MEMS apparatus with a movable waveguide section

Embodiments of the present disclosure are directed towards a micro-electromechanical system (MEMS) sensing device, including a laser arrangement configured to generate a light beam, a first waveguide configured to receive and output a first portion of the light beam, and a second waveguide having a section that is evanescently coupled to the first waveguide and configured to receive and output a second portion of the light beam. The section of the second waveguide is configured to be movable substantially parallel to the first waveguide, wherein a movement of the section of the second waveguide may be caused by an inertial change applied to the sensing device. The movement of the section may cause a detectable change in light intensity between the first and second portions of the light beam. Based on the detected change, the inertial change may be determined. Other embodiments may be described and/or claimed.

FIELD

Embodiments of the present disclosure generally relate to the field of opto-electronics, and more particularly, to using micro-electronic systems for accelerometric and gyroscopic measurements.

BACKGROUND

The market demands and revenues for displacement-sensing devices, such as accelerometers and gyroscopes including micro-electronic systems (MEMS)-based sensors have been growing steadily. The integration of inertial MEMS sensors into a wide range of consumer electronics, cars, and defense applications is driving the need for smaller, cheaper, lower-power, lower-noise, and more accurate sensors. However, technologies for producing micro-scale accelerometers and gyroscopes have remained essentially unchanged since their inception years ago. A typical sensor in an accelerometer or gyroscope may include a movable proof-mass with the proof-mass displacement sensed electrically, e.g., using inter-digitated capacitor plates. However, traditional electrostatic sensing may not allow for scalable production of on-chip sensors, lasers, and detectors, and may not provide sufficient sensitivity or desired sensitivity range.

DETAILED DESCRIPTION

In various embodiments, the phrase “a first layer formed, deposited, or otherwise disposed on a second layer,” may mean that the first layer is formed, deposited, or disposed over the second layer, and at least a part of the first layer may be in direct contact (e.g., direct physical and/or electrical contact) or indirect contact (e.g., having one or more other layers between the first layer and the second layer) with at least a part of the second layer.

FIGS. 1 and 2are diagrams schematically illustrating an example MEMS sensing device100for sensing inertial change, in accordance with some embodiments. For purposes of explanation, a section140of the device100demarcated in dashed lines is enlarged and shown within a dashed-line rectangle140′ inFIG. 1. Also for purposes of explanation of the operation of the device100,FIG. 2illustrates a simplified example200of the device100. The device100includes two evanescently coupled waveguides,102and104, at least sections of which are disposed substantially parallel each other. As illustrated by section140ofFIG. 1and shown in greater detail inFIG. 2, at least a section106of waveguide102may be disposed substantially parallel to waveguide104and may be movable substantially parallel to waveguide104, as indicated by arrows150and250inFIGS. 1 and 2respectively. The movement150(indicated by numeral250inFIG. 2) of the waveguide102(or section106) relative to waveguide104will be hereinafter called a “shearing” movement. Cross-axis movement of waveguide102(section106) indicated by arrow152may be undesirable and will be discussed below in greater detail. The waveguide104may be configured to be immovable, e.g., fixed in a determined position relative to waveguide102. A gap between section106and waveguide104indicated in140′ may be configured to provide for evanescent wave effect between waveguides102and104.

A light beam from a light source such as a laser arrangement114may be split into two portions (shown inFIG. 2as INPUT1and INPUT2), which may be sent through both waveguides102and104and outputted (DET1and DET2) to detectors120and122respectively. A phase of light in one waveguide, e.g., waveguide102may be controlled by a phase shifter124. The phase shifter124may comprise a carrier-injection phase shifter, such as a quadrature bias diode or electro-optic phase tuner. In some embodiments, the phase may be controlled such that the light intensity of the light beam may be divided substantially equally between the portions of light passing through waveguides102and104at a rest position of the device100.

