Optical length change measurement via RF frequency shift analysis of incoherent light source based optoelectronic oscillator

Xihua Zou; Ming Li; Wei Pan; Bin Luo; Lianshan Yan; Liyang Shao

doi:10.1364/OE.22.011129

1. Introduction

Since optical length change is usually determined by the variation in refractive index, temperature, strain, displacement or distance, it is one of the essential parameters to be measured in the sensing field and other applications. Therefore, a large variety of sensors or systems for optical length change measurement have been designed and implemented, including for instance Mach-Zehnder/Michelson/Sagnac interferometers, fiber gratings, optical rings or micro-rings, and Fabry-Perot cavities [1–5].

Recently, the optoelectronic oscillator (OEO) is regarded as one promising solution for the measurement of optical length change. An OEO is an optoelectronic hybrid oscillating loop consisting of optical and electrical links, where the optical energy is converted into radio-frequency (RF) or microwave oscillation signals. At the very beginning, the OEO is proposed for generating high-frequency microwave signals which are characterized by low phase noise [6,7]. Then a series of reports regarding enhanced OEOs have been released. In [8–10], by using the injection locking or an intra-loop Fabry-Perot etalon, the frequency stability of OEOs has been improved. While in a coupled OEO [11], the phase noise of generated microwave signals can be reduced to be extremely low, approaching −160 dBc/Hz at 10 KHz offset. With the help of tunable microwave photonics filters, OEOs having continuously tunable oscillation frequency are designed to enlarge the frequency coverage [12–14]. Especially, in [15] a sliced broadband light source was employed to generate microwave signals with high spectral purity, while the derived phase noise was lower than −120 dBc/Hz at 10 KHz offset. Frequency-doubling or frequency-quadrupling are also implemented [16–19], with the limit on high-frequency narrow electrical filters relieved. In addition, OEOs have already found applications in new fields. In [20–25], the optical clock recovery and the generation of optical pulses or optical frequency comb have been realized using the OEO structures. Microwave or optical measurement can be performed as well, such as RF signal channelization [26–28], optical frequency stability measurement [29], and refractive index measurement [30]. After reviewing these new applications of OEOs, it is known that there would be a large space for significant parameters measurement, such as the measurement of optical length change.

In this paper, a novel OEO-based approach is proposed to measure optical length change. The optical length under test is inserted in the optical links of an OEO where an incoherent light source [e.g. amplified spontaneous emission (ASE) in this paper] is employed. The optical length change is measured from the frequency shift of RF oscillation modes. Two different experimental configurations are established for the optical length change measurement, with a linear relationship between the frequency shift and the optical length change obtained. Such an approach extracts the information of the optical length change in the way of electrical frequency analysis, neither intensity information nor optical frequency analysis, resulting in high resolution, stable measurements immune to time-variable or spatial-variation loss of the links. It should be highlighted that the use of an ASE, rather than a laser source, might relieve the complexity and the cost for stabilization control of light source, as well as the power consumption. Meanwhile, a reconfigurable measurement sensitivity is provided by selecting different oscillation modes, for different application requirements.

2. Measurement principle

The proposed OEOs for the measurement of optical length change are illustrated in Fig. 1. The first OEO is comprised of an incoherent light source, an electro-optic modulator (EOM), an optical link with an optical length of $L$ , and an electrical link, as shown in Fig. 1(a). The second one shown in Fig. 1(b) consists of two optical links which are $L_{1}$ and $L_{2}$ in optical length. The optical length, $L_{2}$ , is inserted into a fiber loop which is connected with the optoelectronic hybrid loop via a 3-dB optical coupler. The light of the incoherent source is modulated by the RF signals in the EOM and then is injected into the optical links. After opto-electronic conversion, the RF signals are recovered and divided into two parts; one part returns to the EOM and the other is extracted for measurement purpose. When the net gain of the hybrid loop is large enough, optical or RF oscillation signals will occur. In both OEOs, the frequency of the RF signals is determined by the total lengths of the hybrid loop and of the fiber loop. As the length of the electrical links is assumed to be constant here, the change in optical lengths, such as $L$ , $L_{1}$ and $L_{2}$ , can be measured from the frequency shift of the RF oscillation signals. It is noted that the optical length in this paper is defined as the product of the physical length and the refractive index. For instance, the optical length is the product of its physical length and its refractive index in optical fiber, or just the displacement or the distance in air/vacuum.

