Patent Publication Number: US-11378552-B2

Title: Microscale photoacoustic spectroscopy, imaging, and microscopy

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
     This application claims the priority benefit, under 35 U.S.C. § 119(e), of U.S. application Ser. No. 62/858,351, filed on Jun. 7, 2019, which is incorporated herein by reference in its entirety. 
    
    
     BACKGROUND 
     Photoacoustic imaging (PAI) has attracted much attention over the past two decades for various biomedical applications. PAI is a hybrid imaging modality that synergizes the acoustic and optical domains to generate enhanced images. In PAI, a nonlinear interaction between light and biological tissue causes the biological tissue to emit ultrasound waves generated by biological tissue in response to incident light. These ultrasound waves can be detected and used to generate an image of the biological tissue. PAI can provide functional and metabolic activity information through endogenous and exogenous imaging contrast. PAI can also offer much higher penetration depths than optical imaging techniques because the acoustic scattering mean free path is orders of magnitude longer than the optical scattering mean free path. 
     Common PAI instrumentation uses medical ultrasound imaging transducer technology. However, the generated ultrasound signal in PAI can vary significantly in comparison to conventional ultrasound imaging. Ultrasound imaging uses narrowband signals and transducers for ultrasound imaging operate with narrow bandwidths. A conventional ultrasound imaging system typically uses a bandwidth that is about of its operating bandwidth, e.g., about 2 MHz within an 8-12 MHz operational range. In contrast, photoacoustic signals generated from biological tissue can be broadband signals spanning from sub MHz to hundreds of MHz. In addition, photoacoustic signals generated from the biological endogenous tissues are almost three orders of magnitude weaker than those signals generated by medical ultrasound imaging. There is a desire for PAI transducers than can collect signals over a broad band with a high level of sensitivity. There is also a desire for PAI transducers that can collect ultrasound signals over a wide angle of acceptance. A PAI transducer with these qualities may improve the field of view and resolution for image reconstruction. 
     SUMMARY 
     The present technology addresses the desires for PAI that operates over a broad bandwidth with high sensitivity and a wide angle of acceptance. This technology can be implemented as a miniaturized on-chip PAI device with optical and acoustic modules integrated together. Silicon photonics enables flexible, low-cost, and scalable approaches for the miniaturization of integrated electronic and photonic systems, enabling on-chip PAI for medicine and biology. 
     Embodiments of the present technology include a sensor. The sensor includes an excitation light source, an output coupler, a first resonator, at least one probe light source, at least one detector, and a processor. In operation, the excitation light source emits an excitation beam. The output coupler, which is in optical communication with the excitation beam, couples the excitation beam into an analyte medium, and the excitation beam causes the analyte medium to emit a photoacoustic wave. The first resonator, which is in acoustic communication with the analyte medium, has a first resonance frequency that shifts in response to the photoacoustic wave. At least one probe light source, which is in optical communication with the first resonator, couples a first probe beam into the first resonator. At least one detector, which is in optical communication with the first resonator, detects at least a portion of the first probe beam transmitted or reflected by the first resonator. The processor, which is operably coupled to the at least one detector, determines a shift of the first resonance frequency in response to the photoacoustic wave based on at least a portion of the first probe beam detected by the detector. 
     The sensor may include a collimator to collimate the excitation beam. The collimator may include a meta-surface. The photoacoustic wave may have at least one spectral component in a band from about 1 MHz to about 50 MHz. The photoacoustic wave may have at least one spectral component in a band from about 1 MHz to about 20 MHz. The first resonator may be disposed on a flexible membrane configured to deflect in response to the photoacoustic wave. The first resonator may include a polymer ring resonator. 
     The sensor may additionally include a second resonator. The second resonator, in acoustic communication with the analyte medium and in optical communication with at least one probe light source and at least one detector, may have a second resonance frequency that shifts in response to the photoacoustic wave. The second resonance frequency may be different than the first resonance frequency. At least one probe light source may be configured to couple a second probe beam into the second resonator. At least one detector may be configured to detect at least a portion of the second probe beam transmitted or reflected by the second resonator. The processor may be configured to determine a shift of the second resonance frequency in response to the photoacoustic wave based on at least a portion of the second probe beam detected by the detector. The processor may be configured to determine a temporal shift between the shift in the first resonance frequency and the shift in the second resonance frequency. The first resonator may be disposed on a membrane that vibrates in response to the photoacoustic wave. 
     The sensor may further include a microfluidic channel. The microfluidic channel, in optical communication with the output coupler and the first resonator, may flow the analyte medium past the output coupler and the first resonator. 
     Another embodiment of the present technology includes a neurophotonic probe. The neurophotonic probe includes a substrate, probe ring resonators, at least one input waveguide, and at least one output waveguide. The substrate of the neurophotonic probe has a tip for penetrating neural tissue. In operation, the probe ring resonators, which are disposed along the tip of the substrate, have respective resonance frequencies that shift in response to acoustic excitation. At least one input waveguide, which is disposed on the substrate and evanescently coupled to the probe ring resonators, couples probe light into the ring resonators. At least one output waveguide, which is disposed on the substrate and evanescently coupled to the probe ring resonators, couples probe light out of the probe ring resonators. 
     At least a portion of the tip of the substrate may be configured to deflect in response to the acoustic excitation, thereby shifting the respective resonance frequencies of the probe ring resonators. The neurophotonic probe may further include wavelength-division multiplexing (WDM) ring resonators. The WDM ring resonators may be evanescently coupled to at least one output waveguide and a bus waveguide and may couple the probe light from at least one output waveguide to the bus waveguide. 
     Another embodiment of the present technology includes a method of imaging neural tissue. The method includes inserting a neural probe into the neural tissue, measuring a shift in a resonance frequency of a first optical ring resonator on the neural probe caused by a photoacoustic excitation propagating through the neural tissue, and generating an image of the neural tissue based at least in part on the shift in resonance frequency of the first optical ring resonator. 
     Generating the image may include generating the image with a spatial resolution of about 20 microns to about 50 microns. Generating the image may include generating the image over a volume of about 1 cubic millimeter. The method may additionally include measuring a shift in a resonance frequency of a second optical ring resonator on the neural probe caused by the photoacoustic excitation propagating through the neural tissue. The method may additionally include illuminating the neural tissue with a probe beam to produce the photoacoustic excitation propagating through the neural tissue. 
     All combinations of the foregoing concepts and additional concepts discussed in greater detail below (provided such concepts are not mutually inconsistent) are part of the inventive subject matter disclosed herein. In particular, all combinations of claimed subject matter appearing at the end of this disclosure are part of the inventive subject matter disclosed herein. The terminology used herein that also may appear in any disclosure incorporated by reference should be accorded a meaning most consistent with the particular concepts disclosed herein. 
    