FIG. 3is a schematic diagram illustrating an example simulation300of the waveguide section106of the waveguide104in different positions A, B, C, D, relative to waveguide102of the MEMS sensing device described above, in accordance with some embodiments. More specifically, simulation300illustrates the instances where the waveguide104including the launch field is physically moved by amounts equal to −λ/4 (position A), 0λ/4 (position B), +λ/4 (position C), +2λ/4 (position D), where λ is the wavelength in the waveguide measured, e.g., in microns.FIG. 4illustrates an example simulation400of the light distribution between the waveguides102and104corresponding to the different positions A, B, C, D of the waveguide104inFIG. 3. More specifically, inFIG. 4, light distribution between the waveguides indicated by letter A corresponds to position A of the waveguides inFIG. 3, light distribution between the waveguides indicated by letter B corresponds to position B of the waveguides inFIG. 3, light distribution between the waveguides indicated by letter C corresponds to position C of the waveguides inFIG. 3, and light distribution between the waveguides indicated by letter D corresponds to position D of the waveguides inFIG. 3.

FIG. 5is a graph500illustrating a normalized light signal power output P/P0(detected by the detectors120and122respectively) as a function of light signal phase difference4, where P0is the total input power of the light beam of the MEMS sensing device, in accordance with some embodiments. The light signal power corresponds to light intensity and will be used hereinafter interchangeably with light intensity. As shown, due to the phase shift control of the input signal in one waveguide (e.g.102as described in reference toFIG. 1), the P/P0ratio may be 0.5 at a rest position of the device100. The normalized signal power output corresponds to the examples of light distribution in the waveguides102and104, as shown inFIG. 4, that in turn correspond to positions A, B, C, and D of the waveguides inFIG. 3. As simulation400and graph500illustrate, the effect of superimposition of the light beam portions passing through the waveguides102and104may result in various degrees of interference occurring between the light beam portions, ranging from constructive interference (points B and D in graph500) to destructive interference (points A and C in graph500). Accordingly, light intensity between the portions of light beam passing through the waveguides102and104may change and be detected by the detectors120and122.

As shown inFIGS. 3-5, the displacement of the waveguide104relative to waveguide102from position B to positions A or C is equal to quarter of a wavelength in the waveguide. More specifically, if one waveguide (e.g.,104) including its launch field may be physically movable from its initial position B, each of the relative waveguide displacement indicated by positions A, C, D may be attainable. Accordingly, the motion of the movable waveguide102with respect to the “fixed” waveguide104may be transduced, resulting in detectable and measureable wavelength changes, which in turn may result in detectable change in light intensity between the light beam portions detected by detectors120and122. The physical movement of the waveguide102relative waveguide104may occur in response to an inertial change, such as external acceleration, applied to the sensing device100.

Consider three modes of operation of the sensing device100. Referring to graph500, in the first mode of operation the sensing device100may be calibrated (e.g., using the phase shifter124) to operate within the linear region near point B. The small motions of the sensing device100and corresponding changes in light intensity may be transduced by monitoring the two detectors120,122to determine, for example, a deviation of the output ratio of two light beam portions from 50:50. The slope of the graph500at the linear region near B may be described as dP/dΔφ=P0/2. Assuming, for example, that the wavelength in the material is ˜1μ with 0.1 mW power input, movement of the waveguide104of about ±32 nm may result in power modulation of ±10%. Accordingly, the sensing device100may be calibrated to transduce small movements of the waveguide102relative to the waveguide104. For example, the full wavelength in free space may be 1.3 um. For a particular waveguide configuration this may correspond to a wavelength in the waveguide of 440 nm, and a quarter of this wavelength is 110 nm, corresponding to the displacement from B to C (FIG. 3).

