Ultrasound detection via low-noise pulse interferometry using a free-space Fabry-P&#x00E9;rot

Oleg Volodarsky; Yoav Hazan; Amir Rosenthal

doi:10.1364/OE.26.022405

1. Introduction

Optical detection of ultrasound has attracted significant attention in recent years as an alternative to conventional piezo-electric approaches. Optical detectors are immune to electromagnetic (EM) interference and are often transparent – properties that are highly desirable in hybrid ultrasound assisted imaging modalities such as optoacoustic tomography [1–8] radiofrequency thermo-acoustic tomography [9,10], and magneto-acoustics [11,12].

One of the major challenges in detecting ultrasound via optical means is achieving sufficient sensitivity for the application at hand. Sensitivity is often enhanced by the use of optical resonators [13–21], optical materials with a large photoelastic coefficient [22,23], low-noise read-out schemes [24], or acoustic membranes [25,26]. When optical resonators are used, their interrogation is often performed by continuous wavelength (CW) lasers tuned to the resonance wavelength, where ultrasound-induced shifts of the resonance lead to intensity modulation at the resonator output [13–18]. Two major disadvantages of CW techniques are their susceptibility to environmental disturbances [27] and their limited capabilities in simultaneously interrogating resonators with distinct resonance wavelengths, hindering the development of detector arrays with parallel readout. Accordingly, previous schemes in which CW lasers have been used for parallel measurements of ultrasound signals either did not use resonators [28,29], or used resonators with relatively broad resonances [30], with the possible price of reduced sensitivity

In recent years, a new technique for optical detection of ultrasound has been developed called pulse interferometry (PI) [24,31,32]. PI is designed for the interrogation of resonator-based detectors and involves illuminating the resonator with an optical pulse train whose bandwidth is considerably larger than that of the resonators. Thus, multiple resonators with different resonance wavelengths may be simultaneously illuminated, facilitating future implementations with parallel interrogation of multiple detectors with a single source. In addition, when PI was implemented with passive demodulation schemes, it demonstrated very high robustness against external disturbances [24] and high dynamic range in ultrasound detection [31].

In its original implementation, PI suffered from excessive noise, which had the spectral properties of amplified spontaneous emission (ASE) [32]. In [24], over an order of magnitude reduction in the optical noise of PI was obtained by using a fiber-based Fabry-Pérot filter which rejected most of the incoherent noise while transmitting the pulses. This modified scheme of PI, termed coherence-restored pulse interferometry (CRPI), achieved shot-noise-limited detection over the acoustic band of 4-20 MHz. However, the implementation of CRPI in [24] was not compatible with parallelization due to the fiber-based implementation of the Fabry-Pérot filter. In particular, the spectrum of the Fabry-Pérot filter could match the spectrum of the laser over only a narrow bandwidth due to the dispersion in the fiber. Thus, the potential ability of PI to interrogate with a single source multiple resonators with non-overlapping resonance spectra was lost in the fiber-based implementation of CRPI. In addition, the shot-noise-limited detection demonstrated in [24] was achieved with a modest power level of 180 µW at the resonator output.

In this paper, a new CRPI scheme is demonstrated that is compatible with both parallelized detection of detector arrays and high-power operation. The new scheme involves two modifications to the interrogation source. First, a free-space Fabry-Pérot filter was designed to fully match the entire spectrum of the laser source. By matching the free spectral range (FSR) of the Fabry-Pérot filter to the repetition rate of the laser and matching the Fabry-Pérot input- and output-mode profiles to those of the fiber-collimation system, transmission efficiency of approximately 50% was obtained over a bandwidth of 80 nm in the telecom wavelengths. Accordingly, in the new CRPI scheme, the original advantage of PI of parallelization compatibility via wideband illumination was regained. Second, a high-power optical amplifier was used to increase the sensitivity and experimentally determine the limitations imposed by nonlinear effects. Indeed, it was found that spectral broadening due to Kerr nonlinearity [33] limits the performance of CRPI at typical amplifier outputs of 500 mW. To overcome this limitation, a pulse stretcher was added to the scheme, which reduced the peak power of the pulses, and thus the effect of Kerr nonlinearity.