Fig. 1 Proposed incoherent source based OEOs for the measurement of optical length change. Black lines and red lines indicate the optical links and the electrical links, respectively. (ILS, incoherent light source; EOM, electro-optic modulator; PD, photo-detector; C, electrical coupler; Am: electrical amplifier).

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Mathematically, the transmission response of the first OEO shown in Fig. 1(a) can be expressed as

H (f) = \frac{1}{1 - G \exp (- 2 π f τ)}

where

f

is the RF frequency,

G

is the gain of the optoelectronic hybrid loop,

τ = L^{'} / c

is the single-pass time delay of the hybrid loop,

L^{'}

is regarded as an equivalent optical length in vacuum, and

c

is the light velocity in vacuum. Consequently, among the RF signals, the frequency of the k-th oscillation mode can be derived as

f_{k} = f_{0} + k c / L^{'}

where

f_{0}

is related to the bias condition of the EOM [26], and

k

represents the order of the oscillation mode. We recall that the length of electrical links keeps unchanged and only the change of the optical length is taken into account. Subsequently, from Eqs. (1) and (2), the relationship between the optical length change and the RF frequency shift is written as

Δ f_{k} = - \frac{k c}{{(L^{'})}^{2}} Δ L

where

Δ f_{k}

is the RF frequency shift, and

Δ L

is the optical length change of interest.

Equation (3) reveals a linear relationship under the perturbation condition when the optical length change is regarded as a perturbation. Thus the optical length change can be derived by measuring the frequency shift of the RF signals and the measurement sensitivity can be flexibly adjusted by choosing a customized oscillation mode of the RF signals. Here the optical length change might be induced by one or several parameters, such as temperature, strain, or displacement.

As for the second OEO shown in Fig. 1(b), two optical links are presented and their optical lengths jointly determine the frequency of the oscillation signals. The transmission responses can be expressed as

H_{1} (f) = \frac{2}{2 - G_{1} \exp (- 2 π f τ_{1})}

H_{2} (f) = \frac{1}{1 - H_{1} (f) G_{2} \exp (- 2 π f τ_{2})}

where

H_{1} (f)

and

H_{2} (f)

are the transmission responses of the fiber loop and the hybrid loop,

G_{1}

and

G_{2}

,

τ_{1}

and

τ_{2}

are the gains and the single-pass time delays of the two loops, respectively. The frequency of the k-th oscillation mode,

f_{k}

, corresponds to the transmission peaks of Eq. (5). Likewise, the optical length change,

Δ L_{1}

or

Δ L_{2}

, can be considered as a perturbation, compared with the lengths of the fiber loop and the hybrid loop. The oscillation condition always holds under the perturbation condition, such that the frequency shift can be simplified. When one of the optical lengths suffers a perturbation and the other remains fixed, we have

Δ f_{k 1} \propto - \frac{k_{1} c}{{({L^{'}}_{1})}^{2}} Δ L_{1}

Δ f_{k 2} \propto - \frac{k_{2} c}{{({L^{'}}_{2})}^{2}} Δ L_{2}

where

{L^{'}}_{1}

and

{L^{'}}_{2}

,

k_{1}

and

k_{2}

,

Δ f_{k 1}

and

Δ f_{k 2}

, are the total lengths, the order of the selected oscillation modes, and the frequency shifts of the hybrid loop and the fiber loop, respectively. In Eqs. (6) and (7), a linear expression is established between the frequency shift and the optical length change as well. In other words, the RF frequency shift is proportional to the optical length change (i.e.,

Δ L_{1}

or

Δ L_{2}

) under the perturbation condition.

