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Abstract
The possibility to perform distributed measurements of the effective refractive index difference between distinct modes in few mode optical fibers is demonstrated using phase sensitive optical time domain reflectometry. Effective refractive index differences between LP02, LP21a and LP21b modes are measured with for a spatial resolution of 24m.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical time domain reflectometry (OTDR) is the most common inspection technique used to detect failures in deployed optical fiber networks. Researchers who proposed OTDR for the first time recognized the potential of the technique, but its importance in sustaining passive optical networks was hard to predict back in the 70s [1]. OTDR measurement provides information about spatially resolved optical attenuation which allows events such as fiber breakage, bad splicing, connectors, or splitters to be identified. OTDR is relatively insensitive to more subtle disturbances such as temperature/strain variations or fiber birefringence. To measure these quantities, coherent optical time domain reflectometry (C-OTDR) was proposed [2]. This technique, in comparison to classical OTDR, uses a coherent, tunable light source and measures similarity [3] between the fiber time domain response, called a trace, before and after the induced change. Moreover, it is possible to modify the original C-OTDR setup to measure, for example, the birefringence of birefringent optical fibers [4], optical fiber shape using multicore fibers [5,6], detect seismic waves [7] or perform measurements on multimode fibers [8]. The examples presented, represent only a few amongst many permutations of C-OTDR based sensing techniques [9,10] that can be utilized with new, potential applications that are still arising.
One of the properties of optical fibers that had thus far remained unmeasured in a distributed manner was the intermodal effective refractive index difference in multimode and few mode fibers. The major difference between distributed birefringence measurements and intermodal measurements is the mode spatial distribution that is almost identical in the case of single mode birefringent fibers. In the case of a single mode optical fiber, one can expect that the wavelength shifted C-OTDR wavelength scan will produce identical trace spectra due to the same distribution of scattering points interacting with the incident wave. In the few mode fiber case, the mode spatial distribution varies from mode to mode which means that the light effectively “sees” the different scattering centers and the traditional one dimensional model [11] of scattering centers is no longer valid. The scattering centres are physically positioned identically for all modes, but their relative contribution for the light propagating in distinct modes is clearly different. The phase cumulated by the light backscattered from 2 given scattering centres will depend on the effective indices of the incident and collecting modes. As a result, the correlation of signals originating from spatially different modes will no longer produce straightforwardly comparable traces and therefore statistical analysis is required. In this paper, we show that even though the scattering characteristics of different modes are not identical after a laser frequency change, the statistical average of the maximum cross correlation values is matched with differences in the effective refractive indices of the modes.
Since few mode fibers [12,13] are one of the most promising transmission media that may allow the world capacity record to be broken [14], it can be predicted, with a reasonable degree of certainty, that they will be deployed on the field. This means that potential tools for an in depth characterization of this new type of fiber may prove useful - for example, for the precise spatially resolved differential group delay (DGD) measurements, that are potentially needed to provide the level of complexity required for Multiple Input Multiple Output algorithms [15], or for reducing the cross sensitivity of optical fiber sensors due to the potential accessibility of many independently changing variables under external perturbation. Proposed technique is applicable for measurements of effective refractive indexes but is not capable of performing absolute values measurement which is an inherent property of wavelength scanned C-OTDR system.
2. Theoretical prediction
In order to predict the expected frequency shifts needed to cross correlate traces from different groups present in the examined fiber, we have built a fiber numerical model with refractive index distribution presented in Fig. 1
The fiber model is based on the finite-element method and assumes a 25 µm core diameter with a maximum refractive index difference of Δn = 0.01 for a 1550 nm wavelength with a parabolic refractive index distribution. The core is surrounded by a trench of Δn=−0.005 with a width of 6 µm. The distance between the core and the trench area is equal to 1.5 µm. The refractive indices of the points in the fiber core are calculated using the Sellmeier equations and take into account the chromatic dispersion [16]. The resulting effective refractive indices differences are used to calculate the theoretical frequency shift Δf needed to correlate the mode pairs. We can expect C-OTDR trace matching when following equation is satisfied:
where ${n_{LPn1}}$ is effective refractive index for first mode at wavelength equal to ${\lambda _1}$, ${n_{LPn2}}$ is effective refractive index for second mode at wavelength ${\lambda _2}$. In our calculations we assume that ${\lambda _1}$ is equal to 1550 nm. To calculate spectral shift $\mathrm{\Delta }f$ following equation is used:
Table 1. Theoretical C-OTDR frequency shifts between mode groups in examined few mode fiber bolded numbers indicate mode pairs that are a subject of further analysis. Reference mode is given in column and is assumed to be measured at 1550 nm.
