AMORPHOUS SILICON

CROSS-REFERENCES TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Application No. 62/003,404, filed on May 27, 2014, and U.S. Provisional Application No. 62/044,867, filed on September 2, 2014, the disclosures of which are incorporated by reference in their entirety for all purposes.

BACKGROUND

[0002] This application relates to optical waveguides. More specifically, and without limitation, to coupling a silicon waveguide to an optical fiber.

[0003] Photonic devices, including optical waveguides, are being integrated on semiconductor chips. Photonic devices integrated on semiconductor chips are often designed for use in fiber-optic communication systems.

BRIEF SUMMARY

[0004] This application discloses embodiments of a mode expander for coupling a smaller optical mode, such as a fundamental mode in a semiconductor waveguide, to a larger optical mode, such as a fundamental mode in an optical fiber.

[0005] In some embodiments, a waveguide mode expander comprises a substrate, a shoulder, and a ridge. The shoulder is disposed on the substrate, and the shoulder is made of crystalline silicon. The ridge is made of non-crystalline silicon. The ridge is disposed on the shoulder such that the shoulder is between the ridge and the substrate. The ridge has a narrower width than the shoulder, wherein the ridge and the shoulder are configured to guide and expand an optical beam propagating through the shoulder and the ridge.

[0006] In some embodiments, the waveguide mode expander further comprises cladding disposed on the waveguide, wherein: the cladding has been etched in a pattern to form a recess; and the ridge is formed by filling the recess with non-crystalline silicon. In some embodiments, the ridge has a plurality of stages, and at a cross section of the waveguide mode expander, each stage of the plurality of stages has a different width, and stages closer to the substrate have wider widths. In some embodiments, a stage closer to the substrate is thinner than a stage farther from the substrate. In some embodiments, the ridge comprises one stage, three stages, and/or five stages. In some embodiments, cladding covers the ridge and/or the shoulder. In some embodiments, the waveguide mode expander is fabricated using a silicon-on-insulator wafer. In some embodiments, the ridge comprises one or more tapers to expand an optical beam.

[0007] In some embodiments, a method for manufacturing a waveguide mode expander is described. A substrate having a. waveguide disposed on the substrate is provided. Cladding is deposited on the waveguide. Photoresist is applied on the cladding forming a pattern. A recess is etched in the cladding based on the pattern. Photoresist is removed, and the recess is filled with non-crystalline silicon, wherein: the waveguide forms a shoulder of the waveguide mode expander; the non-crystalline silicon forms a ridge of the waveguide mode expander; the shoulder is between the substrate and the ridge; and the ridge has a narrower width than the shoulder.

[0008] A waveguide mode expander comprises a substrate, a waveguide disposed on the substrate, a shoulder, and a ridge. The waveguide disposed on the substrate comprises crystalline silicon. The shoulder is optically coupled with the waveguide, wherein: the shoulder is disposed on the substrate; and the shoulder comprises non-crystalline silicon. The ridge comprises non-crystalline silicon; the ridge is disposed on the shoulder, such that the shoulder is between the ridge and the substrate; and the ridge has a narrower width than the shoulder, wherein the ridge and the shoulder are configured to guide and expand an optical beam propagating from the waveguide and through the shoulder and the ridge.

[0009] In some embodiments, the waveguide has a rectangular cross section. In some embodiments, the ridge comprises a plurality of stages; at a cross section of the waveguide mode expander, each stage of the plurality of stages has a different width; and a first stage of the plurality of stages, which is closer to the shoulder, has a wider width than a second stage of the plurality of stages, which is farther from the shoulder than the first stage. In some embodiments, the first stage is thinner than the second stage. In some embodiments, the non-crystalline silicon is amorphous silicon. In some embodiments, the plurality of stages has a number of stages; and the number of stages is three. In some embodiments, the waveguide mode expander further comprises a claddmg (e.g., Si02) covering the ridge and the shoulder. The ridge expands the optical beam by tapering from a narrower width near an input end to a wider width near an output end. In some embodiments, the substrate comprises buried-oxide layer and a handle layer; the buried-oxide layer is disposed between the shoulder and the handle layer; the buried- oxide layer is disposed between the waveguide and the handle layer; and the buried-oxide layer acts as a cladding layer to the shoulder and the waveguide. In some embodiments, the waveguide mode expander further comprises an interface between the shoulder and the waveguide, wherein the interface forms a plane that is angled with respect to an optical path of the waveguide such that the plane is not orthogonal to an optical path.

)] In some embodiments, a method for manufacturing a waveguide mode expander is described, the method comprising: providing a substrate having a device layer disposed on the substrate; applying photoresist, on the device layer; etching the device layer to form a first recess, the first recess having a shape of a first pattern; removing photoresist from the device layer; filling the first recess with non-crystalline silicon (e.g., amorphous silicon) to form, a shoulder; etching the device layer to define a waveguide; etching the shoulder, wherein the shoulder to align with the waveguide; covering the shoulder with cladding; applying photoresist on the cladding; etching the cladding to form a second recess, the second recess having a shape of a second pattern; removing photoresist from the cladding; filling the second recess with noncrystalline silicon, wherein: the non-crystalline silicon forms a ridge of the waveguide mode expander; the shoulder is between the substrate and the ridge; and the ridge has a narrower width than the shoulder.

[0011] In some embodiments, etching the cladding uses a highly selective etch such that the cladding is more easily etched than the shoulder. In some embodiments, the second pattern comprises a triangle taper and/or a parabolic taper. Some embodiments further comprise:

applying, wherein the cladding is a first cladding, a second cladding on both the first cladding and the non-crystalline silicon; etching the second cladding to form a third recess, the third recess having a shape of a third pattern; filling the third recess with additional non-crystalline silicon to form a second stage of the ridge, wherein filling the second recess formed a first stage of the ridge, in some embodiments, the first stage is wider than the second stage; and the second stage is thicker than the first stage. Some embodiments further comprise: applying, a third cladding the second cladding; etching the third cladding to form a fourth recess, the fourth recess having a shape of a fourth pattern; and filling the fourth recess with additional non-crystalline silicon to form a third stage of the ridge. In some embodiments, amorphous silicon is converted to polyerystalline silicon.

[0012] Further areas of applicability of the present disclosure will become apparent from the detailed description provided hereinafter. It should be understood that the detailed description and specific examples, while indicating various embodiments, are intended for purposes of illustration only and are not intended to necessarily limit the scope of the disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

[00131 FIG. 1 depicts a perspective drawing of an embodiment of a single-stage mode expander.

[0014] FIG. 2 depicts a cross section of an input end of the single-stage mode expander.