The second mode of operation of the sensing device100may be similar to the first mode of operation, but instead of detecting changes in the output ratio at the two detectors122and120, an active feedback loop may be introduced (not shown) that may control the phase shifter124, keeping the output power ratio fixed at 50:50. In the third mode of operation, the sensing device100may be configured to transduce larger motions of the waveguide104by counting fringes as the output goes from A to B to C to D to A etc. “Counting fringes” means that rather than transducing inertial forces based on a small linear region of the sinusoidal response around B (inFIG. 5), larger displacements may be allowed, which trace out the entire non-linear sine curve A to B to C to D, possibly multiple times. By detecting where along the sine curve period(s) the power output value is, the displacement may be determined. For example, each time the ratio is determined to be around 100:0 the waveguide104may have moved an additional length equal to one wavelength in the waveguide104.

As noted above, “shearing” movement of the waveguide102(or its section106) relative to the waveguide104is desirable, while cross-axis movement of the waveguide104may not be, due to potential distortions of the light intensity changes detected as a result of the “shearing” movement of the waveguide102and subsequent errors in estimating corresponding inertial changes.FIG. 6illustrates an example assembly600including a MEMS sensing device similar to device100and configured to avoid cross-axis movement of the waveguide102. The assembly600may include a proof mass660having four “legs” (e.g., spring arrangements)640,642,644, and646. The assembly600may further include a sensing device670comprising waveguides602and604(similar to102and104), where at least a section606(similar to106) of the waveguide604may be disposed on the proof mass660. As shown, the section606is disposed substantially parallel to the waveguide602.

The assembly600may further include detectors622and620(similar to122and120) and the light source, e.g., laser614configured to provide a laser beam to be split between the waveguides602,604as described in reference toFIG. 1. The legs640,642,644, and646may be fixed on their outermost points to a fixed frame (not shown) and may be configured to be deformable, e.g., stretchable or bendable. Accordingly, the proof mass660may be movable in one direction, e.g., up and down, as shown by arrow670inFIG. 6, due to the legs deformation. The legs may be manufactured with desired thickness so as to avoid cross-axis movement of the proof mass660and corresponding cross-axis movement of the section606of the waveguide604. Furthermore, the legs need not be straight. In some embodiments, the legs may include one or more bent sections with the waveguide running along the bends with a large enough radius of curvature so as not to cause significant optical loss. In operation, an external acceleration may cause the proof mass660to move relative to the frame, deforming the legs640,642,644, and646, and shifting the launch field in the waveguide604attached to the proof mass660. (The deformation of the legs640,642,644, and646is exaggerated for simplicity purposes inFIG. 6.)

Several points may be noted in regard to the assembly600. For example, the bending of the waveguide602due to running along a bending flexure may cause stress-optical effects, shifting the phase of the input light. However, detailed research has shown that this may have a negligible effect on the inertial change sensing described above. In another example, the detector622formed on the assembly600may be sensitive to cross-axis movement. However, installing an additional sensing device (e.g., identical to622) on the other side (e.g., right side) of the proof mass660inFIG. 6may report an opposite result, which may be linear for cross-axis movements. Accordingly, the effect of cross-axis movements may be canceled by providing two sensing devices on each side of the proof mass600and finding the sum of the detector signals.

The assembly600may be relatively power-insensitive, configured to tolerate substantial optical powers, up until nonlinear optical thresholds of the waveguides602and604. Traditional electrostatic MEMS sensing device may require a trade-off between sensitivity (the smallest measurable signal, or the smallest measurable change in signal) and dynamic range (the largest measurable signal before saturation or failure). By contrast, in the described sensing device the sensitivity may be dictated by the geometry of the waveguides602,604and the dynamic range in the third mode of operation described above may be set by the geometry of the “legs”640,642,644, and646, which determines how far the proof mass660may move in a “shearing” motion.

