1. Introduction

Piezoelectric transducers represent a fundamental technology in the field of ultrasound, which has been essential to the development of medical sonography [1]. The success of piezoelectric technology may be attributed to its capability to generate and detect ultrasound with a single device and the availability of ultrasound arrays whose elements may be accessed simultaneously. With the recent emergence of hybrid imaging modalities in which the generation of ultrasound is performed via the absorption of electromagnetic energy in the tissue and subsequent thermal expansion, many imaging systems have been developed that use piezoelectric transducers only in detection mode [2–7]. In the field of optoacoustic tomography, in which light is used to generate ultrasound, the availability of ultrasound arrays has led to the development of imagers capable of producing 2D and 3D images in real time [5,6].

Notwithstanding recent progress, many challenges remain in the development of hybrid imaging modalities that stem from the limitations of piezoelectric technology. Piezoelectric transducers are opaque, susceptible to electromagnetic interference, and often have limited bandwidths and acceptance angles that lead to image artifacts [3]. In addition, the miniaturization of piezoelectric arrays generally leads to loss of sensitivity, limiting minimally invasive applications [4].

One of the alternatives to piezoelectric technology for ultrasound detection in hybrid-imaging applications is optical interferometry [8,9]. Interferometric detectors of ultrasound offer immunity to electromagnetic interference [2], may be produced from transparent materials [10–19], and can achieve wide bandwidths and acceptance angles [11,14,15]. In addition, when optical resonators with high Q-factors are employed, the detector may be miniaturized without compromising sensitivity [14,16]. When acoustic waves impinge on an optical resonator, they modulate its refractive index owing to the elasto-optic effect and deform its structure, leading to a modulation in the resonance wavelength [20]. The advantages of interferometry for ultrasound detection has led to the development of numerous all-optical optoacoustic imaging systems, based on optical excitation and detection of ultrasound [11,21,22].

Conventionally, optical resonators are interrogated with CW lasers tuned to their resonance, where ultrasound induced resonance shifts are translated to intensity [9–17,19] or phase [23] variations at the output of the resonator. While arrays of optical resonators may be produced in a single platform [21,24,25], parallel interrogation with a single CW laser is challenging since it requires a good overlap between the spectra of all the resonators [26]. In addition, external disturbances like vibrations and bending may shift the resonances away from each other, preventing their simultaneous interrogation with a single CW laser; in the case of severe mechanical disturbances, even serially tuning the laser to each resonator separately may be technically challenging [27]. While the challenge of parallelization may be mitigated by using resonators with lower Q-factors [28], or avoided by using schemes that do not rely on resonators [29–31], these approaches may lead to reduced sensitivity or limit the achievable miniaturization. Alternatively, one may post-process the fabricated resonators to tune their spectra to the same wavelength [32]. However, such a post-processing procedure, which significantly complicates the production of the optical resonators, may not be compatible with all platforms, and has yet to be demonstrated with high-Q resonators.

Recently, Wei et al. demonstrated that the robustness of CW methods may be improved if the resonator is integrated in a fiber ring laser [33], but the scaling of the systems was limited by the number of fiber-based components required per detector. More efficient scaling might be possible in schemes in which the laser cavity is formed solely by the sensing resonator, e.g. using erbium-doped fibers [34,35], but the need for active media prevents the use of this approach in passive platforms such as planar polymer waveguides. Overall, while numerous strategies may be used to parallelize optical detection of ultrasound, scalable methods that are compatible with passive high-Q resonators with non-overlapping spectra have yet to be demonstrated.

Pulse interferometry (PI) has been developed as an alternative approach for interrogating optical resonators, which may potentially overcome some of the limitations that have characterized CW interrogation [36–39]. In PI, the source is based on a pulse laser whose bandwidth is sufficiently wide to cover the entire bandwidth in which the resonances may occur. In [37,38], this property was used to achieve a high dynamic range and robust operation under volatile environmental conditions. While PI may in principle be used to interrogate several resonators with non-overlapping spectra with a single source, the demodulation schemes used in [36,37] were not scalable, and would lead to unacceptable cost per channel.

