SHARP ADIABATIC BENDS IN LOW-CONFINEMENT STRUCTURES

In part, the disclosure relates to a photonic device that may include a curved waveguide that includes a plurality of layers; a curved elongate structure defining an upper surface, an inner elongate surface, and an outer elongate surface, the curved elongate structure comprising a first end, and a second end; and a ridge extending from the upper surface, the ridge having a first side and a second side; and a trench defined by one or more of the plurality of layers and the first side; the curved elongate structure defines a first elongate section and a second elongate section, wherein a first cross-section of the ridge has a first shape that substantially extends along the first elongate section of the structure, the first shape is defined by the first side and a step extending from the first side and above the bottom of the trench.

FIELD

This disclosure relates generally to the field of integrated photonics.

BACKGROUND

Contemporary optical communications and other photonic systems make extensive use of photonic integrated circuits that are advantageously mass-produced in various configurations for various purposes.

SUMMARY

In part, in one aspect, the disclosure relates to an efficient bending of waveguides in photonic integrated circuits. In one aspect, the disclosure relates to a particular shape of a bend in a waveguide such that the waveguide curvature transitions adiabatically from a value near zero, corresponding to a substantially straight waveguide, to a substantially constant, finite value encompassing a majority of the bend, and then back to a near-zero curvature as the waveguide completes the bend and returns to a substantially straight path. In part, in one aspect, the disclosure also relates to a microfabricated structure that enhances optical confinement in a waveguide bend. In various embodiments, the waveguide is a multi-layer device. In some embodiments, one of the foregoing layers is a confinement layer. In many embodiments, the confinement layer comprises one or more quantum well structures that prevent vertical leakage of an optical mode into a substrate. More specifically, the disclosure relates to a particular placement of a deep etch near to a waveguide bend such that the deep etch partially overlaps the waveguide bend and induces a net reduction in optical losses through the bend as compared to similar structures wherein a trench is formed adjacent to but not overlapping a waveguide such as by etching one or more layers of a PIC or other layers. In various embodiments, a deep etch refers to an etch having a depth that ranges from about 1 μm to about 10 μm or from about 2 μm to about 5 μm or between about 3 μm to about 4 μm. In part, the disclosure relates to a photonic device. The device may include a curved waveguide that includes a plurality of layers; a curved elongate structure defining an upper surface, an inner elongate surface, and an outer elongate surface, the curved elongate structure comprising a first end, and a second end, the first end in optical communication with the second end; and a ridge extending from the upper surface, the ridge having a first side and a second side; and a trench defined by one or more of the plurality of layers and the first side; wherein the curved elongate structure defines a first elongate section and a second elongate section, wherein a first cross-section of the ridge has a first shape that substantially extends along the first elongate section of the structure, wherein the first shape is defined by the first side and a step extending from the first side and above the bottom of the trench. In some embodiments, the trench follows the first side and bends therewith. In various embodiments, a second elongate section comprises a curvature transition section wherein curvature changes in the curvature transition section are non-linear in curvature space. In some embodiments, at a normalized position of 50 to 75% along the optical path of the curvature transition section, the curvature is reduced by about 10% to about 60% of a linear curvature in curvature space.

In various embodiments, the curvature transition section transitions to a section of constant curvature in the first elongate section, wherein the first elongate section defines a bend. In some embodiments, a curvature of the bend ranges from about 1 mm−1to about 100 mm−1or from about 5 mm−1to about 20 mm−1. In various embodiments, one or more of the plurality of layers comprise a compound semiconductor. In some embodiments, the curved waveguide further comprises a confinement layer disposed below the ridge, the confinement layer comprising a plurality of quantum wells. In various embodiments, the confinement layer is configure to not absorb propagating light in response to being in one or more pumped states.

In some embodiments, the device may further include a third elongate section, wherein the waveguide defines a bend in the first elongate section, wherein the first elongate section has a constant radius of curvature, wherein the second elongate section comprises a non-linear curvature transition, wherein the trench approaches the waveguide in the third elongate section. In various embodiments, the ridge has a ridge width, wherein a percent increase in a normalized ridge width changes in response to a normalized position along the third elongate structure is selected such that when the normalized position is about 20%, the normalized ridge width ranges from about 30% to about 50%; and when the normalized position is about 80%, the normalized ridge width ranges from about 65% to about 85%.

