An all-fiber optical heterodyne detection configuration was proposed based on an all-fiber acousto-optic structure, which acted as both frequency shifter and coupler at the same time. The vibration waveform within a frequency range between 1 Hz to 200 kHz of a piezoelectric mirror was measured using this optical heterodyne detection system. The minimal measurable vibration amplitude and resolution are around 6 pm and 1 pm in the region of tens to hundreds of kilohertz, respectively. The configuration has advantages of compact size, high accuracy and non-contact measurement. Moreover, it is of a dynamically adjustable signal-to-noise ratio to adapt different surface with different reflections in the measurement, which will improve the usage efficiency of the light power.
© 2015 Optical Society of America
Optical heterodyne detection is one of the main methods of optical coherent detection . Because of the advantages of much higher sensitivity and accuracy and stronger anti-interference ability than optical homodyne detection , optical heterodyne detection has been widely used in the fields of laser communication , heterodyne spectroscopy , infrared physics , laser gyroscope , radar , and so on. Besides the applications mentioned above, optical heterodyne detection has also been widely used in the field of vibration sensing such as precision mechanism monitoring  and hydrophone .
The kernel part of an optical heterodyne detection system is an optical frequency shifter which generates frequency shift and forms a carrier signal. Current configurations especially the optical frequency shifter are mainly based on a bulk optic Bragg cell  and integrated optical waveguide [11,12], which are of large size or need precise optical alignment with relatively large insertion loss. An all-fiber frequency shifter could avoid such difficulties spontaneously. Note that the first all-fiber acousto-optic frequency shifter was constructed based on a dynamic grating introduced by acoustic wave in a two-mode fiber (TMF) in 1986 . Although it can convert the LP 01 mode to the LP 11 mode and generate a frequency difference which is equal to the frequency of the propagating acoustic wave inside the fiber, it’s not suitable for the optical heterodyne detection. This is because both the two modes are in the core of TMF and it is relatively difficult to separate them completely . Therefore, a light beat will be generated, which will ruin the heterodyne measurement. Recently, we constructed an all-fiber acousto-optic tunable add/drop coupler based on single mode fiber (SMF). It can not only make the core mode LP 01 be coupled to the cladding mode LP 11 with a downshifted frequency, but also separate them and steer the LP 11 mode into the core of another SMF efficiently through evanescent wave coupling . In this way, the two components with a frequency difference can be separated efficiently into two SMFs, which makes it possible for all-fiber optical heterodyne detection. Moreover, the ratio of the two components can be optimized (see Fig. 3(a) in ) according to different situations (the reflection of measured surfaces), which will result in desirable signal-to-noise ratio (SNR)  in application while keep the efficiency of the usage of light power at the same time.
In this paper, we proposed a configuration of optical heterodyne detection with an all-fiber acousto-optic structure, which acts as both frequency shifter and coupler at the same time. In this configuration, SNR could be adjusted dynamically. The vibration within a frequency bandwidth between 1 Hz to 200 kHz of a piezoelectric mirror (PZM) was measured. The minimal measurable vibration amplitude and resolution are around 6 pm and 1 pm in the frequency region of tens to hundreds of kilohertz, respectively. The performances of the proposed optical heterodyne detection configuration are comparable to commercial vibrometers with the advantage of all-fiber configuration, which makes it more compact in size and could be applied in the compact and portable instruments based on optical heterodyne detection.
2. Principle and experimental configuration
The schematic configuration of the system is shown in Fig. 1. An all-fiber acousto-optic tunable add/drop filter acts as an acoustic-optic frequency shifter (AOFS) , which consists of an acoustic wave generation system and an unjacketed SMF. Applying a radio frequency (RF) signal on the piezoelectric transducer (PZT), an acoustic wave can be generated and then amplified at the tip of the horn-like acoustic transducer. The acoustic wave propagates along the unjacketed SMF and produces a dynamic micro-bend grating, which induces a mode coupling between the LP 01 and LP 1u modes when the phase matching condition 18], Cext =5760 m/s is the speed of the acoustic wave in silica, and fa is the frequency of the acoustic wave. As a result, the core mode LP 01 is coupled and converted to the LP 1u mode, which is downshifted in frequency by an amount equal to the acoustic frequency. Then, the light of LP 1u mode is coupled to the core mode of the TF through the evanescent wave . The coupling efficiency could be controlled by the driving power of the RF signal . Therefore, the AOFS can not only generate a frequency shift, but also act as a tunable light splitter (coupler) in this configuration.