In this paper, we report on a new version of PI that may be scaled to simultaneously interrogate multiple optical resonators with non-overlapping spectra. Our method is based on a phase-modulation scheme performed at the output of the source, which couples between the intensity and wavelength at the output of the resonators. Using a simple demodulation algorithm, ultrasound-induced shifts in the resonators’ wavelengths may be decoded from intensity measurements. Accordingly, only a single photodetector and sampling channel are required per resonator. Using the proposed phase-modulation PI (PM-PI), we demonstrate, for the first time to our knowledge, parallel interrogation of four resonators with non-overlapping spectra.

2. Experimental setup

An illustration of the PM-PI system used in this work is given in Fig. 1. A wideband pulse laser is employed together with optical band-pass filters (BPFs) and an erbium-doped fiber amplifier (EDFA), which are used to increase the spectral power density of the source while maintaining an acceptable bandwidth. An unbalanced Mach-Zehnder interferometer (MZI) with a phase modulator (PM) on one of its arms is connected at the output of the source; where the phase is switched between two values with a difference of π/2. The resonators, implemented by π-phase shifted fiber Bragg gratings (π-FBGs) [15], are connected to photodetectors whose voltage signals are sampled by an oscilloscope (Keysight, DSOX4154A). As the analysis in the following shows, the output of each resonator is switched between two interferometric states, which together enable us to monitor the ultrasound-induced wavelength shifts of its resonance.

 

Fig. 1. A schematic drawing of the PM-PI system used in this work to interrogate 4 resonators, implemented with π-phase shifted fiber Bragg gratings (π-FBGs). A wideband pulse laser with band-pass filters (BPFs) and an erbium-doped fiber amplifier (EDFA) create a source with a high spectral power density and sufficient bandwidth to cover the spectra of all the resonators. The modulation unit is an unbalanced Mach-Zehnder interferometer (MZI), composed of optical fiber couplers (FC) and a phase modulator (PM). The input phase signal to the PM, shown in the top-right plot, alternates between two values with a difference of $\pi /2$. For each phase value, the pulses interfere differently at the output of each resonator depending on the phase difference in the MZI for the specific resonance wavelength of that resonator. The bottom-right plot, shows a typical voltage signal measured for one of the resonators, which alternates between two states that correspond to the two phase values. As the bottom-right plot shows, in the current implementation, the duration of each phase value delivered to the PM corresponded to 5 laser pulses. We note that the limited bandwidth of our measurement did not allow full separation between the pulses in the bottom-right plot.

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In our analysis, we assume that the PM has only two phase states that may be experienced by each pulse; whereas the transition between the two states occurs at times when no light passes through the PM. We follow the electric field at different positions in the PM-PI setup, marked with the red letters a-c in Fig. 1. The electric field at the input of the MZI, i.e. point (a1), marked in red in Fig. 1, is given by $e_1^a = e(\omega )$; where $\omega$ is the angular frequency. We denote the energy forward coupling of the modes in the fiber couplers “a” and “b” in Fig. 1 by ${T_a}$ and ${T_b}$, whereas the energy cross coupling terms are given by $\sqrt {1 - {T_a}}$ and $\sqrt {1 - {T_b}}$, respectively. Accordingly, at the two outputs of the first coupler, points (a3) and (a4) in Fig. 1, the electric fields respectively given by $e_3^a = \sqrt {{T_a}} e(\omega )$ and $e_4^a = \sqrt {1 - {T_a}} ie(\omega )$; whereas at the two inputs of the second coupler, points (b1) and (b2) in Fig. 1, one obtains:

At the final stage of the setup, the electric fields $e_3^b$ and $e_4^b$ are filtered by the resonators, whose field transmission functions we denote by ${H_i}(\omega )$; where $i = 1,\ldots ,4.$ For each resonator, we denote the central frequency by ${\omega _i}$ and its bandwidth by $\Delta {\omega _i}$. We assume that $\Delta l$ is sufficiently small so that $\exp ({i\omega n\Delta l/c} )$ is approximately constant over $\Delta {\omega _i}$ $(i = 1,\ldots ,4)$; the corresponding mathematical condition is given by

Assuming that the two phase states of the PM lead to ${\varphi _{PM}} = 0$ and ${\varphi _{PM}} = \pi /2$ and that ${T_a} = {T_b} = 0.5$, two expressions are obtained for the measured power at each channel, corresponding to the two states:

