# US 2025/0164692 A1 · Waveguide Implementations With Adiabatic Structures

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- Number: US 2025/0164692 A1
- Document ID: US20250164692A1
- Status: Published application
- Kind: A1
- Application number: 18/954,391
- Filed: 2024-11-20
- Published: 2025-05-22
- Earliest claimed: 2023-11-20
- Assignees: Xscape Photonics Inc.
- Applicants: Xscape Photonics Inc.
- Inventors: Asher Novick; Samira Karimelahi; Brian West
- Web page: https://patentgrep.com/patent/US20250164692A1

## CPC

- G02B 6/12007: {forming wavelength selective elements, e.g. multiplexer, demultiplexer}
- G02B 6/125: Bends, branchings or intersections
- G02B 6/1228: {Tapered waveguides, e.g. integrated spot-size transformers (for coupling with fibres G02B6/305)}
- G02B 6/126: using polarisation effects {(G02B6/1226 takes precedence)}
- G02B 6/29343: {Cascade of loop resonators}
- G02B 2006/12097: {Ridge, rib or the like}
- G02B 2006/1215: {Splitter}
- G02B 2006/12159: {Interferometer}
- G02B 2006/12164: {Multiplexing; Demultiplexing}
- G02B 2006/12195: {Tapering}
- G02B: OPTICAL ELEMENTS, SYSTEMS OR APPARATUS

## Abstract

Optical waveguides with adiabatic bends (e.g., hybrid partial Euler bends) are described herein. The optical waveguides are implemented into various optical components of integrated photonic devices to improve the performance of the optical components and allow for more compact manufacturing of the integrated photonic devices. In one example, a waveguide having a geometric path defined in a plane and a width perpendicular to the geometric path is described. The geometric path includes an adiabatic curve connecting a first inflection point to a second inflection point on the geometric path, the adiabatic curve including: a circular arc subtending an angle from a first endpoint to a second endpoint; a clothoid connecting the first inflection point to the first endpoint of the circular arc; and an anti-clothoid connecting the second endpoint of the circular arc to the second inflection point.

## Claims

### Claim 1

A waveguide having a geometric path defined in a plane and a width perpendicular to the geometric path,
wherein the geometric path comprises an adiabatic curve connecting a first inflection point to a second inflection point on the geometric path, the adiabatic curve comprising:
a circular arc subtending an angle from a first endpoint to a second endpoint, wherein the width of the waveguide is equal to a first width along the circular arc;
a clothoid connecting the first inflection point to the first endpoint of the circular arc, wherein the width of the waveguide increases from a second, different width to the first width along the clothoid; and
an anti-clothoid connecting the second endpoint of the circular arc to the second inflection point, wherein the width of the waveguide decreases from the first width to a third width along the anti-clothoid.

### Claim 2 (depends on 1)

The waveguide of claim 1, wherein the adiabatic curve subtends a bending angle from the first inflection point to the second inflection point of 45 degrees, 90 degrees, 135 degrees, 180, or 225 degrees.

### Claim 3 (depends on 1)

The waveguide of claim 1, wherein the first width is equal to the third width.

### Claim 4 (depends on 1)

The waveguide of claim 1,
wherein the adiabatic curve is a first adiabatic curve, the circular arc is a first circular arc, the angle is a first angle, and the first circular arc subtends the first angle in a positive azimuthal direction, and
wherein the geometric path further comprises a second adiabatic curve connecting the second inflection point to a third inflection point on the geometric path, the second adiabatic curve comprising:
a second circular arc subtending a second angle from a first endpoint to a second endpoint in a negative azimuthal direction, wherein the width of the waveguide is equal to a fourth width along the second circular arc;
a second anti-clothoid connecting the second inflection point to the first endpoint of the second circular arc, wherein the width of the waveguide increases from the third width to the fourth width along the second anti-clothoid; and
a second clothoid connecting the second endpoint of the second circular arc to the third inflection point, wherein the width of the waveguide decreases from the fourth width to a fifth width along the second clothoid.

### Claim 5 (depends on 4)

The waveguide of claim 4, wherein the first angle is equal to the second angle, the first width is equal to the fourth width, and the second width is equal to the fifth width.

### Claim 6 (depends on 5)

The waveguide of claim 5, wherein the geometric path further comprise a first line segment connected to the first inflection point, and a second line segment connected to the third inflection point.

### Claim 7 (depends on 6)

The waveguide of claim 6, wherein the first and second line segments are parallel to each other.

