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Burst-mode pulse interferometry for enabling low-noise multi-channel optical detection of ultrasound

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Abstract

Ultrasound detection via optical resonators can achieve high levels of miniaturization and sensitivity as compared to piezoelectric detectors, but its scale-up from a single detector to an array is highly challenging. While the use of wideband sources may enable parallel interrogation of multiple resonators, it comes at the cost of reduction in the optical power, and ultimately in sensitivity, per channel. In this work we have developed a new interferometric approach to overcome this signal loss by using high-power bursts that are synchronized with the time window in which ultrasound detection is performed. Each burst is composed of a train of low-noise optical pulses which are sufficiently wideband to interrogate an array of resonators with non-overlapping spectra. We demonstrate our method, termed burst-mode pulse interferometry, for interrogating a single resonator in which the optical power was reduced to emulate the power loss per channel that occurs in parallel interrogation of 20 to 200 resonators. The use of bursts has led to up 25-fold improvement in sensitivity without affecting the shape of the acoustic signals, potentially enabling parallel low-noise interrogation of resonator arrays with a single source.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Optical detectors of ultrasound represent a promising alternative to piezoelectric technology in applications that require both high sensitivity and miniaturization [17]. While the pressure and displacement associated with acoustic waves may be optically detected in numerous ways, optimizing both the detector sensitivity and size is commonly performed via optical resonators whose resonance frequency is pressure sensitive. Traditionally, the ultrasound-induced modulation of the resonance frequency is monitored by tuning a continuous-wave (CW) to the resonance and monitoring the amplitude [8,9] or phase [10,11] modulation at the output. While this method has the advantages of simplicity and, in some configurations, low-noise operation, it may limit scalability when resonators with high Q-factors are used [12,1316]. Because of fabrication errors, when an array of resonators is produced, each resonator exhibits a slightly different wavelength, and if the resonances are sufficiently narrow, as often is the case when the Q-factor is high, the individual resonances do not overlap, requiring a separate laser per resonator to enable parallel detection. While post-processing techniques, e.g. UV trimming [17], may be used to tune the individual resonators to the same wavelength, it comes at the cost of increased cost and complexity. Furthermore, external disturbances such as differential pressure may shift the resonance wavelengths apart even in the scenario of error-free fabrication.

Over the last decade, an alternative technique has been developed for interrogating optical resonators for ultrasound detection, which could potentially enable scalability. This interrogation technique, called pulse interferometry (PI), uses a pulse laser whose bandwidth is sufficiently broad to cover all the resonators it interrogates [1823]. While the original implementation of PI suffered from relatively high noise levels due to the effect of amplified spontaneous emission (ASE) [21], recent implementations have shown that ASE noise may be effectively eliminated by using a Fabry-Perot filter, leading to shot-noise limited detection [20,22]. More recently, PI has been demonstrated for parallel interrogation of 4-resonators in a setup in which the only optical components that needed scaling with the number of detection channels where the photodetectors [14]. However, extending the scheme of Ref. [20,24] to a high number of detection channels would inevitably come at the cost of reduced sensitivity since the same optical power, provided by a single pulse source, would be split among numerous channels, leading to lower signal strength per channel.

In this work, we have developed a new PI scheme that enables parallel interrogation of resonator arrays while maintaining a high optical power, and thus sensitivity, per resonator. The scheme, termed burst-mode PI (BM-PI), is designed for the applications of pulse-echo ultrasound [25] and time-domain optoacoustics [2629], in which ultrasound detection is performed in short bursts, rather than continuously. Accordingly, BM-PI is based on a pulse source operating in burst mode, which interrogates the resonator only at the time intervals for which ultrasound detection is required. In BM-PI, higher peak optical powers may be achieved without increasing the average power, thus mitigating optical losses in the system, e.g. due to parallel readout of several resonators.

Maximizing the signal gain in BM-PI involves two challenges that have been overcome in this work. First, optical amplifiers suffer from depletion of their inversion level and exponential signal decay when maximum burst amplification is sought. To overcome this challenge, the waveform of the amplifier input was optimized in way that generates a relatively uniform burst at the output. Second, the Fabry-Perot used in PI needs to be locked to the comb-structure of the source, requiring a continuous feedback signal that is provided also between the bursts. This challenge was overcome by a dual-polarization Fabry-Perot in which the feedback signal was generated from a continuous pulse train, rather than from pulse bursts.