We note first that the result shown in Eqs. (7a) and (7b) is valid even if the experimental parameters deviate from their ideal values. First, while standard fiber couplers can deviate from an even split ratio by up to 10%, i.e. 45/55 instead of 50/50, this deviation, when substituted in Eq. (6), translates to only a 1% change in the coefficients in Eqs. (7a) and (7b), thus justifying our approximation. Second, if the phase difference between the two stats of the PM deviates from $\pi /2$ by $\delta \ll 1$, it will lead to an error in the calculated phase which is generally smaller than $\delta $ and given by $\delta {\phi _i} \approx {\delta \mathord{\left/ {\vphantom {\delta {({{{\tan }^2}{\phi_i} + 1} )}}} \right.} {({{{\tan }^2}{\phi_i} + 1} )}}$. Assuming that $\delta $ remains constant over the short duration of the ultrasound measurement, which is usually performed within a time window of 10 µs, the effect of the error $\delta {\phi _i}$ is a mere offset in the calculated phase $\phi$, which does not affect the recovery of the acoustic signal, described in the next paragraph.

When an acoustic pulse impinges on the resonator, it leads to a modulation in ${\omega _i}$. Accordingly, we define ${\omega _i}(t) = \omega _i^{dc} + \omega _i^{ac}(t)$; where $\omega _i^{dc}$ represents the resonance frequency before the arrival of the acoustic pulse, and $\omega _i^{ac}(t)$ is the ultrasound -induced perturbation, which we wish to recover. Assuming that the MZI is not exposed to the acoustic pulse, the term $n\Delta l$ may be regarded as constant during the acoustic measurement. Thus, $\omega _i^{ac}(t)$ may be readily recovered from ${\phi _i}(t)$:

Figure 2 shows the resonance spectra of the four π-FBGs (TeraXion Inc., Quebec, Canada) used in our measurements as a function of detuning from the central wavelength of 1549 nm. The resonances had a full-width-at-half-maximum (FWHM) of approximately 4 pm; whereas the spectral distance between two resonances had a maximum value of approximately 43 pm, preventing parallel interrogation with CW techniques. The pulse laser (M-Comb model, Menlo Systems GmbH, Martinsried, Germany) had a central wavelength of 1560 nm, spectral bandwidth of 40 nm, pulse repetition rate of 250 MHz, pulse duration of approximately 90 fs, and average power of 75 mW. The BPFs had a spectral width of 0.4 nm around the resonance wavelength, sufficiently wide to cover all the four resonances shown in Fig. 2. The output power from each of the π-FBGs was approximately 25 µW when the EDFA was set to 100 mW average power output. All the components in our system were implemented with polarization-maintaining fibers to avoid polarization fading in the setup [41].

 

Fig. 2. The transmission spectra of the four different π-FBG resonances used in the system shown in Fig. 1.

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The MZI in Fig. 1 had an imbalance of $\Delta l = 7$ cm and included a PM with a modulation bandwidth of 20 GHz (PM-5S5-10-PFA-PFA-UV-UL, EOspace). The PM was fed with a square voltage signal with a frequency of 25 MHz and duty cycle of 50% and the modulated signals at the output of the π-FBGs were detected by photodetectors with a bandwidth of 1.5 GHz (DET01CFC, Thorlabs), connected to a 4-channel oscilloscope with a bandwidth of 1.5 GHz (Keysight, DSOX4154A). As shown in Fig. 1, each cycle of the voltage signal corresponded to 10 pulses, half of which with the response given in Eq. (7a) and half with the response of Eq. (7b). Since the voltage signal was not synchronized with the repetition rate of the laser, some the laser pulses occasionally overlapped with the transition between the two states of ${\varphi _{PM}}$. To avoid transition effects, $P_{i,0}^c$ and $P_{i,\pi /2}^c$ were extracted from the photodetector signals by calculating the median value for every 5 pulse peaks within half a cycle of the PM.

