Distributed measurement and characterization of the intermodal beat length between LP01 and LP11 modes in an elliptical-core (e-core) two-mode fiber (TMF) are demonstrated by the analysis of Brillouin dynamic grating (BDG) spectra. The BDG is generated by the stimulated Brillouin scattering (SBS) of the LP01 mode and probed by the LP11 mode, with four different pairs of the spatial and polarization modes in the e-core TMF applied for the pump and the probe (LP01x-LP11y, LP01y-LP11y, LP01x-LP11x, and LP01y-LP11x). A mode selective coupler (MSC) is used for selective launch and retrieval of the LP01 and the LP11 modes in the BDG operation, and the local reflection spectra from the BDG are obtained by an optical time-domain analysis. A distribution map of the intermodal beat length is acquired for each pair of the pump-probe modes with a 1.5 m spatial resolution along a 75 m e-core TMF. Temperature- and strain-dependence of the BDG spectrum is also evaluated for each case.
© 2014 Optical Society of America
A two (spatial) mode fiber (TMF), which was researched for devices and sensors based on unique properties of LP11 mode [1,2], has recently attracted a renewed interest as a potential platform of mode division multiplexing (MDM) for optical communication systems [3–5]. An elliptical-core (e-core) TMF was developed to stabilize the lobe orientation of the LP11 mode [6–9] which is useful for several applications such as fiber sensors, tunable filters, and fiber lasers [10,11], and also applicable to a MDM transmission for the reduction of the modal cross-talk . An intermodal beat length (IBL) is one of key parameters characterizing two- or few-mode fibers, determined by the difference between effective (phase) refractive indices (ERI’s) of two spatial modes. A few techniques have been developed for measuring the IBL such as an acousto-optic tunable filter (AOTF), far-field interference, prism coupler, and Fabry-Perot cavity [13–16], however these methods can provide only the average value within a test fiber.
In this paper we propose and experimentally demonstrate the mapping of the IBL distribution along an e-core TMF based on Brillouin dynamic grating (BDG) operated by different spatial and polarization modes. The BDG is generated by the stimulated Brillouin scattering (SBS) of the LP01 mode (i.e. pump), and analyzed by the LP11 mode (i.e. probe), where four different pairs of the spatial and polarization modes in the e-core TMF are applied for the pump and the probe (LP01x-LP11y, LP01y-LP11y, LP01x-LP11x, and LP01y-LP11x). We show that the BDG spectra can provide the information of not only the IBL between the pump and the probe modes but also the birefringence of each spatial mode, implementing the full characterization of the modal structure in the e-core TMF. A mode selective coupler (MSC) is used for selective launch and retrieval of the LP01 and the LP11 modes in the BDG operations. The local reflection spectra from the BDG are obtained by an optical time-domain analysis which is conducted for each pair of modes with a 1.5 m spatial resolution along a 75 m test fiber. The evaluation of temperature- and strain-dependence of the BDG spectra is also performed, and the results show that the spectral shift of the BDG reflection appears with a slope ranging from −0.16 MHz/°C to 4.9 MHz/°C for temperature and from −0.089 MHz/με to −0.012 MHz/με for strain, respectively, depending on the polarizations of the pump and the probe.
The BDG represents an acoustic wave generated in the process of SBS which plays a role of moving index grating. In general, the BDG is operated in a polarization maintaining fiber (PMF) utilizing the birefringence between orthogonally polarized pump and probe waves, where the BDG is generated by counter-propagating pump waves in one polarization and used to reflect the probe wave in the orthogonal polarization. The frequency offset between the pump and the probe (called BDG frequency, νD) in the BDG operation is determined by the ERI difference between the two polarization modes, which is several tens of GHz in PMF’s . The BDG has proven to be useful for a variety of applications such as distributed sensing based on the birefringence variation, optical signal processing and microwave photonics [17–23]. Recently the operation of BDG in a circular-core few-mode fiber was reported by applying the ERI difference between the LP01 and the LP11 modes guided in the fiber .
In a circular-core fiber, the LP11 mode is an approximated mode composed of almost degenerate TM01, TE01, and HE21 modes. Since the intensity lobes of the LP11 mode is constructed by the interference of the TM01 (or TE01) mode and HE21 mode with slightly different propagation constants, the orientation of the lobes is not maintained in the propagation along the fiber. In an e-core fiber, on the contrary, the LP11 mode splits into two groups, i.e. LP11odd and LP11even modes, with considerably different ERI’s and well-defined and stable intensity patterns [6–9]. When the size and the ellipticity of the e-core are properly set, the LP11odd mode can be cut-off while the LP11even mode is still guided. This fiber is called an e-core TMF supporting two stable spatial modes, i.e. the LP01 and the LP11even modes [8, 25]. Since the e-core also produces internal birefringence, overall four spatial and polarization modes – i.e. LP01x, LP01y, LP11even x (or simply LP11x), LP11even y (or LP11y) – are guided in the e-core TMF .
