Patent Description:
Laser vibrometers have been used to make non-contact vibration measurements of a surface. In some instances, a test beam is transmitted to the surface of interest and a reflected laser beam is received and analyzed to extract a Doppler shift due to the motion of the surface of interest. A typical laser vibrometer requires access to a reference beam that is identical in frequency to the test beam. Prior to reaching the surface of interest, the test beam passes through a Bragg cell, which adds a frequency shift. The reflected beam has a frequency containing the frequency of the test beam, the frequency shift, and the Doppler shift. The reflected beam and the reference beam are fed into a photodetector and the Doppler shift is thereafter estimated by investigating the beat frequency between the two beams.

Despite the usefulness of conventional vibrometers in many applications, the requirement of access to a local copy of the test beam (i.e., a reference beam) makes the conventional approach ill suited for remote sensing. Accordingly, new systems, methods, and other techniques are needed. Document <CIT> discloses an optical system providing information about tangential vibration components of a surface at remote location. The optical system includes a light source that emits two beams directed at the interrogated surface. A detector system detects a third beam formed by the reflected beams, and provides information on a phase change.

The present invention relates to a method of performing remote sensing as defined in claim <NUM> and to an apparatus as defined in claim <NUM>.

Further details of the invention are set forth in the dependent claims.

Numerous benefits are achieved by way of the present invention. For example, with conventional laser Doppler vibrometers, a local oscillator or a local copy of the interrogation laser signal is required so as to detect the frequency differences between the interrogation laser signal and the reflected laser signal caused by the surface of interest. Additionally, embodiments of the present invention are not limited by the coherence length of the laser source, thereby extending the usable range of the device. Furthermore, embodiments of the present invention include a chip scale inteferometer that can be fabricated significantly more compactly and inexpensively compared to conventional interferometers. The chip scale interferometer is not limited to vibrometry applications, but can be used in a wide variety of frequency measurement systems. Examples of possible applications beyond vibrometry include a number of laboratory-scale measurement setups, medical imaging, telecommunication networks, navigation systems, radar systems, and the like. Other benefits of the present invention will be readily apparent to those skilled in the art.

Weak value amplification (WVA) and inverse weak value amplification (IWVA) using free space optics have enabled ultrasensitive measurements in applications such as beam deflection, frequency shifts, and phase shifts. The weak value technique allows the amplification of small signals by introducing a weak perturbation to the system and performing a post-selection to the data.

Bringing weak value techniques to the field of integrated photonics improves its applications. For example, it largely reduces the size of the measuring system to millimeter scale. Also, an integrated photonic device is inherently stable; therefore it is less susceptible to environmental factors such as vibrations. With an on-chip weak value amplification device, precision measurements can be carried out in a small volume with reliable performance.

In some instances, IWVA can be demonstrated using free space optics and a misaligned Sagnac interferometer. One goal may be to measure the relative phase shift φ between the two paths of the interferometer. The misalignment introduces a phase front tilt k to one path of the interferometer and -k to the other. <MAT>
When the two paths interfere at the beam splitter, considering a Gaussian input, the dark port becomes,
<MAT>
By measuring the mean location shift -φ/(<NUM>k) of the dark port pattern, the phase shift φ is determined.

To bring free space IWVA to the integrated photonics regime, the above expressions are expanded into Hermite-Gaussian (HG) modes. The beams are composed mainly of the HG<NUM> mode with a small contribution of the HG<NUM> mode. Contribution of the higher modes is negligible. Therefore, the phase front tilt can be considered as coupling the initial HG<NUM> mode partially into the HG<NUM> mode. <MAT>
<MAT>.

Eigenmodes of a waveguide are similar to Hermite-Gaussian modes. The theory described above can be applied to waveguide eigenmodes TE<NUM> and TE<NUM>. Assuming that a TE<NUM> mode is sent into an upper waveguide of the device. Its power is split in half and the fields become,
<MAT>
<MAT>
Then a relative phase φ between the two paths is added,
<MAT>
<MAT>.

Similar to free space case, part of the TE<NUM> mode is coupled to the TE<NUM> mode with opposite phases in the two paths. a is the percentage of the TE<NUM> mode coupled to the TE<NUM> mode, which is a small number. <MAT>
<MAT>.

After the two paths interfere at the second <NUM>/<NUM> splitter, the dark port becomes,
<MAT>
Since φ is very small,
<MAT>
Therefore, by analyzing the ratio between the TE<NUM> and TE<NUM> modes, the phase φ can be determined.

Embodiments of the invention are related to methods and systems for performing long range vibrometry using weak measurement amplification (WMA). Specifically, embodiments relate to a chip scale integrated optics WMA sensor for detecting vibration signals of remote vibrating targets. According to some embodiments, an interrogation laser is transmitted toward a remote vibrating target and return vibration signals (micro-Doppler) are imaged with a chip scale WMA receiver sensor to produce target vibration profiles. This approach enables ultra-sensitive vibrometry without the need for long coherence length lasers and significantly reduces technical noise. The approach also enables longer range vibrometry missions than the current state of the art of commercial remote vibrometers. An integrated photonics implementation at the chip scale provides for significant reduction in platform vibration sensitivity of the vibrometer platform, allowing the WMA sensor to measure the target effects versus the platform effects. The implementation of weak value and inverse weak value based detection with several different interferometer geometries using guided waves in a monolithic geometry enables the implementation of the WVA effect in an ultrasmall package (compared to conventional interferometer packages). This advances WMA to real world applications by reducing effects related to the vibrometer platform.