    
     
       BRIEF DESCRIPTIONS OF THE DRAWINGS 
       The skilled artisan will understand that the drawings primarily are for illustrative purposes and are not intended to limit the scope of the inventive subject matter described herein. The drawings are not necessarily to scale; in some instances, various aspects of the inventive subject matter disclosed herein may be shown exaggerated or enlarged in the drawings to facilitate an understanding of different features. In the drawings, like reference characters generally refer to like features (e.g., functionally and/or structurally similar elements). 
         FIG. 1A  is a diagram of a microscale photoacoustic sensor. 
         FIG. 1B  is another view of the microscale photoacoustic sensor of  FIG. 1A . 
         FIG. 1C  is a diagram of a miniature photoacoustic sensor within a microfluidic channel. 
         FIG. 2A  is diagram of a probe in a neurophotonic microscale photoacoustic imaging sensor. 
         FIG. 2B  is a diagram of a neurophotonic microscale photoacoustic imaging sensor with multiple probes for super resolution PAI. 
         FIG. 2C  is a closer view of a collimator and resonator on the neurophotonic microscale photoacoustic imaging sensor probes of  FIGS. 2A and 2B , where the collimator is designed for acoustic resolution. 
         FIG. 2D  is a closer view of a collimator and resonator on the neurophotonic microscale photoacoustic imaging sensor probes of  FIGS. 2A and 2B , where the collimator is designed for optical resolution. 
         FIG. 3A  is a diagram of a photonic waveguide-based metasurface collimator. 
         FIG. 3B  is a diagram depicting dimensions of the photonic waveguide-based metasurface collimator of  FIG. 3A . 
         FIG. 3C  is a diagram depicting another view of the waveguide-based metasurface collimator of  FIG. 3A . 
         FIG. 4  shows a process for fabricating a waveguide in a PAI sensor. 
         FIG. 5  is an image of a waveguide-based metasurface collimator produced with a scanning electron microscope (SEM). 
         FIG. 6A  shows a front view of a simulated emission from a binary grating. 
         FIG. 6B  shows a top view of a simulated emission from the binary grating of  FIG. 6A . 
         FIG. 6C  shows a front view of a simulated emission from a waveguide-based metasurface collimator. 
         FIG. 6D  shows a top view of a simulated emission from the waveguide-based metasurface collimator of  FIG. 6C . 
         FIG. 7A  shows a side view of an experimentally measured emission from a waveguide-based metasurface collimator at 1× magnification. 
         FIG. 7B  shows a top view of the experimentally measured emission from the waveguide-based metasurface collimator at 1× magnification in  FIG. 7A . 
         FIG. 7C  shows a side view of an experimentally measured emission from a conventional binary grating at 1.5× magnification. 
         FIG. 7D  shows a top view of the experimentally measured emission from the waveguide-based metasurface collimator at 1.5× magnification in  FIG. 7C . 
         FIG. 8  is a cross-sectional diagram of an on-chip photoacoustic transducer. 
         FIG. 9A  shows a simulation of a first resonance frequency of a membrane within the photoacoustic transducer of  FIG. 8 . 
         FIG. 9B  shows a simulation of a second resonance frequency of a membrane within the photoacoustic transducer of  FIG. 8 . 
         FIG. 10  shows a simulation of a deflection/stress profile of a membrane within the photoacoustic transducer of  FIG. 8  with a waveguide on top of it. 
         FIG. 11A  shows a simulated profile of a mode supported by a photonic waveguide within a photoacoustic transducer before deflection. 
         FIG. 11B  shows a simulated profile of the mode supported by the photonic waveguide within the photoacoustic transducer of  FIG. 11A  after deflection. 
         FIG. 12  shows a microscope image of two fabricated photoacoustic transducers. 
         FIG. 13  is a diagram of an array of photoacoustic transducers. 
         FIG. 14  shows the process to fabricate a photoacoustic transducer. 
         FIG. 15  is a graph of the time series response of the velocity of a deflecting membrane within a photoacoustic transducer with application of an external ultrasound signal of a 1 MHz. 
         FIG. 16  is a graph of the shift in resonance frequency of a ring resonator within a photoacoustic transducer with and without an external ultrasound signal. 
     
    
    
