Feedthrough rejection for optomechanical devices

An optomechanical device for producing and detecting optical signals comprising a proof mass assembly, one or more laser devices, and a circuit. The one or more laser devices are configured to generate a first optical signal and a second optical signal. The circuit is configured to modulate, with an electro-optic modulator (EOM), the second optical signal, output the first optical signal and the second optical signal to the proof mass assembly, generate a filtered optical signal corresponding to a response by the proof mass assembly to the first optical signal without the second optical signal, and generate an electrical signal based on the filtered optical signal, wherein the EOM modulates the second optical signal based on the electrical signal.

TECHNICAL FIELD

This disclosure relates to optomechanical devices, such as accelerometers configured to measure acceleration using an optical signal.

BACKGROUND

Optomechanical devices include devices for detecting acceleration, velocity, vibration, and other parameters. For example, in an optomechanical accelerometer, the resonance frequency of a mechanical structure is shifted under acceleration in the optomechanical device. The mechanical resonance frequency can be read out with an optical field by applying near-resonant light to the structure's optical resonance and measuring the transmitted or reflected optical signal.

SUMMARY

In general, this disclosure is directed to devices, systems, and techniques for reducing drive feedthrough in optomechanical devices. As used herein, drive feedthrough may refer to the portion of the optical driving field which leaks into the detection path and is independent of acceleration. Drive feedthrough may limit the ultimate noise floor and hence performance of the optomechanical device. For example, a circuit may be configured to output the first optical signal as a driving field to drive a mechanical response to a proof mass assembly and output the second optical signal as a sensing field to the proof mass assembly to detect one or more of a modulation in phase or frequency of mechanical vibrations in the proof mass assembly.

In one example, an optomechanical device for producing and detecting optical signals includes a proof mass assembly; one or more laser devices configured to generate a first optical signal and a second optical signal, wherein the first optical signal comprises a frequency different than a frequency of the second optical signal; and circuitry configured to: modulate, with an electro-optic modulator (EOM), the second optical signal; output the first optical signal and the second optical signal to the proof mass assembly; generate a filtered optical signal corresponding to a response by the proof mass assembly to the first optical signal without the second optical signal; and generate an electrical signal based on the filtered optical signal, wherein the EOM modulates the second optical signal based on the electrical signal.

In another example, a method for producing and detecting optical signals including: generating, by one or more laser devices, a first optical signal and a second optical signal, wherein the first optical signal comprises a frequency different than a frequency of the second optical signal; modulating, by an electro-optic modulator (EOM) of circuitry, the second optical signal; outputting, by the circuitry, the first optical signal and the second optical signal to a proof mass assembly; generating, by the circuitry, a filtered optical signal corresponding to a response by the proof mass assembly to the first optical signal without the second optical signal; and generating, by the circuitry, an electrical signal based on the filtered optical signal, wherein the EOM is configured to modulate the second optical signal based on the electrical signal.

In another example, an optomechanical system for producing and detecting optical signals includes one or more laser devices configured to generate a first optical signal and a second optical signal, wherein the first optical signal comprises a frequency different than a frequency of the second optical signal and a circuit configured to: modulate, with an electro-optic modulator (EOM), the second optical signal; output the first optical signal and the second optical signal to a mechanical assembly; generate a filtered optical signal corresponding to a response by the mechanical assembly to the first optical signal without the second optical signal; and generate an electrical signal based on the filtered optical signal, wherein the EOM modulates the second optical signal based on the electrical signal.

The summary is intended to provide an overview of the subject matter described in this disclosure. It is not intended to provide an exclusive or exhaustive explanation of the systems, device, and methods described in detail within the accompanying drawings and description below. Further details of one or more examples of this disclosure are set forth in the accompanying drawings and in the description below. Other features, objects, and advantages will be apparent from the description and drawings, and from the claims.

Like reference characters denote like elements throughout the description and figures.

DETAILED DESCRIPTION

This disclosure describes devices, systems, and techniques for reducing drive feedthrough into the detection for optomechanical devices, such as, for example, but not limited to, optomechanical accelerometers, electrical filters (e.g., high pass filters, low pass filters, and band pass filters), strain sensors, pressure sensors, force sensors, and gyroscopes, where the structures have a coupled optical degree of freedom, and could help improve performance of such optomechanical devices. For example, in an optomechanical accelerometer, a resonance frequency of a mechanical structure is shifted under acceleration in the optomechanical device. The mechanical resonance frequency can be measured with an optical field by applying near-resonant light to the structure's optical resonance and measuring the transmitted or reflected light (as the mechanical resonance frequency is imprinted as modulation of the phase and/or amplitude of the light by virtue of optical-mechanical coupling in the device). To increase the signal to noise of the mechanical frequency measurement, systems may drive the mechanical resonance to a larger amplitude by strongly amplitude modulating the light field at or near the mechanical resonance frequency, which may be referred to as a “driving modulation” of the input optical field. In contrast, the “sense modulation” may refer to a modulation induced on the outgoing optical field by the mechanical vibrations and can be less than, or even much less than, the driving modulation of the incoming driving optical field. In optomechanical devices in which a single laser field is used to both drive and sense, the outgoing sense optical field thus can have a deleterious “feed-through” modulation present on the optical field, which can fundamentally distort, obscure, or otherwise decreases the quality of the optical signal.

Techniques described herein may mitigate or help to eliminate distortion from feed-through modulation. In some examples, an optomechanical accelerometer may use one laser wavelength for the driving field and another laser wavelength for the sensing field. The laser wavelength for the driving field and the laser wavelength for the sensing field can be separated through the use of wavelength selective optical components, such as, for example, but not limited to, filters or dichroics. Combined with appropriate readout and feedback system, techniques described herein may provide a detection signal that is free of “feed-through,” can be locked to the mechanical resonance, and is advantageously almost free or completely free of distortions or noise that is present in systems in which the feed-through has not be eliminated.

For example, the optomechanical device may include an electro-opto-mechanical system configured to precisely measure very high acceleration values (e.g., up to 500,000 meters per second squared (m/s2)). The electro-opto-mechanical system may use a combination of electrical signals, optical signals, and mechanical signals to determine the acceleration of the object.

An optomechanical device may be configured to measure the acceleration, velocity, vibration, etc. of the object in real-time or near real-time, such that processing circuitry may analyze the acceleration, velocity, vibration, etc. of the object over a period of time to determine a positional displacement of the object during the period of time. For example, the optomechanical device may be a part of an Inertial Navigation System (INS) for tracking a position of an object based, at least in part, on an acceleration of the object. Additionally, the optomechanical device may be located on or within the object such that the optomechanical device accelerates, moves, vibrates, etc. with the object. As such, when the object accelerates, moves, vibrates, etc., the optomechanical device (including the mechanical assembly, proof mass assembly, etc.) accelerates, moves, vibrates, etc. with the object. In some examples, because acceleration over time is a derivative of velocity over time, and velocity over time is a derivative of position over time, processing circuitry may, in some cases, be configured to determine the position displacement of the object by performing a double integral of the acceleration of the object over the period of time. Determining a position of an object using the accelerometer system located on the object—and not using on a navigation system separate from the object (e.g., a Global Positioning System (GPS))—may be referred to as “dead reckoning.”