BM-PI was experimentally demonstrated using a π-phase-shifted FBG (π-FBG) resonator as the detection element in an optical setup emulating the signal loss expected for parallel interrogation of an array with 20 to 200 elements. Measurements were performed for two types of sources: low-frequency piezoelectric transducer and wideband optoacoustic source, revealing a noise equivalent pressure (NEP) of 50 Pa over a bandwidth of 15 MHz for BM-PI with 20 channels. The measurements were repeated with continuous-mode PI (CM-PI) performed with full power, i.e. a single-channel configuration, resulting in an NEP of 73 Pa. However, the NEP of CM-PI in the 20-channel configuration was 525 Pa, an order of magnitude less sensitive than BM-PI in the same configuration. In the case of the 200-channel configuration, the sensitivity benefit of BM-PI was even higher with noise levels 25-times lower than those of CM-PI.

2. Experimental setup

2.1 System overview

The experimental setup of BM-PI is presented in Fig. 1. The system was composed of three parts: the source, the sensing element (resonator), and the demodulation module that transformed the optical output of the resonator into a voltage signal. The optical pulses were generated by a femtosecond laser (M-Comb model, Menlo Systems GmbH, Germany) with a central wavelength of 1560 nm, pulse repetition tunable from 248.65 MHz to 251.15 MHz, a pulse duration of 90 fs, and average power of 75 mW. The laser’s output was filtered by an optical bandpass filter (BPF) tuned to the wavelength of the resonator to a bandwidth of approximately 0.4 nm, resulting in picosecond pulses at the BPF output. Similar to the CM-PI setup of Ref. [22], a pulse stretcher was used to broaden the pulse width to approximately 0.67 ns to reduce the effect of Kerr nonlinearity. The stretched pulses were delivered to a high-power erbium-doped fiber amplifier (EDFA) and sequentially filtered by a BPF to reject the amplified spontaneous emission (ASE) outside the 0.4 nm illumination bandwidth.

 figure: Fig. 1.

Fig. 1. A schematic drawing of BM-PI. EDFA is erbium-doped fiber amplifier; B-EDFA an EDFA optimized for burst-mode operation; AOM is acousto-optic modulator; CRF is dual-polarization coherence restore filter; PZ is piezoelectric fiber stretcher; BPF is band-pass filter; and π-FBG is π-phase-shifted fiber Bragg grating. The pulse train from the laser is filtered to a bandwidth of 0.4 nm, amplified, and then split to the burst (bottom) and continuous (top) channels. The burst channel was shaped by the AOM and then again amplified. Then, the two channels are filtered by the CRF. The continuous channel is passed to the feedback circuit, to lock the spectrum of the CRF on that of the laser, whereas the burst channel is transmitted to π-FBG. Shifts in the resonance of the π-FBG are measured by an` optical demodulator, implemented by a Mach-Zehnder interferometer locked to quadrature.

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The output of the BPF was split to two fibers: one maintaining a continuous operation and the other operating in burst mode. The optical bursts were created by an acousto-optic modulator (AOM, Fiber-Q, G&H, UK), used to shape the bursts, and a custom-made burst-mode EDFA (B-EDFA), which amplified the AOM’s output (AMONICS). The radio-frequency (RF) input of the AOM was generated by a voltage driver operating at a frequency of 80 MHz with an amplitude modulation provided by an arbitrary function generator. Accordingly, the intensity-modulated optical output of the AOM was also frequency shifted by 80 MHz. To assure that both the CM and BM channels had the same optical frequencies, the same AOM module was used also in the CM channel, but with constant-amplitude RF input. Similar to Ref. [22], a coherence restoring filter (CRF) was used whose transmission spectrum matched the comb structure of the optical pulses. The CRF was implemented by a free-space Fabry-Perot with a free spectral range (FSR) of 250 MHz, which was locked on the CM channel using the same feedback scheme employed in [22]. Since the BM and CM channels possessed the same comb structure, the CRF was effectively locked also on the BM channel. To enable the separation of the BM and CM channels at the output of the CRF, two orthogonal polarizations were used, as described in detail in Section 2.3.

After exiting the CRF, the BM channel was delivered to the optical resonator, which was a π-phase-shifted fiber Bragg grating (π-FBG) with a central wavelength of 1549 nm, a bandgap width of approximately 1 nm, and a transmission notch with full-width-at-half-maximum (FWHM) of approximately 1 GHz (TeraXion Inc., Canada). The transmission notch in the π-FBG was a result of a resonance mode, spatially localized around the π-phase shift in the FBG [30]. The optical bandpass filters in the source were tuned to the central wavelength of the π-FBG, and thus, the spectrum at the output of the π-FBG included only the transmission notch. The ultrasound-induced shifts were monitored by a Mach-Zehnder interferometer (MZI), stabilized to quadrature point using a piezoelectric fiber stretcher and a feedback system [31]. The MZI outputs were split by a 90/10 fiber coupler, where the 90% branch, used to measure the acoustic signal, was connected to custom-made low-noise balanced photodetector with a transimpedance amplification of 104 V/A and bandwidth of 150 MHz, and the 10% branch, used to generate the feedback signal, was connected to balanced photodetector with an adjustable gain (Model PDB450C, Thorlabs), which was adjusted between 104 and 105 V/A, according to the optical power used in the measurement, in order to achieve optimal stability of the feedback circuit.