The performance of PM-PI was tested using an acoustic setup similar to the one used in [16,36,38], presented in Fig. 3. The π-FBGs were placed in a water bath along with an ultrasound transducer with a central frequency of 1 MHz. To maximize the resonance frequency shift in the fibers, the orientation of the transducer was adjusted to an angle of 30° with respect to the optical fibers, leading to excitation of a guided acoustic wave in the fibers, which has been previously shown to generate a stronger response than normal-incidence waves [42,43]. The position of the π-FBGs with respect to the ultrasound transducer was adjusted to lead to a delay of approximately 0.5 µs between the arrival times of the acoustic signals for neighboring π-FBGs.

 

Fig. 3. The acoustic setup used to test the performance of PM-PI. The part of the optical system that was submerged in water and exposed to the acoustic waves is marked by the green rectangle. The magnified part presented on the top of the figure shows guided acoustic waves (GAWs) that propagated in the fibers and modulated the resonance wavelength of the π-FBGs. The excitation of the GAWs was performed by using an ultrasound transducer positioned with a 30° angle with respect to the fibers – a technique previously used in [42,43].

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3. Results

In the first measurement, the signal from a single π-FBG was measured using PM-PI and the original implementation of PI developed in [36], in which active stabilization of the MZI was used (A-PI). Since A-PI suffers from non-linear signal folding when the acoustic signal is too strong [38], the magnitude of the ultrasound burst was chosen to be sufficiently small to fit the linear-operation range of the MZI, which was 600 MHz in our implementation. In Fig. 4(a), the sine and cosine component of the measured PM-PI signal (Eqs. (7a) and (7b)) are shown in addition to the demodulated PM-PI signal, whereas in Fig. 4(b) the demodulated PM-PI signal is compared to the one obtained by A-PI; in Fig. 4(c) the spectra of the PM-PI and A-PI signals are compared. The demodulated signals in Fig. 4(b) are represented in terms of the modulation of the central frequency of the resonator $\Delta \nu (t) = {\omega ^{ac}}(t)/2\pi$. We note that the frequency modulation $\Delta \nu$ may be alternatively expressed via the modulation in the central wavelength of the resonator $\Delta \lambda = - (\lambda _0^2n/c)\Delta \nu$, where ${{\lambda }_0}$ is the central wavelength of the resonator.

 

Fig. 4. (a) The raw signal of active demodulation (A-PI) and the two separated signals of phase modulation (PM-PI) given in Eq. 7. The acoustic signals, expressed in terms of modulation of the resonance frequency ${\Delta }\nu $ measured using both A-PI and PM-PI techniques. The resonance shifts presented in time domain (b) and frequency domain (c).

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The acoustic signals and corresponding spectra measured by the two techniques are in very good agreement as shown in Figs. 4(b) and 4(c), respectively. The small differences may be attributed to a deviation from the π/2 phase difference between the two interleaved signals in the implementation of PM-PI. The measurement bandwidth in PM-PI was limited to 12.5 MHz, i.e. half of the phase-modulation frequency. Using this bandwidth, the minimum detectable values for $\Delta \nu$ were 3 MHz and 10 MHz for A-PI and PM-PI, respectively.

In the second measurement, we demonstrated the linearity of the PM-PI in the case of ultrasound bursts with high pressure levels. Figure 5(a) shows the signals measured with PM-PI for two different settings of the gain of the electric pulser. The signals of PM-PI in Fig. 5(a) are expressed as the ultrasound induced resonance frequency modulation, $\Delta \nu (t)$. The figure shows the capability of PM-PI to reconstruct high pressure signals with peak-to-peak values of over 3000 MHz, equivalent to 8.8 rad in the phase of the sine and cosine of Eq. (7a) and Eq. (7b). For comparison, we present in Fig. 5(b) the signals measured by A-PI for the same gain settings (G = 1 and G = 4.3). As the figure clearly shows, at the high gain level the signal folded due to the nonlinear response of the MZI spectrum of A-PI, limiting the peak-to-peak values to 600 MHz, equivalent to 3.14 rad.

 

Fig. 5. PM-PI (a) and A-PI (b) signals expressed as the as the ultrasound induced resonance frequency modulation, $\Delta \nu (t)$, for two different gain values (G).