In some embodiments, a tapered fiber coupler couples light from a specific target location within the receiver's field of view onto an individual chip scale silicon waveguide, which is designed to form an interferometer by creating two beam splitters in the waveguide's propagation path. The signal injected into the waveguide from the remote vibrating target contains both the initial laser frequency (i.e., the interrogation frequency) and the Doppler and Micro-Doppler signals superimposed on top of the initial laser frequency (e.g., a THz laser frequency). The waveguide is designed with a given refractive index difference to create two modes of propagation, for example, by spatially varying the index of refraction across the transverse profile of the waveguide. The two beam splitters cause constructive interference of a higher, information-containing mode and destructive interference of the lowest mode.

<FIG> illustrates a block diagram of a vibrometer <NUM>, according to some embodiments of the present invention. Vibrometer <NUM> includes a transmitter module <NUM> configured to transmit an interrogation signal <NUM> to a remote vibrating target <NUM> and a receiver module <NUM> configured to receive a reflected signal <NUM> generated by interrogation signal <NUM> being reflected off remote vibrating target <NUM>. Transmitter module <NUM> may include an interrogation laser <NUM> for modulating interrogation signal <NUM> at an interrogation frequency fo, typically in the THz frequency range. Optionally, an afocal expander <NUM> can be used to expand interrogation signal <NUM> prior to transmission thereof to reduce beam divergence. Receiver module <NUM> may include a receiver telescope <NUM> for collecting reflected signal <NUM><NUM> from a specific target location within the field of view of vibrometer <NUM> and for imaging reflected signal <NUM> onto a WMA interferometer <NUM>. As described herein, WMA interferometer <NUM> processes reflected signal <NUM> in a way that allows extraction of a Doppler frequency fd introduced onto reflected signal <NUM> by remote vibrating target <NUM>.

In some embodiments, vibrometer <NUM> includes control/processing electronics <NUM> that is communicatively coupled to each of transmitter module <NUM> and receiver module <NUM>. For example, control/processing electronics <NUM> may send control signals to and receive information signals from each of transmitter module <NUM> and receiver module <NUM>. According to at least one embodiment, control/processing electronics <NUM> may send a set of control signals to transmitter module <NUM> so as to turn on interrogation laser <NUM>, set the interrogation frequency fo, and cause interrogation laser <NUM> to point at remote vibrating target <NUM>. The set of control signals may implement more sophisticated control algorithms in which, as an example, the interrogation frequency fo may be driven over a range of frequencies while remote vibrating target <NUM> is spatially scanned by directing interrogation laser <NUM> across the field of view. Control/processing electronics <NUM> may generate target vibration profiles such as Doppler images <NUM> based on the output of WMA interferometer <NUM>.

<FIG> illustrates an example of vibrometer <NUM> comprising a plurality of WMA interferometers <NUM>, according to some embodiments of the present invention. In some embodiments, receiver telescope <NUM> may include an objective lens <NUM> configured to image reflected signal <NUM> onto a particular WMA interferometer <NUM> of a plurality of WMA interferometers <NUM> based on the angle of arrival of reflected signal <NUM>. In some embodiments, each of the plurality of WMA interferometers <NUM> corresponds to a pixel of Doppler image <NUM>. Outputs of the plurality of WMA interferometers <NUM> may be fed into a digital readout integrated circuit <NUM> that processes the outputs and/or serializes the outputs into a data stream that is provided to control/processing electronics <NUM>. In some embodiments, digital readout integrated circuit <NUM> behaves as a multiplexer that forwards one or more of the outputs of the plurality of WMA interferometers <NUM> as requested by control/processing electronics <NUM>.

<FIG> illustrates an example of WMA interferometer <NUM>, according to some embodiments of the present invention. WMA interferometer <NUM> includes a first waveguide <NUM>-<NUM> and a second waveguide <NUM>-<NUM> for propagating reflected signal <NUM>. WMA interferometer <NUM> may include one or two input ports, such as a first port <NUM>-<NUM> coupled to first waveguide <NUM>-<NUM> and a second port <NUM>-<NUM> coupled to second waveguide <NUM>-<NUM>. A tapered fiber coupler <NUM> may be coupled to first port <NUM>-<NUM> and may be configured to receive reflected signal <NUM>. In the illustrated embodiment, second port <NUM>-<NUM> is coupled to vacuum or to an ambient atmosphere.

Portions of first waveguide <NUM>-<NUM> may be positioned in close proximity (e.g., within a threshold distance) to portions of second waveguide <NUM>-<NUM> to implement first beam splitter <NUM>-<NUM> and second beam splitter <NUM>-<NUM>. First beam splitter <NUM>-<NUM> may be configured to split reflected signal <NUM> into a first portion of reflected signal <NUM>-<NUM> and a second portion of reflected signal <NUM>-<NUM>, where first portion <NUM>-<NUM> corresponds to the portion of reflected signal <NUM> that propagates down first waveguide <NUM>-<NUM> after being split by first beam splitter <NUM>-<NUM> and second portion <NUM>-<NUM> corresponds to the portion of reflected signal <NUM> that propagates down second waveguide <NUM>-<NUM> after being split by first beam splitter <NUM>-<NUM>. Second beam splitter <NUM>-<NUM> splits first portion of reflected signal <NUM>-<NUM> and second portion of reflected signal <NUM>-<NUM> into third portion of reflected signal <NUM>-<NUM> and fourth portion of reflected signal <NUM>-<NUM>, where third portion <NUM>-<NUM> corresponds to the portion(s) of first portion <NUM>-<NUM> and second portion <NUM>-<NUM> that propagates down first waveguide <NUM>-<NUM> after being split by second beam splitter <NUM>-<NUM> and fourth portion <NUM>-<NUM> corresponds to the portion(s) of first portion <NUM>-<NUM> and second portion <NUM>-<NUM> that propagates down second waveguide <NUM>-<NUM> after being split by second beam splitter <NUM>-<NUM>.