[0015] FIG. 3 depicts a cross section of an output end of the single-stage mode expander.

[0016] FIGs. 4-6 depict simulations of mode confinement in mode expanders and an optical fiber.

[0017] FIG. 7 depicts a top view of an embodiment of a three-stage mode expander.

[0018] FIGs. 8-12 depict cross sections of the three-stage mode expander.

[0019] FIGs. 13-18 depict cross sections of an embodiment of a five-stage mode expander.

[0020] FIGs. 19-28 depict simplified sketches of the five-stage mode expander during fabrication.

[0021] FIG . 29 depicts an embodiment of a flowchart of a process for manufacturing a mode expander. [00221 FIG. 30 depicts a graph showing simulated loss due to misalignment between a single-stage mode expander and an optical fiber.

[00231 FIG. 31 depicts an optical mode confined in a three-stage mode expander having a crystalline silicon shoulder and a non-crystalline silicon ridge.

[0024] FIG. 32 depicts an optical mode confined in a three-stage mode expander having a non-crystalline silicon shoulder and a non-crystalline silicon ridge.

[002S] FIG. 33 is a plot of simulated mode divergence of a three-stage mode expander.

[0026] FIGs. 34-39 depict views of an embodiment of forming a non-crystalline silicon shoulder of a mode expander.

[0027] FIG. 40 depicts a top view of a three-stage mode expander with a non-crystalline silicon shoulder.

[0028] FIGs. 41 -43 depict views of a single-stage mode expander with a non-crystalline silicon shoulder.

[0029] FIG . 44 shows a flowchart of an embodiment of a process for forming a non-crystalline silicon shoulder of a mode expander.

[0030] FIGs. 45-48 depict an embodiment of a multistage coupler for coupling a first semiconductor waveguide with a second semiconductor waveguide.

[0031] In the appended figures, similar components and/or features may have the same reference label. Further, various components of the same type may be distinguished by following the reference label by a dash and a second label that distinguishes among the similar

components. If only the first reference label is used in the specification, the description is applicable to any one of the similar components having the same first reference label irrespective of the second reference label.

DETAILED DESCRIPTION

[0032] The ensuing description provides preferred exemplary embodiment(s) only, and is not intended to limit the scope, applicability, or configuration of the disclosure. Rather, the ensuing description of the preferred exemplary embodiment(s) will provide those skilled in the art with an enabling description for implementing a preferred exemplary embodiment. It is understood that various changes may be made in the function and arrangement of elements without departing from the spirit and scope as set forth in the appended claims.

[0033] Embodiments generally relate to a mode expander for coupling a semiconductor waveguide (e.g., crystalline-silicon waveguide) to an optical fiber.

[0034] Referring first to FIG. 1, a perspective drawing of an embodiment of a single-stage mode expander 100 is shown. The single-stage mode expander 100 comprises a shoulder 104 and a ridge 108. The single-stage mode expander 100 has an input end 1 16 and an output end 1 18. In some embodiments, the input end 1 16 is coupled to a waveguide 120 having a rectangular cross section. In some embodiments, the waveguide 120 has a cross section that is not rectangular (e.g., trapezoidal or inverted 'T' shape with a crystalline-silicon ridge on top of a crystalline-silicon shoulder). The output end 1 18 is coupled with an optical fiber having a round cross section (e.g., an optical fiber having normal or high Numerical Aperture (NA)).

[0035] In FIG. 1 , both the shoulder 104 and the ridge 108 taper from the output end 1 18 to the input end 1 16 so that an optical beam expands that is transmitted from the input end 1 16 to the output end 1 18. For example, a beam is transmitted from a waveguide 120 (e.g., a

crystalline-silicon waveguide), through the input end 1 16 of the single-stage mode expander 100, through the output end 1 18 of the single-stage mode expander 100, and to an optical fiber having a larger core than the waveguide 120. In some embodiments, as the beam, propagates through the single-stage mode expander 100, the beam expands adiabatically, A direction of beam

propagation .124 is shown as an arrow going from the input end .1 16 to the output end 1 1 8. A. person of skill in the art will recognize a beam propagating from the output, end 118 to the input end 1 16 will be compressed.

[0036] FIG, 2 depicts a cross section of the single-stage mode expander .100 at the input end 1. 1.6 of the single-stage mode expander .100. The single-stage mode expander 1.00 at the input end comprises the shoulder 104, but not the ridge 108. The shoulder 104 has a thickness, S _t , and a width, Sw. The shoulder 104 has an input width, S _w -i, at the input end 1 16. In some

embodiments, the input width, S _w -i, of the shoulder 104 ranges between 0.2 and 5 μτη. (e.g., 0.2, 0,5, 1 , 2, 3, 4, or 5 u rn}. The thickness (sometimes referred to as height) of the shoulder 104 ranges between 0.2 and 5 tun (e.g., 0.2, 0.5, 1.0, 1 .5, 2, 3, or 5 um). The shoulder 104 is made of crystalline silicon (c-Si). in some embodiments, the shoulder 104 is simply an extension of the waveguide 120 fabricated on a substrate (e.g., a substrate comprising silicon on insulator and/or Si02). In some embodiments, the single-stage mode expander 100 further comprises a substrate and/or cladding material.

[0037] FIG. 3, depicts a cross section of the single-stage mode expander 100 at the output end 1 18 of the single-stage mode expander 100. The output end 1 18 of the single-stage mode expander 100 comprises the shoulder 104 and the ridge 108. The thickness S _t of the shoulder 104 remains relatively constant from the input end 1 16 to the output end 1 18. The width, S _w , of the shoulder 104 expands to an output width, S _w -o, of the shoulder 104. In some embodiments, the output width S _w -o of the shoulder 104 ranges between 2 and 50+ μη (e.g., 2, 3, 4, 5, 6, 8, 10, 25, or 50+ μιη). In some embodiments, the width S _w -o of the shoulder 104 at the output end 1 18 is not critical because a beam, is contmed laterally (widthwise) by the ridge 108. Thus the width S _w -o of the shoulder 104 at the output end 1 1 8, in some embodiments, is greater than 4.5 μπι. Put another way, in some embodiments mode confinement does not significantly change if the width S _w -o of the shoulder 104 at the output end 1 1 8 is 5 μηι, 20 μηι, 500 μηι, or I. meter.

