1. Introduction

Spatial light modulators (SLMs) have been widely used for precise and dynamic shaping of light beams in applications such as high-speed optical signal processing [1], multiphoton microscopy [2], optical trapping of particles [3], and generation of optical vortices [4]. In particular, SLM-based beam-shaping technologies have been recently employed for improving optical imaging deep inside turbid media [5], for example, for in vivo 2D and 3D biological imaging [6]. In addition to imaging, SLMs have been used for optical manipulation of biological tissue, for example, for simultaneous multipoint photo-manipulation of brain in a dynamic way (e.g., to uncage glutamate at different locations within the brain tissue [7]) and the stimulation or inhibition of multiple neurons at once in different spatial locations [8].

Various implementations of spatial light modulators have been investigated such as fixed SLMs [9], liquid-crystal-based spatial light modulators (LC-SLMs) [10], and digital micro-mirror devices (DMDs) [11]. While SLMs based on fixed optical masks exhibit excellent beam shaping quality [12], reconfigurable SLMs are now highly demanded for fast spatial beam shaping in applications such as biological microscopy [13]. LC-SLMs have been employed in numerous pioneering experiments involving spatial scanning of light with refresh rates in the range of 10 - 200 Hz. The slow response time of LC-SLMs renders their application limited to either a small number of pixels or a very slow reconfiguration of large number of pixels over several minutes [14]. Moreover, strong intrinsic scattering present in LC-SLMs substantially diminishes the optical power efficiency [15]. Digital micro-mirror devices (DMDs) as purely binary amplitude modulators, fabricated using advanced micro electro-mechanical systems (MEMS) technology, have therefore been introduced to address the slow refresh rate problem [16]. However, the power efficiency is low and the number of pixels in each scanning direction is limited, resulting in pixelated images, and thus, a low spatial resolution [15,17]. Acousto-optic deflectors (AODs) have also been used to spatially modulate light in an acousto-optic crystal through forming spatially varying density patterns [18]. Therefore, the phase front is modulated before light is launched into the target medium. These AOD-based SLMs can address both the pixelation and slow refresh rate issues [18–20].

In all of the existing implementations of SLMs, the phase and amplitude of light is shaped on or in the device before it is launched into the medium. Then, light propagates into the target medium and forms a structured beam of light in the far field. If the propagation medium changes over time (e.g., micromotion of the tissue or changes due to respiration over a sub-second timescale in biological contexts [21,22]) or imposes some unwanted modifications of spatial light pattern (e.g., through scattering in a turbid medium), the structured lightwave will be disrupted and will deviate from the intended pattern. Therefore, the depth of penetration for the spatially modulated light will be limited. To account for this challenge, closed-loop methods for active correction of optical phase front based on the feedback from the medium have been devised recently [23,24]. The computation overhead, time delay, and the limited correction capability have been the main shortcomings of such methods [25]. As an example, a newly developed method based on neural network training can provide single- and multi-focus single-shot control over a 5 × 5 pixel area after a long training time of 97 minutes [26], which makes it less appealing for functional biological imaging. Additionally, Cizmar et al. have shown that to focus and pattern light within highly scattering turbid media, in situ phase modulation is essential [27]. This is particularly important in biological imaging and optical manipulation, where deep penetration of externally patterned light is mainly impeded by the scattering of light in the tissue [15,24]. Implantable optical fibers [28] or waveguides [28–31] have been used to guide light into the tissue, which limit the illumination pattern to fixed positions within the tissue. To overcome this limitation and enable active reconfiguration and steering of light deep into the tissue, it is crucial to devise a new high-throughput and fast in situ reconfigurable spatial light modulator. We have recently shown that non-invasive ultrasound waves can be used to sculpt optical waveguides within tissue to mediate penetration of light into such scattering media [32–34].

Here, we demonstrate that the trajectory of light can be actively defined and controlled as it propagates through the medium by forming 3D spatial interference patterns of ultrasound that modulate the local refractive index of the medium in which light is propagating. We demonstrate that complex interference patterns of ultrasound can be reconfigured to generate reconfigurable spatial patterns of light. This technique will serve as a new toolset to realize next generation in situ nearfield SLMs. The interaction of light with the modulated medium defines the trajectory of light in situ. Moreover, by changing the ultrasound interference pattern, the trajectory of light can be reconfigured, enabling active correction of the spatial lightwave in nearfield. Employing a custom-designed cylindrical ultrasonic array, we demonstrate the feasibility of creating dipole and quadrupole shapes by driving the ultrasonic phased array at the first and second azimuthal modes of the cylindrical cavity. We show (both theoretically and experimentally) that the created shapes can be reconfigured in radial and angular directions. Furthermore, by temporal synchronization of ultrasound and the incident lightwave, we show selective confinement of light to specific locations of ultrasound pressure profile. We experimentally demonstrate the utility of the proposed technique in optically turbid media. Our method is fundamentally different from conventional implementations of SLM, since it uses the medium itself to continuously shape the beam of light in situ to address both shortcomings of low depth of penetration and pixelation of the imaging system.