### Claim 8 (depends on 4)

The waveguide of claim 4, wherein the fifth width is equal to the third width, and the geometric path further comprises a third adiabatic curve connecting the third inflection point to a fourth inflection point on the geometric path, the third adiabatic curve comprising:
a third circular arc subtending the first angle from a first endpoint to a second endpoint in the positive azimuthal direction, wherein the width of the waveguide is equal to the first width along the third circular arc;
a third clothoid connecting the third inflection point to the first endpoint of the third circular arc, wherein the width of the waveguide increases from the third width to the first width along the third clothoid; and
a third anti-clothoid connecting the second endpoint of the third circular arc to the fourth inflection point, wherein the width of the waveguide decreases from the first width to the second width along the third anti-clothoid.

### Claim 9 (depends on 8)

The waveguide of claim 8, wherein the geometric path further comprise a first line segment connected to the first inflection point, and a second line segment connected to the fourth inflection point.

### Claim 10 (depends on 9)

The waveguide of claim 9, wherein the first and second line segments are collinear with each other.

### Claim 11

An integrated photonic device, comprising:
a planar surface;
a looped waveguide disposed on the planar surface, the looped waveguide having a geometric path defined in the planar surface and a width perpendicular to the geometric path, wherein the geometric path comprises:
two adiabatic curves each connecting a respective first inflection point to a respective second inflection point on the geometric path, each adiabatic curve comprising:
a respective circular arc subtending an angle from a first endpoint to a second endpoint, wherein the width of the looped waveguide is equal to a first width along the circular arc;
a respective clothoid connecting the respective first inflection point to the first endpoint of the circular arc, wherein the width of the looped waveguide increases from a second, different width to the first width along the clothoid; and
a respective anti-clothoid connecting the second endpoint of the circular arc to the respective second inflection point, wherein the width of the looped waveguide decreases from the first width to the second width along the anti-clothoid; and
two parallel line segments each connecting one of the first inflections points to one of the second inflection points, wherein the width of the looped waveguide is equal to the second width along each of the two parallel line segments; and
a bus waveguide disposed on the planar surface and evanescently coupled to the looped waveguide, the bus waveguide being parallel and adjacent to one of the two parallel line segments of the looped waveguide.

### Claim 12 (depends on 11)

The integrated photonic device of claim 11, wherein the bus waveguide is a first bus waveguide, and the integrated photonic device further comprises:
a second bus waveguide disposed on the planar surface and evanescently coupled to the looped waveguide, the second bus waveguide being parallel and adjacent to the other one of the two parallel line segments of the looped waveguide.

### Claim 13 (depends on 12)

The integrated photonic device of claim 12, wherein the first and second bus waveguides each have the second width.

### Claim 14 (depends on 11)

The integrated photonic device of claim 11, further comprising:
a dielectric layer having the planar surface; and
a core layer disposed on the planar surface of the dielectric layer, the core layer comprising the looped and bus waveguides.

### Claim 15 (depends on 14)

The integrated photonic device of claim 14, further comprising:
a ridge layer disposed on the planar surface of the dielectric layer, the ridge layer filling an area enclosed by the looped waveguide and having a smaller height from the planar surface than the core layer.

### Claim 16

An integrated photonic device, comprising:
a planar surface;
a circular resonator disposed on the planar surface; and
a bus waveguide disposed on the planar surface and evanescently coupled to the circular resonator, the bus waveguide having a geometric path defined in the planar surface and a width perpendicular to the geometric path,
wherein the geometric path comprises an adiabatic curve connecting a first inflection point to a second inflection point on the geometric path, the adiabatic curve comprising:
a circular arc subtending an angle from a first endpoint to a second endpoint about a central point of the circular resonator, wherein the width of the bus waveguide is equal to a first width along the circular arc;
a clothoid connecting the first inflection point to the first endpoint of the circular arc, wherein the width of the bus waveguide increases from a second, different width to the first width along the clothoid; and
an anti-clothoid connecting the second endpoint of the circular arc to the second inflection point, wherein the width of the bus waveguide decreases from the first width to the second width along the anti-clothoid.

### Claim 17 (depends on 16)

The integrated photonic device of claim 16, wherein the circular resonator is a ring resonator.

### Claim 18 (depends on 17)

The integrated photonic device of claim 17, wherein the ring resonator has a radial width equal to the second width.

### Claim 19 (depends on 16)

The integrated photonic device of claim 16, wherein the circular resonator is a disk resonator.

### Claim 20 (depends on 19)

The integrated photonic device of claim 19, wherein the disk resonator is composed of a semiconductor, and the disk resonator comprises a dopant dispersed within an annular region of the disk resonator.