In both OEOs above, the optical length change is monitored via the frequency shift or frequency coding of RF oscillation signals. Firstly, owing to the available high-resolution frequency analysis in electrical domain, high sensing resolution for optical length change would be resulted in a cost-effective way by using the proposed OEOs, compared with the use of optical frequency analysis in the optical domain. The use of frequency shift or frequency coding also makes the measurement immune to the loss variation or the amplitude change in the OEO configurations. Secondly, from Eqs. (3), (6), (7), different oscillation modes can be selected as target for optical length change measurement, such that multiple different sensitivities are available, providing reconfigurable sensing sensitivity for different application requirements. Moreover, in comparison with the use of a laser in a regular OEO, the use of incoherent light source in the measurement system also cuts the cost on the light source, while the sensing sensitivity and the phase noise performance are good enough for measurement applications.

3. Experiments

Measurement experiments for the proposed approach using OEO will be performed in this section. The setup for the first OEO shown in Fig. 1(a), is present in Fig. 2. An ASE source is employed and an optical variable delay line (OVDL) is inserted into the hybrid loop to emulate the change in the optical length. At the output of the OEO, a number of oscillation modes are generated and the corresponding spectrum is illustrated in Fig. 3.

Fig. 2 Experimental setup for the first OEO in Fig. 1(a). Black lines and red lines indicate the optical links and the electrical links, respectively. (ASE, amplified spontaneous emission; Pol, polarizer; MZM, Mach-Zehnder modulator; EDFA, Er-doped fiber amplifier; OVDL, optical variable delay line; PD, photo-detector; C, electrical coupler; Am: electrical amplifier)

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Fig. 3 Spectrum of RF oscillation signals measured in the experiment setup in Fig. 2.

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As we tune the OVDL step by step, it is known from Eq. (3) that all RF oscillation modes will experience frequency shift and each mode has a unique frequency shift slope or sensing sensitivity. For instance, the first oscillation mode around 29 MHz is chosen for measurement demonstration and the results are shown in Fig. 4(a), wherein $k = 1$ according to Eq. (3). The spectrum of the selected mode is plotted in the left inset of Fig. 4(a) when the optical length change is 3 cm, from which the RF frequency is derived as 29.056 MHz. By tuning the OVDL, we can derive a number of RF frequencies that reflect different optical length changes. Consequently, an excellent linear relationship between the frequency shift and the optical length change within the range of 0~10 cm is observed and the sensing sensitivity of is derived as −28 KHz/cm. For more details, in the right inset of Fig. 4(a), a zoom-in view for the range of 0~2 cm is present and the local linear relationship agrees well with the total linear relationship. From the mode spacing close to 30 MHz shown in Fig. 3, a measurement range up to 100 cm can be achieved. To keep an excellent linear relationship, the perturbation condition is fulfilled in the measurement range of 10 cm.

Fig. 4 Relationship between the frequency shift and the optical length change for the oscillation modes around (a) 29MHz and (b) 490MHz.

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Then we move to another oscillation mode. As $k = 17$ , the corresponding spectrum of the selected mode at 490.6411 MHz is present in the inset of Fig. 4(b) while the optical length change is set as 2.8 cm. After obtaining a number of such RF frequencies, a linear relationship between the frequency shift and the optical length change is achieved as well and plotted in Fig. 4(b). Here the sensitivity is increases to −480 KHz/cm. It is noted that, although linear relationships are observed for the two selected modes, the sensitivity of −480 KHz/cm at the mode around 490 MHz is about 17 times greater than the one of −28 KHz/cm at the mode around 29 MHz. This indicates that a reconfigurable sensitivity will be available for many measurement/sensing scenarios by setting different oscillation modes, which has been already predicted in Eq. (3).