2.2 Burst signal optimization

The main challenge in producing high-power optical bursts was that the output waveform from the high-power B-EDFA did not match its input due to depletion effects in the B-EDFA in high-gain operation. Figures 2(a) and 2(b) present a typical measurement scenario in which a square RF signal (Fig. 2(a)) used for the AOM led to an exponentially decaying optical waveform at the output of the B-EDFA (Fig. 2(b)). To achieve an approximately square burst waveform with a high peak power at the output, the input RF signal was optimized in gradient decent algorithm in which the output was monitored during gradual modifications in the RF signal and the cost function was the square error between the monitored output and desired one. We limited the number of optimized parameters to 7 samples of the voltage waveform, serving as anchor points, whereas the rest of the signal was calculated using cubic Hermite interpolation between those 7 points for 200 points in the time window of 0–10 µs.

 figure: Fig. 2.

Fig. 2. Input-output measurements for the B-EDFA for two scenarios: (a) the voltage input of the AOM has a rectangular profile and (c) the voltage input of the AOM is engineered so that the optical output of the B-EDFA achieves an approximately rectangular profile. The left panels (a,c) show the input voltage signals and the right panel (b,d) show the corresponding B-EDFA outputs.

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The optimization protocol for achieving a desired waveform for the power of the B-EDFA output, ${P_d}(t )$, was as follows (Fig. 3):

  • 1. Initial guess: set the sampled voltages ${V_n}$ ($n = 1,2, \ldots ,N)$ to a constant value, corresponding to a square burst with maximum transmission.
  • 2. Calculate the voltage waveform $\; V(t )$ by applying cubic Hermite interpolation on ${V_n}$.
  • 3. Generate $V(t )$ with the signal generator and transmit it to the RF driver of the AOM.
  • 4. Measure the resulting burst-power waveform at the B-EDFA output, $P(t ).$
  • 5. Calculate the cost function $J = \smallint {[{P(t )- {P_d}(t )} ]^2}dt\; /\smallint {P_d}{(t )^2}dt\; $
  • 6. If $\sqrt J < \epsilon $, terminate.
  • 7. For each value of $n = 1,2, \ldots ,N$, perform
    • a. Perturb ${V_n}:$ $V{^{\prime}_n}$=${V_n} + \delta V$
    • b. Repeat steps 2–5 and measure the B-EDFA output, $P{^{\prime}_n}(t )$, for the individually perturbed voltage waveforms.
  • 8. Calculate the N derivatives of J with respect to ${V_n}$: ${\partial _n}J = \smallint {[{P{^{\prime}_n}(t )- {P_d}(t )} ]^2} - [{P_n}(t )- {P_d}(t ) ]^2dt\; /\smallint \delta V{P_d}{(t )^2}dt\; $.
  • 9. Update ${V_n}$ for $n = 1,2, \ldots ,N$: ${V_n} - {\partial _n}J\mathrm{\Delta }V \to {V_n}$.
  • 10. Go to step 2.

 figure: Fig. 3.

Fig. 3. The flow chart of waveform shaping optimization process

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In our experiments, the termination (step 6) was performed with $\epsilon $ =0.05. Once the desired voltage waveform $V(t )$ was found, it could be used in the acoustic measurements, without the need for further updates. Nonetheless, measurements that were performed on different occasions required new optimization of $V(t )$ before the measurement, where a previously optimized $V(t )$ generally led to sub-optimal burst shapes. This behaviour may be explained by the dependence of the B-EDFA gain and saturation on the exact input power and on temperature and the highly nonlinear dynamics of burst amplification.

Figure 2(c) and 2(d) show the optimized RF signal achieved by the optimization procedure and corresponding B-EDFA output, which was used in measurement described in Section 2.1. The maximum peak power achieved was 13W. In comparison, CM-PI has been demonstrated with powers ranging from 100 mW to 1 W at the EDFA output [20,22]. The fluctuations in the output signals within the 10 µs burst duration were approximately 4.3% and may be explained by the fast depletion time scale of the B-EDFA, as can be appreciated from Fig. 2(b), and the small number of anchor points used to form the RF signal.

2.3 Dual polarization CRF

The CRF was designed to filter out the ASE from the output of the EDFA while maintaining high transmission for the optical pulses, as illustrated in Fig. 4. Since the central frequency of both the pulse laser and CRF fluctuate, active stabilization is required to assure stable transmission of the pulses, which was demonstrated in Ref. [22] for CM operation using a feedback circuit. The challenge in BM operation is to maintain continuous locking during the times between the bursts to assure stable operation, which required a new CRF design.

 figure: Fig. 4.