In some embodiments, the ridge has a ridge width, wherein the ridge width increases in an amount that ranges from about 0 to about 1 μm or about 0.25 μm to about 0.5 μm over a transition distance. In various embodiments, a length over which the curved waveguide exhibits a taper in width is between about 50 to about 500 μm or between about 100 to about 250 μm or about 150 μm. In some embodiments, a starting gap between the trench and the ridge ranges from about 1 μm to about 10 μm, or from about 3 μm to about 5 μm, or is about 4 μm. In various embodiments, the gap between the trench and the ridge has been reduced by 50 to 70% from the starting gap at a normalized position of 20% along the third elongate section. In various embodiments, the trench comprises the bottom, an outer trench wall and an inner trench wall, wherein the inner trench wall is defined by the step that extends upwards from the bottom and then towards the waveguide before continuing upwards to end along the first side of the ridge. In some embodiments, the step has a width that ranges from about 0.1 to about 1 μm.

In various embodiments, the waveguide is configured to propagate light having a wavelength that ranges from about 1250 nm to about 1650 nm. In some embodiments, the device may further include one or more optical amplifier devices in optical communication with the first end or the second end. In part, the disclosure relates to a method for curving light in an integrated photonic structure. The method may include providing a curved waveguide comprising a plurality of layers; a curved elongate structure defining an upper surface, an inner elongate surface, and an outer elongate surface, the curved elongate structure comprising a first end, and a second end, the first end in optical communication with the second end; and a ridge extending from the upper surface, the ridge having a first side and a second side; a trench defined by one or more of the plurality of layers and the first side; and a confinement layer disposed below the ridge, the confinement layer comprising a plurality of quantum wells; wherein the curved elongate structure defines a first elongate section and a second elongate section, wherein a first cross-section of the ridge has a first shape that substantially extends along the first elongate section of the structure, wherein the first shape is defined by the first side and a step extending from the first side and above the bottom of the trench; propagating light of a wavelength between 1250 and 1650 nm in the ridge; and applying an electrical signal to pump the plurality of quantum wells through an electrode disposed on ridge to pump one or more quantum wells.

Although, the disclosure relates to different aspects and embodiments, it is understood that the different aspects and embodiments disclosed herein can be integrated, combined, or used together as a combination system, or in part, as separate components, devices, and systems, as appropriate. Thus, each embodiment disclosed herein can be incorporated in each of the aspects to varying degrees as appropriate for a given implementation. Further, the various apparatus, optical elements, passivation coatings/layers, optical paths, waveguides, splitters, couplers, combiners, electro-optical devices, confinement layers, ridges, quantum wells, dielectrics, inputs, outputs, ports, adiabatic bends, trenches, channels, components and parts of the foregoing disclosed herein can be used with any laser, laser-based communication system, waveguide, fiber, transmitter, transceiver, receiver, and other devices and systems without limitation.

DETAILED DESCRIPTION

Applicant has realized that curved waveguides may introduce losses, and that typical approaches to mitigating these losses, namely the use deep etches near the waveguide bend, may be improved. Although counter-intuitive, placement of etches to define a curved trench that tracks the bend of the waveguide over one or more sections of the waveguide offers various advantages. In addition, optimization of the geometry, sections of the waveguide having a constant radius of curvature with other sections of the waveguide having non-linear radiuses of curvature support the construction of a waveguide having an adiabatic bend that deviates from a purely semicircular bend. In various embodiments, the etch/trench and the waveguide follow each other in various sections of the waveguide.

In part, the disclosure pertains to photonic circuits, devices, and components thereof, which involve guiding and manipulating light in structures fabricated using planar microfabrication processes. In particular, this disclosure pertains to bending integrated photonic waveguides more efficiently in various embodiments. In various embodiments, a given waveguide-based device includes a ridge waveguide that is curved and substantially symmetric with a series of segments along its length that have differing cross-sections, tapers, transitions, and curvature changes that are variable or non-linear in curvature space. In various embodiments, a given exemplary curvature is the inverse of the radius of curvature and vice versa.