[0038] The ridge 108, in FIG. 3, has only one stage. In some embodiments, the ridge 108 comprises more than one stage, so that for a given cross section perpendicular to beam propagation 1.24, the ridge 108 has varying widths for different stages (e.g., as discussed later in reference to FIGs. 10-18). The ridge 108 in the single-stage mode expander 100 has a thickness, R _t , and a width, R. _w . The thickness R _t of the ridge 108 at the output end 1 18 is between 0.2 to 10 \im (e.g., 0.2, 0.5, 5 , 2, 3, 5, 7, or 50 p.m). And in some embodiments, the width of the ridge R _w ranges between 0.2 and 10 μηι (e.g., 0.2, 0.5, 1 ,2, 2.5, 3, 3.5, 4, 5, 7, or 10 μηι). Additionally, in some embodiments, a length of the single-stage mode expander 100, from the input end 1 16 to the output end 1 1 8, is between 25 and 500 μ,ηι (e.g., 25, 50, 75, 1 00, 1 50, 200, 250, 300, 400, or 500 μηι).

[0039] The ridge 508, in some embodiments, is made of non-crystalline silicon. In crystalline silicon, a lattice structure is well defined. In non-crystalline silicon, a lattice structure is not wel l defined. Examples of non-crystalline silicon include amorphous silicon (a-Si) and polycrystalline silicon (poly-Si). In polycrystalline silicon, the lattice structure is not well defined, and a polycrystalline-siiicon structure comprises multiple crystal lattices, in some embodiments, though non-crystalline silicon may have more loss than crystalline silicon, non-crystalline silicon is used for manufacturing reasons (e.g., for manufacturing tolerances and/or for expanding a beam larger than a crystalline-silicon layer). Another advantage of non-crystalline silicon, in some embodiments, is that non-crystalline has a. stable and predictable index of refraction that is similar to crystalline silicon (e.g., the ridge 108 has a first index of refraction; the shoulder 104 has a second index of refraction; and the first index of refraction minus the second index of refraction is less than 0.05, 0,1 , 0.2, or 0.3). In some embodiments, the shoulder 104 is made of non-crystalline silicon.

[0040] Referring next to FIGs. 4-6, simulations of mode confinements are shown. In FIG, 4, a simulated profile of a beam at the output end 118 of the single-stage mode expander 100 is shown. In some embodiments, a smaller beam divergence angle and/or a larger spot size is preferred. For example, a beam divergence (half angle) of less than 30, 25, 20, 15, or 10 degrees is targeted. In the simulation in FIG. 4, a beam divergence of about 15 degrees was calculated. In FIG. 4, a spot size of 2.6 μτη in the vertical direction (y-axis) and about 2.8 μηι in the horizontal direction (x-axis) is shown (beam size being measured to l/e ^z of peak intensity). In FIG. 5, a simulation of an optical beam confined in a high NA fiber is shown. In FIG. 6, a simulated profile of a beam at an output of a triple-stage mode expander is shown. In some embodiments, having a cross section roughly rectangular is targeted to assist in matching an optical mode of a coupler with an optical mode of an optical fiber.

[0041] Referring to FIG. 7, a top view of an embodiment of a three-stage mode expander 700 is shown. The three-stage mode expander 700 comprises a shoulder 704 and a ridge 708. The ridge 708 further comprises a first stage 71 1, a second stage 712, and a third stage 753. An input end 756 and an output end 718 are also shown. An optica] beam is expanded going from the input end 716 to the output end 718, Though FIG. 7 shows the ridge 708 having three stages, other embodiments of mode expanders have fewer or more stages.

[0042] The shoulder 704, the first stage 75 5 , the second stage 712, and the third stage 713 taper from the output end 718 to the input end 716. In FIG, 7, the shoulder 704, the first stage 71 1 , the second stage 712, and the third stage 733 have a substantially isosceles-triangle shape tapers (e.g., z ~ njxj). In some embodiments, other taper shapes are used. For example, a taper could be substantially parabolic shaped (e.g., z ~ x ^" ; or z « jxj"), or substantially funnel shaped (e.g., z « ± in(!xj); or z « ± iog _n (|xj)), where n is not constrained to be an integer. Further, tapers for each stage could have a different shape. In FIG. 7, the shoulder 704 has a. length, SL, the first stage 71 1 has a length, the second stage 712 has a length, I _L , and the third stage 713 has a length, Ji _. . In some embodiments, SL =

[0043] FIGs. 8-12 show cross sections of the three-stage mode expander 700 going from the input end 716 (e.g., coupling to a semiconductor waveguide) of the three-stage mode

expander 700 to the output end 718 (e.g., coupling to an optical fiber). In some embodiments, the first stage 71 1 , the second stage 712, and the third stage 713 are made of non-crystalline silicon. In some embodiments, the shoulder 704 is made of crystalline silicon. In some embodiments, the shoulder 704 is made of non-crystalline silicon. In some embodiments, the shoulder 704 is made of crystalline silicon to reduce a manufacturing step (e.g., to not, have to replace some crystalline silicon with non-crystalline silicon). In some embodiments, the shoulder 704 is made of non-crystalline silicon so a mode of an optical beam extends more into the shoulder 704 of the three-stage mode expander 700.

[0044] FIG. 8 depicts a first cross section of the three-stage mode expander 700 at the input end 716. FIG. 8 shows the shoulder 704. The shoulder 704 in the first cross section has a first width, 8 _W ~1 , and a thickness, S _t . In some embodiments, the input end 716 is coupled to the waveguide 120. In some embodiments, the first width S _w -1 of the shoulder 704, and the thickness S _T of the shoulder 704, are equal to a width of the waveguide 120 and a thickness of the waveguide 120, respectively. In some embodiments, the shoulder 704 is an extension of the waveguide 120, In some embodiments, the waveguide 120 is in a device layer of a silicon-on- insulator (SO I) wafer. In some embodiments, the three-stage mode expander 700 further comprises a substrate and/or cladding material.

[0045] FIG . 9 depicts a second cross section of the three-stage mode expander 700. The second cross section shows a starting of the first stage 71 1 of the three-stage mode expander 700. The first stage 71 1 of the three-stage mode expander 700 has a first width, H _w -1, and a thickness, H _E . The first stage 71 1 is disposed on top of the shoulder 704.

[0046] FIG . 10 depicts a third cross section of the three-stage mode expander 700. The third cross section shows a starting of the second stage 712 of the three-stage mode expander 700. The second stage 712 of the three-stage mode expander 700 has a first width, and a thickness, I _t . The first stage 71 1 of the three-stage mode expander 700 has a second width H _w -2, which is wider than the first width H _w -1 of the first stage 711. The shoulder 704 of the three-stage mode expander 700 has a second width S _w -2, which is wider than the first width 8 _W -1 of the shoulder 704.