In the illustrated embodiment, WMA interferometer <NUM> includes a delay element <NUM>, such as a Bragg grating, positioned along second waveguide <NUM>-<NUM> between beam splitters <NUM>. In some embodiments, delay element <NUM> is positioned along first waveguide <NUM>-<NUM> between beam splitters <NUM>. In some embodiments, two delay elements (e.g., two Bragg gratings) positioned along both of waveguides <NUM> are utilized. Delay element <NUM> may be configured to delay the phase of second portion of reflected signal <NUM>-<NUM> such that second portion <NUM>-<NUM> acquires a relative phase ϕ compared to first portion <NUM>-<NUM>. This may be accomplished by fabricating delay element <NUM> to have a periodic variation in the index of refraction.

In some embodiments, WMA interferometer <NUM> includes a first spatial phase shifter <NUM>-<NUM> positioned along first waveguide <NUM>-<NUM> configured to spatially phase shift first portion of reflected signal <NUM>-<NUM> and a second spatial phase shifter <NUM>-<NUM> positioned along second waveguide <NUM>-<NUM> configured to spatially phase shift second portion of reflected signal <NUM>-<NUM> such that the modes TM<NUM> and TM<NUM> acquire opposite tilted phase fronts resulting in a relative phase shift between the two modes. In some embodiments, an extra spatial phase shift is created of the form e±iKx, which is equivalent to bringing out the next mode. In some embodiments, only a single spatial phase shifter is used. One or both of spatial phase shifters <NUM> may be positioned at different positions within WMA interferometer <NUM> than that shown in the illustrated embodiment, such as before delay element <NUM> and/or before beam splitter <NUM>-<NUM> (in reference to the direction of propagation). In some embodiments, one or both of spatial phase shifters <NUM> may include a mode exciter, such as a prism, fabricated within one or both of waveguides <NUM> configured to excite a superposition of odd order modes in reflected signal <NUM>. The mode exciter may include a gradient in the index of refraction across the transverse profile of the waveguide causing some of the electric field amplitude to be transferred to the first excited mode. In some embodiments, spatial phase shifters <NUM> are implemented by widening waveguides <NUM> at a particular widening point along waveguides <NUM><NUM> such that only a single mode is supported prior to the widening point and a second mode is supported after the widening point.

In some embodiments, WMA interferometer <NUM> includes a split detector <NUM> coupled to first waveguide <NUM>-<NUM>. Split detector <NUM> is configured to receive third portion of reflected signal <NUM>-<NUM> and detect an intensity difference S between a first lobe and a second lobe of third portion <NUM>-<NUM>. Due to the TM<NUM> and TM<NUM> modes acquiring opposite tilted phase fronts during propagation in WMA interferometer <NUM>, second beam splitter <NUM>-<NUM> causes destructive interference of the TM<NUM> mode and enhances the relative contribution of the TM<NUM> mode within third portion <NUM>-<NUM>. Accordingly, a significant portion of the detectable power in third portion <NUM>-<NUM> resides in the information-containing TM<NUM> mode.

<FIG> illustrates an example of the signal intensity of the TM<NUM> mode of reflected signal <NUM> within WMA interferometer <NUM>, according to some embodiments of the present invention. Prior to reaching first beam splitter <NUM>-<NUM>, power in the TM<NUM> mode is concentrated in first waveguide <NUM>-<NUM>. When reflected signal <NUM> propagates through first beam splitter <NUM>-<NUM>, power in the TM<NUM> mode is <NUM>/<NUM> split between waveguides <NUM>. When reflected signal <NUM><NUM> propagates through second beam splitter <NUM>-<NUM>, power in the TM<NUM> mode shifts to second waveguide <NUM>-<NUM>.

<FIG> illustrates an example of the signal intensity of the TM<NUM> mode of reflected signal <NUM><NUM> within WMA interferometer <NUM>, according to some embodiments of the present invention. Prior to reaching first beam splitter <NUM>-<NUM>, power in the TM<NUM> mode is concentrated in first waveguide <NUM>-<NUM>. When reflected signal <NUM><NUM> propagates through first beam splitter <NUM>-<NUM>, power in the TM<NUM> mode remains in first waveguide <NUM>-<NUM>. When reflected signal <NUM> propagates through second beam splitter <NUM>-<NUM>, power in the TM<NUM> mode remains in first waveguide <NUM>-<NUM>.

<FIG> illustrates an example of the power transfer between waveguides of the TM<NUM> mode as the beam propagates along the Z-axis, according to some embodiments of the present invention. The Y-axis coming out of the page corresponds to signal intensity level, which is shown on the right. In the illustrated embodiment, the upper and lower waveguides are positioned sufficiently close over a particular propagation distance such that coupling by evanescent waves in the cladding causes power in the TM<NUM> mode to split <NUM>/<NUM> between the waveguides.

<FIG> illustrates an example of the power transfer between waveguides of the TM<NUM> mode as the beam propagates along the Z-axis, according to some embodiments of the present invention. The Y-axis coming out of the page corresponds to signal intensity level, which is shown on the right. In the illustrated embodiment, the upper and lower waveguides are positioned sufficiently close over a particular propagation distance such that coupling by evanescent waves in the cladding causes power in the TM<NUM> mode to remain in the upper waveguide.

<FIG> illustrates an example of detection of the intensity difference S by split detector <NUM>, according to some embodiments of the present invention. In some embodiments, the intensity difference S may be calculated as S = IR-IL where IR is the intensity of the right half of the waveguide and IL is the intensity of the left half of the waveguide. In some embodiments, the intensity difference S may be calculated as S = (IR-IL)/(IR+IL). Split detector <NUM> may include a left area <NUM> and a right area <NUM> for detecting intensities IL and IR, respectively. In the illustrated embodiment, an intensity difference of S<NUM> = <NUM> detected at time T<NUM> is shown in profile <NUM> and an intensity difference of S<NUM> > <NUM> detected at time T<NUM> is shown in profile <NUM>.