     DETAILED DESCRIPTION 
     Miniature Photoacoustic Sensor 
     A miniature, on-chip, platform for both excitation and detection may offer several advantages. First, the field-of-view for imaging may be scaled up by multiplexing a large number of excitation sources. Second, a miniature platform may provide a compact hardware geometry to implement solutions at a low-cost with high volume production. Third, a miniature platform may enable biological analysis, such as cell screening, probing, and automation. 
       FIGS. 1A and 1B  show different views of a microscale photoacoustic sensor  100  with integrated photonic components for stimulating and detecting photoacoustic emissions from biological tissue and other matter. This microscale photoacoustic sensor  100  can be used for spectroscopy, imaging, or microscopy. 
     The sensor  100  includes a coherent excitation light source  110  (e.g., a laser), an output coupler  120 , and a waveguide  170   a  that couples the excitation light source  110  and the output coupler  120 . The excitation light source  110 , output coupler  120 , and waveguide  170   a  may all be fabricated on a flexible substrate or membrane  102 . The excitation light source  110  emits an excitation beam  101 , which is guided by the waveguide  170   a  to the output coupler  120 . The output coupler  120  couples the excitation beam  101  into an analyte medium that is deposited on or flows over the membrane  102 . The output coupler  120  may be a collimator or a binary grating surface, which diffracts light out of the plane of the sensor. The sensor  100  also includes at least one resonator  130 , probe light source  140 , and waveguide  170   b  fabricated on the membrane  102 . The waveguide  170   b  is evanescently coupled to the resonator  130 , which may be a ring resonator or an unbalanced Mach Zehnder interferometer, and connects the probe light source  140  to a detector  150 , which in turn is coupled to a processor  160 . 
     The membrane  102  is a flexible substrate with some elasticity and free boundary conditions. It may be modelled using a spring-mass-damper system with a characteristic resonance. The characteristics of the membrane  102  are its quality factor and center frequency and bandwidth of its resonance peak. A lower quality factor produces a broader bandwidth. These characteristics may be designed so that the membrane  102  vibrates with a certain central frequency and a certain bandwidth. For example, the membrane  102  may vibrate at a 1 MHz central frequency and a 50% bandwidth. 
     In operation, the light source  110  launches the excitation beam  101  into the waveguide  170   a . The output coupler  120  couples the excitation beam  101  out of the waveguide  170   a  and into the analyte medium. Depending on the coupler&#39;s configuration, the coupler  120  may collimate the excitation beam  101  or focus it to a point within or beyond the analyte medium. The excitation beam  101  interacts nonlinearly with analyte medium to produce a photoacoustic wave  105 , which propagates through the analyte medium back towards the sensor  100 . The photoacoustic wave  105  causes the membrane  102  to deflect or vibrate. This deflection or vibration deforms the resonator  130 , shifting its resonance frequency. 
     A probe beam from the probe light source  140  probes the resonant frequency of the resonator  130  via the waveguide  170   b . If the wavelength of the probe beam matches the resonator&#39;s resonant frequency, the probe beam is at least partially coupled from the waveguide  170   b  into the resonator  130 , where it remains until it is coupled out of the resonator  130  (neglecting absorption). This causes the signal sensed by the detector  150  to fluctuate as a function of the (mis)match between the probe beam wavelength and the resonator&#39;s resonance frequency. The processor  160  coupled to the detector  150  can quantify the shift in the resonator&#39;s resonance frequency based on the intensity of the probe light detected by the detector  150 . 
     For instance, if the wavelength of the probe beam matches the resonance frequency of the unperturbed resonator  130 , then the detector  150  should not detect any light when the resonator is in an unperturbed state. Instead, it should detect light when the resonator  130  is perturbed. Similarly, if the wavelength of the probe beam does not match the resonance frequency of the unperturbed resonator  130 , then the detector  150  should detect light unless the resonator is perturbed enough to shift its resonance frequency to overlap in wavelength/frequency with the probe beam. The probe beam&#39;s wavelength can also be chirped or swept (e.g., with a tunable laser) so that it probes different possible resonance frequencies at different moments in time in a repeatable fashion. By sensing when the detected intensity dips, the processor  160  can match the time bin to the probe beam wavelength/frequency that matches the resonator&#39;s instantaneous resonance frequency. This makes it possible to both detect and quantify the resonator&#39;s instantaneous resonance frequency. 
     The processor  160  matches the detected resonance frequency (shift) to the photoacoustic wave that caused the resonance frequency shift. The resonators  130  are in different positions on the sensor and so detect photoacoustic waves from different angles, just like pixels in a photodetector array. If the resonators  130  are ring resonators, they can be driven in a phase-locked loop, with the frequency of the probing beam frozen and the detector  150  and processor  160  measuring the change in intensity of the probing mean. The detector  150  and processor  160  can measure time-domain changes in the intensity output from the ring resonators, thereby giving information on changes in the photoacoustic wave&#39;s phase. In addition to measuring changes in the photoacoustic wave&#39;s phase, the processor  160  may measure changes in the photoacoustic wave&#39;s amplitude using vector analysis. If the resonators  130  are Mach Zehnder Interferometers (MZI), changes in intensity in the time domain can be measured at the detector  150 , thereby giving information on changes in the photoacoustic wave&#39;s phase. 
       FIG. 1C  illustrates how the microscale photoacoustic sensor  100  may be used in a microfluidic application. An integrated microfluidic channel  108  is laid over the output coupler  120  so that the excitation beam  101  emitted by the output coupler  120  passes through a fluid analyte medium  106  that flows through the channel  108 . The membrane  102  that supports the resonator(s)  130  is in acoustic communication with the fluid analyte medium  106 . For example, the fluid analyte medium  106  may flow through the channel  108  over at least a portion of the membrane  102  (though not necessarily the portion that supports the resonator(s)  130 ). In any event, the liquid analyte medium  106  flows through the path of the excitation beam  101  emitted by the output coupler  120 . The excitation beam  101  causes the fluid analyte medium  106  to emit a photoacoustic wave  105 , which in turn moves or shakes the membrane  102 . In turn, this movement of the membrane  102  by the photoacoustic wave  105  may shift the resonance frequency of the resonator  130 . 
       FIGS. 2A-2D  illustrate a microscale photoacoustic sensor  200  suitable for photoacoustic imaging of neural tissue  205  or other biological tissue.  FIG. 2A  shows the sensor&#39;s probe  202 , which has a tip  204  that is sharp enough to penetrate the tissue  205  without damaging it. The probe  202  supports three output couplers  220   a ,  220   b , and  220   c , which are coupled to respective waveguides  222   c ,  222   b , and  222   c . These waveguides  222   a ,  222   b , and  222   c  are coupled to an excitation bus waveguide  226  via respective ring resonators  224   a ,  224   b , and  224   c . The probe  202  also supports ring resonators  230   a ,  230   b , and  230   c , which are evanescently coupled to a probe bus waveguide  232 . The portion of the probe  202  that supports the ring resonators  230  is flexible enough to bend or deflect in response to a photoacoustic wave propagating through the tissue  205 . 
     The resolution of the microscale photoacoustic sensor  200  scales with the number of ring resonators. With a higher number of ring resonators, the microscale photoacoustic sensor has a higher resolution in measuring the temporal shift in the photoacoustic wave. Likewise, with a higher number of ring resonators on the microscale photoacoustic sensor  200 , the image derived from the temporal shift information has better resolution and fewer reconstruction artifacts. As an example, a probe  202  that is about 8 mm to about 10 mm long, 300 μm wide, and about 5 μm to about 10 μm thick can have about 32 to about 128 ring resonators on its surface. 