### Claim 21

An integrated photonic device, comprising:
a planar surface;
an elliptical resonator disposed on the planar surface, the elliptical resonator having a semi-major axis, a semi-minor axis, and a center point defined by an intersection of the semi-major and semi-minor axes; and
a bus waveguide disposed on the planar surface and evanescently coupled to the elliptical resonator, the bus waveguide having a geometric path defined in the planar surface and a width perpendicular to the geometric path,
wherein the geometric path comprises an adiabatic curve connecting a first inflection point to a second inflection point on the geometric path, the adiabatic curve comprising:
an elliptical arc subtending an angle from a first endpoint to a second endpoint about the central point of the elliptical resonator, wherein the width of the bus waveguide is equal to a first width along the elliptical arc;
a clothoid connecting the first inflection point to the first endpoint of the elliptical arc, wherein the normal width increases from a second, different width to the second width along the clothoid; and
an anti-clothoid connecting the second endpoint of the elliptical arc to the second inflection point, wherein the width of the bus waveguide decreases from the auxiliary width to the operational width along the anti-clothoid.

### Claim 22

An integrated photonic device, comprising:
a first waveguide having a first geometric path defined in a plane and a width perpendicular to the first geometric path,
wherein the first geometric path comprises a first adiabatic curve connecting a first inflection point to a second inflection point on the first geometric path, the first adiabatic curve comprising:
a first circular arc subtending an angle from a first endpoint to a second endpoint about a conformal point, wherein the width of the first waveguide is equal to a first width along the first circular arc;
a first clothoid connecting the first inflection point on the first geometric path to the first endpoint of the first circular arc, wherein the width of the first waveguide increases from a second width to the first width along the first clothoid; and
a first anti-clothoid connecting the second endpoint of the first circular arc to the second inflection point on the first geometric path, wherein the width of the first waveguide decreases from the first width to the second width along the first anti-clothoid; and
a second waveguide evanescently coupled to the first waveguide, the second waveguide having a second geometric path defined in the plane and a width perpendicular to the second geometric path,
wherein the second geometric path comprises a second adiabatic curve connecting a first inflection point to a second inflection point on the second geometric path, the second adiabatic curve comprising:
a second circular arc subtending the angle from a first endpoint to a second endpoint about the conformal point, wherein the width of the second waveguide is equal to a third width along the second circular arc;
a second clothoid connecting the first inflection point on the second geometric path to the first endpoint of the second circular arc, wherein the width of the second waveguide increases from a fourth width to the third width along the second clothoid; and
a second anti-clothoid connecting the second endpoint of the second circular arc to the second inflection point on the second geometric path, wherein the width of the second waveguide decreases from the third width to the fourth width along the second anti-clothoid.

### Claim 23

An integrated photonic device, comprising:
an input waveguide extending along an axis from an input end to an output end, the input waveguide having a width that increases from an input width at the input end to an output width at the output end;
a first output waveguide connected to the output end of the input waveguide, the first output waveguide comprising a first adiabatic bend extending from the output end, the first adiabatic bend having positive curvature; and
a second output waveguide connected to the output end of the input waveguide, the second output waveguide comprising a second adiabatic bend extending from the output end, the second adiabatic bend having negative curvature.

### Claim 24 (depends on 23)

The integrated photonic device of claim 23, wherein:
the first adiabatic bend comprises:
a first arcuate section subtending a first angle from a first end to a second end in a positive azimuthal direction;
a first Euler section extending from the output end of the input waveguide to the first end of the first arcuate section; and
a first anti-Euler section extending from the second end of the first arcuate section, and
the second adiabatic comprises:
a second arcuate section subtending a second angle from a first end to a second end in a negative azimuthal direction;
a second anti-Euler section extending from the output end of the input waveguide to the first end of the second arcuate section; and
a second Euler section extending from the second end of the second arcuate section.

### Claim 25

An integrated photonic device, comprising:
an input waveguide extending along an axis from an input end to an output end, the input waveguide comprising:
a first linear section extending from the input end along the axis, the first linear section having an input width; and
a second linear section extending to the output end along the axis, the second linear section having an output width that is larger than the input width;
a first output waveguide connected to the output end of the input waveguide, the first output waveguide comprising a first adiabatic bend extending from the output end, the first adiabatic bend having positive curvature; and
a second output waveguide connected to the output end of the input waveguide, the second output waveguide comprising a second adiabatic bend extending from the output end, the second adiabatic bend having negative curvature.