The optomechanical device may be configured to achieve high levels of sensitivity in order to improve the accuracy of the acceleration, velocity, vibration, etc. values. High sensitivity may enable the optomechanical device to detect very small acceleration, velocity, vibration, etc. values, detect a very small change in acceleration, velocity, vibration, etc. values, detect a large range of acceleration, velocity, vibration, etc. values, or any combination thereof. Additionally, an optomechanical device may be configured to accurately determine the acceleration, velocity, vibration, etc. of the object while the object is experiencing high levels of acceleration, velocity, vibration, etc. In this way, the an optomechanical device may be configured to enable an INS to accurately track the position of the object while a magnitude of the acceleration, velocity, vibration, etc. of the object is very high.

The optomechanical device may, in some examples, include a MEMS accelerometer which includes a light-emitting device, a circuit, and a proof mass assembly which includes a proof mass suspended within a frame by double-ended tuning fork (DETF) structures. In some examples, the optomechanical device may include a single-ended tuning fork or another mechanical assembly. For instance, the optomechanical device may use a mechanical assembly suitable for electrical filters (e.g., high pass filters, low pass filters, and band pass filters), strain sensors, pressure sensors, force sensors, gyroscopes, or another mechanical assembly.

In some examples, the DETF structures may be configured to guide optical signals. Additionally, optical signals may induce mechanical vibration in the DETF structures. In some cases, acceleration causes a displacement of the proof mass relative to the frame, the displacement affecting mechanical vibration frequencies (e.g., mechanical resonance frequencies) corresponding to the DETF structures. In this way, a mathematical relationship may exist between acceleration and the mechanical vibration frequencies of the DETF structures. As such, the mathematical relationship may be leveraged to determine acceleration. The accelerometer device uses, in some examples, a combination of optical signals and electrical signals to measure the mechanical vibration frequencies corresponding to the DETF structures and calculate acceleration based on the mechanical vibration frequencies.

While examples of an optomechanical device are described with respect to an example accelerometer, techniques described herein for noise rejection may be applied to optomechanical device configured to measure various parameters, including, but not limited to, acceleration, velocity, vibration, and other parameters. Moreover, while examples of the optomechanical device are described with respect to an example proof mass assembly that includes a DETF structure, other structures may be used, for example, but not limited to, a single-ended tuning fork structure or another structure.

FIG. 1is a block diagram illustrating an electro-opto-mechanical system10, in accordance with one or more techniques of this disclosure.FIG. 1is merely one non-limiting example system architecture that may utilize the techniques of this disclosure for resonator stabilization. As illustrated inFIG. 1, system10includes light-emitting devices12A,12B (collectively, “light-emitting devices12”), circuit14, and proof mass assembly16. Additionally, in the example illustrated inFIG. 1, circuit14includes electro-optic-modulators (EOM)22A,22B (collectively, “EOMs22”), photoreceivers24A,24B (collectively, “photoreceivers24”), feedback units26A,26B (collectively, “feedback units26”), frequency counters28A,28B (collectively, “frequency counters28”), and processing circuitry30. While the example ofFIG. 1includes two EOMs, two photoreceivers, and two frequency counters, in some examples, an electro-opto-mechanical system may include only one EOM, one photoreceiver, and one frequency counter or more than two EOMs, two photoreceivers, and two frequency counters.

In the example ofFIG. 1, light-emitting device12A, proof mass assembly16, EOM22A, photoreceiver24A, feedback unit26A, and frequency counter28A form a first positive feedback loop. Additionally, in the example ofFIG. 1, light-emitting device12B, proof mass assembly16, EOM22B, photoreceiver24B, feedback unit26B, and frequency counter28B form a second positive feedback loop. In some examples, the second positive feedback loop may be omitted.

System10may be configured to determine an acceleration associated with an object (not illustrated inFIG. 1) based on a measured vibration frequency of a tuning fork structure of proof mass assembly. For example, system10may be configured to determine an acceleration associated with an object (not illustrated inFIG. 1) based on a measured vibration frequency of a set of double-ended tuning fork (DETF) structures which suspend a proof mass of proof mass assembly16, where the vibration of the DETF structures is induced by an optical signal emitted by light-emitting device12. In some examples, the first positive feedback loop generates a first frequency value representing a vibration frequency of a first DETF structure and the second positive feedback loop generates a second frequency value representing a vibration frequency of a second DETF structure. Based on the first vibration frequency and the second vibration frequency, system10may determine a first acceleration value and a second acceleration value, respectively. In some examples, system10determines an acceleration of an object based on the first acceleration value and the second acceleration value. In some examples, system10determines the acceleration of the object based on only the first acceleration value (e.g., the second positive feedback loop is omitted). In some examples, system10determines the acceleration of the object based on only the second acceleration value (e.g., the first positive feedback loop is omitted).

Light-emitting devices12may each include a laser device, also referred to herein as simply “laser,” configured to emit photons that form an optical signal. In some examples, light-emitting devices12emit the photons at an optical power within a range between 0.1 microwatts (μW) and 100 μW. In some examples, light-emitting devices12each include a semiconductor laser which includes a laser diode. In some examples, each of light-emitting devices12may be configured to generate a first optical signal that interacts with proof mass assembly16and, in response to interacting with the proof mass assembly16, is impressed with one or more of a modulation in phase or frequency of mechanical vibrations in proof mass assembly16and a second optical signal that stimulates mechanical vibrations in proof mass assembly16. In this way, the second optical signal (e.g., a driving optical signal) may provide driving modulation at proof mass assembly and feedback unit26A may use the first optical signal (e.g., a sense optical signal) that interacts with proof mass assembly16while the first optical signal drives the mechanical vibration frequency at proof mass assembly16.

In some examples, circuit14may include a set of electrical components for processing and analyzing electrical signals received by photoreceivers24. Components of circuit14are described in further detail below.

EOMs22may represent optical devices configured to modulate, based on electrical signals produced and processed by circuit14, an optical signal emitted by light-emitting device12. EOM22A, for example, may include a set of crystals (e.g., Lithium Niobate crystals), where a refractive index of the set of crystals changes as a function of an electric field proximate to the set of crystals. The refractive index of the crystals may determine a manner in which EOM22A modulates the optical signal. For example, the crystals of EOM22A may receive the optical signal from light-emitting device12while EOM22A is also receiving an electrical signal from feedback unit26A of circuit14. As such, the electrical signal may affect the electric field proximate to the crystals of EOM22A, thus causing EOM22A to modulate the optical signal. In some examples, EOM22A modulates the optical signal for driving a mechanical response in proof mass assembly16by modulating the refractive index of the crystals using the electrical signal. EOM22A, in some cases, may transmit the modulated optical signal to proof mass assembly16. In some examples, EOM22B is substantially similar to EOM22A, with EOM22B controlled by an electrical signal from feedback unit26B.

Photoreceivers24(also referred to herein as “photodiodes”) may each include one or more transistors configured to absorb photons of an optical signal and output, in response to absorbing the photons, an electrical signal. In this manner, photoreceivers24may be configured to convert optical signals into electrical signals. Photoreceivers24A, for example, may include a p-n junction that converts the photons of the optical signal into the electrical signal, where the electrical signal preserves at least some parameters of the optical signal. One or more frequency values and intensity values associated with the optical signal may be reflected in the electrical signal produced by photoreceivers24A in response to photoreceivers24A receiving the optical signal. For example, photoreceivers24A may produce a stronger electrical signal (e.g., greater current magnitude) in response to receiving a stronger (e.g., greater power) optical signal. Additionally, in some cases, photoreceivers24A may produce the electrical signal to reflect the one or more frequency values corresponding to the received optical signal. In other words, processing circuitry (e.g., processing circuitry30) may analyze the electrical signal to determine the one or more frequency values corresponding to the optical signal. Photoreceivers24A may include semiconductor materials such as any combination of Indium Gallium Arsenide, Silicon, Silicon Carbide, Silicon Nitride, Gallium Nitride, Germanium, or Lead Sulphide. In some examples, photoreceivers24B is substantially similar to photoreceivers24A.