In various embodiments, the disclosure relates to non-planar waveguides such as channel waveguides that are curved and disposed relative to air trenches or gaps. The air trenches or gaps may be formed by various etching-based fabrication techniques. In some embodiments, the channel waveguides are curved waveguides such as curved ridge waveguides or curved rib waveguides. In some embodiments, a ridge waveguide is surrounded by air trenches or air gaps or low-index materials to confine optical signals within a wave propagating region within the ridge. A given waveguide may be curved and have different sections or segments along its length. Some waveguides may include various bends that are defined by a bend angle that ranges from about 20 degrees to about 180 degrees. In various embodiments, different layers and region of materials may be arranged, deposited, sandwiched and etched to form a curved waveguide such as ridge waveguide or a photonic device that includes a curved waveguide such as a ridge waveguide. Suitable materials for the various layers and regions may include, without limitation, InP or GaAs containing material, AlGaInAs or InGaAsP containing material, semiconductors, metals, electrode regions, dielectrics, passivation layers or regions, and metallization layers or regions, and combinations of the foregoing. Refer now to the exemplary embodiment ofFIG.1, wherein a top-down view of a waveguide120and a deep etch or trench formed thereby130is illustrated. The waveguide is an elongate structure that may be formed by a stack of two or more layers. In various embodiments, the layers extend along and follow the curve or bend of the waveguide. The height and depth profile of a cross-section of the waveguide in various sections may changes such that the width and presence of various layers and the structures and surfaces they form changes. The waveguide120includes an optical inlet or first end102and an optical outlet or second end103, and a bend that is surrounded by and/or is tracked by a trench130formed by a deep etch. The bend may include various sections or segments such as sections/segments132,133, and134. In some embodiments, the bend may also begin earlier such as in section131.

In some embodiments, a section of the waveguide such as section125amay include the elongate structure of the waveguide120without the trench130/deep etch being present. In addition, as shown, in the subset125bof section125a, the trench130approaches, but does not reach the waveguide until a little after the midpoint of section131. A ridge or ridge wave-guide (not shown) extends from the upper surface of curved waveguide120in various embodiments. As shown in and discussed in more detail with regard toFIGS.3,4,5A, and5Band others, the shape of a given cross-section of the waveguide may change along sections131,132,133,134, and mirrored or symmetric sections on the other side of the waveguide120. In particular, the width of the ridge and the existence of a trench adjacent the ridge and the distance between the ridge and trench changes along the curved length of the waveguide in various sections. Changing the width of the ridge and removing a portion of one or more layers of the stack of layers that form the ridge occurs in one or more sections of the waveguide.

Generally, in various embodiments, the etch and the waveguide follow each other. In various embodiments, the cross-section of the waveguide relative to an axis of light propagation is variable. For example, along the length of a given curved waveguide, the cross-sectional shape along a first segment may be constant and then the cross-sectional area may change along a subsequent section of the waveguide that is continuous with the first. A waveguide120may be formed from various layers including a substrate upon which it may extend or be disposed on or part of. In various embodiments, the cross-sectional area of a slice along the second section will be less than that of the first section and may continue to decrease as a result of the etch approaching the second region of the waveguide.

For example, the cross-sectional area of the waveguide in section125aor125bwould be greater than the cross-sectional area of the waveguide in section125cor130. This follows from the etch approaching the waveguide and removing a portion of the stack of layers that form the structure of the waveguide and thus reducing its cross-sectional area and other measurable length changes. In some embodiments, the waveguide may be initially fabricated with a width wider than a final target width, in anticipation of a loss of some of the cross-sectional area of the waveguide to the deep etch. In a region131of the waveguide, the trench130begins to approach the waveguide. The curved waveguide ofFIG.1shows a 180 degree bend with light entering waveguide on one side and existing the waveguide on the other side. Various bends for the curved waveguide may be used without limitation, including, for example, bends that range from about 0 degrees to about 360 degrees.