For a purpose of comparison, the ASE in the Fig. 2 is replaced by a tunable single-frequency laser source. At the output of the OEO, the RF oscillation signals are tested and shown in Fig. 5. The derived frequency shifts versus the optical length changes are then illustrated in Fig. 6 and a zoom-in view is shown in the inset, indicating a total measurement range of 0~10 cm and a local range of 0~2 cm. It is clear that a linear relationship with a slope of −28 KHz/cm is obtained, which corresponds to a sensing sensitivity of −28 KHz/cm. Thus, compared with the use of a laser source, the use of an ASE is also able to realize the same measurement performance and an identical measurement sensitivity.

Fig. 5 Spectrum of oscillation signals measured in the case of using a laser source.

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Fig. 6 Relationship between the frequency shift and the optical length change with the use of a laser source.

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Also, the phase noise spectra of the two cases using ASE and using laser source are measured for the purpose of comparison. A similar reduction trend in the two phase noise spectra is observed for the same oscillation mode. At the 10-KHz and the 100-KHz offsets, the phase noise obtained using ASE is 5 dB higher than that achieved using laser source. Such a small phase noise difference between two cases exerts little influence on the optical length change measurement using frequency shift analysis. In addition, it is noted that the measured phase noise performances in the two cases are not as good as those in the microwave signal generation approaches [8–14,16–18] which were designed for high-spectral-purity microwave signal generation.

Next, the experimental setups for the second OEO shown in Fig. 1(b) are illustrated in Fig. 7. From Eqs. (4) and (5), the introduction of the fiber loop into the optoelectronic hybrid loop could enlarge the mode spacing of the RF oscillation signals. Subsequently, a larger measurement range will be offered. The spectrum of the RF signals is recorded and illustrated in Fig. 8, where an increased mode spacing of 84.2 MHz is formed. Meanwhile, according to Eq. (6), the linear relationship between the frequency shift and the optical length change still holds under the perturbation condition.

Fig. 7 Experimental setups for the second OEO shown in Fig. 1(b) with optical length change in (a) $L_{1}$ and (b) $L_{2}$ . (ASE, amplified spontaneous emission; MZM, Mach-Zehnder modulator; EDFA, Er-doped fiber amplifier; OVDL, optical variable delay line; PD, photo-detector; C, electrical coupler; Am: electrical amplifier)

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Fig. 8 Spectrum of the oscillation signals obtained from the experimental setup in Fig. 7(a).

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As we adjust the OVDL to emulate the optical length change in $L_{1}$ , the first oscillation mode around 67 MHz is selected for demonstration and the corresponding spectrum is shown in Fig. 9 and its inset. The distribution of the frequency shift versus the optical length change is then given and a linear relationship with a sensitivity of −13 KHz/cm is achieved. Meanwhile, the corresponding phase noise spectrum is also measured, and a value of −80 dBc/Hz is achieved at 10 KHz offset. This phase noise is much close to that achieved using laser source, indicating that excellent phase noise performance for measurement applications can be obtained in the second OEO shown in Fig. 1(b) as well.

Fig. 9 Relationship between the frequency shift and the optical length change in $L_{1}$ .

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Further, the OVDL is moved into the fiber loop to emulate the optical length change in $L_{2}$ . Likewise, when the oscillation mode around 57 MHz is chosen, the obtained frequency shifts are illustrated in Fig. 10 and a sensitivity of −14 KHz/cm is achieved, showing a linear relationship in line with the prediction of Eq. (7).

Fig. 10 Relationship between the frequency shift and the optical length change in $L_{2}$ .

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Up to now, using the proposed OEOs, the optical length change measurement has been experimentally performed via the frequency shift analysis of the RF signals, owing to the linear relationship between the optical length change and the frequency shift. Moreover, the use of an incoherent source yields identical measurement results and sensing sensitivities, and similar phase noise performances, compared with that achieved by using a laser source. For instance, an identical measurement sensitivity of −28 KHz/cm was derived for OEOs using ASE and laser source. Similar phase noise spectra were observed, with only a 5-dB degradation to the phase noises at the 10-KHz and the 100-KHz offset frequencies in the ASE-based OEO. The phase noise performance also can be verified from the results in [31] where an OEO configuration using ASE and fiber loops was implemented. Therefore, the use of an ASE not only provides similar measurement specificaitons, but also relieves the complexity and the cost for stabilization control of optical source for measurement applications.