Feedback units26may each include a set of circuit components for processing electrical signals. In some examples, the set of circuit components included in feedback unit26A may include any combination of a band pass filter, a phase shifter, an electronic amplifier, and a voltage limiter. Such components may process, or filter, the electrical signal such that certain aspects of the electrical signal may be more efficiently measured (e.g., frequency values or intensity values). In the example ofFIG. 1, feedback unit26A may receive an electrical signal from photoreceiver24A and output a processed electrical signal to EOM22A, frequency counter28A, and light-emitting device12A. In this way, feedback unit26A acts as a part of a first positive feedback loop by processing an electrical signal which EOM22A uses to modulate an optical signal emitted by light-emitting device12A, where the modulated optical signal passes through proof mass assembly16before arriving back at circuit14for processing by feedback unit26A.

Feedback unit26B may be substantially similar to feedback unit26A in that feedback unit26B receives an electrical signal from photoreceiver24B and delivers a processed electrical signal to frequency counter28B, EOM22B, and light-emitting device12B. As such, feedback unit26B operates within a second feedback loop in a similar manner to which feedback unit26A operates within the first feedback loop. Again, feedback unit26B may be omitted.

Frequency counters28are circuit components that are each configured for measuring a frequency of an electrical signal. For example, frequency counter28A may determine one or more frequency values corresponding to the processed electrical signal produced by feedback unit26A. Frequency counter28A may measure frequency values corresponding to the processed electrical signal in real-time or near real-time, such that frequency counter28A tracks the frequency values as a function of time. Frequency counter28B may be substantially similar to frequency counter28A, except frequency counter28B receives an electrical signal from feedback unit26B rather than from feedback unit26A.

Processing circuitry30, and circuit14generally, may include one or more processors that are configured to implement functionality and/or process instructions for execution within system10. For example, processing circuitry30may be capable of processing instructions stored in a storage device (not illustrated inFIG. 1). Processing circuitry30may include, for example, microprocessors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or equivalent discrete or integrated logic circuitry, or a combination of any of the foregoing devices or circuitry. Accordingly, processing circuitry30may include any suitable structure, whether in hardware, software, firmware, or any combination thereof, to perform the functions ascribed herein to processing circuitry30. Processing circuitry30, and circuit14may include only analog circuitry, only digital circuitry, or a combination of analog circuitry and digital circuitry. The term “processor” or “processing circuitry” may generally refer to any of the foregoing analog circuitry and/or digital circuitry, alone or in combination with other logic circuitry, or any other equivalent circuitry.

Proof mass assembly16may include a proof mass, a frame, a set of tethers, and a set of DETF structures. The proof mass, in some examples, is suspended within the frame by the set of tethers and the set of DETF structures. For example, proof mass assembly16may include a set of DETF structures that suspend the proof mass in a first direction relative to the frame. Additionally, the set of tethers may suspend the proof mass in a second direction and a third direction relative to the frame. The first direction, the second direction, and the third direction may represent three axes (e.g., x-axis, y-axis, and z-axis) of a Cartesian space. In some cases, the set of DETF structures enable the proof mass to be displaced in the first direction. Additionally, in some cases, the set of tethers prevent the proof mass from being displaced in the second direction and the third direction. In this way, proof mass assembly16may only allow the proof mass to be displaced along a single axis (e.g., a displacement axis). Because the displacement of the proof mass may determine the acceleration measured by circuit14, system10may be configured to determine the acceleration relative to the displacement axis.

In some examples, the first positive feedback loop (e.g., light-emitting device12A, proof mass assembly16, EOM22A, photoreceiver24A, feedback unit26A, and frequency counter28A) and the second positive feedback loop (e.g., light-emitting device12B, proof mass assembly16, EOM22B, photoreceiver24B, feedback unit26B, and frequency counter28B) are configured to independently determine an acceleration value representative of an acceleration of an object including system10. For example, light-emitting device12may emit an optical signal, EOM22A may modulate the optical signal for driving a mechanical response in proof mass assembly16to obtain a first modulated optical signal, and EOM22A may transmit the first modulated optical signal to proof mass assembly16. Photoreceiver24A may receive the first modulated optical signal from proof mass assembly16, where properties of the first modulated optical signal received by photoreceiver24A may be affected by mechanical vibrations of a first DETF structure of proof mass assembly16. Photoreceiver24A converts the first modulated optical signal into a first electrical signal and transmits the first electrical signal to feedback unit26A.

Feedback unit26A may process the first electrical signal to obtain a first processed electrical signal. For example, feedback unit26A may use any combination of a first band pass filter, a first phase shifter, a first electronic amplifier, and a first voltage limiter to process the first electrical signal. Frequency counter28A may receive the first processed electrical signal and determine a first frequency value corresponding to the first processed electrical signal. In some cases, the first frequency value represents a mechanical vibration frequency of the first DETF structure of proof mass assembly16, which carries the first modulated optical signal ultimately received by photoreceiver24A.

In addition to transmitting the first processed electrical signal to frequency counter28A, feedback unit26A may transmit the first processed electrical signal to EOM22A. In turn, EOM22A may modulate the optical signal emitted by light-emitting device12based on the first processed electrical signal, where the first modulated optical signal is transmitted to photoreceiver24A via the first DETF structure of proof mass assembly16, thus completing the first positive feedback loop. As such, a future mechanical vibration frequency of the first DETF structure depends, at least in part, on a current mechanical vibration frequency of the first DETF structure.

Additionally, in some examples, the second positive feedback loop may determine a second frequency value. For example, light-emitting device12may emit an optical signal, EOM22B may modulate the optical signal to obtain a second modulated optical signal, and EOM22B may transmit the second modulated optical signal to proof mass assembly16. Photoreceiver24B may receive the second modulated optical signal from proof mass assembly16, where properties of the second modulated optical signal received by photoreceiver24B may be affected by mechanical vibrations of a second DETF structure of proof mass assembly16. Photoreceiver24B converts the second modulated optical signal into a second electrical signal and transmits the second electrical signal to feedback unit26B.

In some examples, feedback unit26B processes the second electrical signal to obtain a second processed electrical signal. For example, feedback unit26B may use any combination of a second band pass filter, a second phase shifter, a second electronic amplifier, and a second voltage limiter to process the second electrical signal. Frequency counter28B may receive the second processed electrical signal and determine a second frequency value corresponding to the second processed electrical signal. In some cases, the second frequency value represents a mechanical vibration frequency of the second DETF structure of proof mass assembly16, which carries the second modulated optical signal ultimately received by photoreceiver24B.

In addition to transmitting the second processed electrical signal to frequency counter28B, feedback unit26B may transmit the second processed electrical signal to EOM22B. In turn, EOM22B may modulate the optical signal for driving a mechanical response in proof mass assembly16and emitted by light-emitting device12based on the second processed electrical signal, where the second modulated optical signal is transmitted to photoreceiver24B via the second DETF structure of proof mass assembly16, thus completing the second positive feedback loop. As such, a future mechanical vibration frequency of the second DETF structure depends, at least in part, on a current mechanical vibration frequency of the second DETF structure.