3. Experimental setup
The scheme of the setup is shown in Fig. 2(a)) [17]. A DFB laser operating at a central wavelength of 1550 nm is used as a light source. By changing the operating current of the laser, we tune the central frequency up to 20 GHz in steps of 75 MHz. Using a pulse generator, a 4 ns optical pulse is generated with an extinction ratio of more than 50 dB, which is more than sufficient for measurements of 1 km of fiber and corresponds to a 40 cm spatial resolution of the system. To increase the pulse power, an erbium doped fiber amplifier (EDFA) is inserted. Then the pulse goes through a mode multiplexer, which enables a single mode to be selectively excited in a few-mode fiber with a selectivity better than 15 dB and an average insertion loss of 3.5 dB. The generated pulse is sent in the LP01 mode of the fiber under test (FUT). The examined fiber is a 1 km long few-mode-fiber with cross section presented in Fig. 1. At each point of the FUT, the propagating pulse is partially scattered into all modes that are guided by the fiber and propagates backwards [18]). The FUT is stabilized in a water bath to reduce the influence of environmental perturbations such as vibrations or random temperature changes. By using a pair of optical switches, it is possible to select a signal backscattered into chosen higher order modes. In this experiment, modes LP21a, LP21b, LP02 have been measured because, according to Table 1, the expected frequency shifts from these modes can be potentially measured using a 20 GHz frequency scan range. The spatial distributions of all the measured modes for a particular fiber are presented in Fig. 2(b), (c), (d) respectively. The returning signal is then amplified by a second EDFA. After the amplifier, a tunable filter with a bandwidth of 1 nm is used to filter out the amplified spontaneous emission. The filtered signal is measured by a DC-coupled photodetector with a 1 GHz bandwidth and digitized by a 4 GHz bandwidth oscilloscope with a sampling rate of 5 GSamples/s.
Fig. 2. Experimental setup. PC - polarization controller, PG – optical pulse generator, EDFA – erbium doped fiber amplifier, MUX – Mode Multiplexer, FMF – few-mode fiber, OS-optical switch, PD – photodiode. Spatial distribution of b) LP02, c) LP21a, d) LP21b
To verify the performance of the assembled setup we calculated the visibility of the obtained time domain trace according to the following formula:
where Imax and Imin are respectively the maximum and the minimum intensity of the trace [19]. The visibility is calculated using a 40 m calculation window which corresponds to 100 spatial resolutions. The sample data obtained from acquiring a backscattered signal for LP02, LP21a and LP21b from one pulse launched into mode LP01 is presented in Fig. 3. Measured traces are quasi random in nature and there is no simple similarity between them even though they originate from the same pump pulse with exactly the same wavelength. This proves that each trace has its origin from differently distributed scattering centers in an optical fiber. Such behavior is expected due to a different spatial overlap of incident light field and distribution of scattering points in cross section of any arbitrary fiber. In all cases the visibility is above 0.9 which means that the measurement system is working properly and information contained in the C-OTDR trace can be used for wavelength scanning C-OTDR [20]. Only at the beginning of the fiber the visibility is lower due to a strong reflection from the mode multiplexer.Fig. 3. Example of the measured time trace for LP02, LP21a and LP21b modes under LP01 excitation (blue line) and the calculated visibility of the traces (red line).
4. Results
To obtain the difference in effective refractive index between the measured higher order modes, the cross-correlation spectrum at every sampling point along the fiber is calculated. The cross correlation between two frequency scans for a signal scattered to the same mode LP02-LP02 results in a clearly visible maximum at a 0 GHz frequency shift, which can be seen in Fig. 4(a)). When performing the same operation on signals originating from different modes, one can observe at first glance, quasi random cross correlation values with a maximum centered at 0 GHz due to the cross-correlation window envelope. The quasi-random cross-correlation spectra for LP21b-LP02, LP21a-LP02 and LP21a-LP21b are presented on Fig. 4(b)), Fig. 4(c)) and Fig. 4(d)) respectively. Second given mode is a reference. Observed randomness of cross-correlation spectra is caused by the fact that each mode has substantially different spatial distribution and thus interacts with different scattering points distribution perpendicular to the light propagation direction. In the case of few mode fiber, one can’t expect perfect trace matching because only a fraction of refractive index fluctuations (parallel to the propagation direction) are common for all modes. This is a major difference comparing to single mode C-OTDR scenario when fluctuations of refractive index perpendicular to the light propagation does not play a role Performing further analysis of the intermodal cross-correlation spectra, we define the coefficient κ as the average of the cross-correlation value which can be expressed by equation:
Fig. 4. Cross correlation values as a function of spectral shift and fiber distance for a) LP02-LP02 b) LP21b-LP02, c) LP21a-LP02 and d) LP21a-LP21b mode pairs. Second given mode is a reference.