[0047] FIG. 1 1 depicts a fourth cross section of the three-stage mode expander 700. The fourth cross section shows a starting of the third stage 713 of the three-stage mode expander 700. The third stage 713 of the three-stage mode expander 700 has a first width, J _w -L and a thickness, J _t . The second stage 712 of the three-stage mode expander 700 has a second width, I _w -2, which is wider than the first width I _w -1 of the second stage 712. The first stage 711 of the three-stage mode expander 700 has a third width H _w -3, which is wider than the second width H _w -2 of the first stage 711. The shoulder 704 of the three-stage mode expander 700 has a third width 8 _W ~3, which is wider than the second width S _w -2 of the shoulder 704.

[0048] FIG. 12 depicts a fifth cross section of the three-stage mode expander 700. The fifth cross section of the three-stage mode expander 700 is a cross section of the output end 718 of the three-stage mode expander 700. The third stage 713 of the three-stage mode expander 700 has a second width, J _w -2, which is wider than the first width J _w -i of the third stage 713. The second stage 712 of the three-stage mode expander 700 has a third width, I _w -3, which is wider than the second width I _w -2 of the second stage 712. The first stage 711 of the three-stage mode expander 700 has a fourth width H _w -4, which is wider than the third width H _w -3 of the first stage 71 1. The shoulder 704 of the three-stage mode expander 700 has a fourth width S _w -4, which is wider than the third width S _w -3 of the shoulder 704.

[0049] A table of dimensions of the shoulder 704 and of the ridge 708 in FIGs. 7-12 is shown below. The ranges and values below are meant to be exemplary for the three-stage mode expander 700 in FIGs. 7-32, and not meant to limit the scope of the invention. In some embodiments, ranges of dimensions belo are used to adiabatically expand an optical mode from a silicon waveguide to an optical fiber. In some embodiments, ranges below are used to adiabatically expand an optical mode from a silicon waveguide to an optical fiber in a compact distance to save room on a chip. Dimension Example Ranges (μηι) Example Values (μπι)

{00501 Referring to FIGs. 13-18, cross sections of an embodiment of a five-stage mode expander are shown. The five-stage mode expander has a shoulder 1304 and a ridge. The ridge of the five-stage mode expander has a first stage 131 1 , a second stage 1312, a third stage 1313, a fourth stage 1314, and a fifth stage 1315. FIGs. 13-18 show successive cross sections of the five-stage mode expander going from an input end 1316 of the five-stage mode expander (e.g., coupling to the waveguide 120) toward an output end 1318 of the five-stage mode expander (e.g., coupling to an optical fiber). In some embodiments, the first stage 131 1 , the second stage 1312, the third stage 1313, the fourth stage 1314, and/or the fifth stage 1315 of the five-stage mode expander are made of non-crystalline silicon.

[0051] FIG. 13 depicts a first cross section of the five-stage mode expander. The first cross section of the five-stage mode expander shows the shoulder 1304 of the five-stage mode expander. The first cross section of the five-stage mode expander is at the input end 1316. The shoulder 1304 of the five-stage mode expander in the first, cross section has a first, width,

SHR _W -1 , and a thickness, SHR _t . In some embodiments, the input end 1316 is coupled to the waveguide 120. In some embodiments, the first width 8HR _W -1 of the shoulder 1304, and the thickness SHR _t of the shoulder 1304, are equal to the width of the waveguide 120 and the thickness of the waveguide 120, respectively. In some embodiments, the shoulder 1304 is an extension of the waveguide 120. In some embodiments, the waveguide 120 is in a device layer of a silicon-on-insulator (SOI) wafer. In some embodiments, the five-stage mode expander further comprises a substrate and/or cladding material. In some embodiments, the shoulder 1304 is made of crystalline silicon to reduce a manufacturing step (e.g., to not have to replace some crystalline silicon with non-crystalline silicon). In some embodiments, the shoulder 5304 is made of noncrystalline silicon so a mode of an optical beam extends more into the shoulder 1304 of the five- stage mode expander.

[0052] FIG . 14 depicts a second cross section of the five-stage mode expander. The second cross section shows a starting of the first stage 135 5 of the five-stage mode expander. The first stage 131 1 of the five-stage mode expander has a first width, A _w -5 , and a thickness, A _t . The first stage 131 1 is disposed on top of the shoulder 1304,

[0053] FIG . 15 depicts a third cross section of the fi ve-stage mode expander. The third cross section shows a starting of the second stage 5352 of the five-stage mode expander. The second stage 1312 of the five-stage mode expander has a first width, B _w -1, and a thickness, B _t . The first stage 131 1 of the five-stage mode expander has a second width A _w -2, which is wider than the first width A _w -1 of the first stage 1311 , The shoulder 1304 of the five-stage mode expander has a second width SHR _w -2, which is wider than the first width SHR _W -1 of the shoulder 1304.

[0054] FIG. 16 depicts a fourth cross section of the five-stage mode expander. The fourth cross section shows a starting of the third stage 1313 of the five-stage mode expander. The third stage 1313 of the five-stage mode expander has a first width, C _w -1, and a thickness, Q. The second stage 1312 of the five-stage mode expander has a second width, B _w -2, which is wider than the first width B _w -1 of the second stage 1312. The first stage 131 1 of the five-stage mode expander has a third width A _w -3, which is wider than the second width A _w -2 of the first stage 1311. The shoulder 1304 of the five-stage mode expander has a third width SHR _w -3, which is wider than the second width SHR _w -2 of the shoulder 1304.

[0055] FIG. 17 depicts a fifth cross section of the five-stage mode expander. The fifth cross section shows a starting of the fourth stage 1314 of the five-stage mode expander. The fourth stage 1314 of the five-stage mode expander has a first width, D _w -i, and a thickness, D _t . The third stage 1313 of the five-stage mode expander has a second width, Cw-2, which is wider than the first, width C _w -1 of the third stage 1313. The second stage 1312 of the five-stage mode expander has a third width, B _w -3, which is wider than the second width B _w ~2 of the second stage 1312. The first, stage 1311 of the five-stage mode expander has a fourth width A _w -4, which is wider than the third wid th A _w -3 of the first stage 131 1. The sho ulder 1304 of the five-stage m ode expander has a fourth width SHR _w -4, which is wider than the third width SHR _w -3 of the shoulder 1304.