     The tip  204  may be coated with a bio-compatible material. For example, the tip  204  may be coated with PDMS or parylene. The tip  204  may be inserted up to about 1 cm into biological tissue. The bio-compatible coating has a Young&#39;s modulus within about 1 MPa of the Young&#39;s modulus of the neural or biological tissue penetrated. The similar Young&#39;s modulus may help to decrease any mechanical stress or immune response in the tissue when the microscale photoacoustic sensor  200  is inserted. 
     Like the sensor  100  in  FIGS. 1A-1C , the sensor  200  in  FIGS. 2A-2D  operates by illuminating the tissue with a pump or excitation beam  201  that generates a photoacoustic wave, which the sensor  200  detects and uses to generate a photoacoustic image of the tissue  205 . More specifically, an excitation light source (not shown) generates the excitation beam  201 , which is coupled into the tissue via the output collimators  220 , excitation bus waveguide  226 , ring resonators  224 , and waveguides  222 . The ring resonators  224  may have equal radii, to couple light  201  of the same wavelength to their respective output couplers  220 , or different radii, to couple light  201  of different wavelengths to the different output couplers  220 . This enables the probe  200  to illuminate the tissue with light  201  at different wavelengths. This light generates one or more photoacoustic waves  203  that propagate within the tissue  205 . Wavelength-division multiplexing (WDM) may be used to channel light  201  of different wavelengths into different output couplers  220  for multispectral photoacoustic imaging. WDM can be used to identify the source of the excitation light  201  when deriving an image from the photoacoustic signal. 
     The microscale photoacoustic sensor&#39;s ring resonators  230  sense the photoacoustic waves  203 . Each ring resonator  230  has a resonance frequency that shifts in response to movement of the corresponding probe  202  by the photoacoustic waves  203 . The ring resonators  230  may have the same resonance frequency or different resonance frequencies. If the ring resonators  230  have different resonant frequencies, and those resonant frequencies are separated by more than the expected frequency shifts, then the resonant frequencies can be uniquely mapped to the ring resonators  230 . In other words, the resonance frequencies can be spectrally multiplexed, making it possible to interrogate all of them using a single probe beam  207  from a tunable probe light source (not shown) swept over a range that spans the range of the resonance frequencies. Each ring resonator  230  reflects and/or transmits a portion of the probe beam  203 . The probe waveguide  232  guides the transmitted and reflected portions of the probe beam to a detector (not shown). 
       FIG. 2B  is an illustration of a microscale photoacoustic sensor  200  with an array of four probes  202  inserted into neural tissue  205 . Microscale photoacoustic sensor components (output couplers  220 , ring resonators  230 , and waveguides) reside on each of the four probes  202 . Each probe  202  may emit one or more excitation beams  201  to excite one or more photoacoustic signals  203  within the neural tissue  205 . The probes  202  may emit excitation beams  201  sequentially or simultaneously; for instance, each probe  202  may emit excitation beams  201  in turn, with all of the probes  202  “listening” for the corresponding acoustic waves  203 . This may make it possible to localize the sources of the acoustic waves  203  for generating a 3D image of the neural tissue  205 . In this manner, the microscale photoacoustic sensor  200  with an array of neural-penetrating probes  202  may be used to perform photoacoustic tomography. A microscale photoacoustic sensor with an array of tips may be used to image up to about 10,000 neurons with single-neuron spatial resolution in a 1 mm 3  sampling volume of neural tissue  205 . 
       FIGS. 2C and 2D  illustrate the tunability of spatial resolution in the microscale photoacoustic sensor  200 . As explained above, the output coupler  220 , which may be a metasurface lens or collimator as described below, emits probe light  201  into the neural tissue  205 . The output coupler  220  may be designed to diffract the excitation beam  201  with a range of different beam shapes and focus parameters. For example, the output coupler  220   a  may diffract light  201  with a lateral resolution of about 100 μm for acoustic resolution PAI, as shown in  FIG. 2C . As another example,  FIG. 2D  shows a modified output coupler  220 ′ that diffracts light  201 ′ with a lateral resolution of about 0.22 μm for optical resolution PAI. Optical resolution results in a smaller field of view and higher spatial resolution, whereas acoustic resolution results in a larger field of view and lower spatial resolution. 
     Acoustic resolution and optical resolution offer different advantages. Acoustic resolution offers better depth penetration and a larger field of view, while also having lower resolution. With acoustic resolution, output couplers  220  and resonators  230  can be placed with less spatial precision. Acoustic resolution is appropriate for measuring photoacoustic waves in larger volumes. In contrast, optical resolution offers higher resolution, lower penetration, and a smaller field of view. With optical resolution, output couplers  220  and resonators  230  may need to be placed with more care. Optical resolution is appropriate for measuring photoacoustic waves with higher resolution within smaller volumes. For example, optical resolution can be used to image individual neural cells. 
     Photonic Waveguide-Based Metasurface Collimator 
       FIGS. 3A-3C  show different views of a photonic waveguide-based metasurface collimator  320  suitable for use in a photoacoustic sensor. The photonic waveguide  370  terminates in a metasurface collimator structure  320 , which has an array of metasurface elements or diffracting grooves  322  with a pitch of about 60 to about 80 μm. Each metasurface element  322  is about 400 nm thick. The metasurface collimator  320  receives a light beam  301  from an excitation light source  310 . The light beam  301  propagates through a waveguide  370 . The diffracting grooves  322  diffract the light beam out of the plane of the waveguide  370 , forming an excitation beam  305  that can cause an analyte medium to emit a photoacoustic wave. 
     A photonic waveguide-based metasurface collimator  320  may enable the miniaturization of excitation sources and may enable integrated on-chip photon routing and manipulation. A diffracting metasurface collimator  320  can collimate light more uniformly and/or over a wider area than the binary gratings used in conventional out-of-plane couplers. The metasurface collimator  320  may achieve a more uniform emission along the waveguide  370  propagation direction than a binary grating by controlling the amount of energy diffracted from each diffracting groove  322  in proportion to the power loss along the optical path. The power loss may be controlled by designing a unique arrangement of light diffractors  322  along the direction of light propagation. 
     An inverse modelling approach can be used to design the metasurface grating structure on the photonic waveguide-based metasurface collimator  320  shown in  FIGS. 3A-3C . For instance, the collimator can be designed to create a wide collimated beam, which is useful for on-chip optical excitation and detection in bio-sensing applications. Finite difference time domain (FDTD) modeling can be used to design the collimator. The collimator&#39;s light diffraction properties are mathematically related to critical design parameters. Rectangular light diffracting grooves  322  in the grating structure on the metasurface collimator can be defined by their duty cycle (C), row period (Λ y ) along the transverse direction, and line period (Λ x ) along the propagation direction, as shown in  FIG. 3B . 
     The metasurface collimator  320  may offer a high index region to support orthogonally polarized modes propagating along the axial direction. Assuming the incoming optical wave  301  in the waveguide  370  is of the form E 0   inc (y,z)e i(βx−ωt) , where E 0   inc (y,z) is the amplitude of the electric field and β is the propagation constant, the diffracted beam profile is given by, E 0   diff  (y,z)e i(k     xn     x−ωt)  with the propagation constant as 
     