A displacement and corresponding power change for the waveguides602,604may be calculated as follows. If the power of the light beam in waveguide604is 100%, then the power in waveguide602may be calculated as:

P=Pmax⁢⁢sin2⁡(π⁢⁢neffλ0⁢x+δ)Equation⁢⁢1
Where Pmax is the peak power of the sine-squared function, λ0is the wavelength in free space so that the wavelength in the waveguide is λ0/neff), x is the displacement of one of the waveguides relative to the other, and δ is initial phase offset, which may be controlled using a phase shifter such as electro-optic phase tuner. It is desired to have the P at the point of steepest slope of the sine-squared function above, accordingly, a baseline power output at the detector is not Pmax, but approximately one half of Pmax:
P0=Pmax/2  Equation 2
Accordingly, the Equation 1 may be rewritten as follows:

Differentiating this gives the resulting fractional power change at the detector d (P/P0) when a small displacement dx occurs:

d⁡(P⁢/⁢P0)dx=π⁢⁢neffλ0⁢sin⁡(2⁢π⁢⁢neffλ0⁢x+2⁢δ)Equation⁢⁢4
Note that in one mode of operation, it is desired to have a steepest point of the original function, i.e., at the point where the slope is maximized. Accordingly, the “sine” part of the last equation may be equal to +1 (or −1). Thus, the displacement sensitivity for small displacements around the point of steepest slope is:

In other words, the measured output power may change by 0.7% for every nanometer of displacement. For example, for 14 nm of displacement we may have 10% output power change. Accordingly, reasonable fabrication lengths of a few tens of wavelengths long may be provided for manufacturing waveguides602and604.

Once we have the x-displacement measurement, acceleration may be calculated considering the following: the force causing the acceleration of the proof mass obeys Hooke's law, F=kx, where k is the spring constant of the springs. It also obeys Newton's second law, F=ma, where m is the mass. Thus, kx=ma. Accordingly, acceleration may be calculated as
a=(m/k)*xEquation 7

The above described embodiments may be directed towards accelerometry sensing and measurements. Different types of sensors such as MEMS gyroscopes may also be provided using the above-described technique.FIGS. 7-11illustrate example embodiments of MEMS sensing devices configured to measure angular velocity using the above described technique.

FIG. 7as an example configuration of a MEMS sensing device700such as a gyroscope, in accordance with some embodiments. The sensing device700includes an outer proof mass702affixed to a fixed frame704. The proof mass702may be configured similar to one described in reference toFIG. 6and accordingly may include a sensing device similar to one described in reference toFIG. 6(not shown inFIG. 7for simplicity). The proof mass702may be configured to move in the direction indicated by arrow720(drive mode).

The device700may further include an inner proof mass706(also configured similar to one described in reference toFIG. 6and including a similar sensing device that is not shown for simplicity) that is free to move in the direction indicated by arrow722(sense mode), e.g., perpendicular to the drive mode. In some embodiments, the inner proof mass706may be disposed within the outer proof mass702. In other embodiments, the inner and outer proof masses702and706may be disposed separately due to inertial forces and affixed to the frame704. The outer proof mass702may be excited at a determined drive frequency “ω drive,” e.g., using a “drive” set of comb fingers (not shown for clarity), in order to provide for the Coriolis force (calculated to determine rotation speed) to be measurable.

Calculation of x displacement may be conducted in the same way as described above and applied to a formula below in order to obtain rotation rate. In the presence of an overall rotation in the z-direction, there is an acceleration (“Coriolis acceleration”) of the inner proof mass of a C=−2Ω×v, where Ω is the rotation rate vector and v is the velocity vector. For simplicity, assume Ω and v are perpendicular. Again using ma=kx, and applying the Coriolis acceleration above, we have:
Ω=(−k/2mv)xEquation 8
where m is the mass of the inner mass and k is its spring constant.

FIGS. 8-11illustrate an example MEMS sensing device700in different modes pertaining to an gyroscope, specifically, configured to measure the gyroscope's sense and drive modes with or without applied external rotation, e.g., gyroscopes800,900,1000, and1100configured as described in reference toFIG. 7. More specifically, device700may be configured to sense the drive mode and sense mode without or with applied external rotation. For example, device700may sense the drive mode and sense mode without applied external rotation in states800and900respectively and may sense the drive mode and sense mode with applied external rotation in states1000and1100respectively. When subject to external rotation (in plane with the page), the inner proof mass706may move at a frequency “ω sense”=“ω drive.” The device700may be configured to detect the motion of either the sense mode or the drive mode in states800,900,1000, and1100at the locations of the black ellipses indicated by numerals802,902,1002, and1102respectively.