[0056] FIG. 1 8 depicts a sixth cross section of the five-stage mode expander. The sixth cross section shows a starting of the fifth stage 1315 of the mode expander. The fifth stage 1315 of the five-stage mode expander has a first width, E _w -1, and a thickness, E _t , The fourth stage 5314 of the five-stage mode expander has a second width, D _w -2, which is wider than the first width D _w -1 of the fourth stage 1314, The third stage 1313 of the five-stage mode expander has a third width, C _w -3, which is wider than the second w idth C _w -2 of the third stage 1313. The second stage 1312 of the five-stage mode expander has a fourth width, B _w ~4, which is wider than the third width B _w -3 of the second stage 1312. The first stage 131 1 of the five-stage mode expander has a fifth width A _w -5, which is wider than the fourth width A _w -4 of the first stage 131 1 . The shoulder 1304 of the five-stage mode expander has a fifth width SHR _w -5, which is wider than the fourth width SHRw-4 of the shoulder 1304.

(00571 in some embodiments, S _w -1 < S _w -2 < S _w -3 < S _w -4 < Sw-5; A _w -1 < A _w -2 < A _w -3 < A _w -4 < A _w -5; B _w -1 < B _w -2 < B _w -3 < B _w -4; Cw-1 < C _w -2 < C _w -3; and D _w -1 < D _w -2. In some embodiments A, < B _t < Q < D _t < E _t , and/or A _w > B _w > C _w > D _w > E _w , In some embodiments, thicknesses of stages is constrained: if the thickness of a stage is too great, the mode doesn't adiabatically diverge vertically. If the thickness of the stage is too small it adds potentially unneeded steps to manufacturing. As the mode gets larger, thicker stages are tolerated. That is one reason why some embodiments have A _t < B _t < Q < D _t < E _t . Additionally, in some embodiments, a narrow tip width is desired (tip width being a most narrow portion of a stage), and the tip width of a stage is limited by manufacturing capabilities. Similarly, in the three-stage mode expander 700, in some embodiments, H _t < I _t < J, and/or H _w > I _w > J _w ; and for mode expanders having more or less than three or five stages, widths of upper stages (stages farther from a shoulder) are thicker and/or narrower than lower stages (stages closer to a shoulder).

[0058] A table of dimensions of the shoulder 1304 and ridge in FIGs. 13-18 is shown below. The ranges and values below are meant to be exemplary for the five-stage mode expander in FIGs. 13-1 8, and not meant, to limit the scope of the invention. In some embodiments, ranges below are used to adiabatically expand an optical mode from a silicon waveguide to an optical fiber (e.g., UFfNAl fiber from. Nufern). In some embodiments, the first stage 131 1 and the second stage 1312 have thicknesses are +/- 100 nm. In some embodiments, thickness of the third stage 1313, the fourth stage 1314, and the fifth stage 1315 (if present) vary by +/- 200nm. In some embodiments, other tolerances are within 100 nm.

Dimension Example Ranges (μηι) Example Values (μηι)

SHRw5 0.1-12; 10-15 11, 13, 15

At 0.2-10; 0.2-1.2 0.5,0.6,0.8, 1.0

Aw-1 0.1-10; 0.4-1.2 0.6,0.8, 1

A _w -2 0.1-10; 1-4 2.5, 3, 3.5, 4

A _w -3 0.1-10; 3-9 3.5, 4.0, 4.5

A _w -4 0.1-11; 5-11 6,7,8

Aw-5 0.1-12; 6-13 10, 11, 13

B _t 0.2-10; 0.5-1.4 0.8, 1.2, 1.3, 5.4

B _w -1 0.1-10; 0.4-0.8 0.5, 0.6, 0.7

Bw-2 0.1-10; 2-6 3.0,3.5,4

B _w -3 0.1-10; 2-8 5,6,7

Bw-4 0.1-10; 6-13 9, 11, 12

c _t 0.2-10; 1-4 1,2,3

Cw-1 0.1-10; 0.6-1.5 0.8, 1.0, 1.2, 1.4

0.1-10; 4-6 4,5, 5, 5.5

C _w -3 0.1-12; 8-12 8, 10, 11

D _t 0.2-10; 1-5 2, 3, 4

D _w -1 0.1-10; 1-2 1, 1.5,2

Dw-2 0.1-11; 5-11 6, 7, 8.5

E _t 0.2-10; 2-7 4, 5, 6

Ew-1 0.1-10; 1.5-3 1.5,2,2.5,3

(0059| Referring next to FIGs.19-28, simplified sketches of the five-stage mode expander during fabrication of the five-stage mode expander are shown. Similar techniques are used to manufacture the single-stage mode expander 100, the three-stage mode expander 700, and mode expanders having different number of stages. In FIG. 19, a waveguide 120 made of crystalline silicon is sandwiched between a substrate 1908 and a first cladding layer 1904. The substrate 1908 comprises a buried-oxide (BOX) layer 1912 and a handle layer 1916. The waveguide 120 is made by processing a device layer of a silicon-on-insuiator (SOI) wafer, wherein the BOX layer 1912 and the handle layer 1916 are part of the SOI wafer. The BOX layer 1912 is made of Si02, and the handle layer is made of crystalline silicon. In some embodiments, the BOX layer 1912 acts as a lower cladding layer to the waveguide 120 and/or shoulder 1304. The direction of beam propagation 124, from left to right, is also shown. As mentioned previously, the direction of beam propagation 124 is defined to facilitate explanation. A person of skill in the art will recognize that mode expanders, such as the five-stage mode expander, can be used in a reverse direction of the beam propagation 124 (e.g., to couple light from an optical fiber to a silicon waveguide).

[0060] In some embodiments, the first cladding layer 1904 is made of Si02. The first cladding layer 1904 is polished (e.g., using chemical-mechanical planarization (CMP)) to a thickness equal to the thickness A _t of the first, stage 1311 of the five-stage mode expander. The shoulder 1304 of the five-stage mode expander is also shown, contiguous with the waveguide 120. In some embodiments, shoulder 1304 is formed while forming the waveguide 120.

[0061] In FIG. 20, a first photoresist 2004 is placed in a first pattern on top of the first cladding layer 1904. The first pattern covers part of the first cladding layer 1904, but leaves part of the first, cladding layer 1904 exposed. The first, pattern is used to form the first stage 1311, so the first pattern will be similar to a top view of the first stage 135 5. As mentioned previously, stages can have a linear taper (e.g., similar to an isosceles triangle), a funnel-shape taper, and/or an exponential-shaped taper. In some embodiments, photolithography methods are used in placing photoresist layers (e.g., preparing the cladding layer; applying the photoresist; aligning a mask; exposing photoresist to UY light; and removing photoresist exposed to the UV light).

