# US 10,481,463 B2 · All optical fast fourier transform on chip with heating tunability design, simulation, fabrication, and performance analysis

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- Number: US 10,481,463 B2
- Document ID: US10481463B2
- Status: Granted
- Kind: B2
- Application number: 15/830,747
- Filed: 2017-12-04
- Published: 2019-03-07
- Granted: 2019-11-19
- Earliest claimed: 2017-09-07
- Assignees: The George Washington University
- Applicants: The George Washington University
- Inventors: Hani Nejadriahi; Volker J. Sorger
- Web page: https://patentgrep.com/patent/US10481463B2

## CPC

- G02F 1/225: in an optical waveguide structure
- G02F 1/0147: {based on thermo-optic effects (G02F1/132 takes precedence)}
- G06E 3/003: {forming integrals of products, e.g. Fourier integrals, Laplace integrals, correlation integrals; for analysis or synthesis of functions using orthogonal functions}
- G02F 1/212: {Mach-Zehnder type}
- G02F 1/215: {Michelson type}
- G02F: OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
- G06E: OPTICAL COMPUTING DEVICES (digital storage using optical elements G11C13/04)

## Abstract

The present invention provides optical computing by means of fast Fourier transform Integration on Silicon On Insulator chip technology with implementation in the analog and temporal domain. This is done by cascading (N−2) stages of delayed interferometers (couplers and phase shifters) where a parallel set of N time samples are taken and using the delay lines and phase of the optical components (constructive/deconstructive interference) the DFT is computed. The Optical Fast Fourier Transform (OFFT) design was built on passive components (2×2 couplers: cascaded Mach Zehnder Interferometer) used for addition and subtraction through optical interference, waveguides with short path differences are used for phase shifting and waveguides with long path differences are used for signal delay based on the needed number of outputs. Since the OFFT is a system of imbalanced interferometers, there are additional bends designed to compensate for the difference in power ratios of the arms.

## Claims

### Claim 1

A temporal photonic integrated Fast Fourier Transform circuit, comprising:
a photonic integrated on-chip input for receiving an optical signal from a source; and
a photonic integrated on-chip first stage having a first interferometer with a first stage output, and a photonic integrated on-chip second stage having a second interferometer and a third interferometer, the second and third interferometers receiving the first stage output and having a second stage output, wherein each of said first, second and third interferometers each comprise a first arm and a second arm parallel to the first arm, the first arm forming a first waveguide and the second arm having a spiral waveguide, and further comprising first arm output from the first waveguide and a second arm output from the spiral waveguide, said first, second and third interferometers further comprising a coupler to couple the first arm output and the second arm output, wherein the spiral waveguide imparts a phase delay to the optical signal whereby said circuit conducts Fast Fourier Transform.

### Claim 2 (depends on 1)

The circuit of claim 1, wherein the optical signal is modulated.

### Claim 3 (depends on 1)

The circuit of claim 1, wherein the first waveguide is straight.

### Claim 4 (depends on 1)

The circuit of claim 1, wherein the first waveguide has one or more bends.

### Claim 5 (depends on 4)

The circuit of claim 4, wherein the one or more bends compensate for optical power loss by the spiral waveguide.

### Claim 6 (depends on 1)

The circuit of claim 1, wherein the first waveguide has a plurality of inversely positioned U-shaped bends that compensate for optical power loss by the spiral waveguide.

### Claim 7 (depends on 4)

The circuit of claim 4, wherein the bends provide a power on the first arm that substantially matches power on the second arm.

### Claim 8 (depends on 1)

The circuit of claim 1, further comprising an integrated on-chip heater formed on the first waveguide.

### Claim 9 (depends on 8)

The circuit of claim 8, wherein the heater modifies the phase of the optical signal on the first arm to compensate for a phase shift on the second arm and align the phase of the optical signal on the first arm with the phase of the optical signal on the second arm.

### Claim 10 (depends on 1)

The circuit of claim 1, wherein the first, second and third interferometers are each Mach Zehnder Interferometers (MZI).

### Claim 11 (depends on 1)

The circuit of claim 1, further comprising a photonic integrated on-chip modulator receiving an output from the second and third interferometers.

### Claim 12 (depends on 11)

The circuit of claim 11, wherein the modulator comprises a Michelson Interferometer Modulator (MIM).