Still referring toFIG.1, an axis A is also shown which intersects the waveguide120in a section of constant curvature133and divides or sections the waveguide bend. For example, region or section133is divided by axis A and regions or sections132and134, which have the same cross-sectional shape in various embodiments, are on either side of the A axis. A section that includes non-linear and/or adiabatic transitions in curvature132is shown as a section that extends from section of constant curvature133. Similarly, section134also exhibits a curvature transition for the structure of the waveguide. In various embodiments, the curvature transition and changes in the shape of the cross-sectional areas of the waveguide structure in sections132and134are substantially the same. In some embodiments, another section134that includes non-linear and/or adiabatic transitions in curvature extends from the other end of section133. In some embodiments, one or more of the features above may interface with or be disposed relative to a substrate. An exemplary substrate, in another embodiment, could be a Si wafer with patterned waveguides. In other embodiments, the various materials and layers disclosed herein may be used as the substrate or disposed on or near the substrate. In various embodiments, the various sections shown inFIG.1and described elsewhere herein may be referenced to as first, second, third, fourth, fifth, etc., sections with regard to how they are depicted and arranged inFIG.1. These terms may be used for selection sections and describing their structure, layers, and geometry without limitation.

As shown inFIG.1, the waveguide has an overall U-shaped geometry wherein the bend portion of the U is designed to avoid a pure semicircular bend. Other waveguide shapes with curves and bends that range over various angles are possible. In various embodiments, a straight waveguide such as one having a 180 degree bend is avoided. As shown, the bend is about 180 degrees (which results in input102and output103being oriented as shown), but other bend angles may be selected without limitation. In some embodiments, the waveguide120is symmetric about the axis A shown such that it divides a region of non-linear curvature such as region133.

In various embodiments, the lengths of the sections of the waveguide on either side of the axis A may be the same or different. In various embodiments, waveguide shapes that reduce losses compared to Euler bends and other bends such as circular or elliptical bends are used when selecting the various sections and radiuses of curvature properties for a given waveguide section. In various embodiments, a given curved waveguide embodiment includes segment or section that undergoes curvature changes that are non-linear in curvature space. This is in contrast with an Euler curve, which is linear in a curvature space. In some embodiments, a curvature space is a representation of curvature that compares relationship of curvature versus position, such as a normalized position.

To improve photon confinement within a waveguide bend, a deep etch surrounding the bend may be used to form a trench, such as an air-filled trench or air gap, at either side or both sides of the waveguide. However, placement of air trenches on both sides of the waveguide may create substantial scattering losses. In addition, placement of air trenches on both sides of the waveguide may introduce cooling issues in active waveguides. In various embodiments, a trench may be defined relative to one side of the waveguide bend, such as on the exterior of the bend that has various geometric features that vary along the length of the bend. In some embodiments, the overall length of the curved air-filled trench ranges from about 110 μm to about 2000 μm. In some embodiments, the length of the air-filled trench varies based on radius of curvature and angle of arc of the waveguide and lengths and the region where the trench overlaps with the waveguide.

To improve photon confinement within a waveguide bend, a single deep etch may be used to form a trench near the waveguide bend. The waveguide and the trench are formed in one or more layers, which may be the same or have layers in common in some embodiments. In some embodiments, the waveguide includes various layers including an upper ridge. The upper ridge may include an electrode with a contact layer. In some embodiments, the trench is etched next to the ridge and waveguide and has a step or notch that extends out from the waveguide into the bottom of the trench.

Refer now to the exemplary embodiment ofFIG.1, wherein a waveguide120is bordered by a trench130formed by a deep etch. Certain cross-sectional planes127,128,129indicate locations of cross-sectional views in other figures. The etch130is defined by various lengths, sections, regions, depths, widths and other parameters. In some embodiments, the etch is defined, in part, by an approach length131, a gradual, continuous, two sections of non-linear and/or adiabatic transitions in radius of curvature132,134and a section or arc of constant curvature133.