Processing circuitry30may be configured to calculate, based on the first frequency value, a first acceleration value. In some examples, to calculate the first acceleration value, processing circuitry30may subtract a baseline frequency value from the first frequency value to obtain a first frequency difference value. The baseline frequency value may represent a resonant mechanical frequency of the first DETF structure of proof mass assembly16while the proof mass is not displaced from a resting point along the proof mass displacement axis. In other words, the modulated optical signal emitted by EOM22A may induce or drive the first DETF structure to vibrate at the baseline frequency value while the proof mass is not displaced from the resting point along the proof mass displacement axis. As such, when the object is not accelerating, the first frequency difference value may be equal to zero since the first acceleration value—which represents the mechanical frequency of the first DETF structure—is equal to the baseline frequency value when the proof mass is not displaced (e.g., the object carrying system10is not accelerating). The first frequency difference value, in some examples, may be correlated with an acceleration of the object. In other words, an increase of a magnitude of the first frequency difference value may indicate an increase in the acceleration of the object and a decrease of a magnitude of the first frequency difference value may indicate decrease in the acceleration of the object.

Additionally, processing circuitry30may be configured to calculate a second acceleration value based on the second acceleration value. In some examples, to calculate the second acceleration value, processing circuitry30may subtract a baseline frequency value from the second frequency value to obtain a second frequency difference value. The second frequency difference value, in some examples, may be correlated with an acceleration of the object. In other words, an increase of a magnitude of the second frequency difference value may indicate an increase in the acceleration of the object and a decrease of a magnitude of the second frequency difference value may indicate decrease in the acceleration of the object. The first acceleration value and the second acceleration value, which are calculated by processing circuitry30, may, in some cases, be approximately equal.

FIG. 2is a block diagram illustrating circuit14ofFIG. 1in further detail, in accordance with one or more techniques of this disclosure. As illustrated inFIG. 1, circuit14includes EOMs22, photoreceivers24, feedback units26, frequency counters28, and processing circuitry30. Feedback units26may each include band pass filters40A,40B (collectively, “band pass filters40”), phase shifters42A,42B (collectively, “phase shifters42”), electronic amplifiers44A,44B (collectively, “electronic amplifiers44), and drivers47A,47B (collectively, “drivers47). The first feedback loop includes band pass filter40A, phase shifter42A, electronic amplifier44A, and driver47A). The second feedback loop includes band pass filter40B, phase shifter42B, electronic amplifier44B, and driver47B.

Circuit14may be configured to receive optical signals from proof mass assembly16, convert the optical signals into electrical signals, process the electrical signals, analyze the processed electrical signals to determine acceleration values, and use the processed electrical signals to modulate optical signals and reject noise, thus completing the first feedback loop and the second feedback loop. While this example is an accelerometer, in some examples, circuit14may be configured to analyze the processed electrical signals to determine other values, such as, for example, but not limited to, velocity, vibration, rotation, and other values. For example, photoreceivers24A may receive a first modulated optical signal from a first DETF structure of proof mass assembly16. The first modulated optical signal may include a frequency component associated with the first DETF structure itself, such as a vibration frequency of the first DETF structure. Photoreceivers24A may convert the first modulated optical signal into a first set of electrical signals, preserving the frequency component indicative of the vibration frequency of the first DETF structure for driver47A. Photoreceivers24A may transmit the first set of electrical signals to feedback unit26A, which includes band pass filter40A, phase shifter42A, electronic amplifier44A, and driver47A.

Band pass filter40A may be an electronic filter that attenuates frequencies outside of a frequency range and “passes” frequencies within the frequency range. In some examples, band pass filter40A includes any combination of passive filters, active filters, infinite impulse response (IIR) filters, finite impulse response (FIR) filters, Butterworth filters, Chebyshev filters, elliptic filters, Bessel filters, Gaussian filters, Legendre filters, or Linkwitz-Riley filters. In some examples, band pass filter40A includes a combination of a high pass filter which passes frequencies above a high pass cutoff point and a low pass filter which passes frequencies below a low pass cutoff point. In some cases, band pass filter40A passes frequencies within a range between 100 kilohertz (kHz) and 10,000 kHz.

Phase shifter42A may be configured to shift a phase of the first electrical signal and the second electrical signal. Phase may be characterized as a position of an instant on a waveform cycle of a periodic waveform. For example, the first electrical signal may include periodic waveforms which represent frequency components of the first electrical signal. A maximum peak of a sine wave for example, may be at a different phase than a minimum peak, or a zero crossing of the sine wave. In some examples, phase shifter42A may “delay” the first electrical signal by a time value in order to shift a timeline in which frequency components of the first electrical signal oscillate and delay the second electrical signal by a time value in order to shift a timeline in which frequency components of the second electrical signal oscillate.

Electronic amplifier44A may amplify the first electrical signal and/or the second electrical signal such that an amplitude of the first electrical signal is increased by a gain factor. In other words, electronic amplifier44A may increase a power of the first electrical signal and second electrical signal. By amplifying the first electrical signal and second electrical signal using electronic amplifier44A, circuit14may improve an ability of processing circuitry30to analyze the first electrical signal and the second electrical signal, and modulate the optical signal emitted by light-emitting device12using EOM22A.

Electronic amplifier44A may include, in some cases, power amplifiers, operational amplifiers, or transistor amplifiers, or any combination thereof. Additionally, in some examples, electronic amplifier44A is configured to limit a voltage of the first electrical signal and/or second electrical signal to a maximum voltage value. In other words, electronic amplifier44A may prevent the first electrical signal and the second electrical signal from exceeding the maximum voltage value, meaning that the first processed electrical signal and the second processed electrical signal produced by feedback unit26A may not exceed the maximum voltage value.

In some examples, the first set of electrical signals may pass through feedback unit26A in an order from band pass filter40A, to phase shifter42A, to electronic amplifier44A, and to driver47A, as illustrated inFIG. 2. However, the order illustrated inFIG. 2is not limiting. Band pass filter40A, phase shifter42A, and electronic amplifier44A may be arranged to process the first electrical signal and second first electrical signal in any order.

Driver47A may be configured to cause EOM22A to modulate the optical signal to drive a mechanical resonance of proof mass assembly16. For example, driver47A may be configured to generate a mechanical resonance feedback signal that causes EOM22A to operate near or at the mechanical resonance of proof mass assembly16. For example, driver47A may generate the mechanical resonance feedback signal using a signal generator set to the mechanical resonance of proof mass assembly16. For example, driver47A may be designed to use a first optical signal (e.g., a sensing optical signal) for sensing a mechanical resonance at proof mass assembly16while system10may use a second optical signal (e.g., a driving optical signal) for driving the mechanical resonance at proof mass assembly16.

Driver47A may transmit a mechanical resonance feedback signal to frequency counter28A. Frequency counter28A may determine a first frequency value, and processing circuitry30may determine a first acceleration value based on the first frequency value. Additionally, driver47A may transmit the mechanical resonance feedback signal to EOM22A and EOM22A may modulate the optical signal for driving a mechanical response and emitted by light-emitting device12A based on the mechanical resonance feedback signal generated based on a sensing optical signal. In this way, proof mass assembly16, photoreceiver24A, band pass filter40A, phase shifter42A, electronic amplifier44A, driver47A, EOM22A, and frequency counter28A are a part of the first positive feedback loop which produces the first acceleration value associated with the object including system10.

The components of feedback unit26B (e.g., band pass filter40B, phase shifter42B, electronic amplifier44B, and driver47B) may be substantially similar to the respective components of feedback unit26A. As such, the second positive feedback loop may be substantially similar to the first positive feedback loop.