In some embodiments, the intensity difference S may be used to calculate the Doppler frequency fd as follows. If the system is calibrated to a fiducial frequency ω (where the balanced signal is <NUM>), then a slight change of frequency from remote vibrating target <NUM> will have the following chain of dependencies. The relative phase shift between the arms of the interferometer (i.e., first and second waveguides <NUM>) is controlled by the combination n(ω)ω ΔL/c, where n is the frequency-dependent index of refraction, ΔL is the path length difference, and c the speed of light. Therefore, a change of frequency δω will result in a change of relative phase of δφ = δω (∂ω/∂φ)-<NUM> ≈ τg δω, where τg is the "group delay", the amount of temporal delay a pulse of light will suffer going through the dispersive medium, which is proportional to the frequency derivative of the index of refraction. The normalized signal read out by the split detector S = (IR-IL)/(IR+IL) is related to the relative phase φ by S = cm φ/(κd), where κ is the tilt of the phase front, d is the width of the waveguide (spatial spread of the mode), and cm is a constant related to the mode function. Thus, for small phase shifts, there is a linear relation between phase and detected signal. Combining the above observations, a shift in frequency δω is related to a shifted signal reading δS as follows: δS = ((cm τg)/κd)δω. Consequently, the larger the group delay, the more signal is obtained for the same amount of Doppler shift. Similarly, the <NUM>/κ is the weak value amplification effect.

<FIG> illustrates spatial and temporal resolution of intensity differences S and Doppler frequencies fd corresponding to the embodiment shown in <FIG>. Each of intensity differences S is characterized by two indexes: the particular WMA interferometer (numbered <NUM> through <NUM>) that detected the intensity difference and the time (numbered <NUM>, <NUM>,. , N) at which the intensity difference was detected. As illustrated, intensity differences S detected across time and spatial values are converted into Doppler frequencies fd over the same time and spatial values.

Referring once again to <FIG>, the spatial map <NUM> of intensity difference S has been converted into a spatial map <NUM> of Doppler frequencies fd at a first time (T<NUM>). Spatial maps of the intensity differences (spatial maps <NUM> and <NUM>) are illustrated for a second time (T<NUM>) and an Nth time, respectively. Additionally, spatial maps of Doppler frequencies fd (spatial maps <NUM> and <NUM>) are illustrated for the second time (T<NUM>) and the Nth time, respectively. Accordingly, embodiments of the present invention enable spatial maps of the vibrometry data associated with remote vibrating target <NUM> to be measured and subsequently utilized as appropriate to the particular application.

<FIG> illustrate a method <NUM> of performing remote sensing using WMA, according to some embodiments of the present invention. One or more steps of method <NUM> may be performed in a different order than the illustrated embodiment, and one or more steps of method <NUM> may be omitted during performance of method <NUM>.

At step <NUM>, interrogation laser <NUM> modulates interrogation signal <NUM> at an interrogation frequency fo. In some embodiments, the interrogation frequency fo is selected to be near the band gap of delay element <NUM>. In various embodiments, the interrogation frequency fo may be any one of <NUM> THz, <NUM> THz, <NUM> THz, <NUM> THz, <NUM> THz, <NUM> THz, <NUM> THz, among other possibilities.

At step <NUM>, afocal expander <NUM> expands interrogation signal <NUM>. In some embodiments, afocal expander <NUM> expands interrogation signal <NUM> to reduce beam divergence so as to maximize energy on remote vibrating target <NUM>. In some embodiments, afocal expander <NUM> includes objective lens <NUM>.

At step <NUM>, transmitter module <NUM> transmits interrogation signal <NUM> to remote vibrating target <NUM>. In some embodiments, step <NUM> may include interrogation laser <NUM> transmitting interrogation signal <NUM> through afocal expander <NUM> toward remote vibrating target <NUM>. When interrogation signal <NUM> is reflected by remote vibrating target <NUM>, a target-own platform Doppler shift is introduced by remote vibrating target <NUM> and a target micro-Doppler shift is induced by localized surface vibrations on remote vibrating target <NUM>.

At step <NUM>, receiver telescope <NUM> collects reflected signal <NUM> from a specific target location within the field of view of vibrometer <NUM> and images reflected signal <NUM> onto tapered fiber coupler <NUM>. In some embodiments, the receiver telescope <NUM> may image reflected signal <NUM> onto a particular tapered fiber coupler <NUM> of a plurality of tapered fiber couplers based on the angle of arrival of reflected signal <NUM>.

At step <NUM>, first port <NUM>-<NUM> receives reflected signal <NUM>. In some embodiments, step <NUM> includes first port <NUM>-<NUM> receiving reflected signal <NUM> from tapered fiber coupler <NUM>. Concurrently with or subsequent to step <NUM>, first waveguide <NUM>-<NUM> may receive reflected signal <NUM> via first port <NUM>-<NUM> and reflected signal <NUM> may propagate down first waveguide <NUM>-<NUM>.

At step <NUM>, first beam splitter <NUM>-<NUM> splits reflected signal <NUM> into first portion of reflected signal <NUM>-<NUM> and second portion of reflected signal <NUM>-<NUM>, where first portion <NUM>-<NUM> corresponds to the portion of reflected signal <NUM> that propagates down first waveguide <NUM>-<NUM> after being split by first beam splitter <NUM>-<NUM> and second portion <NUM>-<NUM> corresponds to the portion of reflected signal <NUM> that propagates down second waveguide <NUM>-<NUM> after being split by first beam splitter <NUM>-<NUM>. In some embodiments, first beam splitter <NUM>-<NUM> is formed by positioning first and second waveguides <NUM> within a threshold distance from each other such that reflected signal <NUM> is coupled into first and second waveguides <NUM> via evanescent wave coupling. By bringing first and second waveguides <NUM> sufficiently close, coupling by evanescent waves in the cladding causes power to shift between each waveguide as a function of propagation distance. Such an effect can be utilized to create a reliable analog for a free space <NUM>/<NUM> beam splitter.