FIG. 12is a process flow diagram illustrating operation of the MEMS sensing device100as described in reference toFIG. 1, in accordance with some embodiments. The process1200may begin at block1202, where the phase of the light beam portion in at least one waveguide (e.g., waveguide102) may be controlled, for example, with a phase shifter124. The phase may be controlled to ensure that in a rest (or initial) position of the device100the light intensity of the light beam may be divided substantially equally between the portions of light passing through the waveguides102and104, in order to ensure detectability of light intensity changes when the device100moves in response to an external acceleration, causing the movable waveguide to move relative to the fixed waveguide, as described above.

At block1204, a change in light intensity between the portions of the light beam passing through each of the two waveguides of the device may be detected, e.g., using detectors120and122. The change may occur in response to a substantially parallel displacement of the waveguide104(or the section106of the waveguide104) relative to the waveguide102. As described above, the displacement may occur as a result of external acceleration applied to the device100or an apparatus including the device100.

At block1206, inertial change (e.g., external acceleration or rotation) applied to the device100(or apparatus including device100) may be determined, based on the detected light intensity change. As described above, the device100may be calibrated to transduce movements of the waveguide104relative to the waveguide102based on detected power (light intensity) changes. The movements of the waveguide104and corresponding changes in light intensity correspond to inertial change resulting from external acceleration or rotation applied to the device100(or apparatus including device100). The acceleration or rotation may be calculated based on these dependencies. Knowing how much the detected light has changed d(P/P0) in Equation 4, and knowing the geometrical and other factors on the right hand side of Equation 4, the displacement dx may be transduced using Equation 4. From that the acceleration may be calculated using Equation 7 or the rotation rate may be calculated using Equation 8. Various operations are described as multiple discrete operations in turn, in a manner that is most helpful in understanding the claimed subject matter. However, the order of description should not be construed as to imply that these operations are necessarily order dependent. Embodiments of the present disclosure may be implemented into a system or apparatus using any suitable hardware and/or software to configure as desired.

FIG. 13schematically illustrates an example system that may be used to practice various embodiments described herein.FIG. 13illustrates, for one embodiment, an example system1300having one or more processor(s)1304, system control module1308coupled to at least one of the processor(s)1304, system memory1312coupled to system control module1308, non-volatile memory (NVM)/storage1314coupled to system control module1308, and one or more communications interface(s)1320coupled to system control module1308.

In some embodiments, the system1300may include a device100, assembly600, or device700and provide logic/module that performs functions aimed at detecting change of light intensity and calculating external acceleration and/or rotation applied to the system and/or other modules described herein. For example, the device100, assembly600, or device700may be disposed in a chip included in the system1300. In some embodiments, the system1300may include one or more computer-readable media (e.g., system memory or NVM/storage1314) having instructions and one or more processors (e.g., processor(s)1304) coupled with the one or more computer-readable media and configured to execute the instructions to implement a module to perform light intensity change detection and inertial change calculation actions described herein.

System control module1308for one embodiment may include any suitable interface controllers to provide for any suitable interface to at least one of the processor(s)1304and/or to any suitable device or component in communication with system control module1308.

System control module1308may include memory controller module1310to provide an interface to system memory1312. The memory controller module1310may be a hardware module, a software module, and/or a firmware module. System memory1312may be used to load and store data and/or instructions, for example, for system1300. System memory1312for one embodiment may include any suitable volatile memory, such as suitable DRAM, for example. System control module1308for one embodiment may include one or more input/output (I/O) controller(s) to provide an interface to NVM/storage1314and communications interface(s)1320.