Fig. 4. The CRF used in Fig. 1, based on a Fabry-Perot cavity operating in two polarization channels: high power BM in the p-polarization state and low-power CM in the s-polarization state. The length of the cavity is controlled by a piezoelectric actuator, enabling fine tuning of the cavity spectrum, and two collimation systems are used to match between the spatial modes of the fiber collimators and those of the cavity. The output of the BM channel is delivered to the $\pi $-FBG, as illustrated in Fig. 1, whereas the output of the CM channel is measured by photodetector to generate the feedback signal used by the piezoelectric actuator to lock the cavity’s spectrum on that of the optical pulses. To reduce cross-talk in the feedback CM signal, a custom-made analog filter is used to filter burst signals that leaked from the BM channel.

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Figure 4 shows the optical setup used to implement the CRF for BM operation, based on a dual-polarization free-space Fabry-Perot cavity in which the transmission spectrum of both polarization states is effectively identical. The input to the cavity was composed of two polarization components, which were combined by a polarization beam splitter (PBS): the high-power BM input in the p-polarization state and the low-power CM input in the s-polarization state. The two beams were spatially aligned using a beam profiler and collimated to assure they both match the fundamental mode of the cavity. At the output of the Fabry-Perot, the two polarization components were split by a second PBS, where the CM optical output was measured by a photodetector with a bandwidth of 510 kHz (PDA50B2, Thorlabs) and used to lock the cavity using the scheme of Ref. [31] and the BM output was delivered to the $\pi $-FBG for optical interrogation. Since the polarization extension ratio of the PBS was 30 dB, whereas the BM channel had a maximum power that was up to 46 dB higher than that of the CM channel, the CM output suffered from severe crosstalk, which destabilized the feedback circuit [31]. Figure 5(a) and 5(b) show the feedback signal from the CM output and its corresponding spectrum, when the burst power was reduced to 6% of its maximum value, clearly demonstrating the strong cross-talk, even for low burst-power levels. To improve stability, an analog band-stop filter was used to block the periodic electric signal in the CM output due to the burst. The analog filter was designed for a burst repetition rate of 8 kHz and exhibited bandstop notches with a 4 kHz width which appeared at five frequencies, $8n$ kHz with $n$=1,2,3,4,5). The spectrum of the analog filter is shown in Fig. 5(c). We note that since the feedback circuit, which is described in detail in Ref. [31], had a bandwidth of 35 kHz, cross-talk contributions at 48 kHz and above were naturally blocked by the circuit, and did not require additional filtering.

 figure: Fig. 5.

Fig. 5. (a) The feedback signal and (b) corresponding spectrum obtained at the output of the CM channel with the burst power reduced to 6% of its maximum power. Despite the low burst power, the cross-talk is clearly visible in both time and frequency domain. (c) The spectrum of a custom-made analog which was designed to reject the BM channel crosstalk, where the bandstop notches appeared at period of 8 kHz and a 4 kHz notch width.

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Figure 6 shows typical outputs for BM and CM channels obtained during the initialization of the locking procedure, in which the Fabry-Perot switches to its locked state. The CM signal was measured at the output of the analog bandpass filter, whereas the BM signal was directly obtained from the photodetector at the BM output (Fig. 4). The periodic optical bursts can be clearly seen on the BM signal, but not in the CM signal, demonstrating the success of the polarization splitting and analog filtering in reducing crosstalk. As the figure shows, the locking procedure did not suffer from instabilities due to transients in the BM channel and the locked operation remained stable during the times between the bursts.

 figure: Fig. 6.

Fig. 6. The optical signal at the CM (blue) and BM (red) of the CRF output in the transition from the unlocked stated, in which the CRF blocks the optical pulses, to the locked state in which the CRF transmits the optical pulses and blocks only the ASE. Each of the spikes in the locked BM channel represents a burst with a width of 10 µs, shown in detail in Fig. 2(d), where the burst repletion rate was 8 kHz.