2. Generating spatial interference patterns of ultrasound pressure waves

Here, we demonstrate that ultrasonic phased arrays arranged in a cylindrical geometry can be used for generating complex patterns of ultrasound pressure waves inside the medium. The ultrasound pressure pattern is extended along the axial direction, which coincides with the direction of light propagation. Therefore, the trajectory of light is adiabatically changed and shaped according to the ultrasound pressure columns inside the medium. Cylindrical ultrasonic arrays generate intense standing ultrasound pressure waves in the center with peak intensities much larger than what can be produced by planar ultrasonic arrays [35]. The standing ultrasonic waves in a cylindrical cavity can be described by solving the wave equation subject to rigid-wall boundary condition in the cylindrical coordinate system [36]. The general ultrasonic cavity pressure [37] can be written as

 

Fig. 1 FEM simulation of the ultrasound pressure profile in 2D (shown in a window of 8 mm × 8 mm) for (a) the fundamental mode (first azimuthal mode, m = 0) at 829 kHz, (b) the dipole mode (second azimuthal mode, m = 1) at 848 kHz, and (c) the quadrupole mode (third azimuthal mode, m = 2) at 867 kHz. (d) Schematic of a multi-segment transducer array and electrodes placement in a cylindrical geometry. (e) Schematic showing the electric potential distribution.

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An appropriate distribution of driving electrical signals around the piezoelectric cylinder will be required to excite the desired acoustic modes. An electric potential distribution pattern in the form of $V\left(\phi \right)=V_0\cos (m\phi )$ can excite the $m_{th}$ azimuthal mode [38]. In this work, we have used a custom-designed 8-element cylindrical ultrasonic array (Fig. 1(d)). Each element of the array is a piezoelectric ceramic (PZT-5A) with a thickness of 3 mm operating at the fundamental thickness mode of vibration. To excite modes with even symmetry, the eight electrodes can be grouped into four pairs as shown in Fig. 1(e). A uniform discrete electric potential pattern, i.e., $V=[V_1,V_2,V_3,V_4]=[V_0\angle 0,V_0\angle 0,V_0\angle 0,V_0\angle 0]$ can selectively excite the fundamental mode (m = 0). The amplitude of the electric potential is $V_0$. To excite the dipole mode (m = 1), the driving electric potential distribution should follow $V=[V_1,V_2,V_3,V_4]=[V_0\angle 0,V_0\angle 0,V_0\angle \pi ,V_0\angle \pi ]$ pattern to create two out-of-phase poles. Similarly, the $V=[V_1,V_2,V_3,V_4]=[V_0\angle 0,V_0\angle \pi ,V_0\angle \pi ,V_0\angle 0]$ configuration will primarily excite the quadrupole mode (m = 2). As shown, to excite all the azimuthally symmetric ultrasonic modes, two out-of-phase (180° phase difference) electric potentials are needed.

To excite the ultrasonic phased array elements and polarize them individually along the radial direction, independent electric potentials need to be applied to the outer and the inner walls of the transducer array elements. In this scheme, each transducer array element would require an independent electric potential source. In this work, we use an innovative approach by driving the transducer array elements in a differential configuration. The positive terminal of the electric potential source is connected to two pairs of transducer array elements and the negative terminal is connected to the opposing pairs (Fig. 1(e)). This way, the opposite pairs are excited out of phase (180° phase difference). In this scheme, we can assume a virtual ground in the center between the two opposing elements. To drive a multi-segment transducer array, a multi-channel two-stage amplifier was custom-designed using a TLE2072 op-amp (Texas Instruments Inc.) and a PB63A dual-channel power amplifier (APEX Inc.), which provides an open-loop gain of 55 dB over a 1.5 MHz bandwidth in the range of f = DC-2 MHz.