FIG. 3illustrates a conceptual diagram of proof mass assembly16including a proof mass50suspended within a frame52by a first DETF structure54, a second DETF structure58, and a set of tethers62A-62R, in accordance with one or more techniques of this disclosure. As illustrated inFIG. 3, proof mass assembly16includes proof mass50, frame52, first DETF structure54including a first pair of mechanical beams56A,56B (collectively, “first pair of mechanical beams56”), second DETF structure58including a second pair of mechanical beams60A,60B (collectively, “second pair of mechanical beams60”), tethers62A-62R (collectively, “tethers62”), first distal tine64, and second distal tine68. Proof mass assembly16is aligned relative to proof mass displacement axis72and proof mass resting plane74, as illustrated inFIG. 3.

Proof mass assembly16is a mechanical component of electro-opto-mechanical system10. Because system10measures acceleration, which is a rate in which a velocity of an object changes over time, it may be beneficial to include proof mass assembly16so that acceleration can be measured based on a physical object such as proof mass50. For example, system10, which includes proof mass assembly16may be fixed to or included within an object. Consequently, as the object accelerates at an acceleration value, proof mass assembly16may also accelerate at the acceleration value. Acceleration may affect a position of proof mass50within frame52relative to proof mass displacement axis72and proof mass resting plane74. For example, non-zero acceleration may cause proof mass50to be displaced from proof mass resting plane74along proof mass displacement axis72. As described herein, if proof mass50is “displaced,” a center of mass of proof mass50is displaced relative to frame52. Increasing a magnitude of acceleration may cause the displacement of proof mass50along proof mass displacement axis72to increase. Additionally, decreasing a magnitude of acceleration may cause the displacement of proof mass50along proof mass displacement axis72to decrease.

In some examples, proof mass50takes the form of a patterned thin film, where the thin film has a mass within a range between 100 nanograms (ng) and 10,000 ng. Additionally, in some cases, the thin film has a thickness within a range between 1 nm and 5,000 nm. Proof mass50may be suspended within frame52along proof mass displacement axis72by first DETF structure54and second DETF structure58(collectively, “DETF structures54,58”). First DETF structure54and second DETF structure58may each have a high level of stiffness. For example, a scale factor of each of first DETF structure54and second DETF structure58may be within a range between 0.1 parts per million per gravitational force equivalent (ppm/G) and 10 ppm/G. In this way, proof mass assembly16may include a very light proof mass50which is secured by very stiff DETF structures54,58. As such, a very high acceleration (e.g., 100,000 m/s2) may cause proof mass50to be displaced along the proof mass displacement axis72by a very small displacement value, for example. In some examples, proof mass50is displaced along the proof mass displacement axis72by a displacement value of up to 100 nm.

To generate acceleration values indicative of the acceleration of the object in which system10is fixed to, system10may quantify, using optical signals, the displacement of proof mass50within frame52. To quantify the displacement of proof mass50, system10may measure and analyze mechanical properties of DETF structures54,58, such as mechanical vibrating frequency values corresponding to DETF structures54,58. Indeed, since DETF structures54,58suspend proof mass50, the mechanical vibrating frequencies of DETF structures54,58may be affected due to a displacement of proof mass50. For example, a displacement of proof mass50towards first DETF structure54and away from second DETF structure58may cause proof mass50to apply a compression force to first DETF structure54and apply a tension force to second DETF structure58. Such a compression force may cause the mechanical vibration frequency of first DETF structure54to decrease and such a tension force may cause the mechanical vibration force of second DETF structure58to increase. Changes in the mechanical vibration frequencies of DETF structures54,58may, in some examples, be proportional to the displacement of proof mass50relative to frame52in the direction of proof mass displacement axis72. In some examples, System10may measure changes in the mechanical vibration frequencies of DETF structures54,58by transmitting modulated optical signals through DETF structures54,58.

First DETF structure54may include, for example, the first pair of mechanical beams56separated by a gap. The first pair of mechanical beams56may include photonic crystal mechanical beams that are configured for guiding a first modulated optical signal while first DETF structure54is oscillating at a first mechanical vibrating frequency. In some cases, the first modulated optical signal is emitted by light-emitting device12(illustrated inFIG. 1), and the first modulated optical signal itself induces vibration in first DETF structure54. Additionally, the vibration of the first DETF structure54may affect certain properties of the first modulated optical signal such that the mechanical vibrating frequency of the first DETF structure54is reflected in the first modulated optical signal. In this way, the first modulated optical signal may cause the mechanical vibration in the first DETF structure54and enable system10to measure the mechanical vibration frequency of the first DETF structure54based on the first modulated optical signal.

Additionally, second DETF structure58may include, for example, the second pair of mechanical beams60separated by a gap. The second pair of mechanical beams60may include photonic crystal mechanical beams that are configured for guiding a second modulated optical signal while second DETF structure58is oscillating at a second mechanical vibrating frequency. In some cases, the second modulated optical signal is emitted by light-emitting device12(illustrated inFIG. 1), and the second modulated optical signal itself induces vibration in second DETF structure58. Additionally, the vibration of the second DETF structure58may affect certain properties of the second modulated optical signal such that the mechanical vibrating frequency of the second DETF structure58is reflected in the second modulated optical signal. In this way, the second modulated optical signal may cause the mechanical vibration to occur in the second DETF structure58and enable system10to measure the mechanical vibration frequency of the second DETF structure58based on the second modulated optical signal.

Proof mass50may be fixed to frame52by tethers62. In some examples, tethers62may suspend proof mass50in proof mass resting plane74such that the center of mass of proof mass50does not move within proof mass resting plane74relative to frame52. Proof mass displacement axis72may represent a single axis (e.g., x-axis) of a Cartesian space, and proof mass resting plane74may represent two axes (e.g., y-axis and z-axis) of the Cartesian space. Since tethers62may restrict proof mass50from being displaced relative to proof mass resting plane74, in some examples, proof mass50may only be displaced along the proof mass displacement axis72. System10may measure an acceleration based on mechanical vibrating frequencies of DETF structures54,58, where the mechanical vibrating frequencies are related to an amount of displacement of proof mass50along proof mass displacement axis72. In this way, the acceleration determined by system10may be an acceleration relative to proof mass displacement axis72.

First DETF structure54may include a proximal end that is proximate to proof mass50, and a distal end that is separated from frame52by a first gap66. First distal tine64may help to suspend first DETF structure54within frame52such that the first DETF structure54is perpendicular to proof mass resting plane74. In some examples, first distal tine64extends perpendicularly to proof mass displacement axis72between two sidewalls of frame52. An optical signal may travel through frame52via a first optical fiber (not illustrated inFIG. 3), the optical signal being coupled across first gap66to first DETF structure54.

Second DETF structure58may include a proximal end that is proximate to proof mass50, and a distal end that is separated from frame52by a second gap70. Second distal tine68may help to suspend first DETF structure58within frame52such that the second DETF structure58is perpendicular to proof mass resting plane74. In some examples, second distal tine68extends perpendicularly to proof mass displacement axis72between two sidewalls of frame52. An optical signal may travel through frame52via a second optical fiber (not illustrated inFIG. 3), the optical signal being coupled across second gap70to second DETF structure58.

FIG. 4illustrates a conceptual diagram of system10, in accordance with one or more techniques of this disclosure. The conceptual diagram ofFIG. 4includes light-emitting devices12, components of circuit14, and proof mass assembly16. In some examples, an object may be fixed to system10. The object, in some cases, may accelerate. System10, including proof mass assembly16, may accelerate with the object. As proof mass assembly16accelerates, proof mass50may be displaced relative to frame52. In the example illustrated inFIG. 4, if proof mass assembly16accelerates in direction78, proof mass50is displaced in direction78. Direction78, in some examples, is aligned with a proof mass displacement axis (e.g., proof mass displacement axis72ofFIG. 3.