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3. Results

The optical and acoustic performance of the BM-PI (Fig. 1) were experimentally characterized and compared to those of CM-PI. In the first set of measurement (Fig. 7), the noise power spectrum at the output of the MZI was measured for several values of the peak burst power at the output of the π-FBG and compared to the photodetector noise, where the electric noise was measured when the optical channel was turned off. In order to quantify voltage signals in terms of frequency modulation of the resonance, we used the following relation [11]:

$$V = {V_0}\sin ({\alpha \nu + {\phi_0}} ),$$
where $\alpha = {({2\pi c} )^{ - 1}}\mathrm{\Delta }L$, $\mathrm{\Delta }L$ is the optical path difference of the MZI, and c is the speed of light in the fibers. Two calibration measurements were performed: first, we measured spectrum of the MZI using an optical spectrum analyzer and calculated $\alpha $ from the period of the spectrum; second, we the maximum voltage swing of the MZI when the feedback loop was disconnected to find ${V_0}$. Reconnecting the feedback loop and locking the MZI to quadrature led to the following linearized scaling equation for small signals [11]:
$$V(t )= {\alpha ^{ - 1}}{V_0}\mathrm{\Delta }\nu (t ),$$
used to express the measured voltage signals in terms of frequency modulation of the resonance, expressed in units of Hz. Accordingly, the noise spectral density (NSD), obtained by averaging the square of 40–100 noise spectra (Fig. 7), is expressed in units of Hz2/Hz. The figure shows that at the higher power level, the main noise source was optical for frequencies up to 100 MHz. The inset of Fig. 7 shows the total noise power integrated over the frequency band 10–60 MHz for the different power levels, exhibiting a linear dependency of the electric noise power on the optical power, indicative of shot-noise-limited operation at this frequency band. In contrast, when ASE is the leading noise factor, the standard deviation of the voltage noise is proportional to the optical power, and the electric noise power is proportional to the square of the optical power.

 figure: Fig. 7.

Fig. 7. Measured noise spectral density (NSD) at the output of the demodulation module (Fig. 1) for different peak powers achieved in BM operation. The linear dependency of the electric noise power on the optical power presented at the inset (red line), by total integration of noise over the frequency band 10–60 MHz for different power level, (blue circles).

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In the second set of measurements, the interferometric system was demonstrated for ultrasound detection. A flat ultrasound transducer with a diameter of 12.7 mm and a central frequency of 1 MHz (Olympus), connected to an electric pulser (US Ultratek, PicoPulser), was used to generate a guided acoustic mode [32,33]. That was detected by the π-FBG, as illustrated in Fig. 8(a). The optical bursts of the interferometric system (Fig. 1) were synchronized to the trigger signal from the electric pulser with an additional delay corresponding to the acoustic propagation time from the transducer to the π-FBG. Figure 8(b) shows the acoustic signal measured using BM-PI with a peak power of 6 mW at the output of the π-FBG (blue curve). The result is compared to the signal obtained with CM-PI performed with the setup shown in Fig. 1, but without the AOMs and second B-EDFA stage, for which the power achieved at the output of the π-FBG was 0.17 mW. The figure clearly shows that the same waveform is obtained in both measurements, but with a considerably higher signal-to-noise ratio (SNR) for the signal acquired using BM-PI.

To further compare between the performance of BM-PI and CM-PI, the acoustic measurement was repeated for several power levels at the output of the π-FBG, where the highest power level was obtained when the EDFAs operated at maximum amplification. Figure 9(a) shows the minimum detectable frequency shift, $\mathrm{\Delta }f$, in the frequency band 10–60 MHz, in which the main noise source of BM-PI was optical, as shown in Fig. 7. The figure is presented with both axes in log scale to reveal the polynomial dependence of Δf on power: for the CM-PI a slope of approximately 1 is obtained, expected when the main noise source is additive photodetector noise [22], whereas for BM-PI at high powers a slope of approximately 1/2 is obtained, characteristic of shot-noise-limited detection. To quantify the SNR gain of BM-PI over CM-PI, the SNRs need to be compared for the same percentage of the maximum power achieved by each method. Figure 9(b) shows the ratio between the SNR in both methods, revealing an SNR gain of 10 at the maximum power and approximately 25 at lower powers. We note that reducing the power percentage effectively emulates a higher number of interrogation channels with respect to the 20 channels emulated in the setup (Fig. 1), e.g. the result for 10% represent the SNR gain that would be obtained for 200 channels.

 figure: Fig. 8.

Fig. 8. (a). The experimental setup was submerged in water where an ultrasound transducer was used to generate ultrasound bursts with a central that excites a guided acoustic wave in the optical fiber, detected by the π-FBG. (b). The measured resonance frequency shifts in a system that emulated the power loss due anticipated for a 20-channel system using BM-PI (blue) and CM-PI (red). The figure shows that while both methods captured the same waveform, BM-PI achieved a considerably higher SNR.

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 figure: Fig. 9.

