figure 5(b), when the relative refractive index difference between the first region 121 and the third region 123 is set to 0.6%, and the relative refractive index difference between the third region 123 and the second regions 122a and b is set to 1.1%, it can be seen that the coupling length is approximately 1900 μm, and the combined light of the 500 nm light input from the input terminal 110aI and the 770 nm light input from the input terminal 110bI is output from the output terminal 210aO.

[0030] Based on the above, in the directional coupler 100, the refractive indices of the cores 110a and 110b, the first region 121, the second region 122a and 122b, and the third region 123 are set to n core By configuring the coupler such that >n1 > n3 > n2, it becomes possible to realize a directional coupler with a shorter coupling length compared to conventional technology, and consequently, a smaller directional coupler. Note that even if n1 and n3 are the same value, the coupling length can be shortened if the relationship n3 > n2 is satisfied, thus achieving a similar effect. Therefore, the refractive indices of the core, first region, second region, and third region in the directional coupler according to this disclosure are, more generally, n core It should be constructed such that >n1 ≥ n3 > n2.

[0031] Furthermore, in a directional coupler 100 having such a configuration, as described above, the dimensions of the first region 121, second region 122a, b, and third region 123 constituting the core 110a, b, and cladding 120, as well as the interaction region 130, can be arbitrarily set according to the design, as long as the relative magnitudes of their respective refractive indices are satisfied. Therefore, tolerance to manufacturing variations is improved compared to the conventional technology.

[0032] The above description concerns the case where the directional coupler 100 according to this disclosure combines light with a wavelength of 500 nm and light with a wavelength of 770 nm. This is for illustrative purposes only and does not limit the wavelength of the input light. The directional coupler 100 according to this disclosure can be applied to the combination of visible light with visible light, visible light with near-infrared light, and near-infrared light with near-infrared light. For example, the directional coupler 100 according to this disclosure is effective as a multiplexer for two wavelengths of light in the range of 400 nm to 800 nm, which has been in demand in recent years.

[0033] (Combiner Configuration) Figure 6 is a schematic top view showing the structure of a combiner 600 in which multiple directional couplers 100 according to this disclosure are connected in stages. The directional couplers according to this disclosure (for example, directional couplers 100, 200) described above can be extended to combiners that combine light of more wavelengths by connecting them in stages.

[0034] The combiner 600 shown in Figure 6 has a four-input configuration, but this is for illustrative purposes only and can actually be extended to a combiner that combines N wavelengths of light (where N is an integer greater than or equal to 3).

[0035] As described above, the directional coupler 100 can be applied to the combination of visible light with other visible light, visible light and near-infrared light, and near-infrared light with other near-infrared light. Similarly, the combiner 600 can also be applied to the combination of visible light with other visible light, visible light and near-infrared light, and near-infrared light with other near-infrared light. In particular, the directional coupler 100 according to this disclosure is effective as a combiner for visible light to near-infrared light (for example, light with three or more wavelengths in the range of 400 nm to 2500 nm), which has been in demand in recent years. Furthermore, of these three or more wavelengths of light, two wavelengths are in the range of 400 nm to 800 nm, and these two wavelengths of light can also be the light combined by the directional coupler 100 that constitutes the combiner 600.

[0036] (Manufacturing Method) Figure 7 is a flowchart showing the manufacturing method 700 for the directional coupler 200 according to this disclosure. Although Figure 7 illustrates the manufacturing method for the directional coupler 200, the principle is the same for the manufacturing method of the directional coupler 100.

[0037] As shown in Figure 7, the manufacturing method 700 comprises forming a lower cladding layer on a substrate (S701), forming a core layer on the lower cladding layer, wherein the core layer has a higher refractive index than the lower cladding layer (S702), forming waveguide patterns for cores 110a and 110b, wherein the waveguide patterns include an interaction region 130 where cores 110a and 110b are in close proximity (S703), depositing an upper cladding layer on the lower cladding layer and cores 110a and 110b to form a third region 123 (S704), and the core in the interaction region 130. The method includes forming a first groove between 110a and core 110b (S705), forming a second groove on the side opposite to the first groove for each of core 110a and core 110b (S706), forming a first region 221 in the first groove, wherein the first region 121 has a refractive index lower than that of cores 110a and b and a refractive index higher than or the same as that of a third region 123 (S707), and forming second regions 222a and b in each of the second grooves, wherein the second regions 222a and b have a refractive index lower than that of a third region 123 (S708).