3. Modulating refractive index of the medium to shape optical beam patterns

The ultrasound pressure interference patterns sculpted in the medium locally change the density of the medium. As a result, the local refractive index of the medium is modulated. The refractive index pattern can be modeled as

 

Fig. 2 (a) Dipole and (b) quadrupole acoustic modes at the ultrasound frequencies of 848 kHz and 867 kHz, respectively. (c) Radial cross section of the pressure profile of the dipole mode. The radial distance between the first extrema is shown as $r_1$. (d) Radial cross section of the pressure profile of the quadrupole mode. The radial distance between the first extrema is shown as $r_2$. (e) and (f) The refractive index profile corresponding to the dipole and quadruple ultrasound pressure profiles, respectively. The red dashed lines in (e) and (f) represent the background refractive index of the medium. (g) and (h) Ray-tracing simulation showing the axial profile of the light beam passing through a modulated medium.

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To study the behavior of light as it propagates through the index-modulated medium, we adopted a paraxial approximation to the Maxwell’s equations and solved the Eikonal equation [42]. This way, we can trace the path of light in the modulated medium, assuming that the input light is a plane wave. The paraxial approximation holds true as long as the maximum refractive index change is much smaller than the background refractive index [43]. The ray tracing simulations show that as light propagates through the index-modulated medium along the axial direction, it branches and adiabatically converges toward the locations of the refractive index profile extrema both for the dipole and the quadrupole modes (Figs. 2(g) and 2(h)).

4. Experimental demonstration

To experimentally demonstrate the possibility of in situ shaping of spatial light patterns using ultrasound, we designed a customized characterization setup (schematically illustrated in Fig. 3(a)), in which an 8-element piezoelectric transducer array (PZT-5A, Inner Diameter (ID) = 38 mm, Outer Diameter (OD) = 44 mm, L = 30 mm, APC International, Ltd.) was immersed in deionized water (as a proof-of-concept demonstration medium). A collimated beam of red laser at λ = 650 nm was expanded (beam diameter = 6 mm) and vertically deflected to pass through the medium surrounded by the cylindrical transducer array. A microscope assembly was built to image the patterned beam of light in the medium onto a CMOS camera from top. The patterned beam of light was imaged at the axial level of the top surface of the cylindrical array.

 

Fig. 3 (a) Schematic of the experimental setup. (b) Top view of the dipole beam pattern. The inset shows the image taken with a zoom lens (6X magnification compared to image (b)). Only the first lobes are captured in this image. The radial distance between the two lobes is $r_1$. (c) Top view of the quadrupole beam pattern. The inset shows the image taken with a zoom lens (3X magnification compared to image (c)), showing the four focal points and the distance between them ($r_2$). (d) and (e) The axial reconstruction of the two beam patterns depicted in the insets of (b) and (c) at the cross-section of y = 0, showing that the incident light is gradually converged to the focal points after passing through the modulated medium.

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Different patterns of light beam modulation can be realized by applying appropriate electric potential distribution to the phased array elements. As an example, to shape the dipole pattern at one of the resonant frequencies (i.e., f = 850 kHz), the electric potential distribution was set to $\text{V}=[23\angle 0 V,23\angle 0 V,23\angle \pi V,23\angle \pi V]$. The top image of the ultrasonically sculpted second azimuthal optical beam pattern (dipole beam pattern, m = 1) is shown in Fig. 3(b). The third azimuthal mode (quadrupole beam pattern, m = 2) can also be achieved by changing the electric potential distribution to $\text{V}=[19 \angle 0V,19\angle \pi V,19\angle \pi V,19\angle 0 V]$ at 829 kHz (Fig. 3(c)).

The axial profiles of the dipole and the quadrupole beam patterns after passing through the corresponding index-modulated medium are shown in Figs. 3(d) and 3(e), respectively. These images are reconstructed from different cross-sectional images along the axial direction. The input light is adiabatically branched to converge to the high-pressure regions of the ultrasonic interference patterns, as predicted by our numerical simulations (Figs. 2(g) and 2(h)).

5. Reconfigurable ultrasonically sculpted spatial light patterns

So far, we have shown that dipole and quadrupole patterns of light can be sculpted in the medium by forming different azimuthal modes using an 8-element ultrasonic transducer array. These complex spatial beam patterns can be reconfigured by changing the ultrasound interference pattern. For a fixed number of transducer array elements in the cylindrical geometry, we have three degrees of freedom: 1) the frequency of ultrasound, that affects the expansion of optical beam patterns; 2) the azimuthal sequence of the applied electric potential, that enables rotation of the beam patterns; and 3) the relative phase between ultrasound and the laser pulses, that enables selective temporal coupling of light to different ultrasound pressure profile extrema. We will demonstrate how these degrees of freedom can be utilized to generate a reconfigurable complex spatial pattern of light in the medium.