Fig. 9. (a) The minimum detectable frequency shift Δf in the 10–60 MHz band for different peak powers at the output of the π-FBG using BM-PI (blue) and CM-PI (red). As the figure shows, CM-PI operated in considerably lower peak power in which Δf dependent linearly on the power, as expected for low-power operation in which the photodetector noise is dominant. In contrast, in the high powers of BM-PI, Δf was proportional to the square root of the power, indicating shot-noise-limited detection. (b) The SNR gain between two methods BM-PI and CM-PI dependence of power input. For low power levels relative for each method the SNR gain remains constant due to dominant photodetector noise in each method, whereas at higher powers the effect of shot noise in BM-PI diminishes the SNR gain.

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In the final measurement, the acoustic sensitivity of the setup was characterized using an ultrasound source generated by the optoacoustic effect, as illustrated in Fig. 10(a), placed at a distance of 21 mm from the π-FBG. The optoacoustic source was a pulse laser (Nd: YAG, Optogama Waveguard-D) with the following parameters: wavelength of 1064 nm, 1 ns pulse duration, repetition rate of 1kHz, and pulse energy of 120 µJ. The laser illuminated a glass slide coated with a weakly absorptive film (10 nm Ti / 300 nm Au) produced using electron-beam physical vapor deposition (EBPVD). The acoustic signal generated by the absorptive film was characterized by a needle hydrophone (NH0075, Precision Acoustics), revealing a peak-to-peak pressure of 4.5 kPa and a frequency band of 20–35 MHz. The optical signal detected by the π-FBG using BM-PI is shown in Fig. 10(b) (blue curve) and is compared to the signal obtained using CM-PI when the 95/5 coupler was removed, emulating the case of single-channel detection. The NEPs were calculated for both signals in the frequency band 20–35 MHz, revealing the following values: 50 Pa for BM-PI in the 20-channel configuration and 73 Pa for CM-PI in the single-channel configuration. Similar to Fig. 8, no significant differences were observed between the waveforms of CM-PI and BM-PI.

 figure: Fig. 10.

Fig. 10. The experimental setup was submerged in water, where detection of wideband ultrasound generated via the optoacoustic effect. (a) The experimental setup used in the measurement in which optical pulses illuminated a gold-coated glass substrate, leading to the generation of ultrasound bursts detected by the π-FBG. (b) The acoustic signals measured using two different configurations of the PI system: BM with 95% loss to emulate a 20-channel system (blue curve) and CM without additional losses, representing a single-channel system. The NEPs of the BM and CM configurations were 50 Pa and 73 Pa, respectively. Accordingly, despite the high losses in the BM configuration, it achieved a slightly higher sensitivity than the CM configuration. As the figure shows, using the BM configuration did not introduce any significant distortions in the measured waveform.

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4. Discussion

PI enables the parallel interrogation of optical resonators with high Q-factors owing to its wideband source without being affected by fabrication errors or external disturbances that lead to non-overlapping resonance spectra [21]. However, PI exhibits low power efficiency since only a fraction of the source’s spectral span reaches the photodetector. Thus, although PI has been demonstrated with low-noise levels for single-channel detection, extending it to multi-channel detection, at the price of additional loss of optical power, would compromise its sensitivity.

In this work, BM-PI was developed to provide additional optical gain in the PI setup to compensate for losses that may occur in multi-channel detection. While in conventional CM-PI the optical resonator is continuously illuminated with optical pulses, even when no interrogation is needed, in BM-PI the pulse illumination is provided in bursts that are synchronized with the time windows in which acoustic detection is required. This BM operation enables significant enhancement in the peak optical power without increasing the average power, which may be limited by the EDFA technology and by the damage thresholds of the optical components in the system. The bursts are produced from the pulse source used in CM-PI by first performing amplitude modulation to obtain the burst waveform and subsequently performing additional optical amplification during which the excited state of the B-EDFA is nearly depleted to provide maximum signal gain. To avoid an exponentially decaying burst, the input burst shape is engineered iteratively to achieve a square burst at the output using a gradient-decent algorithm in which the derivates are calculated from the measured response of the B-EDFA to perturbations in the input-burst shape. To remove ASE from the bursts, a CRF is used, which is implemented by a free-space Fabry-Perot whose spectrum is locked on the comb structure of the source. Since the bursts are shorter than the response time of the feedback circuit used in the locking scheme, locking the Fabry-Perot on the burst output is challenging due to the fast transients in the burst waveform, which may be misinterpreted by the feedback module. Accordingly, we have implemented the CRF with a dual-polarization Fabry-Perot in which the feedback signal is provided from a CM signal that has an identical comb structure for the BM signal. Our experimental results show that the locking mechanism is stable and is not affected by the fast transients of the bursts.