### Claim 13 (depends on 1)

The circuit of claim 1, further comprising a first and second photonic integrated on-chip modulator coupled with an output from the second interferometer, and a third and fourth photonic integrated on-chip modulator coupled with an output from the third interferometer.

### Claim 14 (depends on 1)

The circuit of claim 1, wherein the coupler adds and/or subtracts the first arm output and the second arm output and splits the added/subtracted first and second arm outputs to provide the first stage output and the second stage output, respectively.

### Claim 15 (depends on 14)

The circuit of claim 14, further comprising a photonic integrated on-chip photodetector that detects an output of said circuit.

### Claim 16

A temporal photonic integrated Fast Fourier Transform circuit having n-stages with 2n outputs, where n is an integer greater than 1, comprising:
a photonic integrated on-chip input for receiving an optical signal from a source; and
a photonic integrated on-chip having n stages, each stage having 2(n−1) interferometers, and each interferometer having a first arm and a second arm parallel to the first arm, the first arm forming a first waveguide providing a first arm output and the second arm having a spiral waveguide providing a second arm output, said interferometers each further having a coupler to couple the first arm output and the second arm output to provide a coupled output, wherein the interferometer of a first stage receives the optical signal from the source and the interferometers from each subsequent stage receives the coupled output from the prior stage, wherein the spiral waveguide imparts a phase delay to the optical signal whereby said circuit conducts Fast Fourier Transform.

### Claim 17 (depends on 16)

The circuit of claim 16, wherein the first arm has one or more bends that compensate for optical power loss by the spiral waveguide of the second arm.

### Claim 18 (depends on 16)

The circuit of claim 16, further comprising a photonic integrated on-chip heater formed on the first waveguide, wherein the heater modifies the phase of the optical signal on the first arm to compensate for a phase shift on the second arm and align the phase of the optical signal on the first arm with the phase of the optical signal on the second arm.

### Claim 19 (depends on 16)

The circuit of claim 16, further comprising a photonic integrated on-chip modulator that modulate the second stage output.

### Claim 20 (depends on 16)

The circuit of claim 16, wherein the coupler adds and/or subtracts the first arm output and the second arm output and splits the added/subtracted first and second arm outputs to provide the first stage output and second stage output, respectively.

### Claim 21 (depends on 20)

The circuit of claim 20, further comprising a photonic integrated on-chip detector that detects the second stage output.

### Claim 22

A temporal photonic, plasmonic, or hybrid photonic/plasmonic integrated Fast Fourier Transform circuit having n stages and 2n outputs, where n is an integer greater than 1, comprising:
a photonic, plasmonic, or hybrid photonic/plasmonic integrated on-chip input for receiving an optical signal from a source; and
a photonic, plasmonic, or hybrid photonic/plasmonic integrated on-chip having n stages, each stage having 2(n−1) interferometers, and each interferometer having a first arm and a second arm parallel to the first arm, the first arm forming a first waveguide providing a first arm output and the second arm having a spiral waveguide providing a second arm output, said interferometers each further having a coupler to couple the first arm output and the second arm output to provide a coupled output, wherein the interferometer of a first stage receives the optical signal from the source and the interferometers from each subsequent stage receives the coupled output from the prior stage, wherein the spiral waveguide imparts a phase delay to the optical signal whereby said circuit conducts Fast Fourier Transform.

### Claim 23 (depends on 22)

The circuit of claim 22, further comprising:
a photonic, plasmonic, or hybrid photonic/plasmonic integrated on-chip heater formed on the first waveguide, wherein the heater modifies the phase of the optical signal on the first arm to compensate for a phase shift on the second arm and align the phase of the optical signal on the first arm with the phase of the optical signal on the second arm;
a photonic, plasmonic, or hybrid photonic/plasmonic integrated on-chip modulator that modulate the second stage output; and
a photonic, plasmonic, or hybrid photonic/plasmonic integrated on-chip detector that detects the second stage output.

### Claim 24 (depends on 22)

The circuit of claim 22, wherein each interferometer comprises a Mach Zehnder interferometer (MZI).

### Claim 25 (depends on 16)

The circuit of claim 16, wherein each interferometer comprises a Mach Zehnder Interferometer (MZI).