In some embodiments, a deep etch placed near a waveguide bend may approach the waveguide bend, i.e. the path of the etch may begin some distance away from the bend before coming nearly into contact with the bend and following approximately the same path as the bend. In this way, a trench is formed that tracks the curve of the waveguide. An etch/trench near a waveguide bend may approach the bend along a substantially linear path; however, Applicant has realized that a specific non-linear approach results in a net reduction of optical losses over a linear or circular approach. In various embodiments, the shape and length of waveguide bend are selected to result in reduced or minimized losses. In another embodiment, the etch may approach the waveguide before the waveguide is bent, and the curvature of the waveguide being adiabatically changed only after the etch approach is complete.

Refer now to the exemplary embodiment ofFIG.2wherein a deep etch approach to a waveguide bend exemplary of the disclosure is illustrated in a plot. This plot shows the curvature of the etched boundary. The approach, plotted236as a normalized distance of the etch away from the waveguide as a function of normalized position along the waveguide/light propagation path, is substantially non-linear. Typical and preferred values of etch approach are identified below as a function of normalized position along the light propagation path in the waveguide as shown in Table 1. In some embodiments, the full range may be used. In many embodiments, the preferred range is used.

A curved trench formed near a waveguide bend may be located immediately adjacent, adjacent, or positioned to otherwise track the bend of the waveguide. That is, the edge of the etched trench may be coincident with the edge of the waveguide. However, any etched trench will have uncertainty in its alignment, and an exact placement of an etch wherein the edge of the etch and the edge of a waveguide exactly coincide is difficult in practice. A trench formed by etching near a bend is often placed a distance away from the bend. Etching at a specified distance from the waveguide may accommodate average or worst-case expectations in etch alignment due to process variations, so that no part of the waveguide is etched away.

In various designs, etching into the waveguide, as part of trench formation, may introduce additional sidewall roughness in the waveguide and hence additional scattering losses. However, Applicant has realized that an etch overlapping a bend is preferable in net reduction of worst-case radiation loss when compared to an etch placed some distance away from the bend and that waveguide material lost during the etch may be compensated by widening the waveguide. This is understood when considering the inherent alignment uncertainty in planar fabrication between the placement of the ridge and the trench etch and the resulting worst-case radiation loss penalty. When accounting in design for the narrowing of the waveguide by the etch overlap, the worst-case performance penalty of the etch overlap, within the fabrication alignment uncertainty to the ridge, can be substantially smaller than the worst-case performance penalty resulting from the etch being away from the ridge in a bend, within the same etch alignment uncertainty to the ridge.

Refer now to the exemplary embodiment ofFIG.3wherein a cross-sectional view through a plane or slice327of elongate structure of waveguide near a waveguide bend is illustrated. In some embodiments, the slice327may correspond to slice127shown inFIG.1. The cross section includes a substrate311, typically including Si, InP, and/or GaAs, a confinement layer312, typically containing SiO2, AlGaInAs, and/or InGaAsP, and a ridge of a waveguide320, typically including Si, InP, and/or GaAs. In some embodiments, the confinement layer is configured to vertically confine light when the light is propagating in a horizontal direction. In some embodiments, the confinement layer includes a low refractive-index dielectric layer for a Si ridge, a high index dielectric layer for a dielectric waveguide or at least one quantum well for a compound semiconductor waveguide. An electrode may be disposed above the confinement layer to receive an electrical signal and pump the quantum wells. In some embodiments, a compound semiconductor includes a semiconductor material made of more than one element such as InP, GaAs, InGaAs, AlGaInAs, etc. and combinations thereof. In some embodiments, a dielectric material is used such as an optically transparent material with high bandgap and low carrier mobility such as SiO2, Si3N4, SiON, combinations thereof, etc., and other suitable semiconductor or optically transmissive materials.

In most embodiments of the disclosure, a waveguide includes a ridge and a confinement layer, though some amount of light extends into the substrate. Generally, a waveguide is any structure that guides the propagation of light. Generally, the ridge and the confinement layer will form the waveguide in many embodiments. The width of the ridge and its distance from the trench and/or proximity to a step in the trench varies.