       
         
           
             
               k 
               
                 x 
                 n 
               
             
             = 
             
               
                 
                   β 
                   n 
                 
                 + 
                 
                   i 
                   ⁢ 
                   α 
                 
               
               = 
               
                 
                   β 
                   0 
                 
                 + 
                 
                   
                     2 
                     ⁢ 
                     n 
                     ⁢ 
                     π 
                   
                   
                     Λ 
                     x 
                   
                 
                 + 
                 
                   i 
                   ⁢ 
                   α 
                 
               
             
           
         
       
     
     Here, β n  is the propagation constant of the diffracted beam that depends on the periodicity of diffracting grooves  322  in the x direction, α is the energy leakage factor and n is the diffraction order. The angle of diffraction measured from the vertical axis, for nth order of diffraction is given by 
               ϕ   n     =       sin     -   1       ⁢           ⁢     (       β   n       k   0       )             
Specifically, for out-of-plane diffraction of the beam without any higher-order diffraction, it is customary to satisfy the following conditions,
 
                          n     w   ⁢   g       -     (     λ     Λ   x       )            ≤       ɛ   a         =   1     ,         2   ⁢     (     λ     Λ   x       )       -     n     w   ⁢   g         &gt;       ɛ     SiO   2                 
where n wg  is the effective index of the waveguide and ε α  is the permittivity of the cladding. The cladding may be air or a liquid surrounding the sensor. If the microscale photoacoustic sensor is used as an opto-fluidic integrated sensor, the permittivity of air is replaced by a permittivity value of a surrounding liquid.
 
     The leakage energy in the diffracted beam is given by,
 
α=α h (ω, D,f f )(ε wg −ε α ) 2  sin 2 (π× f f )
 
Here, α h (ω, D, f f) is a coefficient that is a strong function of light wave frequency (ω) and of the etch depth (D) and fill factor (ff) of the diffraction grooves. ε wg  and ε α  are the permittivities of the waveguide and air, respectively. The parameters that control light diffraction are row and line period (in the y- and x-direction respectively) (Λ y , ζ x ) and duty cycles (C) of the diffraction grooves. Line period (Λ x ) controls the angle of diffraction, ϕ 1 , line period (Λ y ) and duty cycles modulate the effective permittivity of the individual row.
 
     As an example, the width, w, and length, l of the metasurface collimator were maintained at 10 μm and 20 μm, respectively. The center wavelength of the excitation light beam  301  was set to be in the C-band (1550 nm). The metasurface collimator  320  can operate over a wide (˜70 nm) range of wavelengths depending on its structure. 
     Tuning the metasurface collimator  320  for a certain set of conditions is performed in two steps. The first step initializes the duty cycle of an individual row in the metasurface collimator and then performs an iterative gradient descent inverse optimization to collimate the excitation beam  305 . The gradient descent method has many advantages, such as enabling the tuning of the metasurface collimator with relatively large degrees of freedom as compared to other gradient-free tuning schemes. Further, the gradient descent method requires fewer simulation steps and does not rely on parametric sweeps or random mathematical perturbations to find optimum values. 
     The gradient descent method may initialize parameters with relevant values, given the method&#39;s sensitivity to initial conditions. To find initial values, an effective mirror model was used for the metasurface collimator. The diffracting grooves  322  can be approximated by the cascaded mirror model to understand light propagation through the structure.  FIG. 3C  shows the metasurface collimator  320  with its cascade mirror model. Transmission, diffraction, and scattering coefficients of the diffracting groove are assumed as t, d, and s, respectively. Diffraction intensity output from the first diffracting groove is proportional to d, and is given by,
 
 I   1   =d   1   (i)
 
Using the cascaded mirror model, we can write intensity I 2  and I n  in general, given as,
 
 I   2   =t   1   d   2   (ii)
 
 I   n   =t   1   t   2    . . . t   n−1   d   n   (iii)
 
     The collimated beam requires uniform emission from an individual groove. Mathematically, the condition is represented as,
 
 I   1   =I   2   = . . . =I   n = . . .  (iv)
 
Substituting the equations (i), (ii), (iii) in the condition (iv) results in
 
 d   1   =t   1   d   2   =t   1   t   2   d   3   = . . . =t   1   t   2    . . . t   n−1   d   n   (v)
 
Assuming f i (x), d i (x) as functions of the duty cycle, length x and width w, of the groove. For constant width, we sweep the duty cycle and obtain the functions, f i (x) and d i (x).
 