As proof mass50is displaced in direction78relative to frame52, proof mass50applies a compression force to first DETF structure54, and proof mass50applies a tension force to second DETF structure58. Such forces may affect mechanical vibrating frequencies of DETF structures54,58, where mechanical vibration is induced in first DETF structure54and second DETF structure58by electro-optic modulator22A and electro-optic modulator22B, respectively. For example, the compression force applied to first DETF structure54may cause the mechanical vibration frequency of first DETF structure54to decrease, and the tension force applied to second DETF structure58may cause the mechanical vibration frequency of second DETF structure58to increase.

Light-emitting devices12may emit a driving optical signal to EOMs22and a sensing optical signal to proof mass assembly16. For example, each of light-emitting devices12may be configured to generate a sensing optical signal that interacts with proof mass assembly16and, in response to interacting with the proof mass assembly16, is impressed with one or more of a modulation in phase or frequency of mechanical vibrations in proof mass assembly16and a driving optical signal that is modulated by EOMs22and that stimulates mechanical vibrations in proof mass assembly16. In this way, the driving optical signal may provide driving modulation at proof mass assembly and feedback unit26A,26B may use the sensing optical signal that interacts with proof mass assembly16while the driving optical signal drives the mechanical vibration frequency at proof mass assembly16.

In turn, EOM22A and EOM22B may modulate a respective driving optical signal according to a processed electrical signals produced by feedback unit26A and feedback unit26B, respectively. As such, EOM22A may produce a first modulated optical signal for driving a mechanical response in proof mass assembly16and EOM22B may produce a second modulated optical signal for driving a mechanical response in proof mass assembly16. EOM22A, for example, may transmit the first modulated optical signal to proof mass assembly16. The first modulated optical signal may cross frame52. In some examples, frame52includes an aperture or another opening bridged by a first optical fiber which allows the first modulated optical signal to pass. Additionally, the first modulated optical signal may couple across first gap66to the first DETF structure54. The first modulated optical signal for driving a mechanical response in proof mass assembly16may propagate through first DETF structure54, inducing mechanical vibration in first DETF structure54. In some examples, the first modulated optical signal propagates the length of first DETF structure54towards proof mass50along mechanical beam56A and subsequently propagates the length of first DETF structure54away from proof mass50along mechanical beam56B. In some examples, the first modulated optical signal propagates the length of first DETF structure54towards proof mass50along mechanical beam56B and subsequently propagates the length of first DETF structure54away from proof mass50along mechanical beam56A.

Similarly, the first sensing optical signal may cross frame52. The first sensing optical signal may couple across first gap66to the first DETF structure54. The first sensing optical signal may propagate through first DETF structure54to impress mechanical vibrations in first DETF structure54onto the first sensing optical signal. In some examples, the first sensing optical signal propagates the length of first DETF structure54towards proof mass50along mechanical beam56A and subsequently propagates the length of first DETF structure54away from proof mass50along mechanical beam56B. In some examples, the first sensing optical signal propagates the length of first DETF structure54towards proof mass50along mechanical beam56B and subsequently propagates the length of first DETF structure54away from proof mass50along mechanical beam56A. In any case, by propagating the length of first DETF structure54, the first sensing optical signal may retain information indicative of mechanical properties (e.g., the mechanical vibration frequency) of first DETF structure54. After the first sensing optical signal propagates through first DETF structure54, the first sensing optical signal may exit proof mass assembly16via first gap66and the first optical fiber of frame52.

After exiting proof mass assembly16, the first sensing optical signal, which may include fluctuations in amplitude and/or frequency, may arrive at photoreceiver24A. Photoreceivers24A convert the first modulated optical signal into a set of electrical signals for rejecting noise in light-emitting device12A and for driving EOM22A to a mechanical resonance of proof mass assembly16. Frequency counter28A may determine a first frequency value corresponding to the first processed electrical signal, where the first frequency value is indicative of the mechanical vibrating frequency of the first DETF structure54. Processing circuitry30may subtract a baseline frequency value from the first frequency value to obtain a first frequency difference value and calculate a first acceleration value based on the first frequency difference value. EOM22A may use the first processed electrical signal to modulate the optical signal emitted by light-emitting device12.

EOM22B, for example, may transmit the second modulated optical signal to proof mass assembly16. The second modulated optical signal may cross frame52. In some examples, frame52includes an aperture or another opening bridged by a second optical fiber which allows the second modulated optical signal to pass. Additionally, the second modulated optical signal may couple across second gap70to the second DETF structure58. The second modulated optical signal may propagate through second DETF structure58, inducing mechanical vibration in second DETF structure58. In some examples, the second modulated optical signal propagates the length of second DETF structure58towards proof mass50along mechanical beam60A and subsequently propagates the length of second DETF structure58away from proof mass50along mechanical beam60B. In some examples, the second modulated optical signal propagates the length of second DETF structure58towards proof mass50along mechanical beam60B and subsequently propagates the length of second DETF structure58away from proof mass50along mechanical beam60A.

Similarly, the second sensing optical signal may cross frame52. Additionally, the second sensing optical signal may couple across second gap70to the second DETF structure58. The second sensing optical signal may propagate through second DETF structure58to impress mechanical vibrations in first DETF structure28onto the second sensing optical signal. In some examples, the second sensing optical signal propagates the length of second DETF structure58towards proof mass50along mechanical beam60A and subsequently propagates the length of second DETF structure58away from proof mass50along mechanical beam60B. In some examples, the second sensing optical signal propagates the length of second DETF structure58towards proof mass50along mechanical beam60B and subsequently propagates the length of second DETF structure58away from proof mass50along mechanical beam60A. In any case, by propagating the length of second DETF structure58, the second sensing optical signal may retain information indicative of mechanical properties (e.g., the mechanical vibration frequency) of second DETF structure58. After the second sensing optical signal propagates through second DETF structure58, the second sensing optical signal may exit proof mass assembly16via second gap70and the second optical fiber of frame52.

After exiting proof mass assembly16, the second sensing optical signal, which may include thermal noise, may arrive at photoreceivers24B. Photoreceivers24B convert the second modulated optical signal into a set of electrical signals for rejecting noise in light-emitting device12B and a second electrical signal for driving EOM22B to a mechanical resonance of proof mass assembly16. Frequency counter28B may determine a second frequency value corresponding to the second processed electrical signal, where the second frequency value is indicative of the mechanical vibrating frequency of the second DETF structure58. Processing circuitry30may subtract a baseline frequency value from the second frequency value to obtain a second frequency difference value and calculate a second acceleration value based on the second frequency difference value. EOM22B may use the second processed electrical signal to modulate the optical signal emitted by light-emitting device12.

FIG. 5depicts additional aspects of system10, in accordance with one or more techniques of this disclosure. For example,FIG. 5illustrates the first DETF structure54including the first pair of mechanical beams56. The optical signal emitted by light-emitting device12may induce a force between the first pair of mechanical beams56, and the force may be modelled by a spring force.FIG. 5illustrates a spring force provided by laser light between beams in an optical zipper in the gap between photonic crystal mechanical beams56A,56B of DETF structure54(502), a perspective view depiction of vibration modes in beams in an optical zipper in one common direction together (504), and a perspective view depiction of vibration modes in beams in an optical “zipper” in opposing directions of oscillation (506).

FIG. 6is a conceptual diagram illustrating example techniques for reducing drive feedthrough in optomechanical devices, in accordance with one or more techniques of this disclosure.FIG. 6is discussed with reference toFIGS. 1-5for example purposes only. As shown, electro-opto-mechanical system610, which may be an example of system10, may include light-emitting device612, intensity stabilizer617, EOM622, optical circulator672, proof mass assembly616(also referred to herein as “device616”), and feedback unit626.