[0062] In FIG. 21 , a portion of the first cladding layer 1904 has been etched to form a first recess 2504 in the first cladding layer 1904. Walls 2108 of the first cladding layer 1904 form walls of the first recess 2104. A top surface of the shoulder 1304 forms a bottom surface of the first recess 2104. The first recess 2104 has an outline in the shape of the first pattern. In some embodiments, a highly selective etch is used so that etching through Si02 of the first cladding layer 1904 happens more quickly than etching the shoulder 1304. In FIG. 22, the first photoresist 2004 is removed.

[0063] in FIG. 23, the first recess 2104 is filled with non-crystalline silicon 2304, e.g., a-Si. In some embodiments, the first cladding layer 1904 is also, partially or fully, covered with noncrystalline silicon 2304 to ensure the first recess 2104 is completely filled.

[0064] In FIG. 24, a-Si is converted into poly-Si (e.g., by heating), and excess poly-Si is removed (e.g., using CMP) so that the poly-Si has a thickness equal to the first cladding layer 1904. In some embodiments, a highly selective CMP process is used that polishes the poly-Si more aggressively than Si02 of the first cladding layer 1904, Polishing the poly-Si finishes the first stage 1311 of the five-stage mode expander.

[0065] Successive stages are created by applying a cladding layer, opening a recess in the cladding layer, filling the opened recess in the cladding layer with non-crystalline-silicon, and polishing the non-crystailine-silicon to a height of the cladding layer. Thus a mode expander can be created that has a finial height greater than a height of a device layer of an SOI wafer. In some embodiments, the number of stages made is a tradeoff between performance and

manufacturability. Thus widths of stages are controlled by photolithography, and thickness controlled by deposition, high-selectivity etching, and CMP. Thus, in some embodiments, this process provides a way to manufacture a mode expander precisely with favorable manufacturing tolerances (e.g., as compared to simply etching a mode expander from crystalline silicon).

[0066] To further illustrate successive stages being formed, FIGs. 25-29, provide illustrations of forming the second stage 1312 of the five-stage mode expander. In FIG. 25, a second cladding layer 2504 is deposited on top of the first cladding layer 1904 and on top of the first stage 131 1 of the five-stage mode expander. The second cladding layer 2504 is polished to the thickness B _t of the second stage 1312 of the fi ve-stage mode expander. FIG. 25 represents a start in making the second stage 1312 of the five-stage mode expander.

[0067] In FIG. 26, a second photoresist 2602 is placed in a second pattern on top of the second cladding layer 2504. The second pattern covers part of the second cladding layer 2504, but, leaves part of the second cladding layer 2504 exposed. The second pattern is used to form the second stage 1312 of the five-stage mode expander, so the second pattern will he similar to a top view as the second stage 1312.

[0068| A portion of the second cladding layer 2504 has been etched to form a second recess 2604 in the second cladding layer 2504. Walls 2608 of the second cladding layer 2504 form walls of the second recess 2604. A top surface of the first stage 1311 forms a bottom surface of the second recess 2604. The second recess 2604 has an outline in the shape of the second pattern.

[0069| in FIG. 27, the second photoresist 2602 is removed and the second recess 2604 is filled with no - crystalline silicon 2304, e.g., a-Si. In some embodiments, the second cladding layer 2504 is also covered with non-crystalline silicon 2304 to ensure the second recess 2604 is completely filled.

(0070| In FIG. 28, a-Si is converted into poly-Si, and excess poly-Si is removed so that the poly-Si has a thickness equal to the first cladding layer 1904. In some embodiments, a highly selective CMP process is used that polishes the poly-Si more aggressively than Si02 of the second cladding layer 2504. Polishing the poly-Si finishes the second stage 1312 of the five-stage mode expander. Similar steps are performed to form all five stages of the five-stage mode expander.

[0071] Referring to FIG, 29, a flowchart of an embodiment of a process 2900 for

manufacturing a mode expander is shown. In step 2904 a cladding layer is deposited (e.g., Si02 as cladding for a waveguide). The cladding layer is polished to a predetermined height (e.g., using CMP), step 2908, In some embodiments, the predetermined height is a height of a stage of the mode expander. Polishing the cladding layer creates a fiat surface. In step 2912, photoresist is placed on the flat surface. In some embodiments, before photoresist is placed on the flat surface, a thin layer of silicon nitride (S1 ₃ N ₄ ) is placed on the fiat surface (e.g., the thin layer of silicon nitride being 50, 75, 100, 125, 150, or 200 nm thick). The thin layer of silicon nitride is used as a stop layer for CMP polishing instead of Si02, as discussed in step 2932. In step 2916, a recess is etched in the cladding layer.

[0072] In step 2920, photoresist is removed. In step 2924, the recess is filled with a-Si. In some embodiments, the recess and the cladding layer are blanketed with a-Si. In some embodiments, only a portion of the cladding layer is blanketed with a-Si when filling in the recess. In step 2928, the a-Si is optionally converted to poly-Si (e.g., by heat). In some embodiments, the a-Si is not converted into polysilicon. For example, at 1330 and 1550 nm wavelengths, light has less attenuation in a-Si than polysilicon. Thus lower-temperature processes (e.g., lower than 400, 500, and/or 600 degrees C) are used so that not as much a-Si converts into polysilicon. In step 2932, a highly selective CMP polish is used to remove extra poly-Si so that the polysilicon does not exceed the predetermined height (e.g., using the cladding layer or S13N4 as a. stop layer for the highly-selective CMP polish),

[0073] In step 2936, a decision is made whether or not to add another stage. If the answer is yes, then the process returns to step 2904. If the answer is no, then the process proceeds to step 2938. In Step 2938, an optional final cladding layer is applied. In some embodiments, a final cladding layer is applied to better confine a mode in the mode expander. In some embodiments, the final cladding layer covers the shoulder and/or the ridge. In step 2940, the process ends.

[0074] In some embodiments, a mode expander is designed to reduce coupling loss when end coupling a beam into an optical fiber (e.g., butt coupling). In FIG. 30, a graph shows simulated loss due to misalignment between single-stage mode expander 100 (e.g., FIGs. 1 and 4) and the optical fiber in FIG. 5. An x-axis shows misalignment, measured in microns (misalignment measures an offset of the center of the single-stage mode expander 100 to a center of the optical fiber in FIG. 5). A y-axis shows loss measured in decibels. The graph in FIG. 30 shows a loss less than 1 dB for a 0.5 μηι misalignment; a loss between 2 and 3 dB for a 1 μηι misalignment; a loss between 5 and 6 dB for a 1.5 μηι misalignment; and a loss between 10 and 11 dB for a 2.0 μηι misalignment.