The new CRPI scheme was tested with a π-phase-shifted FBG (π-FBG) resonator, similar to the one used in [24], which was used to detect an ultrasound signal in the frequency range of 4-20 MHz. For this bandwidth, the minimum detectable resonance shift in [24] was 160 kHz, corresponding to a spectral density of 40 Hz/√Hz. In the current work, the use of a high-power optical amplifier and pulse stretcher conjointly enabled shot-noise limited detection with powers up to 5 mW at the output of the π-FBG, over an order of magnitude higher than the powers achieved in [24]. For this power level, the minimum detectable resonance shift had a spectral density as low as 5 Hz/√Hz, i.e. 8 time lower than noise level achieved in [24]. In addition, we note that while the ultrasound measurement was limited to frequencies below 20 MHz, the power spectrum of the measurement noise indicates that shot-noise-limited ultrasound detection may be achieved for an acoustic frequencies up to 50 MHz, making the interrogation scheme compatible with high-resolution imaging applications [34,35].

2. Experimental setup

2.1 Interferometric system

The interferometric system is shown in Fig. 1, where all the components were implemented with single-mode polarization-maintaining fibers. The system was composed of three parts: the source, the sensing element, and the demodulator. The source employed 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 output of the laser was filtered to an optical bandwidth of approximately 0.4 nm. To reduce the effect of Kerr nonlinearity [33], the picosecond pulses were delivered to a pulse stretcher implemented with a chirped Bragg grating (TeraXion Inc., Canada) and a circulator, leading to a broadening of the pulse to approximately 0.67 ns. The stretched pulses were amplified by a high-power erbium-doped fiber amplifier (EDFA) and sequentially filtered to reject the amplified spontaneous emission (ASE) outside the 0.4 nm illumination bandwidth. To reject the noise within the illumination bandwidth, the output of the amplifier was delivered to a coherence restoring-filter (CRF) implemented by a free-space Fabry-Pérot with a free spectral range (FSR) of 250 MHz, matching the comb spectrum of the pulse laser. The transmission through the Fabry-Pérot was monitored by a photodiode that received 5% of the Fabry-Pérot output. Similarly to [24], a feedback system [36] used the 5% monitor signal to lock the spectrum of the CRF on the comb spectrum of the pulse laser.

Fig. 1 A schematic of CRPI. EDFA is erbium-doped fiber amplifier; PZ is piezoelectric fiber stretcher; CRF is coherence-restoring 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 further filtered by the CRF. Shifts of resonance of the π-FBG are measured by optical demodulator, implemented by a Mach-Zehnder interferometer locked to quadrature.

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The sensing element was a π-FBG with a central wavelength of 1549 nm, a bandgap width of approximately 1 nm, and a transmission notch within the bandgap 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. 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. Ultrasound-induced shifts in the resonance were monitored by an active demodulator composed of a Mach-Zehnder interferometer, stabilized to quadrature point using a piezoelectric fiber stretcher and a feedback system [36]. The output of the Mach-Zehnder interferometer was connected to a balanced photodetector with a trans-impedance amplifier (PDB450C, Thorlabs).

2.2 Coherence-restoring filter (CRF)

The CRF, shown in Fig. 2, was implemented with a fiber collimation system and a free-space Fabry-Pérot cavity formed by one spherical mirror with a radius of curvature of $r = 1 m$ and one flat mirror. We note that while the CRF could also be implemented with a Fabry-Pérot cavity that is composed of two spherical mirrors, using one flat mirror reduces the degrees of freedom in the setup, thus simplifying its alignment. The flat mirror was mounted on a piezoelectric actuator (P-080.391, PI piezo Technology) which enabled a fine control of the cavity length. The collimation system at the input (L1 and L2 in Fig. 2) was used to launch only the fundamental spatial mode of the cavity, whereas the collimation system at the output was used to efficiently couple the output of the cavity back to the fiber system.

Fig. 2 The CRF used in Fig. 1, which consists of input and output fiber collimators, lens-based collimation systems (L1-L4), the Fabry-Pérot cavity with a piezo actuator, and alignment mirrors. The piezo actuator controls the cavity length and the collimation systems are used match between the spatial modes of the fibers collimators and those of the cavity.

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The FSR of the cavity was determined by its length according to the following equation:

FSR= c / 2 n d,

where

d

is the distance between the two mirrors,

c

is the speed of light in vacuum, and

n

is the refractive index in the cavity. Accordingly, to achieve an FSR of 250 MHz, a distance of

d =

60 cm was used. The cavity parameters fulfilled the required stability criterion, given by

- 1 \leq (1 - d / r) \leq 1.