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In the third measurement, the ability of PM-PI for parallel interrogation was demonstrated for the acoustic setup shown in Fig. 3. Figure 6 shows the ultrasound-induced frequency modulation, $\Delta \nu (t)$, for all four π-FBGs as simultaneously measured by PM-PI. The results are compared to those obtained by serial measurement performed with A-PI. In the serial A-PI measurement, since only a single stabilized MZI was available, to change between channels the MZI was manually disconnected from the output of one π-FBG and connected to the output of another. The figure clearly shows an agreement between the results of the parallel PM-PI signals and serial A-PI for both the signal shape (as in Fig. 4(b)) and delay.

 

Fig. 6. Optical resonance frequency shifts from four different π-FBGs. The four different channels are measured simultaneously by the PM-PI scheme and compared with the serially measured A-PI signals. The legend is the same for all sub-plots.

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4. Conclusion and discussion

In conclusion, we demonstrated a novel scheme, PM-PI, for parallel interrogation of resonator-based interferometric detectors of ultrasound. Similar to previous PI schemes [36–39], our current PM-PI scheme employs a wideband pulse laser as the interrogation source. However, while in previous PI schemes the demodulation was performed optically at the resonator outputs, thus requiring an optical demodulator for each resonator, in PM-PI a common optical modulation scheme is used at the input of all resonators, which facilitates digital demodulation of the desired signals from simple power measurements. Accordingly, in PM-PI the only optical components that need to be scaled up with the number of resonators are the photodetectors. Our results show that the demodulated signals obtained using PM-PI are identical to the ones produced using our previously published A-PI. Using PM-PI, we demonstrate, for the first time to our knowledge, parallel detection of ultrasound with resonators with non-overlapping spectra.

In our current implementation, the PM operated at only 10% of the laser pulse rate, which enabled us to perform the modulation without synching the modulation signal with the laser signal. In future implementation, the PM modulation frequency could be increased up to 50% of the pulse repetition rate by increasing the modulation frequency to exactly half the laser repetition rate. For the pulse laser used in this work, which had a repetition rate of 250 MHz, PM-PI with a modulation frequency of 125 MHz corresponds to an acoustic bandwidth of 62.5 MHz, which is compatible with most imaging applications.

In terms of sensitivity, the current implementation of PM-PI comes at the price of increased noise in comparison to A-PI owing to the electronics used in the signal modulation. Future implementations of PM-PI will thus require using low-noise signal generators and demodulation electronics to reduce the noise. Further reduction of the noise level may be achieved by using the noise-reduction scheme of [39], which enable shot-noise limited detection, in which the optical signal-to-noise ratio (SNR) is proportional to the square root of the power at the resonator output. In such a case, increasing the number of resonators from 1 to N would lead to a reduction in SNR by a factor of $\sqrt N$. As shown in [39], if the power is reduced below a certain level, shot-noise-limited detection is lost, making the photodetector noise the leading noise term. In such a case, further increase in N will lead to a proportional decrease in SNR. Therefore, to enable the development of ultrasound detectors arrays, high-power versions of PM-PI will be required to offset, at least partially, the loss in sensitivity due to power splitting.

Despite the lower sensitivity achieved for PM-PI in comparison to A-PI, its performance was still considerably better than low-coherence schemes used for dynamic strain sensing [44]. When converting the measured noise in $\Delta \nu$ to corresponding strain, using the analysis of [44], the noise-equivalent sensitivity of PM-PI is given by 19 p $\epsilon /\sqrt {Hz} .$ In comparison, low coherence schemes in which parallelization was achieve via wavelength division multiplexing achieved a much higher noise level of 1.5 n $\epsilon /\sqrt {Hz} $ [44,45]. We note that the higher sensitivity of PM-PI is consistent with our original findings in [36] that pulse lasers are preferable over low-coherence sources in terms of the resulting sensitivity.

Although demonstrated with fiber-based resonators in the current work, PM-PI may be integrated with planar waveguide platforms, such as polymer waveguides [14,18,24,25,33] and silicon photonics [20,46–48], which enable the fabrication of resonator arrays on a single chip. Future ultrasound detector arrays enabled by PM-PI may be used to significantly improve the performance of hybrid imaging systems for which no compatible ultrasound-array technology exist, e.g. in minimally invasive [4,37] or microscopy applications [49,50].