We tested the performance of BM-PI in a series of measurements emulating the power loss expected in parallel interrogation of 20 or more π-FBGs. While in the case of CM-PI, such high-power losses resulted in weak optical signals for which the photodetector noise was the dominating noise source, in BM-PI optical noise was dominant over a bandwidth of 100 MHz, where in the 10–60 MHz, shot-noise-limited detection was demonstrated. Two acoustic measurements were performed: In the first measurement, a 1 MHz transducer was used to excite guided acoustic waves in the optical fiber, detected by the π-FBG using CM-PI and BM-PI performed for the same induced losses. The results showed SNR gain of approximately 25 by BM-PI for losses emulating parallel interrogation of 200 channels. For the case of 20 channels, the SNR gain of BM-PI was reduced to 10 due to signal saturation and increase in the total noise due to shot-noise.

In the second measurement, an optoacoustic source was used for ultrasound generation and the 20-channel BM measurement was compared to CM-PI operating in full power, i.e. with a setup optimized for a single-channel interrogation. The results showed comparable sensitivities for both systems, with BM-PI achieving a slightly lower NEP of 50 Pa, compared to the 73 Pa achieved by CM-PI, although it was performed with only 5% of the maximum optical power. We note that in this measurement, no signal saturation was observed, despite the high optical powers, due to the weak acoustic signals. In both acoustic measurements, the waveform obtained with CM-PI and BM-PI were close to identical, indicating that no significant signal distortion due to BM operation was obtained. Combining the calibrated acoustic measurements with the results of Fig. 9, the NEPs of CM-PI and BM-PI may be calculated for different channel configurations. For example, CM-PI performed with a 20-channel configuration achieves a NEP of 525 Pa.

Our results show that BM-PI is a promising method for enabling parallelized ultrasound detection with multi-element arrays of optical resonators. In contrast to previous parallel-detection schemes, BM-PI does not require spectral overlap between the resonator spectra and is thus more compatible for interrogating resonators with very high Q-factors. Additionally, BM-PI achieves low-noise operation making it suitable for challenging optoacoustic imaging applications. For example, the NEP obtained for BM-PI for 95% loss, emulating a 20-channel system of π-FBGs in silica fibers, is comparable to the value achieved by polymer Fabry-Perot resonators when no additional losses are applied [5,34], despite the weak acoustic response of silica. Further sensitivity enhancement in our scheme may be achieved by using polymer-based resonators, e.g. micro-rings [6,35], or silicon resonators with a polymer cladding [36]. The main fundamental challenge of BM-PI is that it is inherently incompatible with applications that require continuous acoustic detection, e.g. frequency-domain optoacoustics [37] or magneto-acoustics [38]. Nonetheless, medical ultrasound and optoacoustics commonly operate in bursts, rather than continuously, justifying the development of interrogation setups optimized for BM operation.

An additional advantage of BM-PI is its potential for scalability since it uses only a single source, in contrast to some CW-based schemes in which the number of lasers needs to be scaled with the number of detectors. However, in the current work BM-PI was implemented with a fiber-based actively stabilized MZI at the output – a module that hinders scale-up due to its cost and complexity. Full scalability may nonetheless be achieved by combining BM-PI with the phase modulation scheme developed in Ref. [14], in which a single MZI is used in the input of all the resonators and the active-stabilization scheme is replaced by a phase modulation of one of the MZI arms. Although the experimental demonstration in Ref. [14] included only 4 resonators, the scheme is fully scalable, requiring only the photodetectors and sampling electronics to be scaled up with the number of channels, and the addition of burst-mode operation may enable one to achieve the same optical power per channel as reported in our current work. However, since the sensitivity in Ref. [14] is also affected by the noise of the voltage signal used for the phase modulation, reaching shot-noise-limited detection may require electronics optimized for low-noise operation. Alternatively, scalability may be achieved by using the passive demodulation scheme of Ref. [18], in which the stabilized MZI is replaced by two non-stabilized MZIs, enabling low-cost fabrication of numerous duplicates of the demodulation module in a passive photonic circuit [39]. The main advantage of passive demodulation is that it does not introduce additional noise sources, which may limit the achieved sensitivity. However, some loss in sensitivity may still occur due to coupling losses between the optical fibers and the photonic circuit.

Funding

Israel Science Foundation (1709/20, 694/15).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

Data availability

No data were generated or analyzed in the presented research. 

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Data availability

No data were generated or analyzed in the presented research. 