To efficiently couple the fiber-based interferometric system to the free-space cavity, the beam waists of the fundamental cavity mode were calculated at the input and output of the cavity using ABCD matrix analysis. Briefly, the ABCD matrix for a roundtrip in the cavity that starts at the flat mirror (cavity input) is given by [37]

[\begin{matrix} A & B \\ C & D \end{matrix}] = [\begin{matrix} 1 - \frac{2 d}{r} & 2 d - \frac{2 d^{2}}{r} \\ - \frac{2}{r} & 1 - \frac{2 d}{r} \end{matrix}] .

The beam widths of the fundamental mode at the cavity input and output are as follows [37]:

w_{in} = \sqrt{\frac{λ B}{π n}} {[1 - {(\frac{D + A}{2})}^{2}]}^{- 1 / 4},

w_{out} = w_{i n} \sqrt{1 + {(\frac{d λ}{π n w_{i n}^{2}})}^{2}}

where

λ

denotes the optical wavelength. Accordingly, the beam widths of the fundamental mode at the input and output of the cavity had the following values, respectively:

w_{in} = 0.49 mm

and

w_{out} = 0.78 mm

. The collimation system between the fiber-based system and the cavity was designed according to the calculated values of

w_{in}

and

w_{out}

to maximize the fiber-to-fiber coupling.

When ignoring losses due to spatial-mode mismatches and mirror roughness, the maximum transmission through the cavity, achieved at the resonance wavelengths, is given by

T_{\max} = \frac{(1 - R_{1}) (1 - R_{2})}{{(1 - \sqrt{R_{1} R_{2}})}^{2}},

where

R_{1}

and

R_{2}

are the reflectance of the two mirrors. To achieve

T_{\max} = 1

, the reflectance of both mirrors should be identical. In our implementation, the reflectance of the flat mirror was

R_{1} = 99.15 %

, whereas that of the second mirror was

R_{2} = 98.88 %

, leading to a theoretical transmission limit of

T_{\max} = 0.98

. Thus, the mismatch between the reflectance values of the mirrors in our implementation is sufficiently small to be of no practical importance. The finesses of the cavity, defined as the ratio between the spectral FWHM of the cavity’s transmission notches and its FSR, is given by

F = π \frac{^{4} \sqrt{R_{1} R_{2}}}{1 - \sqrt{R_{1} R_{2}}} .

For the reflectance values of the mirrors employed, the theoretically predicted finesses is thus

F = 304

. The maximum noise rejection achievable by the CRF is determined by the minimum value of the transmission function, given by

T_{\min} = \frac{(1 - R_{1}) (1 - R_{2})}{{(1 - \sqrt{R_{1} R_{2}})}^{2} + 4 \sqrt{R_{1} R_{2}}} .

For the mirror reflection values used in the CRF, one obtains

T_{\min} = - 45 .9

dB.

3. Results

3.1 CRF performance

The performance of the CRF was characterized using several methods. First, the optical spectrum of the CRF was measured by an optical spectrum analyzer (OSA, AP2041B, APEX Technologies) around the wavelength of 1550 nm. The transmission spectrum is shown in Fig. 3(a) as a function of the frequency detuning. The figure shows that the minimum transmission was approximately −53dB. The measured value of the FSR of the CRF was 250.15 MHz, within the tunability range of the pulse repetition rate of the pulse laser. The finesse and maximum transmission of the CRF could not be accurately evaluated from Fig. 3(a) because the resolution of the OSA was 5 MHz, i.e., considerably larger than the spectral width of the transmission notches of the cavity.

Fig. 3 (a) The transmission spectrum of the CRF, as a function of frequency detuning measured with an optical spectrum analyzer with a resolution of 5 MHz. (b,c) The power transmission of the CRF in time when the piezo-actuator was scanned with a saw-tooth voltage signal. The measurement was performed with the source shown in Fig. 1, which had a typical linewidth 150 kHz for each of its spectral modes. The figures show that the CRF achieves a maximum transmission of 0.5 and a finesse of 335.