In various embodiments, some light will extend into the substrate. In some embodiments, the confinement layer is configured to prevent the optical mode from leaking into the substrate. The confinement layer has a thickness313between about 10 to 300 nm and some depth314below the ridge, between about 50 to about 2000 nm. In many embodiments, the confinement layer is part of the waveguide. The ridge320of the waveguide has a height321that ranges between about 0.5 to 3 μm or between about 1 to about 2 μm, and some width322, between about 1 to 10 μm or between about 2 μm, to about 4 μm. In some embodiments, the height of the ridge ranges from about 1 μm to about 2 μm and its width ranges from about 2 μm to about 4 μm.

Refer now to the exemplary embodiment ofFIG.4wherein a cross-sectional view through a plane or slice428near a waveguide bend, as the trench or air gap430approaches the bend, is illustrated. In some embodiments, the slice428may correspond to slice128shown inFIG.1. The cross section includes a substrate411, typically InP or GaAs, a confinement layer412, typically AlGaInAs or InGaAsP, and a ridge of a waveguide420, typically InP or GaAs. The same distance ranges, parameters and materials described with regard toFIG.3and otherwise herein may also apply to waveguide410, the confinement layer412, and substrate411, although other materials and combinations of materials may be used in other embodiments. The waveguide has a ridge420that has a width422that ranges from about 1 μm to about 10 μm or from about 2 μm to about 4 μm. The trench430formed by the deep etch has a depth431, between about 1 to 10 μm or between about 2 to about 5 μm or between about 3 to about 4 μm. The trench430has a width432, that ranges from about 1 to about 200 μm or between about 2 to about 30 μm, and some offset423, that ranges from between about 0 to about 1 μm or between about 0.2 to about 0.5 μm, away from the edge of the waveguide420. As the deep etch approaches the waveguide, the offset423tends toward zero.

Referring now to the exemplary embodiment ofFIGS.5A and5Bwherein a cross-sectional view through a plane or slice529near a waveguide bend is illustrated. In some embodiments, the slice529may correspond to slice129shown inFIG.1. InFIG.5Athe trench530formed by an etching process now includes a region530A overlapping the substrate and a region530B overlapping the waveguide, reducing the waveguide width522by the offset523. This region of overlap may correspond to portions of sections125band125cofFIG.1in various embodiments. As discussed, however, the ridge waveguide width522is widened to compensate for the loss of material due to the etch in some embodiments when selecting the initial ridge width/waveguide width. In some embodiments, a step535may be formed as a result of etching the trench which is defined by regions530A and530B.

As a result, as shown inFIG.5B, in various embodiments, the side530C of the ridge waveguide522defines a portion of a trench530, such as defining a sidewall of the trench530C. In some embodiments, the said trench includes a step535that extends from a sidewall530C of the trench530. In various embodiments, the cross-section529shown inFIG.5B, is present in various sections of the waveguide structure such as sections132,133, and134ofFIG.1. InFIG.5B, the deep etch forms a trench530and has a depth531, between about 1 to about 10 μm or between about 2 to about 5 μm or between about 3 to about 4 μm, and some width532, between about 1 to 200 μm or between about 2 to 20 μm. The waveguide520has a height521, between about 0.5 to about 3 μm or between about 1 to about 2 μm.

In some embodiments, in anticipation of loss of waveguide material in an overlap of a deep etch, as part of forming a trench that follows the waveguide bend, the waveguide may be widened. This width can be selected during the initial design phase and prior to the application of an etch to form the trench. In most embodiments, the waveguide is widened/wider in a region where the waveguide is straight such as along section125aand at cross-section127, for example, inFIG.1. As an example of such widening, in the absence of material loss due to the etch, the waveguide width reaches a maximum at the edges of the bend and the width remains constant through the course of the bend. In many embodiments, in the presence of material loss in the waveguide due to the etch, the waveguide may exhibit a non-uniform width through the course of the bend. In some embodiments, the typical lithographic misalignment between the ridge and the trench definition, as will be appreciated by people of skill in the art of microfabrication, will lead to a changing amount of etched away material from the ridge around the bend and hence to a changing final width around the bend.