When a laser beam is launched into the AOFS, it is divided into two parts with a frequency difference fa. One of the beams propagates along the unjacketed SMF without frequency shift. Via a fiber circulator, the beam is led out by a collimator at Port 2 to collect the vibration information of a vibrating object (a piezoelectric mirror (PZM) with resonance frequency of around a hundred of kHz in our experiment, see Fig. 1, which consisted of a mirror around 5 gram and a piezoelectric transducer) to be detected. The vibration will change the light path in the arm, and the reflected beam with the vibration information is led out from the circulator at Port 3 and then it will be combined with the light bearing a downshifted frequency fa in the other arm by a 3-dB coupler. In this way, light beats will be generated, and the beat signal is detected by a photodetector and recorded by an oscilloscope, respectively. Note the ratio of the two beams can be adjusted by changing the driving power of the RF signal applied on the AOFS, which can control the visibility of the light beat (see Fig. 3(a) in ) and thereby control SNR of the system to adapt different object with different reflections .
Assuming the two beams at the 3-dB fiber coupler before the photodetector are E 1(t) = A cos(2πf 1 t − φ 1) and E 2(t) = B cos(2πf 2 t − φ 2), the light beat can be given as I = |E 1(t) + E 2(t)|2 , where f 2 = f 1 − fa; A, f 1 and φ 1 are the amplitude, frequency and initial phase of E 1, respectively; B, f 2 and φ 2 are the amplitude, frequency and initial phase of E 2, respectively. When the light beat is detected by a photodetector with a photo-electric conversion coefficient β, the light beat used as carrier signal can be expressed as S(t) = βAB cos[2πfat − (φ 1 − φ 2)]. Usually, the initial phase difference φ 1 − φ 2 is assumed to be zero in the optical heterodyne detection, and then we obtainEq. (3).
Now, let us consider a simplest vibration u(t) = U sin(2πf 0 t) with only one Fourier component as an example, where U and f 0 are the amplitude and frequency of the vibration, respectively. Then the phase modulation signal of S(t) = βABcos[2πfat + 4πU sin(2πf 0 t)/λ] will produce a sequence of sidebands in frequency domain whose amplitudes are given by a set of standard Bessel function expansions [20, 21]
Under the condition 4πU ≪ λ, Eq. (4) can be approximately given asEq. (5) can be expressed as
From Eq. (6), it is clear that, when the vibration amplitude is much smaller than the light wavelength, the phase modulation signal will result in only three discrete frequency components fa − f 0, fa and fa + f 0, respectively.
In the experiment, an axial mode PZT with a resonant frequency around f = 1.0 MHz was applied to the AOFS. The unjacketed SMF was of a core radius ρco = 4.5 μm, a cladding radius ρcl = 62.5 μm, and a step-index Δ = 0.32%. In the AOFS, the outer diameter of the SMF was etched down to 29 μm by the hydrofluoric (HF) acid to adjust the resonant wavelength based on the phase matching condition and to enhance the overlap between the acoustic and the optical waves, and therefore, to increase the acousto-optic coupling efficiency of the acoustically induced dynamic grating . The length of the etched region was 50 mm. The TF with a uniform waist of 19 μm and a length of 15 mm was fabricated, and the transition zone of the TF was 30 mm. The uniform waist of the TF was attached along the etched SMF of the AOFS with a coupling length of LC = 10 mm. To increase the coupling efficiency of the evanescent wave, the coupling region was dipped into a refractive-index-matched liquid (n = 1.450) , where the acoustic wave was absorbed and therefore the acousto-optic interaction length LAO was limited to 40 mm. The whole coupling region was supported by a piece of MgF2 substrate with a lower refractive index of ∼ 1.37. One noticed that current structure is vulnerable because TF and the etched fiber were not solidly combined. However, the problem could be solved by sealing the whole coupling area on the MgF2 substrate by PDMS or melting two fibers together.
