# US 11,994,715 B2 · Compact waveguide taper and waveguide crossing

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- Number: US 11,994,715 B2
- Document ID: US11994715B2
- Status: Granted
- Kind: B2
- Application number: 17/684,265
- Filed: 2022-03-01
- Published: 2022-09-08
- Granted: 2024-05-28
- Earliest claimed: 2021-03-02
- Assignees: Rockley Photonics Limited
- Applicants: Rockley Photonics Limited
- Inventors: Jin-Hyoung Lee; Andrea Trita
- Web page: https://patentgrep.com/patent/US11994715B2

## CPC

- G02B 6/1228: {Tapered waveguides, e.g. integrated spot-size transformers (for coupling with fibres G02B6/305)}
- G02B 6/125: Bends, branchings or intersections
- G02B: OPTICAL ELEMENTS, SYSTEMS OR APPARATUS

## Abstract

A tapered waveguide. In some embodiments, the waveguide has a narrow end and a wide end. A taper angle of the waveguide may be, at each point along the waveguide, less than an adiabatic taper angle by a margin. The margin may be greater at a first point than at a second point, where the adiabatic taper angle is less at the first point than at the second point.

## Claims

### Claim 1

A tapered waveguide, having:
a narrow end; and
a wide end,
the tapered waveguide having:
a taper angle, at a first point between the narrow end and the wide end, equal to ΩL1−x1, and
a taper angle, at a second point between the narrow end and the wide end, equal to ΩL2−x2,
wherein:
ΩL1=ρ1/LB1 is an adiabatic taper angle at the first point,
ρ1 is one half of the width of the waveguide at the first point,
L
B
⁢
2
=
2
⁢
π
β
12
-
β
22
is a beat length at the first point,
ρ11 is a propagation constant, at the first point, of a fundamental mode,
β21 is a propagation constant, at the first point, of a higher order mode with a greatest overlap with the fundamental mode,
ΩL2=ρ2/LB2 is an adiabatic taper angle at the second point,
ρ2 is one half of the width of the waveguide at the second point,
L
B
⁢
2
=
2
⁢
π
β
12
-
β
22
is a beat length at the second point,
β12 is a propagation constant, at the second point, of a fundamental mode,
β22 is a propagation constant, at the second point, of a higher order mode with a greatest overlap with the fundamental mode,
ΩL1<ΩL2, and
x1>x2.

### Claim 2 (depends on 1)

The tapered waveguide of claim 1,
wherein the tapered waveguide has a taper angle, at each point between the narrow end and the wide end, within 30% of ΩL−α/ΩL,
wherein:
α is a positive constant,
ΩL=ρ/LB,
ρ is one half of the width of the tapered waveguide at the point,
L
B
⁢
1
=
2
⁢
π
β
11
-
β
12
β1 is a propagation constant, at the point, of a fundamental mode, and
β2 is a propagation constant, at the point, of a higher order mode with a greatest overlap with the fundamental mode.

### Claim 3 (depends on 2)

The tapered waveguide of claim 2, wherein the tapered waveguide has:
a width, at the narrow end, within 20% of 1.5 microns,
a width, at the wide end, within 20% of 7 microns, and
a length, between the narrow end and the wide end, of less than 80 microns.

### Claim 4 (depends on 3)

The tapered waveguide of claim 3, wherein the tapered waveguide has an optical loss of less than 0.08 dB.

### Claim 5 (depends on 2)

The tapered waveguide of claim 2, wherein α is between 0.1 and 0.4.

### Claim 6 (depends on 1)

A waveguide crossing, comprising:
a first tapered waveguide, the first tapered waveguide being a tapered waveguide according to claim 1, abutting a crossing slab.

### Claim 7 (depends on 6)

The waveguide crossing of claim 6, further comprising:
a second tapered waveguide;
a third tapered waveguide; and
a fourth tapered waveguide,
wherein:
the crossing slab is a crossing rectangle;
the first tapered waveguide, the second tapered waveguide, the third tapered waveguide, and the fourth tapered waveguide abut four respective sides of the crossing rectangle; and
the crossing rectangle is configured to allow light to propagate from the first tapered waveguide to the third tapered waveguide, and to allow light to propagate from the second tapered waveguide to the fourth tapered waveguide.

### Claim 8 (depends on 7)

The waveguide crossing of claim 7, wherein the crossing rectangle has a side having a length less than 8 microns.

### Claim 9 (depends on 8)

The waveguide crossing of claim 8, wherein the crossing rectangle has a side having a length less than 7 microns.

### Claim 10 (depends on 6)

The waveguide crossing of claim 6, wherein the first tapered waveguide has:
a width, at the narrow end, within 20% of 1.5 microns,
a width, at the wide end, within 20% of 7 microns, and
a length, between the narrow end and the wide end, of less than 80 microns.

### Claim 11 (depends on 10)

The waveguide crossing of claim 10, wherein the first tapered waveguide has an optical loss of less than 0.08 dB.

### Claim 12 (depends on 6)

The waveguide crossing of claim 6, wherein α is between 0.1 and 0.4.

### Claim 13 (depends on 1)

The tapered waveguide of claim 1, wherein the tapered waveguide has:
a width, at the narrow end, within 20% of 1.5 microns,
a width, at the wide end, within 20% of 7 microns, and
a length, between the narrow end and the wide end, of less than 80 microns.

### Claim 14 (depends on 1)

The tapered waveguide of claim 1, wherein the tapered waveguide has an optical loss of less than 0.08 dB.

### Claim 15 (depends on 1)

The tapered waveguide of claim 1, wherein α is between 0.1 and 0.4.

### Claim 16 (depends on 1)

A waveguide crossing, comprising:
a first tapered waveguide, the first tapered waveguide being a tapered waveguide according to claim 1, abutting a crossing slab.

### Claim 17 (depends on 16)

The waveguide crossing of claim 16, further comprising:
a second tapered waveguide;
a third tapered waveguide; and
a fourth tapered waveguide,
wherein:
the crossing slab is a crossing rectangle;
the first tapered waveguide, the second tapered waveguide, the third tapered waveguide, and the fourth tapered waveguide abut four respective sides of the crossing rectangle; and
the crossing rectangle is configured to allow light to propagate from the first tapered waveguide to the third tapered waveguide, and to allow light to propagate from the second tapered waveguide to the fourth tapered waveguide.

### Claim 18 (depends on 17)

The waveguide crossing of claim 17, wherein the crossing rectangle has a side having a length less than 8 microns.

### Claim 19 (depends on 18)

The waveguide crossing of claim 18, wherein the crossing rectangle has a side having a length less than 7 microns.

### Claim 20 (depends on 16)

The waveguide crossing of claim 16, wherein the first tapered waveguide has:
a width, at the narrow end, within 20% of 1.5 microns,
a width, at the wide end, within 20% of 7 microns,
a length, between the narrow end and the wide end, of less than 80 microns, and an optical loss of less than 0.08 dB.