5.1 Radial sweeping

The generated ultrasonic standing wave in the medium depends on the frequency of ultrasound. Equation (1) shows that for a given arrangement of cylindrical ultrasonic transducer arrays, a set of discrete modes (indicated by $k_{r_{m,n}}$) exists. The high-frequency modes have larger number of peaks and troughs that are closely spaced along the radial direction. On the other hand, the low frequency modes have smaller number of peaks and troughs that are spaced farther from each other. Therefore, by driving the piezoelectric transducer array at these discrete resonant frequencies, we can compress or expand the beam patterns. Beam shape compression is experimentally demonstrated in Figs. 4(a)-4(c) for dipole and Figs. 4(d)-4(f) for quadrupole beam patterns, respectively. The expansion and compression of spatial light patterns using mode hopping is discrete and therefore, cannot be used for continuous scanning.

 

Fig. 4 Experimentally imaged dipole and quadrupole beam patterns at different resonance frequencies to demonstrate radial scanning. The driving frequency is shown in the upper left corner of the picture for each case. The driving electric potential distribution of the dipole and quadrupole beam patterns were set as $[{\text{V}}_0\angle 0,{\text{V}}_0\angle 0,{\text{V}}_0\angle \pi ,{\text{V}}_0\angle \pi ]$ and $[{\text{V}}_0\angle 0,{\text{V}}_0\angle \pi ,{\text{V}}_0\angle \pi ,{\text{V}}_0\angle 0]$, respectively. The electric potential amplitude and radial spacing between the focal points are: (a) $V_0=36 V, r_1=1.243 mm$, (b) $V_0=15 V, r_1=0.865 mm$, (c) $V_0=60 V, r_1=0.657 mm$, (d) $V_0=64 V, r_2=1.911 mm$, (e) $V_0=17 V, r_2=1.4 mm$, (f) $V_0=60 V, r_2=1.089 mm$. Each image is normalized to its own maximum intensity and is plotted in the logarithmic scale.

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The radial sweeping of the beam patterns is mediated through the discrete resonance frequencies of the cylindrical cavity, as explained in Eq. (1). The resonance frequencies are determined by the rigid-wall boundary condition, i.e., $J_m^{\text{'}}\left(\frac{2\pi fr}{c_s}\right)=0$ at r = ɑ (ɑ is the inner radius of the ultrasonic array) as

From Eqs. (4) and (5), it can be seen that the radial modes (indicated by n) are periodic in frequency domain. For example, given ɑ = 19 mm and c_s = 1484 m/s in water, the spacing between consecutive radial mode resonant frequencies is $\frac{{\text{c}}_s}{2a} =$ 39 kHz. The radial mode resonant frequencies predicted by this analytical model match the experimental results. For instance, different experimentally measured radial dipole mode resonant frequencies discussed in Figs. 4(a)-4(c) were obtained at f = 735 kHz, f = 1.006 MHz, and f = 1.318 MHz, which closely match with the analytically calculated resonant frequencies of f_1,19 = 732 kHz, f_1,26 = 1.005 MHz, and f_1,34 = 1.318 MHz, respectively. Similarly, the quadrupole modes shown in Figs. 4(d)-4(f) were obtained at f = 752 kHz, f = 1.024 MHz, and f = 1.297 MHz, which are in agreement with the theoretical results at f_2,19 = 751.7 kHz, f_2,26 = 1.025 MHz, and f_2,33 = 1.298 MHz, respectively.

In this coupled piezoelectric-acoustic-optic system, each optical resonance pattern corresponds to an ultrasonic standing wave resonance mode that is manifested as a resonance in the input electrical admittance. Therefore, another way to measure the resonant frequencies of the radial modes is through measuring the input admittance spectrum. We measured the input electrical admittance spectrum using a Vector Network Analyzer (4396B RF VNA, Agilent Technologies Inc.), as shown in Fig. 5(a). The admittance versus frequency is shown in Figs. 5(b) and 5(c) for the dipole and quadrupole arrangements, respectively. The resonance modes happen at an approximately equal frequency spacing of ~38.6 kHz, matching the prediction of our theoretical analysis. As it can be seen from Figs. 5(b) and 5(c), the quality factors of different modes are different since the damping effect varies at different frequencies. The low-Q radial modes require higher input electric potential to generate the required ultrasound pressure intensities to confine light (Figs. 2(c) and 2(d)). We limited the maximum input electric potential to below the threshold of damage to the transducer elements as determined by the manufacturer (i.e., 75 V_max). We obtained 16 radial modes (i.e., n = 19-34) of the second azimuthal mode (m = 1) and 15 radial modes (i.e., n = 19-33) of the third azimuthal mode (m = 2) that meet the electric potential safety limit. In general, excitation of higher order azimuthal modes requires higher input electric potential values. For instance, to achieve the dipole mode shape (m = 1, n = 19) shown in Fig. 4(a), V₀ = 36 V was applied to the transducer array, while to excite the same radial mode number (n = 19) of the quadrupole mode (m = 2), V₀ = 64 V was needed (Fig. 4(b)).