Fig. 5. Average normalized cross correlation value over entire fiber span for for a) LP02-LP02 b) LP21b-LP02, c) LP21a-LP02 and d) LP21a-LP21b mode pairs. Second given mode is a reference.
A comparison of theoretical values with experimental ones is presented in Table 2. The 0.06 GHz frequency shift present for LP02 - LP02 and LP21a-LP21b can be associated with slight (<0.3 K) temperature variations between consecutive measurements. The measured spectral shift between LP21b-LP02 and LP21a-LP02 is in line with the expectations presented in Table 1. Table 2 also presents calculated difference in effective refractive index (Δneff) and DGD as an example of useful output information resulting from proposed technique.
Table 2. Comparison of experimental and theoretical frequency shifts needed to correlate backscattered signals from different modes
In this particular case (Fig. 5 and Table 2) we used the whole fiber length for the calculation of κ; however, it is possible to choose any arbitrary calculation window to resolve the distributed information about the intermodal effective refractive index difference and the corresponding frequency shift variations. Decreased spatial window for calculation of κ results in an increased standard deviation. The relation between the number of spatial resolutions taken for the calculation of κ and the calculated spectral shift is presented in Fig. 6. The error bars indicate one standard deviation of κ.
Fig. 6. Average spectral shift calculated using κ parameter as a function of spatial resolutions used for calculations. Error bars indicate standard deviation for κ. LP21b is a reference mode.
According to Fig. 6, one can conclude that the standard deviation of κ decreases rapidly with the number of spatial resolutions up to the value of 60 spatial resolutions. Rapid decrease of standard deviation with a number of samples taken into calculation is typical statistical property and can be explained by Central Limit Theorem. Therefore, we chose 60 optical spatial resolutions as a calculation window. In this case, each point for cross correlation calculation has 40 cm of optical spatial resolution. As a result, the measurement demonstrated in Fig. 7 has 24 m spatial resolution ($L1 - L2 = 24\textrm{m}$ according to Eq. (2)). Standard deviation for 24 m calculation window is 0.35 GHz. The results are presented in Fig. 7. Black line represents measured maximum value of κ.
Fig. 7. Spatially resolved intermodal spectral shift calculated using κ and 60 spatial resolutions calculation window for a) LP02-LP02 b) LP21b-LP02, c) LP21a-LP02 and d) LP21a-LP21b mode pairs. Second given mode is a reference. Black line represents measured maximum value of κ.
A direct comparison of Fig. 4 and Fig. 7 shows that simple statistical analysis of intermodal cross correlation can result in a reliable measurement even though the traces are hardly comparable at first sight. Potential effects of intermodal crosstalk can be associated with occasionally measurable double maximum of κ especially visible in Fig. 7(c)) at the 200 m-300 m fiber section. Detailed difference between local cross correlation spectrum (blue line) and κ coefficient (black line) calculated at 812 m of the fiber is presented in Fig. 8. While the cross-correlation spectrum does not indicate any clear peak, the κ coefficient is clearly distinguishable. As the scattering points “seen” by different modes do not share the same distribution perpendicular to the light propagation and only the parallel distribution is common, the statistical approach is necessary to extract useful information.
Fig. 8. Comparison between cross correlation spectrum (blue line) measured at 812 m and κ coefficient (black line) calculated from fiber segment starting at 800 m and finishing at 824 m
A downside of this statistical approach is reduction in the real spatial resolution of measurement. The exact relations between interrogating pulse width and necessary number of spatial resolutions that need to be averaged remains to be examined in the future.
5. Conclusion
We demonstrated that it is possible to measure the effective refractive index between modes in few mode optical fibers in a distributed manner. The measured spectral shift matches theoretical values and even though the modes have substantially different spatial distributions resulting in a reduced maximum cross correlation value, it is possible to statistically measure the spectral shift between the modes. The improvement of proposed technique, in terms of the number of modes that can be correlated, is potentially possible using larger scanning range of the laser source. Further study must follow to verify if it is possible to correlate very distinct modes in multimode fibers with reduced spatial overlap. One of the possible ways to corelate distinct modes is to use Optical Frequency Domain Reflectometry(OFDR) technique [21], which can offer tuning range in the order of tens of nanometers but with reduced sensing distance. Potentially, proposed technique opens a possibility to make tens of independent measurements from one fiber. Such feature may be used for multiparameter sensing using a few mode fiber as well as for in depth characterization of fiber uniformity.
Funding
Fundacja na rzecz Nauki Polskiej (NODUS, TEAMTECH); Narodowe Centrum Badań i Rozwoju (TECHMATSTRATEG1/348438/16/NCBR/2018).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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