Refer now to the exemplary embodiment ofFIG.6wherein a percent increase in the waveguide width as a function of normalized position in the waveguide bend is plotted625. A normalized position of 100% corresponds to the end of the etch approach into the waveguide and the beginning of the waveguide bend or the waveguide curvature transition region. Typical and preferred values of the normalized waveguide increase, for various embodiments, are shown below in Table 2 as a function of normalized position along the waveguide. In various embodiments, the values below correspond to the width of the ridge referenced herein which is a ridge waveguide.

In some embodiments, power losses in a waveguide bend are sensitive to the shape of the bend. For example, some non-circular bends, i.e. bends having non-constant curvature, may exhibit lower power loss than a bend with constant curvature. Waveguide bends composed of Euler curves or waveguide bends featuring linear transitions in curvature may reduce power loss in the bend. In contrast with these approaches, which are preferably avoided in some embodiments, Applicant has realized that a non-linear transition in curvature paired with a section of constant curvature reduces power loss in the bend further still.

Refer now to the embodiment ofFIG.7Awherein a non-linear transition in curvature738exemplary of the disclosure is illustrated by way of a plot of waveguide curvature745as a function of normalized waveguide position. The axis A shown corresponds to the axis A ofFIG.1. The plot745shown inFIG.7Aillustrates a non-linear transition in curvature space that deviates from the linear transition742that would be associated with a Euler bend. A circular bend would exhibit an abrupt change, or a step change, in curvature space (not pictured). With regard toFIG.7A, the waveguide curvature is adjusted adiabatically and in a non-linear fashion from zero to a constant 1/Rminwhere Rminis the radius of curvature of the bend section with constant curvature. Similarly, continuing through the curve of the bend, the waveguide's cross-sectional profile varies from the same adiabatic and non-linear fashion from the constant 1/Rminback to zero. This curve may be mapped to the A axis inFIG.1by adding the A axis toFIG.7Ato show how the different sections (central constant radius of curvature section133and the two sections of non-linear curvature changes132,134are oriented). The waveguide begins at 0% in the normalized position axis and with zero curvature (or zero bend angle), corresponding to a straight waveguide. The normalized position refers to the relative position along the light propagation path in the bend.

Relative to a linear transition742in curvature, an adiabatic transition745is numerically optimized to provide better overall transition loss. In various embodiments, optimization routines may be selected to produce a reduction749in curvature in the third quadrant748that ranges from about 10% to about 60% of the curvature in the linear curvature case. The ridge waveguide curvature shape transition can be optimized using either eigenmode expansion with a cylindrical mode solver, 3D finite difference time domain or combinations thereof. The etch approach transition can be optimized using either eigenmode expansion or 3D finite difference time domain. These computational techniques can be combined with optimization routines such as particle swarm optimization or a kriging predictor.

In many embodiments, after a non-linear transition738in curvature, the waveguide exhibits a constant curvature, before transitioning back to a straight waveguide with the same non-linear pattern738. The length of the constant curvature section739is given by Rmin(θtotal−2θtaper) where θtotalis the desired full change in waveguide angle induced by the bend and θtaperis the change in waveguide angle induced by each curvature taper section. The absolute length of the curvature taper section738may range from about 5 μm to about 200 μm and preferably between about 10 to about 100 μm. The curvature taper angle may vary from between about 2 to about 45 degrees and preferably between about 10 to about 35 degrees. The maximum curvature 1/Rminis between about 1 to about 100 mm−1and preferably between about 5 to about 20 mm−1. In various embodiments, any change greater than 2θtaperin waveguide angle induced by the bend is acceptable.