 

Fig. 5 (a) Schematic of the VNA connection configuration used to measure the admittance spectrum of the transducer array for exciting the dipole and quadrupole modes, while immersed in water. (b) and (c) The measured admittance spectrum when the transducer array was connected to VNA in the dipole and quadrupole mode excitation signal arrangement, respectively, showing well-defined resonant frequencies starting from f_1,19 = 734 kHz to f_1,34 = 1.313 MHz (dipole) and f_2,19 = 753 kHz to f_2,33 = 1.297 MHz (quadrupole). (d) List of the resonant frequencies at which the transducer array has been driven to excite consecutive radial modes in both m = 1 and m = 2 azimuthal modes. The table also shows the repetitive resonance behavior, with a free spectral range of ~38.6 kHz both for the dipole and the quadrupole modes.

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The spatial pattern of light can be reconfigured through mode hopping between different discrete radial modes. As discussed earlier, the light pattern foci happen at extrema of the refractive index profile, where the first derivative of the Bessel function is zero, i.e., when $J_m^{\text{'}}\left(kr\right)=0$. For the dipole mode, the radial distance between the two peaks of the light intensity pattern (i.e., r₁) can be obtained through solving for the zeros of the first derivative of the standard first-order Bessel function of the first kind (Fig. 6(a)). Similarly, the zeros of the first derivative of the standard second-order Bessel function of the first kind reveal the distance between the light intensity profile extrema of the quadrupole modes (i.e., r₂). Therefore, the radial spacing in both acoustic modes can be expressed as

 

Fig. 6 (a) The distances between the first extrema (r₁ and r₂) of the first- and second-order Bessel function of the first kind, corresponding to the dipole and quadrupole beam patterns. Comparison between the theory, simulation, and experiment for (b) the radial spacing (r₁) between the crescents in the dipole beam pattern, (c) and the radial spacing (r₂) between the focal points in the quadrupole beam pattern for discrete modes in the frequency range f = 730 kHz-1.320 MHz.

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The experimental results were obtained by sweeping the frequency of the electrical signal applied to the transducer array elements and imaging the output optical spatial pattern using the top microscope assembly. To ensure the repeatability of the results, the experiments were carried out using two different ultrasonic arrays with the same number of elements and dimensions and the results agreed well (maximum error = 2%). For example, for the case of dipole beam patterns, our experimental results agree well with our analytical calculations from Eq. (6) (shown in Fig. 6(b)). The maximum error, i.e., δ_max is defined as the maximum difference between experimental and theoretical $r_i ; i=1,2$ among all the resonant frequencies. For the case of dipole beam shape presented in Fig. 6(b), δ_max = 21 µm, which corresponds to a negligible 5% discrepancy between the theoretical and experimental results. The main reason behind this small discrepancy is that the analytical model does not include the mechanical damping effect. The maximum difference between the analytical and the experimental resonant frequencies is max(Δf) ~3 kHz over a frequency range of 733 kHz - 1.318 MHz, enabling us to sweep the radial distance from r₁ = 0.657 mm to r₁ = 1.243 mm. Both r₁ and r₂ are inversely proportional to the ultrasound frequency (Eqs. (6) and (7)). Therefore, the radial sweeping step ($\Delta r_i$ when f_1,i → f_{1,i + 1}) is a nonlinear function of frequency, i.e., it is larger at lower frequencies and becomes smaller as the frequency is increased. The step size ($\Delta r_i$) is ~104 µm for a transition from f_1,19 = 735 kHz to f_1,20 = 773 kHz and ~21 µm when changing the resonant frequency from f_1,33 = 1.280 MHz to f_1,34 = 1.318 MHz.