The NVM/storage1314may be used to store data and/or instructions, for example. NVM/storage1314may include any suitable non-volatile memory, such as flash memory, for example, and/or may include any suitable non-volatile storage device(s), such as one or more hard disk drive(s) (HDD(s)), one or more compact disc (CD) drive(s), and/or one or more digital versatile disc (DVD) drive(s), for example. The NVM/storage1314may include a storage resource physically part of a device on which the system1300is installed or it may be accessible by, but not necessarily a part of, the device. For example, the NVM/storage1314may be accessed over a network via the communications interface(s)1320.

Communications interface(s)1320may provide an interface for system1300to communicate over one or more network(s) and/or with any other suitable device. The system1300may wirelessly communicate with the one or more components of the wireless network in accordance with any of one or more wireless network standards and/or protocols.

For one embodiment, at least one of the processor(s)1304may be packaged together with logic for one or more controller(s) of system control module1308, e.g., memory controller module1310. For one embodiment, at least one of the processor(s)1304may be packaged together with logic for one or more controllers of system control module1308to form a System in Package (SiP). For one embodiment, at least one of the processor(s)1304may be integrated on the same die with logic for one or more controller(s) of system control module1308. For one embodiment, at least one of the processor(s)1304may be integrated on the same die with logic for one or more controller(s) of system control module1308to form a System on Chip (SoC).

In various embodiments, the system1300may have more or less components, and/or different architectures. For example, in some embodiments, the system1300may include one or more of a camera, a keyboard, liquid crystal display (LCD) screen (including touch screen displays), non-volatile memory port, multiple antennas, graphics chip, application-specific integrated circuit (ASIC), and speakers.

In various implementations, the system1300may be, but is not limited to, a mobile computing device (e.g., a laptop computing device, a handheld computing device, a tablet, a netbook, etc.), a laptop, a netbook, a notebook, an ultrabook, a smartphone, a tablet, a personal digital assistant (PDA), an ultra mobile PC, a mobile phone, a desktop computer, a server, a printer, a scanner, a monitor, a set-top box, an entertainment control unit, a digital camera, a portable music player, or a digital video recorder. In further implementations, the system1300may be any other electronic device.

The embodiments described herein may be further illustrated by the following examples. Example 1 is an apparatus method comprising micro-electromechanical system (MEMS) apparatus, comprising: a laser arrangement configured to generate a light beam; a first waveguide configured to receive and output a first portion of the light beam; and a second waveguide having a section that is evanescently coupled to the first waveguide, the second waveguide configured to receive and output a second portion of the light beam, wherein the section of the second waveguide is configured to be movable substantially parallel to the first waveguide, wherein a movement of the section of the second waveguide may cause a detectable change in light intensity between the first and second portions of the light beam.

Example 2 may include the subject matter of Example 1, and further specifies that the apparatus comprises a phase shifter coupled with the second waveguide and configured to control a phase shift to the second portion of the light beam relative to the first portion of the light beam, to provide substantially equal division of the light intensity between the first and second portions of the light beam before the detectable change in light intensity occurs.

Example 3 may include the subject matter of Example 2, and further specifies that the phase shifter comprises a carrier-injection phase shifter, including a quadrature bias diode or electro-optic phase tuner.

Example 4 may include the subject matter of Example 1, and further specifies that the apparatus includes a first detector coupled to the first waveguide and configured to detect light intensity of the first portion of the light beam; and a second detector coupled to the second waveguide to detect light intensity of the second portion of the light beam.

Example 5 may include the subject matter of any of Examples 1 to 4, and further specifies that the apparatus further comprises a first proof mass movably affixed to a frame such that the first proof mass is movable at least in one direction relative to the frame, wherein the section of the second waveguide is disposed on the first proof mass, wherein a movement of the first proof mass causes the section of the second waveguide to move substantially parallel to the first waveguide.

Example 6 may include the subject matter of Example 5, and further specifies that the first proof mass structure is affixed to the frame by at least two spring arrangements.