     Using a plot of the functions, the duty cycle for individual meta surface row can be initialized to satisfy the condition given by, 
     
       
         
           
             
               
                 
                   
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     After the initialization process explained above, the duty cycle of the individual diffracting groove  322  in the metasurface collimator  320  can be tuned to obtain a collimated excitation beam output  305 . 
     Lumerical FDTD software was used to model the way that diffracted power from an individual row increases with an increase in its duty cycle. The spatial distribution of diffracted power and its variance was calculated. The duty cycle of each groove was then tuned to minimize the variance across the rows of the metasurface collimator. Every update in the iterative process was performed as 
               C   i     =         C   i     -     δ   ⁢         P   i     -     P   average         P   average           =       C   i     -     δ   ⁢           I   i     ⁢     A   i       -       I   average     ⁢     A     t   ⁢   o   ⁢   t   ⁢   a   ⁢   l               I   average     ⁢   A                   
where i is the row number, δ is the learning rate of the gradient descent method and P i  is the output power calculated by integrating the intensity over the ith row area of meta surface and P average  is the average power over the entire meta surface.
 
     With every iteration, the uniformity in the power distribution of the excitation beam collimation may increase. When the duty cycle and the grating period change, the effective index of the structure changes. As a result, the center wavelength of the excitation beam  305  may shift. This may result in poor convergence of the duty cycle in the iterative procedure. Therefore, the central emission wavelength of the excitation beam  305  may be stabilized by modifying the grating period. An additional step may be added to the process to tune the line period (Λ x ) and stabilize the emission wavelength of the excitation beam  305 . Some spatial randomness may be incorporated in each row to avoid lattice diffraction patterns in the profile of the excitation beam  305 . This method is wavelength independent and can be used across different photonic materials. 
     As an example, a metasurface collimator using SiN was designed to operate at C and L bands, the most commonly used wavelength ranges in communication industries. 
       FIG. 4  shows the steps  400  to fabricate the metasurface collimator. The metasurface collimator may be fabricated by depositing a single layer of patterned SiN  412  on a Si substrate. A low-pressure chemical vapor deposition (LPCVD) system  401  may be used to deposit a 400 nm thick SiN layer  404  onto a 3 μm SiO 2  layer  402  on a 6-inch Si substrate. The Si substrates, known as thermal oxide wafers, may be procured from Wafer Pro LLC, CA. The grating structures and waveguides  408  may be patterned via e-beam lithography  403 , followed by reactive ion etching to define the geometry of the structures  410 . Fluorine chemistry may be used in the dry etching step. After etching, any remaining resist  406  may be stripped  405  using oxygen chemistry and acetone rinsing. 
       FIG. 5  shows an SEM image of a metasurface collimator  520  with an array of diffracting grooves  522  that can diffract an excitation beam out of the plane of the metasurface collimator to create a collimated excitation beam. The excitation beam can elicit a photoacoustic signal from an analyte medium. 
       FIGS. 6A-6D  illustrate how the metasurface collimator may produce a more uniform excitation beam than the excitation beam produced by a binary grating structure.  FIGS. 6A and 6B  show front and top views, respectively, of a simulated excitation beam exiting from a binary grating.  FIGS. 6C and 6D  show front and top views, respectively, of a simulated excitation beam exiting from a metasurface collimator. The metasurface collimator produces an excitation beam spot that is larger and more uniform than the spot produced by the binary grating. In a comparison of a binary grating and a metasurface collimator with equal surface areas, the excitation beam spot from the metasurface collimator was 8 times larger in the direction of propagation of the input waveguide. The collimated excitation beam from a metasurface collimator can have an operating bandwidth of about 50 nm. 
       FIGS. 7A-7D  show an experimental analysis of excitation beam profiles from a metasurface collimator and a binary grating structure.  FIGS. 7A and 7B  show side and top views, respectively, of a 1.0× magnified excitation beam profile from a metasurface collimator.  FIGS. 7C and 7D  show side and top views, respectively, of a 1.5× magnified excitation beam profile from a binary grating structure. The beam profiles shown in  FIGS. 7A-7D  were measured using an Agilent 81640A (tunable across C and L band) laser system coupled to an 8164A optical test mainframe. The output of the laser was fiber-coupled terminating with a lensed tip. The lensed tip fibers (with 1 μm working distance) were procured from Nanonics Imaging Ltd. The lensed tip fiber was aligned to either the metasurface collimator or the binary grating structure with a 3-axis stage (XYZ Linear Stage, ULTRAlign) obtained from Newport Inc. A NIR camera from microViewer Inc aligned the fiber tip to the waveguide. During the experimental characterization, a CinCam InGaAs SWI camera (from Axiom Optics, Somerville, Mass.) analyzed the excitation beam profile. 
       FIGS. 7A-7D  show that a metasurface collimator can improve the quality of the excitation beam in several ways. The total power received at the detector that was delivered through the metasurface collimator is approximately 1.4 times higher than that of the binary grating structure. The signal-to-noise ratio (SNR) of illumination from the metasurface collimator was 23 dB. (SNR as used here refers the ratio of the signal when the excitation beam is on to the ambient noise when the excitation beam is off.) The SNR of illumination from the binary grating structure was 15 dB. The binary grating structure has a lower SNR than the metasurface collimator because more energy is lost in scattering and radiation in the binary grating structure. The area of the beam spot from the metasurface collimator was 0.1 mm 2 , whereas that from the binary grating was 0.06 mm 2 . The metasurface collimator produced a uniform excitation beam with a width of about 3 dB. The homogeneity of the excitation beam from the metasurface collimator was approximately two times higher than the excitation beam from the binary grating. The metasurface collimator increased the power, SNR, spot size, homogeneity, and illumination efficiency of the excitation beam. 
     The metasurface collimator may be a component of a microscale optical sensor. The sensor may be placed on a chip for on-chip probing. The metasurface collimator may be an attractive option to couple excitation light from an excitation source and diffract the light out of the plane of the chip. A metasurface collimator may be coupled with an excitation source within a photoacoustic sensor to induce an analyte to produce a photoacoustic signal. However, the metasurface collimator may be designed to work at many different wavelengths of light. A metasurface collimator may be used in on-chip applications of fluorescence imaging, Raman, and IR spectroscopy. 