In our experiments, the frequency range for the quadrupole mode was limited to 751 kHz to 1.297 MHz to ensure the required input electric potential does not exceed the threshold of damage to the transducer array, i.e., 75 V. We obtained 15 resonant frequencies in this range. Ideally, the horizontal and vertical distances between the four foci of the quadrupole beam pattern must be identical. However, in practice, asymmetries arising from manufacturing and packaging of the transducer array elements in the ultrasonic array cause these two distances to be slightly different. The experimental results for $r_2$ are reported as the average between the two distances (Fig. 6(c)). In the case of quadrupole beam patterns, the discrepancy between the analytical and experimental results for the radial distance is relatively small (δ_max = 22 µm), corresponding to a 2% difference. The radial distance can be swept from r₂ = 1.089 mm to r₂ = 1.921 mm and the step size changes from $\Delta {\text{r}}_2$ = 94 µm for a transition from f_2,19 = 752 kHz to f_2,20 = 792 kHz to $\Delta {\text{r}}_2$ = 57 µm for a transition from f_2,32 = 1.259 MHz to f_2,33 = 1.297 MHz.

5.2 Rotation (angular sweeping)

The beam patterns can be rotated around the central axis of the ultrasonic array by changing the sequence of the driving electrical signals. As shown in Fig. 7, the dipole and quadrupole beam pattern shapes can be rotated by discrete angles. The electric potential distribution $V=[V_0\angle 0,V_0\angle 0,V_0\angle \pi ,V_0\angle \pi ]$ results in a horizontal dipole beam pattern (Fig. 7(a)), whereas changing the electric potential distribution to that shown in Fig. 7(b) will result in a π/4 rotation of the dipole beam pattern (Fig. 7(b)). Changing the electric potential distribution by one additional element results in another π/4 rotation of the beam pattern (Fig. 7(c)). Similarly, the quadrupole beam pattern can be rotated by changing the distribution of the applied electric potentials as shown in Figs. 7(d) and 7(e). The step size of the rotation is determined by the number of elements. For an M-element ultrasonic array, the spatial beam pattern can be rotated by 2π/M steps. In this work, we have designed an 8-element ultrasonic array, and therefore, the smallest rotation step is π/4.

 

Fig. 7 The experimental results showing the rotation of the dipole pattern (6X magnification) by changing the sequence of the applied electric potentials, when the axis is at (a) π/2 (with respect to the horizontal axis), (b) π/4, and (c) 0, and in the quadrupole beam pattern (3X magnification) at (d) π/4 and (e) 0.

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5.3 Temporal multiplexing of the spatial optical pattern

The spatial locations of the pressure nodes in the standing ultrasonic interference pattern are steady over time. However, the peaks and troughs of ultrasound pressure are interchanged every half cycle (Fig. 8(a)). Therefore, a periodic compression and rarefaction of the medium density happens at the locations of the ultrasound pressure profile extrema. As a result, the refractive index of the medium changes periodically over time and consequently, the spatial optical pattern is changed over time. The operating frequency of ultrasound in our experiments (700 kHz - 1.3 MHz) is much higher than the frame rate of commonly used CMOS cameras. Therefore, for many practical applications, time-averaged spatial light patterns (over many cycles of ultrasound waves) can be used. All of the presented experimental results so far have been obtained by using a continuous wave (CW) laser (LT-301, Ultra Laser Co.) (Fig. 8(b)) and time averaging the output spatial light pattern. To reconfigure the spatial light pattern for a given ultrasound pressure standing wave, we can pulse the laser and synchronize it with ultrasound (Fig. 8(c)) to temporally multiplex the spatial optical patterns arising from periodic changes of ultrasound pressure waves. Furthermore, the temporal synchronization of ultrasound and laser pulses will enhance the signal to background ratio, since in this case, light is on only when the intended pattern of ultrasound is formed in the medium. In our experiments, we used a direct current modulation of the input laser using a commercial arbitrary waveform generator (DG 1000Z, RIGOL Technologies Inc.), which was synchronized with the electrical signal driving the ultrasonic array. The temporal width of the laser pulse determines the interaction time between the modulated medium and light. The relative phase delay between the laser modulation signal and ultrasound wave determines the spatial optical pattern, since light will only interact with the modulated medium at a specific instance in time. We used a square laser pulse with a duty cycle of 30%. As an example, for the dipole beam pattern at f_1,22 = 851 kHz, a continuous illumination using a CW laser and time-averaged imaging result in the spatial optical pattern shown in Fig. 8(d), whereas if the laser is pulsed and synchronized with the peak of ultrasound at a phase delay of φ = 0, only half of the dipole beam pattern is shaped (Fig. 8(e)), because at the time when the pressure peak that corresponds to this half of the dipole beam is at the highest positive peak value, the other half is at the peak negative pressure and cannot confine light. By changing the phase delay to π, we can couple light to the other half of the dipole beam pattern (Fig. 8(f)). Similarly, for the quadrupole beam pattern at f_2,21 = 830 kHz, instead of the complete quadrupole pattern obtained by the CW laser (Fig. 8(g)), two orthogonal patterns can be selectively excited by changing the relative phase delay from 0 to π (Figs. 8(h) and 8(i)).