Additionally, the measurement experiments would suffer from the environmental instabilities, such as temperature and vibration. As the experiments were performed under a relative stable room temperature, the selected oscillation mode experiences little frequency shift as the loop length is fixed. This operation stability can be indirectly confirmed from the linear variation between the frequency shift and the optical length change in Fig. 4.

4. Discussions

In the experiments in Section 3, the VODL is adopted as the emulator for the optical length change such that the physical length of the optical links is adjusted. Actually, the optical length change can defined as the produce of the physical length change of optical links and the change in refractive index. All factors that would result in changes in physical length or refractive index can be measured using the proposed OEOs, such as the displacement, the strain, the temperature, the refractive index, and so on. Here, we take the measurement of the displacement in air for demonstration, while the refractive index is assumed to be 1 and the displacement can be exactly regarded as the optical length change in OEOs. When the first oscillation mode is selected for frequency analysis, a sensitivity of −28 KHz/cm, −13 or −14 KHz/cm has been obtained in the first OEO and the second one, respectively. When higher order oscillation modes are selected, the measurement sensitivity will be further enhanced, such as −480 KHz/cm for the oscillation mode around 490 MHz. In this way, a comparable sensitivity as that in [30] can be achieved if a oscillation mode at 3 GHz is employed for measurement. Here, the use of low-order oscillation mode is beneficial in twofold. For one thing, only low-frequency modulator, photodetector, and spectrum analyzer or setups are needed, making the measurement cost-effective for practical applications. For another, a relative larger measurement range (i.e., FSR) can be provided as 30 MHz or 84.2 MHz (see Figs. 3, 5, and 8), compared with the 8.367-MHz measurement range in [30].

In addition, in our experiments, a spectrum analyzer (R&S FSV) with a frequency resolution of 0.01 Hz is used. Therefore, in theory, a resolution to displacement measurement is estimated to be 3.57 nm in the first OEO configuration, 7.69 and 7.14 nm in the second one. If a spectrum analyzer with a finer resolution bandwidth (RBW) is used, higher measurement resolutions can be achieved.

5. Conclusion

Incoherent light source based OEOs were proposed for the optical length change measurement. Two configurations for the OEOs were established, one with a single hybrid loop and the other having a fiber loop and a hybrid loop. In both OEOs, a linear relationship between the frequency shift and the optical length change was theoretically predicted. By analyzing the frequency shift of the selected oscillation mode, the optical length change was estimated. In the first OEO without fiber loop, the predicted linear relationship was experimentally confirmed via the frequency shift analysis of two oscillation modes at 490 and 29 MHz. Measurement sensitivities of −28 and −480 KHz/cm were observed respectively, indicating a reconfigurable sensitivity. For the second OEO with a fiber loop, linear relationships with a sensitivity of −13 and −14 KHz/cm were obtained. Compared with the use of a laser source, the use of ASE source enabled identical linear measurement relationship, sensing sensitivity, and similar phase noise performance for measurement applications. More importantly, the proposed measurement approach using incoherent source based OEOs has the advantages of low cost, high resolution, reconfigurable sensitivity, and immunity to power variation in electrical and optical links.

Acknowledgment

The work was supported in part by the National Natural Science Foundation of China (61378008), the 973 Project (2012CB315704), the Research Fund for the Doctoral Program of Higher Education of China (20110184130003), and the Program for New Century Excellent Talents in University of China (NCET-12-0940).

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Optical length change measurement via RF frequency shift analysis of incoherent light source based optoelectronic oscillator

Abstract

1. Introduction

2. Measurement principle

3. Experiments

4. Discussions

5. Conclusion

Acknowledgment

References and links

Cited By

Figures (10)

Equations (7)

Optics Express