3. Experimental results and discussions
Before our measurement, the background noise of the system has to be measured to evaluate its measurement limit in the condition of PZM without driving voltage. With a RF driving signal of f = 0.9 MHz applied on the acoustic transducer, the mode coupling between the LP 01 and LP 11 modes at the central wavelength λ = 1550 nm was achieved and the light with a downshifted frequency f 1 − fa was led out via TF. By setting the two arms of the system be of the same optical path, the carrier signal was of good temporal stability. Meanwhile, the visibility of the carrier signal had also been optimized by adjusting the RF driving power and the polarization of the two beams. A typical optimized carrier wave signal, which was recorded with an oscilloscope (Tektronix DPO 7054, sampling rate: 10 MS/s, sampling time: 1 s), is shown in Fig. 2(a). Figure 2(b) is the Fourier frequency spectrum of Fig. 2(a) with a frequency bandwidth of 1 Hz, which shows that the carrier signal has only one frequency component of 0.9 MHz equal to the acoustic frequency fa with an acceptable SNR of ∼ 80 dB [24, 25]. By changing the driving power of the RF signal, SNR could be varied in a range of 70–110 dB. Figure 2(c) is the background noise spectrum of the system obtained by demodulating the carrier signal according to Eq. (3). As the frequency increases, the background noise decreases from 10 nm to 6 pm, which determines the minimal amplitude that can be measured by the system.
After the system was ready, we applied a sine electrical signal with f 0 = 90 kHz and a peak-to-peak voltage Vpp = 1.0 V to the PZM, and recorded the phase modulated signal with an oscilloscope. Figures 3 (a) and 3(b) are the waveform of the phase modulated signal carrying the vibration information of PZM and its Fourier frequency spectrum, respectively. It is seen that there are two new frequency components fa − f 0 and fa + f 0 on the two sides of the basic frequency fa as predicted by Eq. (6). The demodulated results (black circles) are shown in Fig. 3(c), which agrees well with the theoretical calculation (blue curve) with U = 0.09 nm and f 0 = 90 kHz.
By decreasing Vpp applied to PZM from 10.0 V to 0.1 V, the vibration amplitude of PZM was measured. The results are shown in Fig. 4(a). There is a good linearity between the vibration amplitude of PZM and the driving voltage with a slope of 0.1 nm/V. The vibration amplitude decreases from 0.900 nm to 0.009 nm with Vpp decreasing from 10.0 V to 0.1 V. As Vpp decreased further, the vibration from the driving signal was blended with the background noise. Therefore, the minimum measurable vibration of the current system is limited by the background noise (see Fig. 2(c)) and the minimum measurable vibration can be as small as ∼ 6 pm for our system (see the inset in Fig. 4(a)). The resolution is around 1 pm with the controlling voltage accuracy to be as small as 0.01 V, which is presented in the inset of Fig. 4(a). We also measured the frequency response of PZM at Vpp = 10.0 V together with its electric impedance. The black circles in Fig. 4(b) show different amplitudes as the driving frequency changes. The vibration amplitude of PZM decreases in general as the driving frequency increases. Meanwhile, the vibration amplitude becomes large at the resonant frequencies such as 37 kHz, 61 kHz and 156 kHz, as shown by the blue curve in Fig. 4(b), which is similar with the case reported in .
Besides the sinusoidal vibration, complicated waveforms and related displacements could also be measured. As proofs of the principle, the displacements induced by four special wave-forms with a frequency of 1.0 kHz and Vpp = 10.0 V applied on PZM were measured. The results are shown in Fig. 5, in which the demodulated displacement waveforms (black curves) show good agreement with the normalized waveforms of the driving signals (blue curves). Subsequently, we also measured the programmed displacements generated by a compact Multi-Axis Piezo Nanopositioning System with a positioning resolution of 0.2 nm (PI, P-611.3, driven by the NanoCube Piezo Controller PI-E503). By programming the output voltage, we can control the displacement of the stage, which were shown as the black curve in Fig. 6, and the measured displacements were shown as the blue curve. One can see that both curves are in good agreement with each other.
In conclusion, we proposed a configuration of optical heterodyne detection with an all-fiber acousto-optic structure, which acts as both frequency shifter and coupler at the same time. The mechanical vibration from 1 Hz to 200 kHz can be measured. The minimal measurable vibration and resolution can reach around 6 pm and 1 pm, respectively. The configuration is characterized with compact size, high accuracy and non-contact measurement. Moreover, it is capable to dynamically adjust the SNR to adapt different surface reflections in the measurement with high efficiency in the light power usage. With the coupling region sealed by PDMS or melted together and all parts of the structure sealed in a dust-proof shell, it will be useful in the compact and portable instruments based on optical heterodyne detection.
This work is financially supported by the 973 Programs ( 2013CB328702, 2013CB632703), the CNKBRSF ( 2011CB922003), the NSFC ( 11174153, 11404263, 61176085 and 61405161), the 111 Project ( B07013), the Natural Science Foundation of Tianjin ( 12JCQNJC00900), the Fundamental Research Funds for the Central Universities ( 3102015ZY060), and the International S&T Cooperation Program of China ( 2011DFA52870).
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