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Figures (10)

Fig. 1.
Fig. 1. A schematic drawing of BM-PI. EDFA is erbium-doped fiber amplifier; B-EDFA an EDFA optimized for burst-mode operation; AOM is acousto-optic modulator; CRF is dual-polarization coherence restore filter; PZ is piezoelectric fiber stretcher; BPF is band-pass filter; and π-FBG is π-phase-shifted fiber Bragg grating. The pulse train from the laser is filtered to a bandwidth of 0.4 nm, amplified, and then split to the burst (bottom) and continuous (top) channels. The burst channel was shaped by the AOM and then again amplified. Then, the two channels are filtered by the CRF. The continuous channel is passed to the feedback circuit, to lock the spectrum of the CRF on that of the laser, whereas the burst channel is transmitted to π-FBG. Shifts in the resonance of the π-FBG are measured by an` optical demodulator, implemented by a Mach-Zehnder interferometer locked to quadrature.
Fig. 2.
Fig. 2. Input-output measurements for the B-EDFA for two scenarios: (a) the voltage input of the AOM has a rectangular profile and (c) the voltage input of the AOM is engineered so that the optical output of the B-EDFA achieves an approximately rectangular profile. The left panels (a,c) show the input voltage signals and the right panel (b,d) show the corresponding B-EDFA outputs.
Fig. 3.
Fig. 3. The flow chart of waveform shaping optimization process
Fig. 4.
Fig. 4. The CRF used in Fig. 1, based on a Fabry-Perot cavity operating in two polarization channels: high power BM in the p-polarization state and low-power CM in the s-polarization state. The length of the cavity is controlled by a piezoelectric actuator, enabling fine tuning of the cavity spectrum, and two collimation systems are used to match between the spatial modes of the fiber collimators and those of the cavity. The output of the BM channel is delivered to the $\pi $-FBG, as illustrated in Fig. 1, whereas the output of the CM channel is measured by photodetector to generate the feedback signal used by the piezoelectric actuator to lock the cavity’s spectrum on that of the optical pulses. To reduce cross-talk in the feedback CM signal, a custom-made analog filter is used to filter burst signals that leaked from the BM channel.
Fig. 5.
Fig. 5. (a) The feedback signal and (b) corresponding spectrum obtained at the output of the CM channel with the burst power reduced to 6% of its maximum power. Despite the low burst power, the cross-talk is clearly visible in both time and frequency domain. (c) The spectrum of a custom-made analog which was designed to reject the BM channel crosstalk, where the bandstop notches appeared at period of 8 kHz and a 4 kHz notch width.
Fig. 6.
Fig. 6. The optical signal at the CM (blue) and BM (red) of the CRF output in the transition from the unlocked stated, in which the CRF blocks the optical pulses, to the locked state in which the CRF transmits the optical pulses and blocks only the ASE. Each of the spikes in the locked BM channel represents a burst with a width of 10 µs, shown in detail in Fig. 2(d), where the burst repletion rate was 8 kHz.
Fig. 7.
Fig. 7. Measured noise spectral density (NSD) at the output of the demodulation module (Fig. 1) for different peak powers achieved in BM operation. The linear dependency of the electric noise power on the optical power presented at the inset (red line), by total integration of noise over the frequency band 10–60 MHz for different power level, (blue circles).
Fig. 8.
Fig. 8. (a). The experimental setup was submerged in water where an ultrasound transducer was used to generate ultrasound bursts with a central that excites a guided acoustic wave in the optical fiber, detected by the π-FBG. (b). The measured resonance frequency shifts in a system that emulated the power loss due anticipated for a 20-channel system using BM-PI (blue) and CM-PI (red). The figure shows that while both methods captured the same waveform, BM-PI achieved a considerably higher SNR.
Fig. 9.
Fig. 9. (a) The minimum detectable frequency shift Δf in the 10–60 MHz band for different peak powers at the output of the π-FBG using BM-PI (blue) and CM-PI (red). As the figure shows, CM-PI operated in considerably lower peak power in which Δf dependent linearly on the power, as expected for low-power operation in which the photodetector noise is dominant. In contrast, in the high powers of BM-PI, Δf was proportional to the square root of the power, indicating shot-noise-limited detection. (b) The SNR gain between two methods BM-PI and CM-PI dependence of power input. For low power levels relative for each method the SNR gain remains constant due to dominant photodetector noise in each method, whereas at higher powers the effect of shot noise in BM-PI diminishes the SNR gain.
Fig. 10.
Fig. 10. The experimental setup was submerged in water, where detection of wideband ultrasound generated via the optoacoustic effect. (a) The experimental setup used in the measurement in which optical pulses illuminated a gold-coated glass substrate, leading to the generation of ultrasound bursts detected by the π-FBG. (b) The acoustic signals measured using two different configurations of the PI system: BM with 95% loss to emulate a 20-channel system (blue curve) and CM without additional losses, representing a single-channel system. The NEPs of the BM and CM configurations were 50 Pa and 73 Pa, respectively. Accordingly, despite the high losses in the BM configuration, it achieved a slightly higher sensitivity than the CM configuration. As the figure shows, using the BM configuration did not introduce any significant distortions in the measured waveform.

Equations (2)

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V = V 0 sin ( α ν + ϕ 0 ) ,
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