[0075] FIG, 31 depicts an optical mode in a first three-stage mode expander 700-1. The first three-stage mode expander 700-1 comprises the shoulder 704 and the ridge 708 (which includes the first stage 71 5 , the second stage 712, and the third stage 713). The shoulder 704 of the first three-stage mode expander 700-1 is made of crystalline silicon. The ridge 708 is made of non-crystalline silicon.

[0076] FIG, 32 depicts an optical mode in a second three-stage mode expander 700-2. The second three-stage mode expander 700-2 comprises the shoulder 704 and the ridge 708 (which includes the first stage 71 1 , the second stage 712, and the third stage 733). The shoulder 704 of the second three-stage mode expander 700-2 is made of non-crystalline silicon. The ridge 708 of the second three-stage mode expander 700-2 is made of non-crystalline silicon.

{0077] Non-crystalline silicon can have a refractive index higher, perhaps slightly, than crystalline silicon. The difference between an index of refraction of non-crystalline silicon and crystalline silicon, in some embodiments, is caused during processing of a mode expander (e.g., heating a-Si and/or chemicals used). A difference of index of refraction can vary from

fabrication unit to fabrication unit (e.g., using different temperatures and/or chemicals). Having differences in the indices of refraction between the shoulder 704 and the ridge 708 results in an optical mode being more tightly confined to the ridge 708, as seen in comparing the optical mode in the first three-stage mode expander 700-1 in FIG. 31 to the optical mode in the second three stage mode expander 700-2 in FIG, 32. Put another way, due to the higher refractive index of a-Si, a-Si placed on top of crystalline Si produces a confined mode in the a-Si and results in a smaller optical mode than would result if the shoulder 704 and the ridge 708 had identical indices of refraction. In some embodiments, a smaller optical mode limits coupling efficiency. Thus, in some embodiments, some or all of a crystalline-silicon shoulder and/or waveguide 120 is replaced with non-crystalline silicon before forming a ridge (e.g., to preserve a larger mode). Therefore, in some embodiments, a mode expander has a shoulder and a ridge of the same material.

[0078] Referring to FIG. 33, a plot of calculated mode divergence of the three-stage mode expander 700 at the output end 718 is shown. The calculated mode divergence is about 14 degrees horizontal, full- width, half-max (FWHM); and about 16 degrees Vertical FWHM. A beam having a wavelength of 1310 nm has a beam width (horizontal) of about 4.6 μηι and a beam height (vertical) of about 4.0 μηι. A beam having a wavelength of 1550 nm has a beam width (horizontal) of about 4.6 μηι and a beam height (vertical) of about 4.0 μηι.

[0079] Losses coupling to an optical fiber are estimated to be less than 1 .8 dB (Taper < 0.1 dB, Misalignment (0.5 μηι) < 0.5 dB, splicing < 0.2 dB, a-Si (20 dB/cm) < 0,6 dB, epoxy gap (5 μηι) < 0.4 dB).

{0080| Referring to FIG, 34, a side view of an embodiment of a device layer 3404 disposed on a substrate 3408 is shown. The substrate 3408 comprises a BOX layer 3412 and a handle layer 3416. The device layer 3404 and the handle layer 3416 are made of crystalline silicon. The device layer 3404, BOX layer 3412, and the handle layer 3416 are part of an SOI wafer. In some embodiments, the device layer has a thickness (vertical) of 1.5 μηι. A CMP stop 3420 is disposed on the device layer 3404. An example of a CMP stop 3420 is silicon nitride. The direction of beam propagation 124, from left to right is also shown.

[0081] Part of the device layer 3404 has been removed (e.g., etched) to form a recess 3424 in the device layer 3404. The part of the device layer 3404 removed to form the recess 3424 has been performed to make a non-crystalline shoulder for a. mode expander,

[0082] FIG. 35 is a top view of FIG. 34. In some embodiments, a width 3504 of recess 3424 is greater than a shoulder width. A width of non-crystalline silicon can be reduced to a proper width later by etching.

[00831 FIG. 36 is a side view of an embodiment of a device with a non-crystalline shoulder 3604. The non-crystalline shoulder 3604 is formed by filling recess 3424 with non-crystalline silicon (e.g., a-Si). FIG. 37 is a top view of FIG. 36. Excess non-crystalline silicon is removed by CMP. In some embodiments, non-crystalline shoulder 3604 is over etched so the

non-crystalline shoulder 3604 has a height lower than the CMP stop 3420. An interface 3608 is formed between the non-crystalline shoulder 3604 and the device layer 3404.

[0084] In FIGs. 38 and 39, the CMP stop 3420 is removed (e.g., by etching) and additional portions of the device layer 3404 are etched (e.g., to the BOX layer 3412) to form a waveguide 120 in the device layer 3404 and/or in the non-crystalline shoulder 3604. Edges of the non-crystalline shoulder 3604 are also formed by etching.

[0085] Light travels from the waveguide 120, through the interface 3608, and into the non-crystalline shoulder 3604. An optical path 3804 is shown by a dashed line. The interface 3608 is angled (e.g., not orthogonal to the optical path 3804) with respect to the optical path 3804 to reduce reflections in the waveguide 120 (e.g., back along the optical path 3804). But, in some embodiments, the interface 3608 is perpendicular to the optical path 3804.

[0086] FIG, 40 shows a top view of an embodiment of the second three-stage mode expander 700-2, after additional stages are added to the non-crystalline shoulder 3604. {0087] Referring to FIGs. 41-43, an embodiment of a single-stage mode expander 100 having an non-crystalline silicon shoulder is shown. FIGs. 41 -43 are similar to FIGs. 1-3, except the shoulder 104 is made of non-crystalline silicon (e.g., a-Si or poly-Si) instead of crystalline- silicon as the shoulder 104 in F Gs. 2-3.

{0088] Referring next to FIG, 44, an embodiment of a process 4400 of forming a mode expander with a non-crystalline silicon shoulder is shown. Process 4400 begins in step 4404 where a substrate is provided having a device layer made of crystalline-semiconductor material (e.g., crystalline silicon). A portion of the device layer is removed and replaced with noncrystalline, semiconductor material, step 4408. The non-crystalline, semiconductor material is not lattice matched to the device layer. A waveguide is formed in the device layer and in the non-crystalline, semiconductor material, step 4412. In step 4416, process 4400 proceeds to step 2904 of FIG. 29.

{0089] The specific details of particular embodiments may be combined in any suitable manner without departing from the spirit and scope of embodiments of the invention. However, other embodiments of the invention may be directed to specific embodiments relating to each individual aspect, or specific combinations of these individual aspects.