At step <NUM>, delay element <NUM> delays the phase of second portion of reflected signal <NUM>-<NUM> such that second portion <NUM>-<NUM> acquires a relative phase ϕ compared to first portion <NUM>-<NUM>. In some embodiments, delay element <NUM> includes a Bragg grating. In some embodiments, delay element <NUM> may be fabricated to have a periodic variation in the index of refraction. Traveling waves within delay element <NUM> have solutions of the form β = βB±(δ<NUM>-κ<NUM>)<NUM>/<NUM> which yields a photonic bandgap where the group velocity goes to <NUM> as Vg = ∂β/βω, implying competition between high dispersion and high transmission. In some embodiments, a double Bragg grating may be employed having two band gaps with couplings κ<NUM> and κ<NUM> providing two spatial wavelengths. Such embodiments comprising two band gaps create a frequency window of high transmission, high dispersion, and low group velocity.

Although delay element <NUM> is described herein as being positioned along second waveguide <NUM>-<NUM>, in some embodiments delay element <NUM> may be positioned along first waveguide <NUM>-<NUM> so as to delay the phase of first portion of reflected signal <NUM>-<NUM>. In some embodiments, a first delay element may be positioned along first waveguide <NUM>-<NUM> so as to delay the phase of first portion <NUM>-<NUM> and a second delay element may be positioned along second waveguide <NUM>-<NUM> so as to delay the phase of second portion <NUM>-<NUM>. In some embodiments, delay element <NUM> acts like a Rubidium cell that may be implemented in free space embodiments, causing a relative phase ϕ between the two arms.

At step <NUM>, first spatial phase shifter <NUM>-<NUM> positioned along first waveguide <NUM>-<NUM> spatially phase shifts first portion of reflected signal <NUM><NUM>-<NUM> and second spatial phase shifter <NUM>-<NUM> positioned along second waveguide <NUM>-<NUM> spatially phase shifts second portion of reflected signal <NUM>-<NUM> such that the modes TM<NUM> and TM<NUM> acquire opposite tilted phase fronts resulting in a relative phase shift between the two modes. In some embodiments, only a single spatial phase shifter is used. In some embodiments, one or both of first-spatial phase shifter <NUM>-<NUM> and second-spatial phase shifter <NUM>-<NUM> are configured to excite a superposition of odd order modes in first portion <NUM>-<NUM> and second portion <NUM>-<NUM>, respectively. This may be accomplished by fabricating a prism within one or both of first waveguide <NUM>-<NUM> and second waveguide <NUM>-<NUM>. For example, the prism may include a gradient in the index of refraction across the transverse profile of first waveguide <NUM>-<NUM> and/or second waveguide <NUM>-<NUM> causing some of the electric field amplitude to be transferred to the first excited mode. In some embodiments, the prism may excite a superposition of odd order modes from an initial zeroth-order mode input. The prism may thereby cause reflected signal <NUM> to propagate in accordance with two modes of propagation.

At step <NUM>, second beam splitter <NUM>-<NUM> splits first portion of reflected signal <NUM>-<NUM> and second portion of reflected signal <NUM>-<NUM> into third portion of reflected signal <NUM>-<NUM> and fourth portion of reflected signal <NUM>-<NUM>, where third portion <NUM>-<NUM> corresponds to the portion(s) of first portion <NUM>-<NUM> and second portion <NUM>-<NUM> that propagates down first waveguide <NUM>-<NUM> after being split by second beam splitter <NUM>-<NUM> and fourth portion <NUM>-<NUM> corresponds to the portion(s) of first portion <NUM>-<NUM> and second portion <NUM>-<NUM> that propagates down second waveguide <NUM>-<NUM> after being split by second beam splitter <NUM>-<NUM>. In some embodiments, second beam splitter <NUM>-<NUM> is formed by positioning first and second waveguides <NUM> within a threshold distance from each other such that first portion <NUM>-<NUM> and second portion <NUM>-<NUM> are coupled into first and second waveguides <NUM> via evanescent wave coupling. Due to the TM<NUM> and TM<NUM> modes acquiring opposite tilted phase fronts in step <NUM>, second beam splitter <NUM>-<NUM> causes destructive interference of the TM<NUM> mode and enhances the relative contribution of the TM<NUM> mode within third portion <NUM>-<NUM>.

At step <NUM>, split detector <NUM> receives third portion of reflected signal <NUM>-<NUM> and detects an intensity difference S between a first lobe and a second lobe of third portion <NUM>-<NUM>. When WMA interferometer <NUM> is tuned to operate in the inverse weak value region, a double lobe pattern is produced on split detector <NUM>. In some embodiments, split detector <NUM> comprises a two element detector or two separate detectors having a right-side and a left-side. In some embodiments, split detector <NUM> identifies two relative maximum intensity values and determines a difference between them. In some embodiments, split detector <NUM> determines two intensity values at two predetermined spatial positions (e.g., x = ±<NUM>·<NUM>-<NUM> m). In some embodiments, a Y-branch may be used to spatially split the profile of third portion <NUM>-<NUM> to measure and detect the intensity difference S.

At step <NUM>, a processor of vibrometer <NUM> calculates the Doppler frequency fd based on the intensity difference S. When WMA interferometer <NUM> is properly tuned, the intensity difference S will shift due to changes in frequency (Doppler change). As such, the rate of change of the intensity difference S with respect to the rate of change in frequency can be calculated. Step <NUM> may be performed by a processor within receiver module <NUM> or control/processing electronics <NUM>, among other possibilities.