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In order to accurately assess the cavity finesse and maximum transmission, the pulse laser, which had a typical linewidth 150 kHz for each of its spectral modes, was connected directly to the CRF. The piezo-actuator was fed with a saw-tooth voltage signal to scan the cavity mirror, and the voltage signal was measured as a function of time (Fig. 3(b) and Fig. 3(c)). As Fig. 3(b) shows, for each linear scan of the voltage signal supplied to the actuator, two transmission notches were captured. Taking the ratio between the delay between two notches (Fig. 3(b)) and notch temporal width (Fig. 3(c)), a finesse of 335 was obtained, in agreement with the theoretical value. The maximum transmission of the CRF was 50%, where losses may be attributed to coupling losses between the input and output fibers of the CRF due to mode mismatches. Accordingly, the experimental value of $T_{\min} / T_{\max}$ was approximately 50 dB, in general agreement with the analysis performed in Sec. 2.2.

In the next measurements, the ability to use the CRF over the entire bandwidth of the pulse laser was tested. The measurement was performed by connecting the pulse laser directly to the CRF. The output of the CRF was connected to a 95/5 splitter, where the 5% output was monitored with a photodiode and used to lock the CRF on the spectrum of the laser, and the 95% output was connected to an optical spectrum analyzer (OSA) with a spectral coverage of 1520-1610 nm (AP2041B, APEX). The repetition rate of the laser was finely tuned to achieve the highest photodiode signal. Figure 4 shows the spectrum at the CRF output in comparison to the spectrum at the CRF input. The figure clearly shows that the CRF achieves approximately −3dB transmission over the entire laser bandwidth. This result indicates that the comb structure of the pulse laser and Fabry-Pérot cavity overlapped over the entire laser bandwidth.

Fig. 4 The spectrum of the pulse laser in Fig. 1 (red curve) compared to the spectrum at the output of the CRF when the pulse laser is connected directly to its input (blue curve). The repetition rate of the laser was finely tuned to match the FSR of the CRF. The light-blue area represent the 3dB level above the CRF output. The figure clearly shows that the CRF approximately maintains a −3dB trasmission across the entire 80 nm bandwidth of the laser.

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3.2 Interferometric-system characteristics

The characteristics of the interferometric system shown in Fig. 1 was investigated in a series of measurements. First, a direct measurement of the noise-reduction capabilities of the CRF was performed by connecting the OSA to the output of the π-FBG. The high spectral resolution of the OSA, which was equal to 5 MHz, enabled the visualization of the fine comb structure of the spectrum. The measurement was performed with a power of 1 W at the output of the EDFA, corresponding to approximately 250 mW power at the input of the π-FBG and 5 mW at its output. The spectrum measurement at the output of the π-FBG was repeated without the CRF, while keeping the input to the π-FBG at 250 mW. The spectra measured with and without the CRF are shown in Fig. 5. The figure clearly shows that when the CRF is not used, e.g. as in the work in [29], the pulses are accompanied by incoherent noise. Analyzing the spectrum in Fig. 5, it was obtained that when the CRF was not used, the power of the noise component accounted for 0.05% of the total power at the output of the π-FBG. When the CRF was used, a noise reduction of up to 30 dB, down to the noise-floor level of the OSA, could be measured.

Fig. 5 The spectrum at the output of the π-FBG in the system in Fig. 1 with (red curve) and without (blue curve) the CRF for a power level of 250 mW at the input of the π-FBG. The figure shows that the CRF achieves noise rejection of at least 30 dB, down to the noise-floor level of the measurement.

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The effect of the CRF was additionally tested at the output of the active demodulator shown in Fig. 1. The voltage signal at the demodulator output was supplied to an electrical spectrum analyzer (E4446A, Agilent) to measure the noise spectrum. The measurement was performed for a power level of 5 mW at the output of the π-FBG with and without the CRF in the interferometric system. The noise spectra are shown in Fig. 6 and compared to that of the dark-current noise of the balanced detector in the demodulator. The measurements were performed with the balanced detector set to a gain level of 10⁴ V/W and with a −3dB drop at modulation frequency 45 MHz. Over the spectral band of 10-45 MHz, the noise reduction due to the CRF was approximate −35 dB and the minimum detectable frequency shift was 21 kHz, corresponding to a spectral density of approximately 5 Hz/√Hz.

Fig. 6 Measured noise spectrum density (NSD) dependence on frequency for different system configuration: the interferometric system of Fig. 1 with and without CRF, and dark photodiode current.