Light-emitting device612may include sense laser611and drive laser613. Sense laser611and drive laser613may be output at different intensities. For example, sense laser611may be configured to generate a sensing optical signal such that the sense optical signal interacts with the proof mass assembly and, in response to interacting with the proof mass assembly, is impressed with one or more of a modulation in phase of mechanical vibrations in the proof mass assembly and a frequency of mechanical vibrations in the proof mass assembly. In contrast, drive laser613may be configured to generate a driving optical signal such that the driving optical signal stimulates mechanical vibrations in proof mass assembly616. For instance, drive laser613may be configured to generate the drive optical signal with an amplitude that is greater than ten times ( ) an amplitude of a sense optical signal output by sense laser611.

Sense laser611and drive laser613may be two intensity stabilized lasers, each tuned to a slightly different frequency. For example, sense laser611may be tuned to vopt+Γ/4 and drive laser613may be tuned to vopt−Γ/4, where vopt is the optical resonance frequency and Γ is the FWHM. In another example, driver laser613may be tuned to vopt+Γ/4 and sense laser611may be tuned to vopt−Γ/4.

Sense laser611and drive laser613may be each tuned to a slightly different frequency that is offset from the optical resonance frequency. For example, Sense laser611may be tuned to vopt+Γ/4+Δ and drive laser613may be tuned to vopt+Γ/4−Δ, where Δ is a resolvable frequency difference that is larger than the mechanical frequency. In some examples, driver laser613may be tuned to vopt+Γ/4+Δ and sense laser611may be tuned to vopt+Γ/4−Δ. In some examples, Sense laser611may be tuned to vopt−Γ/4+Δ and drive laser613may be tuned to vopt−Γ/4−Δ. In some examples, driver laser613may be tuned to vopt−Γ/4+Δ and sense laser611may be tuned to vopt−Γ/4−Δ, where vopt is the optical resonance frequency and Γ is the FWHM.

Intensity stabilizer617may be configured to regulate an intensity of the optical signal output by sense laser611to regulate an intensity of the optical signal to a predetermined light intensity value. For example, the optical signal output by sense laser611passes through a Variable Optical Attenuator (VOA)671, which may be configured to attenuate a portion of the optical signal. Tap673may be configured to output a first portion of the optical signal output from VOA671to photodiode675and a second portion of the optical signal output from VOA671to optical circulator672. In this example, intensity servo677may be configured to use an electrical signal output by photodiode675to stabilize the overall light level of the optical signal.

Intensity stabilizer617may be configured to regulate an intensity of the optical signal output by drive laser613to regulate an intensity of the optical signal to a predetermined light intensity value. For example, the optical signal output by drive laser613passes through VOA686, which may be configured to attenuate a portion of the optical signal. Tap676may be configured to output a first portion of the optical signal output from VOA686to photodiode674and a second portion of the optical signal output from VOA686to optical EOM622. In this example, intensity servo677may be configured to use an electrical signal output by photodiode674to stabilize the overall light level of the optical signal.

Intensity servo677may be configured to regulate an intensity of the optical signal output by sense laser611to a first predetermined light intensity value before outputting the optical signal to proof mass assembly616. In some examples, intensity servo677may be configured to regulate an intensity of the optical signal output by drive laser613to a second predetermined light intensity value before outputting the optical signal to proof mass assembly616. In some examples, the second predetermined light intensity value may be larger (e.g., more than 10 times, more than 20 times, etc.) than the first predetermined light intensity value.

EOM622may be configured to modulate the optical signal output by tap676(e.g., the driving optical signal) to an optical resonance of proof mass assembly616. For example, EOM622may be configured to drive the optical signal output by tap676to a peak optical resonance of proof mass assembly616using an electrical signal generated by feedback unit626.

Optical circulator672may be configured to output an optical signal (e.g., a driving optical signal) output by EOM622and an optical signal output (e.g., a sensing optical signal) by tap673to proof mass assembly616and receive an optical signal reflected from proof mass assembly616. For example, an optical signal output by sense laser611and stabilized by intensity stabilizer617and an optical signal output by driver laser613and stabilized by intensity stabilizer617are combined to generate a combined optical signal and the combined optical signal passes into port ‘1’ of optical circulator672and out of port ‘2’ of optical circulator672, where the modulated optical signal interacts with proof mass assembly616(e.g., a zipper cavity measured in reflection).

After reflection back into port ‘2’ of optical circulator672, the optical signal is output from port ‘3’ of optical circulator672to feedback unit626. Feedback unit626may be configured to use the optical signal resulting from proof mass assembly616to drive the mechanical response of proof mass assembly616.

As shown, feedback unit626may include dichroic684, photodiode624A,624B (collectively, “photodiodes624” (photodiode624A is optional)), Band-Pass Filter (BPF)620, frequency servo and data acquisition module628, and signal generator646. Frequency servo and data acquisition module628may be an example of drivers47A,47B.

Dichroic648may be configured to separate the drive and sense optical signals, which are at different wavelengths. For example, dichroic648may be configured to output a first optical signal corresponding to vopt+Γ/4 and a second optical signal corresponding to vopt−Γ/4 or output a first optical signal corresponding to vopt−Γ/4 and a second optical signal corresponding to vopt+Γ/4. In some examples, dichroic648may be configured to output a first optical signal corresponding to vopt+Γ/4+Δ and a second optical signal corresponding to vopt+Γ/4−Δ or output a first optical signal corresponding to vopt+Γ/4−Δ and a second optical signal corresponding to vopt+Γ/4+Δ. In some examples, dichroic648may be configured to output a first optical signal corresponding to vopt−Γ/4+Δ and a second optical signal corresponding to vopt−Γ/4−Δ or output a first optical signal corresponding to vopt−Γ/4−Δ and a second optical signal corresponding to vopt−Γ/4+Δ.

Photodiode624A may be configured to convert the first portion of the optical signal output by dichroic684into a first electrical signal. Similarly, photodiode624B may be configured to convert the second portion of the optical signal output by dichroic684into a second electrical signal.

BPF620may be configured to pass electrical signals within a band of frequencies around the mechanical frequency of proof mass assembly616. For example, BPF620may be configured to pass electrical signals within a band of frequencies at about 1 Mhz.

Frequency servo and data acquisition module628may be configured to cause EOM622to drive the optical signal output by tap676to a mechanical resonance of proof mass assembly616. For example, signal generator646may be configured to generate a mechanical resonance feedback signal that causes EOM622to operate near or at the mechanical resonance of proof mass assembly616. For example, signal generator646may generate a mechanical resonance feedback signal using signal generator646to set to the mechanical resonance of proof mass assembly616. Frequency servo and data acquisition module628may determine a first frequency value to determine an acceleration value for proof mass assembly616. Frequency servo and data acquisition module628may be configured to measure, using the mechanical resonance feedback signal, an acceleration at proof mass assembly616.