<FIG> illustrates an example layout of a WMA interferometer <NUM>, according to some embodiments of the present invention. WMA interferometer <NUM> includes a first and second directional couplers (DC1 and DC2), multi-mode interferometers (MMI), and outputs (O1, O2, O3, and O4). In some embodiments, for the design of the device, silicon nitride can be used as the guiding material, silicon dioxide can be used as the cladding material, and the testing wavelength can be <NUM>. These materials and wavelength have good compatibility with existing fabrication and testing techniques. A thickness of <NUM> for silicon nitride is chosen for balance of confinement and ease of coupling.

A free space Mach-Zander interferometer can be achieved by two beam-splitters. On a photonic chip, the analog of a beam-splitter is a directional coupler. When two waveguides are close and the modes in them are phase matched, light in one of the waveguides will couple to the other. The coupling ratio depends on the separation between the two waveguides and the length of the coupling region. This structure is called a directional coupler.

<FIG> illustrates an example layout of a mode converter <NUM>, according to some embodiments of the present invention. Mode converter <NUM><NUM> can be used to introduce a phase front tilt by coupling part of the fundamental mode (TE<NUM>) to the second order mode (TE<NUM>). The input waveguide W<NUM>, which may be the bottom waveguide, may be a single mode waveguide that only supports the TE<NUM> mode. At the first directional coupler, a small portion of the input TE<NUM> mode is coupled to the TE<NUM> mode of an identical waveguide W<NUM>, which may be the top waveguide. W<NUM> then enters a tapering region where the width of W<NUM> gradually increases until it becomes a multimode waveguide that supports both the TE<NUM> and TE<NUM> modes. Because the change in width is slow, light in the TE<NUM> mode will tend to stay confined in the TE<NUM> mode instead of coupling to higher order modes and dissipating.

The TE<NUM> mode supported by W<NUM> can be designed to be phase matched with TE<NUM> in W<NUM>. Therefore, at the second directional coupler, TE<NUM> in W<NUM> will couple to TE<NUM> in W<NUM>. Since TE<NUM> in W<NUM> is not phase matched with any mode in W<NUM>, it will stay in W<NUM>. As a result, W<NUM> will contain mostly the TE<NUM> mode with a small amount of the TE<NUM> mode at the end of this structure. The ratio between the two modes depends on the coupling ratio of the first directional coupler. And the phase difference between the two modes depends on the optical path difference of W<NUM> and W<NUM> between the two couplers.

<FIG> illustrates a plot showing the mode effective index change as a function of waveguide width, according to some embodiments of the present invention. <FIG> demonstrates that the widths of the waveguide can be designed to match the TE<NUM> and TE<NUM> modes with an effective index of <NUM>, which corresponds to a width of <NUM> for W<NUM> and <NUM> for W<NUM>.

<FIG> illustrates an example layout of a multimode interferometer <NUM>, according to some embodiments of the present invention. In some embodiments, the mean location shift can be measured by measuring the ratio of TE<NUM> and TE<NUM> mode in the dark port. Therefore, a multimode interference waveguide can be used, which reacts differently to the TE<NUM> and TE<NUM> modes. An multimode interference waveguide is a segment of waveguide that supports many modes followed by two single mode waveguides. In the multimode interference region, light is coupled to a number of modes, which have different propagation velocity. Therefore, their interference pattern changes as they propagate, thus changing the output power of the two single mode waveguides.

<FIG> illustrates a plot showing a simulated output of a multimode interference waveguide as a function of the ratio of TE<NUM> and TE<NUM> mode. As illustrated, simulations of the multimode interference waveguide using the eigenmode multimode interference expansion method (FIMMPROP, Photon Design) show that, while the output ratio of the TE<NUM> mode or the TE<NUM> mode is <NUM>/<NUM>, the addition of the two modes gives a different result. As the percentage of the TE<NUM> mode increases, one of the outputs decreases. This allows the ratio of the TE<NUM> and TE<NUM> modes to be determined with the output light signal.

<FIG> illustrates an example layout of a WMA interferometer <NUM> with heaters, according to some embodiments of the present invention. For the purpose of testing the device, a source of phase φ may be required. A common method to add phase tunability to waveguides is to use micro-heaters. By depositing metal wires on top of the waveguide cladding and applying voltage on them, they can generate heat and increase the temperature of the waveguide underneath. The temperature change will induce a refractive index change of the waveguide material, introducing a phase difference compared to the unheated waveguide. A first heater (H1) may be placed after the first directional coupler to introduce a deliberate phase difference for measurement.

Heaters are also useful for the undesired phase accumulation throughout the device due to fabrication errors. In theory, when phase φ = <NUM>, the TE<NUM> and TE<NUM> modes need to be in phase before they interfere. Other sources of phase accumulation will reduce the sensitivity of the measurement. To compensate for these undesired sources of phase, two other heaters may be placed on each path of the device to tune the two modes in phase before applying the target phase φ. Heater <NUM> (H2) may control the relative phase of the TE<NUM> mode to the TE<NUM> mode. Heater <NUM> (H3) may compensate for the phase difference between the TE<NUM> and TE<NUM> due to their different propagation velocities.

In some implementations, WMA interferometer <NUM> can be fabricated from a <NUM>-inch silicon wafer with <NUM> of thermally grown silicon dioxide. A layer of <NUM> of silicon nitride can be deposited with low pressure chemical vapor deposition (LPCVD). The waveguides can then be patterned with e-beam lithography and the silicon nitride can be etched with inductively coupled plasma reactive ion etching (ICP-RIE). The waveguides can be cladded with <NUM> of silicon dioxide deposited via plasma enhanced chemical vapor deposition (PECVD).