 

Fig. 8 (a) Temporal dynamics of the ultrasound wave. (b) Schematic illustrating illumination by a CW laser and (c) illumination by a pulsed laser. φ is the phase delay between the pulsed laser and ultrasound. (d) Experimentally imaged dipole beam pattern at 851 kHz and V₀ = 17 V with a CW laser, and with a pulsed laser when (e) φ = 0 and (f) φ = π. (g) The quadrupole beam pattern imaged at 830 kHz and V₀ = 19 V with a CW laser and with a pulsed laser when (h) φ = 0 and (i) φ = π.

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All the experimental demonstrations of spatial light patterning using ultrasound presented in this section were carried out in a homogeneous transparent medium (i.e., water with negligible scattering). This technique can also be used in turbid media. However, the scattering of light in turbid media will affect the ultrasonically sculpted optical patterns. In the following section, we will explore the feasibility of spatial light modulation using ultrasound in a scattering medium.

6. In situ spatial light modulation in a turbid medium

As discussed earlier, to shape light in a scattering medium, in situ modulation of light is essential [27]. Our method can address this need for shaping light in situ as it propagates through the medium. To demonstrate the feasibility of using ultrasound to sculpt spatial light patterns in a turbid medium, we immersed the ultrasonic array in scattering media with a range of different scattering levels made of 0.103%, 0.111%, 0.119%, and 0.127% Intralipid (IL, Sigma-Aldrich, Inc.) mixed with deionized water.

The experimental setup is the same as the one shown in Fig. 3(a). When a collimated beam of light propagates through the turbid medium with ultrasound off, light is scattered (Fig. 9(a)). When ultrasound is on, dipole and quadrupole spatial light patterns can be formed in the medium (Figs. 9(b) and 9(c)). The reduced scattering coefficient of this turbid medium (0.119% IL + water) is 1.667 cm⁻¹, measured using Oblique Incidence Reflectometry (OIR) [45]. The optical thickness of the medium defined as $OT= \frac{{\mu }_s^{\text{'}}d}{(1-g)}$, where d is the geometrical thickness and $g$ is the anisotropy factor of the medium, can be used as a normalized measure of light penetration into the scattering medium. For Intralipid, we can assume $g_{IL}\approx 0.9$ [46]. Therefore, the optical thickness of our turbid medium can be obtained as OT = 50 mean free path (MFP), which is a rather thick scattering medium. As shown in Figs. 9(b) and 9(c), the dipole and quadrupole beam patterns at f_1,22 = 853 kHz and f_2,21 = 833 kHz are formed in this scattering medium similar to the spatial light patterns formed in a homogeneous non-scattering medium. By increasing the concentration of IL from 0.103% to 0.127%, with incremental steps of 0.008%, the scattering in the medium is increased. The reduced scattering coefficients are measured to be ${\mu }_{s_1}^{\text{'}}$ = 1.489 cm⁻¹, ${\mu }_{s_2}^{\text{'}}$ = 1.578 cm⁻¹, ${\mu }_{s_3}^{\text{'}}$ = 1.667 cm⁻¹, and ${\mu }_{s_4}^{\text{'}}$ = 1.756 cm⁻¹, respectively. The optical thicknesses for the employed samples, considering their physical thickness d = L = 30 mm, are 44.67 MFP, 47.34 MFP, 50 MFP, and 52.67 MFP, respectively. As shown in Figs. 9(b) and 9(c), the spatial light patterns are dispersed as the scattering in the medium is increased. To quantify this effect, we define the extinction ratio (ER) as the ratio of the peak intensity to background intensity (when ultrasound is off) as illustrated in Figs. 9(d) and 9(e). We have plotted ER in Figs. 9(f) and 9(g) for different cases of OT = 44.67 - 52.67 MFP. Figure 9(f) shows ERs larger than 1.1 can be obtained in a highly scattering turbid medium with an optical thickness of OT ~52 MFP.

 

Fig. 9 Demonstration of ultrasonic spatial light modulation in a turbid medium with an optical thickness of OT = 50 MFP when (a) ultrasound is off and (b) when ultrasound is on and the dipole beam pattern is shaped in the turbid medium at f = 853 kHz. The magnified (6X) image of the dipole pattern is shown in the inset. (c) The quadrupole pattern formed in the turbid medium when ultrasound is on at f = 833 kHz. e) The magnified (3X) image of the quadrupole pattern is shown in the inset. The normalized intensities at the cross section passing through y = 0 are shown for (d) dipole and (e) quadrupole beam patterns. Blue curve shows the signal and the red curve shows the average background (ultrasound off). (f) and (g) Extinction ratio (ER) vs. optical thickness of the turbid medium.