     All-Optical Photoacoustic Transducer 
       FIG. 8  shows a cross-sectional diagram of an optical photoacoustic transducer  800  for the detection of a photoacoustic signal  801 . The optical transducer  800  may be a component of a microscale photoacoustic sensor. The optical photoacoustic transducer  800  includes a mechanical membrane  832 , a membrane cavity  890 , and a resonator  830 . The resonator  830  sits on top of the membrane  832 . A probe beam produced by a probe light source is evanescently coupled to the resonator  830  via a waveguide  870 . The resonator  830  has a resonance frequency that shifts in response to deflection of the membrane  832 , where the deflection is caused by the photoacoustic wave  801 . The shift of the resonance frequency can be detected by a detector that is coupled to the resonator  830  and a processor can determine the frequency shift detected by the detector. 
     Photoacoustic sensitivity is defined as the smallest pressure signal that is detectable using a photoacoustic transducer. Photoacoustic sensitivity is defined in terms of the noise level of the detector. Photoacoustic sensitivity is expressed in terms of pressure units and is known as noise equivalent pressure (NEP). Typically, the pressure generated in biological organs or tissues is in the kPa range. An optical photoacoustic transducer can be more sensitive to photoacoustic signals, making it possible to detect weaker signals (e.g., signals from deep tissue). The optical photoacoustic transducer may have a sensitivity ranging from sub-Pa to kPa. For example, the sensitivity of the optical photoacoustic transducer can be as low as 0.2-2.0 mPa/sqrt(Hz). The dynamic range of the photoacoustic transducer can be, e.g., about 100 Pa to about 1 kPa. 
     The size of the receive aperture, which is set by the size of the membrane, can play a role in determining spatial resolution in photoacoustic transducers. Aperture size also plays a large role in conventional piezoelectric photoacoustic transducers. The spectral bandwidth and resolution of conventional piezoelectric photoacoustic transducers can decrease drastically with decreasing size. In contrast, optical photoacoustic transducers show less of a performance reduction with decreasing size. For example, a piezoelectric photoacoustic transducer with a diameter of 1 mm may have a NEP of about 1.8 kPa and a bandwidth of 16 MHz, while an optical photoacoustic transducer of the same size may have a NEP of about 100 Pa and a bandwidth of about 75 MHz. An optical photoacoustic transducer may respond to photoacoustic signals in a frequency range spanning sub-MHz to 150 MHz. This frequency range may allow an optical photoacoustic transducer to detect absorbing species with a spatial resolution of about 10 μm to about 200 μm. 
     The NEP of the transducer is affected by the compliance of the membrane, losses in the photonic waveguides, and the quality factor of the ring resonator. The compliance of the membrane is controlled by its thickness and material. Losses in the photonic waveguides result in lower NEP. The frequency of the transducer is controlled by the diameter and thickness of the membrane. Higher frequencies can be detected with membranes with smaller diameters. The bandwidth of the transducer is controlled by the compliance and damping of the materials used in the transducer as well as damping of the surrounding medium. 
     Finite element modeling can be used to design the optical photoacoustic transducer, the membrane cavity  890  within the optical transducer  800 , and the effect of an acoustic pressure wave  801  on a photonic waveguide  870 . This finite element analysis can be performed using COMSOL Multiphysics in two steps. The first step investigates structural mechanics of a membrane  832 . Structural mechanics studies can be used to design membrane parameters such as diameter and thickness for a given central frequency. The second step investigates the coupling of acoustic wave propagation with optical wave propagation. 
     The resonant frequency of a membrane depends on its material, diameter, and thickness. The relationship between the size of a membrane and its resonant frequency can be studied using finite element modeling. A parametric sweep of diameter and thickness was performed to obtain eigenfrequencies of a membrane. 
       FIGS. 9A and 9B  show the first and second resonant frequencies, respectively, of an SiO 2  membrane with a 90 μm diameter and 3 μm thickness. The first resonant frequency is 1.0 MHz and the second resonant frequency is 2.0 MHz. 
     The effect of acoustic pressure waves on a membrane can be studied using finite element modeling.  FIG. 10  shows the deflection of a membrane  1032  with a photonic waveguide  1070  on top in response to an external pressure wave. For an input pressure of 100 kPa, an SiO 2  membrane experienced a stress of 1.64×10 7  N/m 2  and a SiN waveguide on top of the membrane experienced a stress of 4.1×10 5 N/m 2 . 
     The propagating mode in a photonic waveguide on top of a membrane changes due to the developed stress in the waveguide in response to an external pressure wave.  FIG. 11A  shows a photonic waveguide  1170   a  on top of a membrane  1132   a  at rest. The photonic waveguide  1170   a  has an effective refractive index of 1.5.  FIG. 11B  shows a photonic waveguide  1170   b  on top of a membrane  1132   b  in response to an external pressure wave. The effective refractive index of the waveguide changes in response to the external pressure wave. The photonic waveguide  1170   b  has an effective refractive index of 1.56. 
     The change in the mode of a photonic waveguide on top of a membrane in response to an external pressure wave can be monitored with a resonator. Examples of a resonator include a micro ring resonator and a Mach Zehnder interferometer.  FIG. 12  shows a microscopic image of two micro ring resonators  1230   a  and  1230   b , and their respective waveguides  1270   a  and  1270   b . These ring resonators each have a diameter of 100 μm and an 800 nm wide waveguide. The ring resonators and waveguides are patterned from 400 nm thick SiN. 
       FIG. 13  shows an array of optical photoacoustic transducers  1300  on a chip  1390  for detecting a photoacoustic signal  1301 . The array  1300  may be a component of a microscale photoacoustic sensor. Each transducer within the array includes a resonator  1330 , a waveguide  1370 , a membrane  1332  and a membrane cavity  1390 . Waveguides may be coupled to more than one transducer. A probe light source supplies a probe beam  1303  to each waveguide  1370 . A shift in the resonance frequency of a resonator  1330  due to a photoacoustic signal can change a property of the probe beam  1305 . This change is detected by a detector and processed by a processor to determine a shift of the resonance frequency in response to a photoacoustic signal. 