To place heaters on top of the waveguides, a "lift-off" method can be employed as follows. First, a layer of photoresist is spun on top of the silicon dioxide and the shape of the heaters can be patterned with DUV photolithography (ASML 300C DUV Stepper - <NUM>). Then, deposit <NUM> of chrome is deposited for adhesion to the silicon dioxide and <NUM> of platinum as the heaters. Next, the wafer is immersed in acetone, which dissolves the photoresist and thus removes the extra metal. The metal left on the surface of the cladding forms the heaters over the waveguides.

<FIG> illustrates an example of a testing setup for testing a WMA interferometer <NUM>. In some implementations, the light source for testing the device is a tunable laser centered at <NUM> run wavelength (Santec TSL-<NUM>). The power of the laser output is <NUM> mW. Light can be coupled into the waveguide with a tapered single mode fiber <NUM> and the output can be imaged with a 40x objective <NUM> onto InGaAs detectors <NUM>. Objective <NUM> allows measurement of the two outputs of the MMI simultaneously by putting one detector at each output image location. A fiber polarization paddle can be used on the input fiber and a polarizer can be placed before the detector to eliminate the effects of stray TM modes.

To apply voltage to the heaters, metal probes that are attached to electric cables can be used. The probes can be put in contact with the heaters on the chip and the electric cables can be connected to a voltage source <NUM>. Without applying any voltage to the heaters, the wavelength of the laser can be scanned and the output spectrum of the device can be recorded. For clarity reasons, only a connection for one heater is illustrated.

<FIG> illustrates a plot showing the output light power as a function of input laser wavelength. The general trend of the spectrum shows the sinusoidal behavior we expect from a Mach-Zehnder interferometer. However, the ratio of the output powers is not as expected. This is most likely due to an undesired accumulation of phase, which can be compensated for by tuning heaters <NUM> and <NUM>. The small fluctuation is due to the vibration of the input fiber during the scan. This can be largely improved by integrated photonics packaging techniques, such as fusing the fiber to the chip.

Because of the fiber fluctuation, it is difficult to determine the cause of light signal change when a constant phase signal is applied. Therefore, a modulated phase signal can be sent. When heater <NUM> is tuned with a sine wave voltage signal, a light signal with a corresponding frequency can be observed at the output.

<FIG> illustrates plots showing a modulated voltage signal (on the left) and an output light signal (on the right) measured using an radio-frequency (RF) spectrum analyzer. The modulation frequency components from the signal generator are <NUM>, <NUM> and <NUM>. Since the response of the refractive index goes as the square of the applied voltage (i.e. power dissipated by the heater), the difference between the frequency components doubles in the measured output light. Accordingly, signal frequencies of <NUM> and <NUM> can be observed at the output. This demonstrates the ability of the device to measure changes to the phase difference between the interferometer arms by detecting the output light.

<FIG> illustrates a simplified computer system <NUM> according to some embodiments described herein. Computer system <NUM> as illustrated in <FIG> may be incorporated into devices such as transmitter module <NUM>, receiver module <NUM>, or control/processing electronics <NUM> as described herein. <FIG> provides a schematic illustration of one example of computer system <NUM> that can perform some or all of the steps of the methods provided by various embodiments. It should be noted that <FIG> is meant only to provide a generalized illustration of various components, any or all of which may be utilized as appropriate. <FIG>, therefore, broadly illustrates how individual system elements may be implemented in a relatively separated or relatively more integrated manner.

Computer system <NUM> is shown comprising hardware elements that can be electrically coupled via a bus <NUM>, or may otherwise be in communication, as appropriate. The hardware elements may include one or more processors <NUM>, including without limitation one or more general-purpose processors and/or one or more special-purpose processors such as digital signal processing chips, graphics acceleration processors, and/or the like; one or more input devices <NUM>, which can include without limitation a mouse, a keyboard, a camera, and/or the like; and one or more output devices <NUM>, which can include without limitation a display device, a printer, and/or the like.

Computer system <NUM> may further include and/or be in communication with one or more non-transitory storage devices <NUM>, which can comprise, without limitation, local and/or network accessible storage, and/or can include, without limitation, a disk drive, a drive array, an optical storage device, a solid-state storage device, such as a random access memory ("RAM"), and/or a read-only memory ("ROM"), which can be programmable, flash-updateable, and/or the like. Such storage devices may be configured to implement any appropriate data stores, including without limitation, various file systems, database structures, and/or the like.

Computer system <NUM> might also include a communications subsystem <NUM>, which can include without limitation a modem, a network card (wireless or wired), an infrared communication device, a wireless communication device, and/or a chipset such as a Bluetooth™ device, an <NUM> device, a WiFi device, a WiMax device, cellular communication facilities, etc., and/or the like. The communications subsystem <NUM> may include one or more input and/or output communication interfaces to permit data to be exchanged with a network such as the network described below to name one example, other computer systems, television, and/or any other devices described herein. Depending on the desired functionality and/or other implementation concerns, a portable electronic device or similar device may communicate image and/or other information via the communications subsystem <NUM>. In other embodiments, a portable electronic device, e.g. the first electronic device, may be incorporated into computer system <NUM>, e.g., an electronic device as an input device <NUM>. In some embodiments, computer system <NUM> will further comprise a working memory <NUM>, which can include a RAM or ROM device, as described above.

Computer system <NUM> also can include software elements, shown as being currently located within the working memory <NUM>, including an operating system <NUM>, device drivers, executable libraries, and/or other code, such as one or more application programs <NUM>, which may comprise computer programs provided by various embodiments, and/or may be designed to implement methods, and/or configure systems, provided by other embodiments, as described herein. Merely by way of example, one or more procedures described with respect to the methods discussed above, might be implemented as code and/or instructions executable by a computer and/or a processor within a computer; in an aspect, then, such code and/or instructions can be used to configure and/or adapt a general purpose computer or other device to perform one or more operations in accordance with the described methods.