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In the next measurements, the interferometric system were tested for ultrasound detection. A cylindrically focused ultrasound transducer with a diameter of 12.7 mm and a central frequency of 15 MHz (Olympus) was used to generate ultrasound bursts that were focused on the center of the π-FBG. The detected signal obtained by the CPRI system is shown in Fig. 7(a) (blue curve) for a power level of 5 mW at the output of the π-FBG. For comparison, the same signal is shown for the same power level for the PI system without the CRF (red curve). The measurement was repeated for several power levels at the output of the π-FBG, with and without the CRF. In Fig. 7(b), noise level, represented by the minimum detectable frequency shift ∆f in the measurement, is shown for the different power levels at the output of the π-FBG. To minimize the effect of dark current and incoherent noise in the analysis, the spectral range over which the noise analysis was performed was 15-30 MHz. The figure shows that, similarly to our previous study in [24], the noise in PI without the CRF does not improve with increasing the power level. In contrast, the noise in CRPI was proportional to the optical power for power levels at the output of the π-FBG up to approximately 0.65mW and to the square root of the optical powers above for powers above 0.65 mW, indicating a shot-noise-limited detection.

Fig. 7 (a) The resonance frequency shifts measured with the CRPI system due to ultrasound bursts with a central frequency of 15 MHz. The figure shows that the same signals were obtained with (blue curve) and without the CRF (red curve), but that the CRF measurement obtained a higher SNR. (b) The minimum detectable frequency shift ∆f in the 15-30 MHz band with (blue circles) and without (red circles) the CRF as a function of the power at the output of the π-FBG. When the CRF was not used ∆f was constant, indicating that classical optical noise is the main noise source in that scheme. In contrast, when the CRF was used, ∆f decreased linearly for powers below approximately 0.65 mW and in proportion to the square root of the power for powers above approximately 0.65 mW. The dashed line shows the extrapolation of ∆f for the hypothetical case of photodiode-noise-dominant measurement for all power levels.

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3.3 Non-linear propagation effects

In this sub-section, we investigate the limitation Kerr nonlinearity imposes on CRPI when high powers are used. The propagation of picosecond pulses in single-mode fibers in the telecom wavelengths is commonly described by the nonlinear Schrödinger equation (NLSE) that models the effects of Kerr nonlinearity and second-order dispersion [33]. We first theoretically show that for pulse parameters and fiber type used in this work Kerr nonlinearity is expected to be the dominant effect of the two in our experimental setup. The dispersion length is given by $L_{D} = Τ_{0}^{2} / | β_{2} |$ , where $Τ_{0}$ is the pulse duration and $β_{2}$ is the dispersion parameter, which is typically equal to 20 ps²/km for standard telecom fibers [33]. The nonlinear length is given by $L_{N L} = {(γ P_{0})}^{- 1}$ , where $P_{0}$ is the peak power of the pulse and $γ$ is the nonlinearity parameter that is typically equal to 1.2 W⁻¹km⁻¹ in standard telecom fibers [33]. To calculate $L_{D}$ and $L_{N L}$ , one needs to know the pulse width and peak power. Although these parameters cannot be directly measured in our setups, their approximate magnitude may be roughly deduced from their bandwidth. For pulses with a spectral FWHM of 0.4 nm, the corresponding temporal FWHM is 8 ps, assuming chirp-free sech pulses. Since the delay between two pulses is 4 ns, the ratio between the peak power and average power, should be approximately 500 when the pulse stretcher is not used. For the highest EDFA setting of 1 W average power, the approximate values for the dispersion and nonlinearity lengths are $L_{D} \approx 5 km$ and $L_{N L} \approx 1.7 m$ , respectively.

Our analysis indicates that for the typical fiber lengths of several meters used in CPRI Kerr nonlinearity alone is significant when the pulse stretcher is not used. Particularly, the spectrum of the pulses is expected to widen due to Kerr-induced self-phase modulation (SPM). When the pulse stretcher is used, a temporal broadening of the pulse and a corresponding reduction in peak power by a factor of approximately 84 is expected, leading to an acceptable nonlinearity length of approximately 142 m. In our experimental setup, the length of the fiber from the high-power EDFA to the filter connected to its input (Fig. 1) is 1 m; from the filter output to the collimation system of the CRF is 4 m; and from the output of the CRF collimation system to the π-FBG is 3 m. Accounting for a −3 dB insertion loss of both the filter and CRF, the effective propagation length from the output of the EDFA to the π-FBG is estimated to be $2.2 L_{N L}$ – a value for which SPM is expected to lead to pulse broadening. To verify this analysis, we measured the optical spectrum at the output of the CRF for average power levels of 500 mW at the EDFA output, corresponding to an effective propagation length of $1.1 L_{N L}$ . The measurement was performed with and without the use of the pulse stretcher at the input of the EDFA (Fig. 1), and the results are shown in Fig. 8. The results indicate that spectral broadening was obtained when the pulse stretcher was not used, leading to reduced spectral power density delivered to the π-FBG.