[0038] In S701, a lower cladding layer is formed on a substrate. The substrate can be, for example, an undoped Si wafer commonly used as a substrate for a PLC. Also, the lower cladding layer can be formed, for example, by deposition by a flame deposition method followed by heat treatment.

[0039] In S702, a core layer is formed on the lower cladding layer. Here, in order to satisfy the above-described refractive index magnitude relationship, the core layer has a higher refractive index than the lower cladding layer (a location that will later become the third region 123). On the other hand, the thickness of the core layer may be arbitrarily set according to the design. Also, the technique for forming the core layer may be a general film formation method such as a physical vapor deposition method such as a vacuum evaporation method or a sputtering method, a chemical vapor deposition method such as plasma CVD or photo CVD, or a liquid phase growth method such as a sol-gel method.

[0040] Incidentally, the manufacturing method 700 may further include performing heat treatment (not shown) to planarize the core layer after S702 and before S703. The temperature of the heat treatment can be, for example, 1000 - 1400°C.

[0041] In S703, a waveguide pattern is formed. In the case of the directional coupler 200, the waveguide pattern corresponds to the shapes of the cores 110a and b. The waveguide pattern can be formed, for example, by photolithography followed by plasma etching.

[0042] In S704, an upper cladding layer is formed on the lower cladding layer and the formed cores 110a and b. The upper cladding layer and the lower cladding layer substantially correspond to the third region 123. The upper cladding layer can be formed by the same method as the formation of the lower cladding layer in S701.

[0043] In S705, a first groove is formed between the cores 110a and b in the interaction region 130. Such a first groove corresponds to a location where the first region 121 will later be formed. The first groove can be formed, for example, by photolithography followed by plasma etching.

[0044] In S706, for each of the cores 110a and 110b, a second groove is formed on the side surface opposite to the first groove. Such a second groove corresponds to the location where the second regions 122a and 122b will be formed later. The second groove can be formed, for example, by photolithography and then plasma etching, similar to the first groove.

[0045] In S707, the first region 121 is formed in the first groove. From the perspective of satisfying the above-described refractive index relationship, the first region 121 is formed to have a refractive index lower than that of the cores 110a and 110b and higher than or the same as that of the third region 123. The first region 121 can be formed, for example, using a flame deposition method.

[0046] In S708, the second regions 122a and 122b are formed in the second groove. From the perspective of satisfying the above-described refractive index relationship, the second regions 122a and 122b are formed to have a refractive index lower than that of the third region 123. The second regions 122a and 122b can be formed, for example, using a flame deposition method, similar to the first region 12,1.

[0047] By using such a method, it becomes possible to manufacture the directional coupler 200 according to the present disclosure. Note that S701 - S708 do not necessarily need to be performed in the order described above, and some of them may be performed in a different order or in parallel.

[0048] As described above, the directional coupler according to the present disclosure can realize a directional coupler with a shorter coupling length compared to the prior art, and is a smaller directional coupler. Furthermore, in the directional coupler according to the present disclosure, the tolerance to manufacturing variations is improved compared to the prior art. Such a directional coupler is expected to be put into practical use as a multiplexer or combiner for multiplexing in a wider wavelength range.

Claims

1. A waveguide-type directional coupler comprising two cores and a cladding, wherein the cladding comprises: a first region between the adjacent sides of the two cores; a second region on the side opposite to the first region for each of the two cores; and a third region which is the portion other than the first and second regions, wherein the refractive indices of the two cores are n core The refractive index of the first region is n1, the refractive index of the second region is n2, and the refractive index of the third region is n3, n core A directional coupler configured such that >n1 ≥ n3 > n2.

2. A combiner configured to combine N wavelengths of light (where N is an integer of 3 or more) by connecting multiple directional couplers as described in claim 1, wherein the N wavelengths of light are light with wavelengths in the range of 400 nm to 2500 nm, and two of the N wavelengths of light are two wavelengths of light in the range of 400 nm to 800 nm, which are combined by the directional couplers.

3. A method for manufacturing a waveguide-type directional coupler, comprising: forming a lower cladding layer on a substrate; forming a core layer on the lower cladding layer, wherein the core layer has a higher refractive index than the lower cladding layer; forming a pattern of two cores, wherein parts of the two cores are in close proximity; depositing an upper cladding layer on the lower cladding layer and on the cores to form a third region; forming a first groove between the two adjacent cores; forming a second groove on each of the two cores on the side opposite to the first groove; forming a first region of cladding in the first groove, wherein the first region has a lower refractive index than the core and a higher or the same refractive index as the third region; and forming a second region of cladding in each of the second grooves, wherein each of the second regions has a lower refractive index than the third region.

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