# US 12,007,579 B2 · Machine learning based regression of complex coefficients of a linear combination of spatial modes from multimode optical fiber

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- Number: US 12,007,579 B2
- Document ID: US12007579B2
- Status: Granted
- Kind: B2
- Application number: 17/081,900
- Filed: 2020-10-27
- Published: 2021-05-06
- Granted: 2024-06-11
- Earliest claimed: 2019-10-30
- Assignees: NEC Corporation
- Applicants: NEC Laboratories America, Inc.
- Inventors: Giovanni Milione; Philip Ji; Eric Cosatto
- Web page: https://patentgrep.com/patent/US12007579B2

## CPC

- G02B 27/283: {used for beam splitting or combining}
- G06F 18/214: Generating training patterns; Bootstrap methods, e.g. bagging or boosting
- G06F 18/24: Classification techniques
- G06V 10/764: using classification, e.g. of video objects
- G06V 10/82: using neural networks
- G02B: OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- G06V: IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING

## Abstract

Aspects of the present disclosure describe systems, methods, and structures for the machine learning based regression of complex coefficients of a linear combination of spatial modes from a multimode optical fiber.

## Claims

### Claim 1

A method for classifying higher-order spatial modes comprising:
providing a light beam emitted from an output of a multimode optical fiber, the light beam having two orthogonal polarization components, each including a linear combination of higher-order spatial modes;
separating the two orthogonal polarization components into two separate light beams;
recording digital images of the two separate light beams; and
classifying, using a machine learning based classifier, the recorded digital images.

### Claim 2 (depends on 1)

The method of claim 1 further comprising training the classifier using numerically calculated training examples.

### Claim 3 (depends on 1)

The method of claim 1 wherein the recording digital images is effected by a digital camera.

### Claim 4 (depends on 3)

The method of claim 3 further comprising:
optically imaging the emitted light beam through the effect of imaging optics prior to the separation of the two orthogonal polarization components into two separate light beams.

### Claim 5 (depends on 4)

The method of claim 4 wherein the imaging optics include one or more lenses.

### Claim 6 (depends on 5)

The method of claim 5 wherein the multimode optical fiber and the digital camera are not placed in a focal region of the lenses.

### Claim 7 (depends on 3)

The method of claim 3 wherein the camera records digital images of the transverse, spatial dependencies of the intensities of the two orthogonal polarization components of the light beam, whose alignment, size, and wavefront vary with respect to the digital camera.

### Claim 8 (depends on 7)

The method of claim 7 wherein the center of an imaged light beam is displaced in the x-direction.

### Claim 9 (depends on 7)

The method of claim 7 wherein the center of an imaged light beam is displaced in the y-direction.

### Claim 10 (depends on 7)

The method of claim 7 wherein the direction of propagation of an imaged light beam forms an angle in the y-z plane.

### Claim 11 (depends on 7)

The method of claim 7 wherein the direction of propagation of an imaged light beam forms an angle in the x-z plane.

### Claim 12 (depends on 7)

The method of claim 7 wherein a waist size of an imaged light beam varies in time.

### Claim 13 (depends on 7)

The method of claim 7 wherein a wave front of an imaged light beam exhibits an aberration.

### Claim 14 (depends on 1)

The method of claim 1 wherein the higher order spatial modes are Hermite-Gaussian modes.

### Claim 15 (depends on 1)

The method of claim 1 wherein the higher order spatial modes are Laguerre-Gaussian modes.

### Claim 16 (depends on 1)

The method of claim 1 wherein the two orthogonal polarization components of the light beam are one selected from the group consisting of: horizontal/vertical, diagonal/antidiagonal, and right/left circular.

### Claim 17 (depends on 1)

The method of claim 1 wherein the classifier is trained using numerically calculated training examples including varying alignments, sizes, and wave fronts.

### Claim 18 (depends on 17)

The method of claim 17 wherein the numerically calculated training examples include higher order spatial modes having waists that vary.

### Claim 19 (depends on 17)

The method of claim 17 wherein the numerically calculated training examples include at least one of: higher order spatial modes displaced in the x-direction, or higher order spatial modes displaced in the y-direction.