Fig. 8 The optical spectrum at the input of the π-FBG in Fig. 1 with (blue curve) and without (red curve) the pulse stretcher for a power level at the output of the EDFA of (a) 30 mW and (b) 500 mW. Significant spectral broadening due to SPM is observed for the higher power setting when the pulse stretcher was not used. In contrast, when the pulse stretcher was used, no broadening is observed.

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To further evaluate the performance of the pulse stretcher in minimizing the effect of Kerr nonlinearity, we performed an additional measurement in which a single-mode fiber with a length of 200 meters was connected to the output of the second filter. Figure 9 shows the spectrum at the output of the 200-meter fiber measured with (blue curve) and without (red curve) the pulse stretcher for different levels of average power at the output of the EDFA. For the highest power in Fig. 9, the effective propagation length was $22 L_{N L}$ , i.e. an order of magnitude larger than the value achieved for the CRPI system in Fig. 1 with maximum amplification. Nonetheless, for all power levels, no spectral broadening was observed in the measurement performed with the pulse stretcher. In contrast, when the pulse stretcher was not used, the spectrum broadening increased with power, and spectral splitting, a known feature of SPM, was observed for the two highest power level.

Fig. 9 The optical spectrum at the output of the 200 m single-mode fiber connected to the second optical filter in the CRPI setup (Fig. 1) obtained for following power levels at the output of the EDFA: (a) 22 mW, (b) 88 mW, (c) 350 mW. When the pulse stretcher was not used (red curve), significant broadening was observed for all power levels, whereas no broadening was obtained with the pulse stretcher (blue curve).

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4. Discussion

CRPI is a pulse-laser-based alternative to CW-based methods for interrogating ultrasound detectors based on optical resonances. The source in CRPI has the attractive features of being wideband, and thus useful for simultaneous interrogation of several resonances with different wavelengths, and low noise. The optical noise in CRPI may be reduced to the fundamental shot-noise limit by using a CRF that rejects wideband noise between the modes of the pulse laser. Accordingly, CRPI enables one to improve the optical SNR by simply increasing the power. Clearly, practical considerations limit the extent to which the power, and thus SNR, may be increased. In the original implementation of CRPI in [24], shot-noise limited detection was obtained for a relatively modest power of 180 µW. An additional limitation of the implementation in [24] was that its fiber-based version of the CRF reduced the source’s bandwidth. Thus, in the implementation in [24], the properties of low-noise and wide optical spectrum were mutually exclusive.

In the current study, a new scheme for CRPI is developed which achieves both wideband operation and shot-noise limited sensitivity at power levels of up to 5 mW, enabling 8 times lower noise levels than those achieved in [24]. The current scheme involves 2 main modifications. The first is the introduction of a pulse stretcher to reduce spectral broadening due to Kerr non-linearity, and the second is the replacement of the fiber-based Fabry-Pérot cavity by a free-space version, thus significantly minimizing spectral mismatches between the laser and the CRF. Despite the free-space implementation, the use of a collimation system to match the spatial mode of the cavity to that of the fibers enabled 50% transmission from the input to output fiber of the CRF. The FSR of the free-space cavity was designed to be approximately 250 MHz, and fine tuning of the pulse repetition rate of the laser enabled matching its spectrum exactly to that of the cavity’s. In contrast, in [24], a cavity with an FSR of 25 MHz was used with a laser that had a pulse repetition rate of 100 MHz, which transmitted not only the laser’s comb structure, but also noise at specific frequencies between the comb teeth.

The performance of the new CRPI scheme was tested in several measurements. In the first set of measurements, the properties of the optical spectrum were studied. To demonstrate that the CRF does not reduce the optical bandwidth of the source, the laser was connected directly to the CRF, and the optical spectrum was measured before and after the source. Indeed, a transmission efficiency of approximately 50% was achieved over the entire effective bandwidth of 80 nm. The noise characteristics were studied by measuring the optical spectrum at the output of the π-FBG with and without the CRF used in the source. The measurement provided the first direct evidence that the CRF indeed reduces excessive broadband noise between the teeth of the laser spectrum. In addition, the high-resolution spectral measurement enabled us to quantify the power content of the noise component, which was 0.05% of the total optical power.