Example 7 may include the subject matter of Example 5, and further specifies that the movement of the first proof mass is caused by an external acceleration applied to the apparatus, wherein the apparatus comprises an accelerometer.

Example 8 may include the subject matter of Example 5, and further specifies that the apparatus comprises a first assembly, wherein the apparatus further includes a second assembly comprising a third waveguide configured to receive and output a third portion of the light beam; a fourth waveguide having at least a section that is evanescently coupled to the third waveguide, the fourth waveguide configured to receive and output a fourth portion of the light beam that is phase-shifted relative to the third portion; a third detector coupled to the third waveguide and configured to detect light intensity of the third portion of the light beam; and a fourth detector coupled to the fourth waveguide and configured to detect light intensity of the fourth portion of the light beam, wherein the section of the fourth waveguide is configured to be movable substantially parallel to the third waveguide in response to another displacement of the apparatus, wherein a movement of the portion of the fourth waveguide causes a detectable change in light intensity between the third and fourth portions of the light beam.

Example 9 may include the subject matter of Example 8, and further specifies that the section of the fourth waveguide is disposed on a second proof mass, wherein a movement of the second proof mass causes the portion of the fourth waveguide to move substantially parallel to the second waveguide.

Example 10 may include the subject matter of Example 9, and further specifies that the second proof mass structure is movably affixed to the frame such that the proof mass is movable at least in another direction relative to the frame, the another direction being perpendicular to the at least one direction.

Example 11 may include the subject matter of Example 10, and further specifies that the second proof mass is disposed on the first proof mass.

Example 12 may include the subject matter of Example 9, and further specifies that the movement of the second proof mass is caused by an external rotation of the frame, wherein the apparatus comprises a gyroscope.

Example 13 is a system, comprising a computing device; and a micro-electromechanical system (MEMS) apparatus coupled to the computing device, the apparatus comprising: a laser arrangement configured to generate a light beam; a first waveguide configured to receive and output a first portion of the light beam; and a second waveguide having a section that is evanescently coupled to the first waveguide, the second waveguide configured to receive and output a second portion of the light beam, wherein the section of the second waveguide is configured to be movable substantially parallel to the first waveguide, wherein a movement of the section of the second waveguide causes a detectable change in light intensity between the first and second portions of the light beam.

Example 14 may include the subject matter of Example 13, and further specifies that system further comprises a first detector coupled to the first waveguide and configured to detect light intensity of the first portion of the light beam; and a second detector coupled to the second waveguide to detect light intensity of the second portion of the light beam.

Example 15 may include the subject matter of Example 14, and further specifies that the system includes circuitry coupled to the first and second detectors to determine an inertial change associated with the system based on light intensities of the first and second portions respectively detected by the first and second detectors.

Example 16 may include the subject matter of Example 15, and further specifies that the MEMS apparatus is disposed in a chip coupled to the computing device.

Example 17 may include the subject matter of Example 16, and further specifies that the system comprises a mobile computing device.

Example 18 includes a method, comprising: controlling light intensity of at least one of a first and second portions of a light beam passing through a first and second waveguide of a micro-electromechanical system (MEMS) apparatus to provide a substantially equal division of light intensities between the first and second portions, wherein at least a section of the second guideline is evanescently coupled to the first waveguide and is configured to be movable substantially parallel to the first waveguide in response to an inertial change associated with the apparatus; detecting a change in the light intensities between the first and second portions caused by a movement of the portion of the second waveguide relative to the first waveguide; and determining the inertial change applied to the apparatus that caused the change in the respective light intensities, based on a result of the detecting.

Example 19 may include the subject matter of Example 18, and further specifies that the controlling includes phase-shifting the second portion of the light beam relative to the first portion of the light beam.

Example 20 may include the subject matter of any of Examples 18-19, and further specifies that the inertial change includes external rotation of the apparatus or external acceleration of the apparatus.