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The possibility of in situ sculpting of arbitrary spatial patterns of light in turbid media, enables a plethora of applications, including spatial light patterning in scattering biological tissue. For example, the ultrasound pressure interference patterns can be actively tailored in situ to compensate for the dispersive effect of light in the tissue. The attenuation of ultrasound in the frequency range of 700 kHz to 1.3 MHz is negligible in tissue (i.e., ~0.3-0.6 dB/(cm·MHz) [47]). Therefore, ultrasound in this range of frequency can be used to shape light deep into the tissue without undergoing major perturbation or damping. Our experimental results show that the proposed technique can be used in different turbid media. When it comes to using this method for spatial patterning of light in biological tissue, care should be taken to ensure the safety of tissue. An advantage of our method is that light is patterned when interacting with the ultrasonically modulated medium only during a brief time interval of the ultrasonic wave period. Therefore, ultrasound does not have to be continuously on and it can be pulsed. Since the transient time to form a standing wave within the ultrasonic cavity is less than a couple of hundred microseconds [48], the ultrasonic signal can be pulsed at a frequency of ~10 Hz or less to prevent heating the tissue. The introduced technology can find applications in medical therapy and diagnostics. The safety measures for diagnostic ultrasound as regulated by the United States Food and Drug Administration (FDA) [49] require that the de-rated spatial-peak pulse-average intensity (I_SPPA), spatial-peak temporal average intensity (I_SPTA), and mechanical index (MI) of ultrasound waves be less than 190 W/cm², 720 mW/cm², and 1.9, respectively. We have recently shown that by pulsing the ultrasonic signal at a duty cycle of 1% with a pulse repetition frequency of 250 Hz, the safety measures are met [32]. In any particular application, depending on the region of the tissue and whether or not our technique is used for diagnostics or therapeutic intervention, the parameters of ultrasound pulses need to be designed to prevent damage to the tissue.

7. Conclusion

The tantalizing notion of sculpting reconfigurable spatial light patterns in situ using ultrasound demonstrated in this paper is a novel addition to the spatial light modulators toolset. Our combined theoretical and experimental results show that interference ultrasound pressure patterns in a compressible medium locally change the refractive index of the medium. When light propagates through a medium that is spatially and temporally modulated, the phase front of light is changed and spatiotemporal patterns of light are formed in the medium. We demonstrated that an 8-element cylindrical ultrasonic array can be used to form multipole optical patterns inside the medium. In particular, we showed how specific resonance modes of the cylindrical cavity encompassed by the ultrasound array can form dipole and quadrupole patterns of light. The ultrasound frequency, the arrangement of the electric potential distribution, and the temporal phase delay between the pulsed laser and ultrasound can be used to spatially and temporally reconfigure the optical patterns. We demonstrated spatial reconfiguration of the optical patterns over a radial distance of ~0.6 mm and ~0.84 mm with the best resolution (the minimum step size between two consecutive radial modes) of ~20 µm and ~60 µm for dipole and quadrupole beam patterns, respectively. By increasing the number of elements, higher order azimuthal modes can be excited with a greater number of focal points. Furthermore, a finer sweeping along the angular direction can be achieved with a step size of 2π/M, where M is the number of elements in the phased array. Additionally, more complex optical beam patterns can be obtained by exciting the transducer array elements using a linear combination of the electric potential distributions discussed in this paper. This technique works in homogeneous non-scattering media as well as turbid media. The scattering of light in turbid media degrades the signal to background ratio. We experimentally demonstrated that a distinguishable spatial pattern of light can be formed through a thick turbid medium with an optical thickness of OT = 52.67 MFP. While these open-loop experiments clearly show that this novel technique works in a turbid medium, the in situ nature of ultrasonically-mediated light patterning can be leveraged to actively compensate for dispersion of light through scattering media by adjusting the ultrasound array parameters in a closed-loop arrangement. Therefore, this method can be employed to conquer the grave challenge of light dispersion in turbid media. One of the challenges, especially in biological tissue is the heating effect due to long-term continuous exposure of the medium to ultrasound, which gradually changes the background refractive index and the mechanical properties of the medium, thus affecting the desired spatial light pattern and also potentially damaging the tissue. This issue can be easily avoided by modulating ultrasound (on/off) at a low repetition rate to prevent the accumulation of heat.