In the second set of measurements, the noise properties of the detected voltage signal were studied. The noise power spectrum was measured with and without the CRF and was compared to that due to the photodiode’s dark current. The results showed that over the 10-45 MHz frequency band, a −35 dB reduction in the noise power was achieved by using the CRF for the maximum output power of 5 mW. Since the noise power obtained with the CRF was above the photodiode’s dark current level, this level of noise reduction represents the noise reduction in the optical noise of the beam, unhindered by electrical noise in the detection. To determine the origin of the optical noise, the noise level was measured for different optical power levels. To minimize the effect of the photodiode noise, the analysis was performed in the spectral band of bandwidth of 15-30 MHz, where the noise spectrum was relatively flat and significantly higher than the photodiode noise for the maximum power setting. The results show that for power levels above approximately 0.65mW, the minimum detectable frequency shift ∆f was proportional to the square root of the optical power, indicating shot-noise limited detection, whereas below 0.65mW, ∆f was proportional to the power, indicating that the photodiode noise was the main noise source. We note that when the highest power level of 5 mW was used, Fig. 6 indicates that shot-noise limited detection is maintained for frequencies as high as 50 MHz, in which stronger rejection of ASE than in the 15-30 MHz band is observed (Fig. 3(a)), yet the photodiode noise is still not dominant. In contrast, when the CRF was not used, ∆f was independent of the optical power, as expected from our previous studies.

In the last set of measurements, the susceptibility of CRPI to Kerr-induced SPM was tested. Estimates of the pulse width and peak powers indicate that from the output of the high-power EDFA to the output of the CRF, the pulses propagate an effective distance of approximately $2.2 L_{N L}$ when the output of the EDFA is set to 1 W and no pulse stretcher is used. Indeed, when the optical spectrum was measured for an EDFA output power of 0.5 W with no pulse stretching, equivalent to an effective propagation of $1.1 L_{N L}$ , a significant spectral broadening was observed. In contrast, when the pulse stretcher was used, no spectral broadening was observed even in the measurements of Fig. 9 in which the effective propagation length was increased to approximately $22 L_{N L}$ , indicating that the current CRPI system can operate with amplifier outputs as high at 10 W without being affected by SPM. Nonetheless, at such high power levels, nonlinear propagation effects within the amplifier and nonlinear optical damage may become a limitation. The invulnerability of CRPI to SPM demonstrated in Fig. 9 also indicates that CRPI may be used in applications that require a long distance between the resonator and the electro-optical components of the system. For example, when immunity to EM interference is sought, placing the electro-optical components far from the EM source is desired since such components may be susceptible to EM interference, whereas the optical resonator, being a passive optical device, is immune to them.

The current version of CRPI may be extended to interrogate multiple resonators by exploiting the large bandwidth of the source. For example, one may split the output of the source (after the 95/5 coupler in Fig. 1) to several outputs, each with its own resonator. In such a scheme, the bandwidth of the optical filters in Fig. 1 may be increased to cover all the resonances, which may be found at non-overlapping spectral bands. For each resonator, a demodulator should be used, which may be based on active stabilization as in Fig. 1, or on a passive scheme that may be economically implemented with photonic circuits, as discussed in [31].

The new scheme for CRPI may be particularly useful for high-resolution optoacoustic imaging based on high-frequency ultrasound detection. While our scheme achieved shot-noise-limited detection for frequencies up to 50 MHz, from Nyquist sampling theorem it follows that the 250 MHz repetition rate of the laser enables ultrasound detection with bandwidths up to 125 MHz. Shot-noise-limited detection may be extended to the entire 125 MHz bandwidth if photodetectors with lower noise and higher bandwidth are used.

Funding

Israel Science Foundation (ISF) (694/15, 942/ 15); Volkswagen Foundation (ZN3172); EVPR fund at the Technion.

Disclosures

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

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Ultrasound detection via low-noise pulse interferometry using a free-space Fabry-Pérot

Abstract

1. Introduction

2. Experimental setup

2.1 Interferometric system

2.2 Coherence-restoring filter (CRF)

3. Results

3.1 CRF performance

3.2 Interferometric-system characteristics

3.3 Non-linear propagation effects

4. Discussion

Funding

Disclosures

References and links

Cited By

Figures (9)

Equations (8)

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