Refer now to the embodiment ofFIG.7Bwherein a top-down view near a waveguide bend exemplary of the disclosure illustrates an etch approach to forming a trench exterior to the waveguide, a waveguide widening, and an overlap between the etch730and the ridge waveguide720in a normalized position along the waveguide. The total path length over which the waveguide720exhibits a taper in width is between about 50 to about 500 μm or between about 100 to about 250 μm or about 150 μm. At the beginning of the etch approach 737 the gap723between the etch and waveguide is between about 1 to about 10 μm or between about 3 to about 5 μm or about 4 μm. In various embodiments, near normalized position 100%, the gap723may correspond to step that remains in the trench, bounded by edge of the ridge, in part, after the deep etch forms a trench that overlaps with the ridge. For example, the gap723may correspond to step535inFIGS.5A and5Bin various embodiments. In some embodiments, the upper extent of region730may correspond to the width of the etch. Over the course of the taper, the ridge width722is increased by some value between about 0 to about 1 μm or between about 0.25 to about 0.5 μm. Note that the interior border of the waveguide is moved725to widen the waveguide while the exterior border remains straight726in the normalized-position coordinates. Referring back to the plot inFIG.6, this plot corresponds to the transition inFIG.2andFIG.7B.FIG.7Aconsiders curvature of the waveguide, there is no waveguide curvature onFIGS.2,6and7B. In some embodiments, the etch approach and waveguide width transition described inFIGS.2,6, and7Bare placed before and after the curvature transitions described inFIG.7A.

Finally, refer to the embodiment ofFIG.8wherein a summary schematic diagram is depicted that cross-references various illustrations of various curved waveguide embodiments. These waveguides may be fabricated with various materials. In some embodiments, compound semiconductor materials, etch, and fabrication techniques are used.FIG.8shows how the ridge waveguide embodiments820,820aand etch/trench830, experience cross-sectional changes including with regard to the etch approach, and waveguide widening825, and waveguide curvature transition845, and constant curvature870in the various sections of the center plot890. In some embodiments, the waveguide widens825only when the waveguide is straight, i.e. when waveguide curvature is zero. In other embodiments, the waveguide may be widened and the curvature transition may occur before the etch transition is complete. In various embodiments, as shown, the etch/trench830approach occurs outside the region of waveguide curvature as shown in cross-sections A1and A2. In cross-sections B1, B2, the trench830is defined by the ridge820aand include a step833. A1, A2, B1, and B2are also shown relative to center plot890. Specifically, the ridge820adefines a sidewall840such as an inner sidewall of the trench820a. In various, embodiments, the width of ridge820ais smaller than ridge820. In some embodiments, this distance in width corresponds to the width of step833. An exemplary confinement layer850is also shown below the ridge820,820ain the various cross-sections in the bottom portion ofFIG.8. In some embodiments the step833may be rounded, sloped or substantially roughened.

In various embodiments, the curved waveguides disclosed herein avoid an Euler bend, which involves a linear change of curvature with path resulting in triangular curvature plot with position. The proposed curved waveguides disclosed herein have lower losses when compared to an Euler bend. Further, the inclusion of an air trench on both sides of waveguide having an Euler bend also creates substantial scattering losses. Further, including air trenches on both sides of the waveguide creates cooling issues in active waveguides, which the present disclosure avoids. The present disclosure also advantageously supports the use of compound semiconductors.

Having thus described several aspects and embodiments of the technology of this application, it is to be appreciated that various alterations, modifications, and improvements will readily occur to those of ordinary skill in the art. Such alterations, modifications, and improvements are intended to be within the spirit and scope of the technology described in the application. It is, therefore, to be understood that the foregoing embodiments are presented by way of example only and that, within the scope of the appended claims and equivalents thereto, inventive embodiments may be practiced otherwise than as specifically described. In addition, any combination of two or more features, systems, articles, materials, and/or methods described herein, if such features, systems, articles, materials, and/or methods are not mutually inconsistent, is included within the scope of the present disclosure.

Where a range or list of values is provided, each intervening value between the upper and lower limits of that range or list of values is individually contemplated and is encompassed within the disclosure as if each value were specifically enumerated herein. In addition, smaller ranges between and including the upper and lower limits of a given range are contemplated and encompassed within the disclosure. The listing of exemplary values or ranges is not a disclaimer of other values or ranges between and including the upper and lower limits of a given range.

The use of headings and sections in the application is not meant to limit the disclosure; each section can apply to any aspect, embodiment, or feature of the disclosure. Only those claims which use the words “means for” are intended to be interpreted under 35 USC 112, sixth paragraph. Absent a recital of “means for” in the claims, such claims should not be construed under 35 USC 112. Limitations from the specification are not intended to be read into any claims, unless such limitations are expressly included in the claims.