{0090] The above description of exemplary embodiments of the invention has been presented for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form described, and many modifications and variations are possible in light of the teaching above. For example, many of the dimensions are based on a laser wavelength of 1310 ran propagating through a mode expander. Different dimensions can be used for different wavelengths of light. For example, if a width of 5 microns is used for 1310 nm light, a width of 5.5 microns may be used for 1550 nm light. In some embodiments, a length of a stage remains constant for different wavelengths while widths and/or thicknesses change. Different dimensions can also be used when coupling to different off-chip devices, such as different types of optical fibers with different mode sizes and/or numerical apertures. Further, all or part of a mode expander may be encapsulated in Si()2 and/or other cladding material.

{0091] Additionally, though the examples given above couple an optical mode of a silicon waveguide to an optical fiber, other features could be fabricated using similar methods as those disclosed. For example, a mode expander could be used to couple one silicon waveguide to a second, larger silicon waveguide. In another example, a first waveguide at a first height is coupled to a second waveguide at a second height (non-crystalline silicon stages being used to move a mode vertically over a horizontal distance in addition to, or instead of being used to expand or contract a size of the mode). Thus waveguides can be made to guide a beam in three dimensions. Multiple waveguides can be layered, vertically, on one chip and combined with one another. In another example, a mode expander couples a silicon waveguide to discrete optics instead of an optical fiber.

[0092] FIG. 45 depicts a side view of an example of an multistage coupler 4500 used to optically couple a first waveguide 4504-1 at a first height with a second waveguide 4504-2 at a second height. In some embodiments, both of the waveguides 4504 are semiconductor waveguides. In some embodiments, both of the waveguides 4504 are made of crystalline silicon. The multistage coupler 4500 comprises a first, stage 4508-1, a second stage 4508-2, and a third stage 4508-3. Though, in some embodiments, fewer or more stages 4508 than three are used. The first stage 4508-1 is optically coupled to the first waveguide 4504-1 . The second stage 4508-2 is on top of the first stage 4508-1. The third stage 4508-3 is on top of the second stage 4508-2. The third stage 4508-1 is optically coupled to the second waveguide 4504-2. The second waveguide 4504-2 is higher (vertically, e.g., farther from a substrate) than the first waveguide 4504-1.

[0093] An optical beam propagates from the first waveguide 4504-1 , to the first stage 4508-1 and into the second stage 4508-2. The optical beam is guided into the second stage 4508-2, in part, because the first stage 4508-1 tapers (narrows) as the first stage 4508-1 extends away from the first waveguide 4504-1 . The second stage 4508-2 has a first taper (expanding) in a direction away from the first waveguide 4504-1 , which also assists in guiding the optical beam from the first stage 4508-1 into the second stage 4508-2,

[0094] The stages 4508 of the multistage coupler 4500 are manufactured similar to stages in mode expanders (e.g., using process 2900 in FIG. 29 and/or process 4400 in FIG. 44).

[0095] The optical beam is guided from the second stage 4508-2 and into the third stage 4508- 3 because of an expanding taper in the third stage 4508-3 and/or a narrowing taper in the second stage 4508-2. The optical beam is coupled from the third stage 4508-3 into the second waveguide 4504-2. [0096| FIG. 46 depicts a top view of the first waveguide 4504- 1 and the first stage 4508- 1. The first waveguide 4504-1 is optically coupled to the first stage 4508-1 (e.g., using an angled interface 4604). In some embodiments, the first stage 4508-1 is formed by removing a portion of the first waveguide 4504-1 (or device-layer material), similar to forming a non-crystalline silicon shoulder of a mode expander. In some embodiments, the first stage 4508-1 is not used and the second stage 4508-2 is disposed on top of the first waveguide 4504-1; light is guided into the second stage 4508-2 from the first waveguide 4504-1 because of a difference in index of refraction (e.g., similar to FIG. 31 of a mode expander having a crystalline shoulder).

[0097] FIG, 47 depicts a top view of the second stage 4508-2. The second stage 4508-2 comprises a first taper 4704-1 and a second taper 4704-2. The first taper 4704-1 expands going from the first waveguide 4504-1 toward the second waveguide 4504-2. The second taper 4704-2 narrows going from the first waveguide 4504-1 toward the second waveguide 4504-2.

[0098] FIG, 48 depicts a top view of the third stage 4508-3 and the second waveguide 4504-2. The third stage 4508-3 is optically coupled to the second waveguide 4504-2.

[0099] In some embodiments, a multistage coupler (e.g., multistage coupler 4500) for coupling a first waveguide 4504-1 with a second waveguide 4504-2 comprises a first stage 4508-1, a second stage 4508-2, and a third stage 4508-3, wherein the first stage 4508-1 is coupled with a first waveguide 4504-1; the second stage 4508-2 is, at least partially, on top of the first stage 4508-1 (e.g., farther from a substrate than the first stage 4508-1); the third stage 4508-3 is, at least partially, on top of the second stage 4508-2; the third stage 4508-3 is optically coupled to the second waveguide 4504-2; and the first stage 4508-1 , the second stage 4508-2, and the third stage 4508-3 are configured to guide an optical beam, (e.g., adiabatically and/or vertically) from the first waveguide 4504-1 to the second waveguide 4504-2. In some embodiments, the multistage coupler 4500 guides the optical beam horizontally as well as vertically.

[0100] In some embodiments, the first waveguide 4504-1 is made of silicon and the second waveguide 4504-2 is made of a different material, such as a III-V compound or II- VI compound (e.g., InP, GaAs). In some embodiments, the different material and the first waveguide 4504-1 are integrated on a silicon chip. For example, a III-V chip is secured on a silicon substrate as described in U.S. Patent Application No. 14/509,914, filed on October 8, 2014. {01011 The embodiments were chosen and described in order to explain the principles of the invention and its practical applications to thereby enable others skilled in the art to utilize the invention in various embodiments and with various modifications as are suited to the particular use contemplated.

{0102] Also, it is noted that the embodiments may be described as a process which is depicted as a flowchart, a flow diagram, a data flow diagram, a. structure diagram, or a block diagram. Although a flowchart may describe the operations as a sequential process, many of the operations can be performed in parallel or concurrently. In addition, the order of the operations may be re-arranged. A process is terminated when its operations are completed, but could have additional steps not included in the figure, A process may correspond to a. method, a function, a. procedure, a subroutine, a subprogram, etc,

[0103] A recitation of "a", "an", or "the" is intended to mean "one or more" unless specifically indicated to the contrary.

[0104] All patents, patent applications, publications, and descriptions mentioned here are incorporated by reference in their entirety for all purposes. None is admitted to be prior art.