A set of these instructions and/or code may be stored on a non-transitory computer-readable storage medium, such as the storage device(s) <NUM> described above. In some cases, the storage medium might be incorporated within a computer system, such as computer system <NUM>. In other embodiments, the storage medium might be separate from a computer system e.g., a removable medium, such as a compact disc, and/or provided in an installation package, such that the storage medium can be used to program, configure, and/or adapt a general purpose computer with the instructions/code stored thereon. These instructions might take the form of executable code, which is executable by computer system <NUM> and/or might take the form of source and/or installable code, which, upon compilation and/or installation on computer system <NUM> e.g., using any of a variety of generally available compilers, installation programs, compression/decompression utilities, etc., then takes the form of executable code.

For example, customized hardware might also be used, and/or particular elements might be implemented in hardware, software including portable software, such as applets, etc., or both.

As mentioned above, in one aspect, some embodiments may employ a computer system such as computer system <NUM> to perform methods in accordance with various embodiments of the technology. According to a set of embodiments, some or all of the procedures of such methods are performed by computer system <NUM> in response to processor <NUM> executing one or more sequences of one or more instructions, which might be incorporated into the operating system <NUM> and/or other code, such as an application program <NUM>, contained in the working memory <NUM>. Such instructions may be read into the working memory <NUM> from another computer-readable medium, such as one or more of the storage device(s) <NUM>. Merely by way of example, execution of the sequences of instructions contained in the working memory <NUM> might cause the processor(s) <NUM> to perform one or more procedures of the methods described herein. Additionally or alternatively, portions of the methods described herein may be executed through specialized hardware.

The terms "machine-readable medium" and "computer-readable medium," as used herein, refer to any medium that participates in providing data that causes a machine to operate in a specific fashion. In embodiments implemented using computer system <NUM>, various computer-readable media might be involved in providing instructions/code to processor(s) <NUM> for execution and/or might be used to store and/or carry such instructions/code. In many implementations, a computer-readable medium is a physical and/or tangible storage medium. Such a medium may take the form of a non-volatile media or volatile media. Non-volatile media include, for example, optical and/or magnetic disks, such as the storage device(s) <NUM>. Volatile media include, without limitation, dynamic memory, such as the working memory <NUM>.

Common forms of physical and/or tangible computer-readable media include, for example, a floppy disk, a flexible disk, hard disk, magnetic tape, or any other magnetic medium, a CD-ROM, any other optical medium, punchcards, papertape, any other physical medium with patterns of holes, a RAM, a PROM, EPROM, a FLASH-EPROM, any other memory chip or cartridge, or any other medium from which a computer can read instructions and/or code.

Various forms of computer-readable media may be involved in carrying one or more sequences of one or more instructions to the processor(s) <NUM><NUM> for execution. Merely by way of example, the instructions may initially be carried on a magnetic disk and/or optical disc of a remote computer. A remote computer might load the instructions into its dynamic memory and send the instructions as signals over a transmission medium to be received and/or executed by computer system <NUM>.

Specific details are given in the description to provide a thorough understanding of exemplary configurations including implementations. However, configurations may be practiced without these specific details. For example, well-known circuits, processes, algorithms, structures, and techniques have been shown without unnecessary detail in order to avoid obscuring the configurations. This description provides example configurations only, and does not limit the scope, applicability, or configurations of the claims. Rather, the preceding description of the configurations will provide those skilled in the art with an enabling description for implementing described techniques. Various changes may be made in the function and arrangement of elements.

Also, configurations may be described as a process which is depicted as a schematic flowchart or block diagram. Although each may describe the operations as a sequential process, many of the operations can be performed in parallel or concurrently. In addition, the order of the operations may be rearranged. A process may have additional steps not included in the figure. Furthermore, examples of the methods may be implemented by hardware, software, firmware, middleware, microcode, hardware description languages, or any combination thereof. When implemented in software, firmware, middleware, or microcode, the program code or code segments to perform the necessary tasks may be stored in a non-transitory computer-readable medium such as a storage medium. Processors may perform the described tasks.

The above elements may be components of a larger system, wherein other rules may take precedence over or otherwise modify the application of the technology. Also, a number of steps may be undertaken before, during, or after the above elements are considered. Accordingly, the above description does not bind the scope of the claims.

Also, the words "comprise", "comprising", "contains", "containing", "include", "including", and "includes", when used in this specification and in the following claims, are intended to specify the presence of stated features, integers, components, or steps, but they do not preclude the presence or addition of one or more other features, integers, components, steps, acts, or groups.

Claim 1:
A method (<NUM>) comprising:
receiving (<NUM>), at a port, a reflected signal generated by an interrogation signal being reflected off a remote vibrating target;
propagating the reflected signal down a first waveguide (<NUM>-<NUM>);
splitting (<NUM>), by a first beam splitter (<NUM>-<NUM>), the reflected signal into a first portion propagating down the first waveguide (<NUM>-<NUM>) and a second portion propagating down a second waveguide (<NUM>-<NUM>);
delaying (<NUM>), by a delay element (<NUM>), a phase of one of the first and second portions of the reflected signal;
spatially phase shifting (<NUM>), by one or more spatial phase shifters (<NUM>-<NUM>, <NUM>-<NUM>), one or both of the first or second portions of the reflected signal;
splitting (<NUM>), by a second beam splitter (<NUM>-<NUM>), the first and second portions of the reflected signal into a third portion propagating down the first waveguide (<NUM>-<NUM>) and a fourth portion propagating down the second waveguide (<NUM>-<NUM>);
detecting (<NUM>), by a split detector (<NUM>), an intensity difference between a first lobe and a second lobe of the third portion of the reflected signal; and
calculating (<NUM>) a Doppler frequency based on the intensity difference.