       FIG. 14  shows a procedure  1400  to fabricate an optical photoacoustic transducer. The transducer may be fabricated on a double-sided polished Si wafer. Low pressure CVD (LPCVD) may be used to deposit a layer of SiO 2    1402 , followed by a 400 nm thick ultra-low stress SiN layer  1404 . Photonic ring resonators and waveguides may be patterned using e-beam lithography. Negative e-beam photoresist  1406  may be coated  1401  and patterned  1403  onto the SiN layer  1404 , followed by reactive ion etching  1405  to form waveguide patterns of SiN  1408 . After patterning the SiN, a thick layer of photoresist (AZ4620)  1410  may be coated onto the side of the wafer with SiN as a protective layer  1404 ′. Membrane cavities  1412  are fabricated by patterning circular cavities onto the back side of the wafer using photolithography  1407  with a double-sided alignment procedure using a Maskless Aligner (MLA). Si is etched away using deep reactive ion etching (DRIE)  1409  to create a membrane  1418  and membrane cavity  1420  under the photonic ring resonator structure  1416 . The photonic waveguides, ring resonators, and membranes in the microscale photoacoustic sensor can be fabricated using this approach. Once the components of the sensor have been patterned, the sensor can be patterned into a shape, such as the neural probe shown in  FIG. 2A , for release. 
     An optical photoacoustic transducer was characterized experimentally in two steps. First, the acoustic performance of a membrane was analyzed using an externally generated ultrasound signal.  FIG. 15  shows the transient membrane velocity response of a mechanical membrane as it vibrates acoustically upon exposure to an external pressure of 1 MHz. A laser vibrometer was used to measure the acoustic vibration of the membrane. 
     Second, a photonic ring resonator&#39;s response to deflection of the mechanical cavity was measured. An external pressure of 1 MHz was used to excite the optical photoacoustic transducer.  FIG. 16  shows the shift in the resonance frequency of the ring resonator with and without an external pressure wave. The ring resonator experiences a shift in its optical resonance peak in response to the external pressure wave. The mean shift is about 132 pm. The sensitivity of the optical photoacoustic transducer can be as low as 0.2-2.0 mPa/√Hz. 
     CONCLUSION 
     While various inventive embodiments have been described and illustrated herein, those of ordinary skill in the art will readily envision a variety of other means and/or structures for performing the function and/or obtaining the results and/or one or more of the advantages described herein, and each of such variations and/or modifications is deemed to be within the scope of the inventive embodiments described herein. More generally, those skilled in the art will readily appreciate that all parameters, dimensions, materials, and configurations described herein are meant to be exemplary and that the actual parameters, dimensions, materials, and/or configurations will depend upon the specific application or applications for which the inventive teachings is/are used. Those skilled in the art will recognize or be able to ascertain, using no more than routine experimentation, many equivalents to the specific inventive embodiments described herein. It is, therefore, to be understood that the foregoing embodiments are presented by way of example only and that, within the scope of the appended claims and equivalents thereto, inventive embodiments may be practiced otherwise than as specifically described and claimed. Inventive embodiments of the present disclosure are directed to each individual feature, system, article, material, kit, and/or method described herein. In addition, any combination of two or more such features, systems, articles, materials, kits, and/or methods, if such features, systems, articles, materials, kits, and/or methods are not mutually inconsistent, is included within the inventive scope of the present disclosure. 
     Also, various inventive concepts may be embodied as one or more methods, of which an example has been provided. The acts performed as part of the method may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include performing some acts simultaneously, even though shown as sequential acts in illustrative embodiments. 
     All definitions, as defined and used herein, should be understood to control over dictionary definitions, definitions in documents incorporated by reference, and/or ordinary meanings of the defined terms. 
     The indefinite articles “a” and “an,” as used herein in the specification and in the claims, unless clearly indicated to the contrary, should be understood to mean “at least one.” 
     The phrase “and/or,” as used herein in the specification and in the claims, should be understood to mean “either or both” of the elements so conjoined, i.e., elements that are conjunctively present in some cases and disjunctively present in other cases. Multiple elements listed with “and/or” should be construed in the same fashion, i.e., “one or more” of the elements so conjoined. Other elements may optionally be present other than the elements specifically identified by the “and/or” clause, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, a reference to “A and/or B”, when used in conjunction with open-ended language such as “comprising” can refer, in one embodiment, to A only (optionally including elements other than B); in another embodiment, to B only (optionally including elements other than A); in yet another embodiment, to both A and B (optionally including other elements); etc. 
     As used herein in the specification and in the claims, “or” should be understood to have the same meaning as “and/or” as defined above. For example, when separating items in a list, “or” or “and/or” shall be interpreted as being inclusive, i.e., the inclusion of at least one, but also including more than one, of a number or list of elements, and, optionally, additional unlisted items. Only terms clearly indicated to the contrary, such as “only one of” or “exactly one of,” or, when used in the claims, “consisting of,” will refer to the inclusion of exactly one element of a number or list of elements. In general, the term “or” as used herein shall only be interpreted as indicating exclusive alternatives (i.e. “one or the other but not both”) when preceded by terms of exclusivity, such as “either,” “one of” “only one of,” or “exactly one of.” “Consisting essentially of” when used in the claims, shall have its ordinary meaning as used in the field of patent law. 
     As used herein in the specification and in the claims, the phrase “at least one,” in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase “at least one” refers, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, “at least one of A and B” (or, equivalently, “at least one of A or B,” or, equivalently “at least one of A and/or B”) can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements); etc. 
     In the claims, as well as in the specification above, all transitional phrases such as “comprising,” “including,” “carrying,” “having,” “containing,” “involving,” “holding,” “composed of,” and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases “consisting of” and “consisting essentially of” shall be closed or semi-closed transitional phrases, respectively, as set forth in the United States Patent Office Manual of Patent Examining Procedures, Section 2111.03.