In accordance with techniques described herein, drive laser613may be configured to generate an optical signal that passes through EOM622where light is modulated at the mechanical resonance frequency. The optical signal output by driver laser613is combined with an optical signal output by sense laser611, and is a combination of the optical signal output by driver laser613and optical signal output by sense laser611is passed through optical circulator672to proof mass assembly616(e.g., an optomechanical accelerometer, which may include a photonic zipper cavity). The optical signal output by drive laser613interacts with proof mass assembly616and stimulates mechanical vibrations in proof mass assembly616. The optical signal output by sense laser611interacts with proof mass assembly616, and has impressed on the optical signal a modulation in phase and/or frequency due to the mechanical vibrations simulated by the optical signal output by drive laser613, but also carrying information about the frequency and phase of the mechanical vibrations, including, for example, one or more shifts in the mechanical resonance due to acceleration of proof mass assembly616. Both optical signals generated by sense laser611and drive laser613leave proof mass assembly616(in reflection or transmission). In the case of reflection, the optical signal is passed back through optical circulator672and to dichroic684with sufficient frequency selectivity to separate the drive and sense optical fields, which are at different wavelengths. Photodiode624B, BPF620, frequency servo and data acquisition module628, and signal generator646, may be configured to perform subsequent detection and processing of only the optical signal output sense laser611, thereby helping to provide measure of acceleration which is not contaminated by feed-through. In closed loop oscillator operation, feedback unit626may be configured to electronically detect and process the optical signal from sense laser611and control signal generator646to drive the EOM622to create a modulated drive field. In some examples (e.g., open loop, or scanning, or Phase-Locked-Loop), feedback unit626may be configured to derive the signal to be applied to EOM622from an independent frequency synthesizer.

FIG. 7is a conceptual diagram an example first optical response of a first optical frequency component and a second optical frequency component, in accordance with one or more techniques of this disclosure.FIG. 7is discussed with reference toFIGS. 1-6for example purposes only. The abscissa axis (e.g., horizontal axis) ofFIG. 7represents laser wavelength in nanometers (nm) and the ordinate axis (e.g., vertical axis) ofFIG. 7represents a normalized reflection702. In the example ofFIG. 7, which may be useful for narrow optical resonances, a laser (e.g., drive laser or sense laser) may be set to first frequency704, which is tuned to vopt+Γ/4 and the other laser (e.g., sense laser or drive laser) is tuned to vopt−Γ/4, where vopt is the optical resonance frequency and Γ is the FWHM.

FIG. 8is a conceptual diagram an example second optical response of a first optical frequency component and a second optical frequency component, in accordance with one or more techniques of this disclosure.FIG. 8is discussed with reference toFIGS. 1-7for example purposes only. The abscissa axis (e.g., horizontal axis) ofFIG. 8represents laser wavelength in nanometers (nm) and the ordinate axis (e.g., vertical axis) ofFIG. 8represents a normalized reflection802. In the example ofFIG. 8, a laser (e.g., drive laser or sense laser) may be set to first frequency804, which is tuned to vopt+Γ/4−Δ and the other laser (e.g., sense laser or drive laser) is tuned to vopt+Γ/4+Δ, where vopt is the optical resonance frequency and Γ is the FWHM. In some examples, a laser (e.g., drive laser or sense laser) may be set to first frequency, which is tuned to vopt−Γ/4−Δ and the other laser (e.g., sense laser or drive laser) is tuned to vopt−Γ/4+Δ, where vopt is the optical resonance frequency and Γ is the FWHM.

FIG. 9is a conceptual diagram an example of an optical signal applied to a proof mass assembly, in accordance with one or more techniques of this disclosure.FIG. 9is discussed with reference toFIGS. 1-8for example purposes only. The abscissa axis (e.g., horizontal axis) ofFIG. 9represents laser wavelength in nanometers (nm) and the ordinate axis (e.g., vertical axis) ofFIG. 9represents a normalized reflection902. In the example ofFIG. 9, optical signal912corresponds to an optical signal output by drive laser613before output to optical circulator672and after processing by intensity stabilizer617and optical signal914corresponds to an optical signal output by sense laser611before output to optical circulator672and after processing by intensity stabilizer617.

As shown, optical signal912includes a central frequency with deleterious “feed-through” modulation, which may be represented as a lower sideband and an upper sideband. Optical signal914, however, includes a central frequency with little or no deleterious feed-through modulation.

FIG. 10is a conceptual diagram an example of an optical signal reflected output by a proof mass assembly in response to the optical signal ofFIG. 9, in accordance with one or more techniques of this disclosure.FIG. 10is discussed with reference toFIGS. 1-9for example purposes only. The abscissa axis (e.g., horizontal axis) ofFIG. 10represents laser wavelength in nanometers (nm) and the ordinate axis (e.g., vertical axis) ofFIG. 10represents a normalized reflection1002. In the example ofFIG. 10, optical signal1012corresponds to an optical signal output by drive laser613before output to dichroic684and after output by optical circulator672and optical signal1014corresponds to an optical signal output by sense laser611before output to dichroic684and after output by optical circulator672.

As shown, optical signal1012includes a central frequency with deleterious feed-through modulation after interacting with proof mass assembly616. Accordingly, while optical signal1012includes an impression from interactions with proof mass assembly616, the impression is obscured by the deleterious feed-through modulation associated with driving the mechanical response at proof mass assembly. In contrast, optical signal1014includes a central frequency with small or no deleterious feed-through modulation. As such, optical signal1014more clearly includes the impression from interactions with proof mass assembly616, which can be seen as additional sidebands, compared to optical signal1012.

FIG. 11is a conceptual diagram an example of a filtered optical signal resulting from filtering the optical signal ofFIG. 10, in accordance with one or more techniques of this disclosure.FIG. 11is discussed with reference toFIGS. 1-10for example purposes only. The abscissa axis (e.g., horizontal axis) ofFIG. 11represents laser wavelength in nanometers (nm) and the ordinate axis (e.g., vertical axis) ofFIG. 11represents a normalized reflection1102. In the example ofFIG. 11, optical signal1114corresponds to an optical signal output by sense laser611after processing by dichroic684.

FIG. 12is a flow diagram illustrating an example for reducing drive feedthrough in optomechanical devices, in accordance with one or more techniques of this disclosure.FIG. 12is discussed with reference toFIGS. 1-11for example purposes only.

Light-emitting device612generates a first optical signal and a second optical signal (1202). In some examples, the first optical signal comprises a frequency different than a frequency of the second optical signal. EOM622modulates the second optical signal (1204). Optical circulator672outputs the first optical signal and the second optical signal to the proof mass assembly (1206). Dichroic684generates a filtered optical signal corresponding to a response by the proof mass assembly to the first optical signal without the second optical signal (1208). Photodiode624B generates an electrical signal based on the filtered optical signal (1210). In some examples EOM622modulates the second optical signal based on the electrical signal.

Frequency servo and data acquisition module628may optionally generate an indication of acceleration at the proof mass assembly based on the electrical signal (1212). However, in other examples, circuitry may generate other indications, such as, for example, an indication of velocity, vibration, rotation, position, or another indication at a mechanical assembly.

The optomechanical device described herein may include only analog circuitry, only digital circuitry, or a combination of analog circuitry and digital circuitry. Digital circuitry may include, for example, a microcontroller on a single integrated circuit containing a processor core, memory, inputs, and outputs. For example, digital circuitry of the optomechanical device described herein may include one or more processors, including one or more microprocessors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), or any other equivalent integrated or discrete logic circuitry, as well as any combinations of such components. The term “processor” or “processing circuitry” may generally refer to any of the foregoing analog circuitry and/or digital circuitry, alone or in combination with other logic circuitry, or any other equivalent circuitry.

The techniques of this disclosure may be implemented in a wide variety of devices or apparatuses that include integrated circuits (ICs) or sets of ICs (e.g., chip sets). Various components, modules, or units are described in this disclosure to emphasize functional aspects of devices configured to perform the disclosed techniques, but do not necessarily require realization by different hardware units. Rather, various units may be combined or provided by a collection of interoperative hardware units, including one or more processors as described above, in conjunction with suitable software and/or firmware.