In our work the BDG is generated by the SBS of the LP01 mode (pump1 and pump2) and analyzed by the LP11 mode (probe) of an e-core TMF as schematically shown in Fig. 1.A MSC composed of a single-mode fiber (SMF) and an e-core TMF is used for high-efficiency and selective launch and retrieval of each mode [25,26]. The frequency offset between the counter-propagating pump1 and pump2 is set to the Brillouin frequency (νB) of the LP01 mode in the TMF for the generation of the BDG. The probe is input to the SMF of the MSC in the LP01 mode to be exclusively coupled to the LP11 mode of the TMF, which is reflected by the BDG and coupled back to the LP01 mode of the SMF as the BDG reflection. The inset ‘A’ of Fig. 1 depicts the spectral positions of relevant waves. It is notable that the frequency offset between the probe and the BDG reflection is expected to be equal to the νB of the LP01 mode, the same as that between the pump1 and the pump2, determined by the frequency of the shared acoustic wave. Since the ERI of the LP11 mode is smaller than that of the LP01 mode, the optical frequency of the probe is set higher than that of the pump waves like the case of the BDG in a PMF [17, 24]. When n01(ν) and n11(ν) are the ERI’s of the LP01 and the LP11 modes, respectively, at an optical frequency ν, the BDG frequency νD is calculated as follows: The acoustic waves are shared in the SBS of the LP01 mode and the BDG reflection of the LP11 mode, so the phase matching condition for each process yields:Eqs. (1) and (2) we obtain the following equation:17, 24], the derivative terms multiplied by ν0 are dominant among the derivatives in Eq. (3). When the group index ng01 (ng11) of the LP01 (LP11) mode at ν0 is introduced and the derivative terms without ν0 are ignored, Eq. (3) is reduced to the following equation:Eq. (4), which leads to a simple relation between IBL (LB) and νD as follows:
Owing to the internal birefringence, the BDG operation in the e-core TMF can take place in four different pairs of the pump-probe modes according to the polarization (LP01x-LP11y, LP01x-LP11x, LP01y-LP11y, and LP01y-LP11x) as depicted in Fig. 2.The polarization-dependent splits of the ERI’s result in corresponding splits of the νD’s. Therefore one can find the ERI difference between any pair of optical modes from the difference of νD’s by Eq. (4), so investigate the modal structure along the fiber.
In experiments, we employed a measurement setup as shown in Fig. 3. Two distributed feedback laser diodes (DFB-LD’s) were used as light sources with the operation wavelength of 1550 nm for the pump and 1547 nm for the probe, respectively. The output of the pump LD was divided by a 50/50 coupler, and one of the output waves was modulated by an electro-optic modulator (EOM) and a pulse generator to generate a 50 ns rectangular pulse for pump1. The other output wave was modulated by a single sideband modulator (SSBM) and a microwave generator to prepare a continuous Stokes wave for pump2 with a frequency offset of νB from the pump1. The output from the probe LD was modulated by another EOM and the pulse generator to generate a 15 ns bell-shaped pulse for the probe. A polarization controller (PC) was used for each of the pump and the probe waves. Er-doped fiber amplifiers (EDFA’s) were used to control the power of the pump1 and the pump2 which counter-propagated in a fiber under test (FUT) to build the BDG by SBS. The peak power of the pump1 and the probe was about 24 dBm and 27 dBm, respectively, and the continuous power of the pump2 was 15 dBm. The probe pulse was propagated in the same direction as the pump1, and the time trace of the BDG reflection was recorded by a 125 MHz photo receiver and an oscilloscope through a fiber Bragg grating (FBG). The pulse propagation of the pump1 and the probe was synchronized with a 30 ns delay as depicted in the inset ‘A’ of Fig. 3 to maximize the signal amplitude, and the pulse repetition rate was 500 kHz. The pump1 and the pump2 were launched to the FUT in the LP01 mode through mode strippers (MS’s, by bending) removing the unwanted LP11 mode from the pump waves which is coupled at the splice point between the lead SMF and the FUT. The probe was launched in the LP11 mode through a MSC, following the schematic of Fig. 1. The coupling efficiency of the MSC was about 80%, and the mode extinction ratio of the LP11 mode to the LP01 mode in the probe wave of the TMF was about 23 dB. The measurement of the BDG spectrum was carried out by sweeping the frequency offset Δν between the pump1 and the probe with about 4 MHz step using the current control of the pump LD.
The FUT used in the experiment is a 75 m e-core TMF with the index difference Δ of 0.6%, the core radius of 5.5 μm x 3.5 μm, and the cladding diameter of 100 μm. The cut-off wavelength of the LP11odd mode is about 1500 nm. The νB of the LP01 mode was 10.614 GHz, and the ERI difference between the LP01 and the LP11 modes was about 3.6 x 10−3 estimated by an AOTF , which corresponds to about 480 GHz by Eq. (5) at a wavelength of 1550 nm with ng11 = 1.45.
First we roughly measured the spectral position of νD using an optical spectral analyzer (OSA) in front of the FBG. The BDG reflection was observed at Δν ~450 GHz as depicted in the inset ‘B’ of Fig. 3 in which the leakage of the continuous pump2 (i.e. the output from the SSBM) is seen together. In order to determine the sweep range of Δν in the acquisition of time traces we carried out a test measurement by sweeping Δν in the vicinity of 450 GHz (from 430 GHz to 470 GHz) while recording the time traces of the BDG reflection with the oscilloscope. We found out that the BDG reflection appeared in three different frequency regions of Δν centered nearly at 445 GHz (low), 449 GHz (middle), and 453 GHz (high) with the reflection amplitude strongly dependent on the polarization states of the pump and the probe waves. According to the theoretical expectation in Fig. 2, we thought that the low, the middle, and the high frequency regions correspond to the pump-probe combinations of LP01y-LP11x, LP01x-LP11x (and LP01y-LP11y), and LP01x-LP11y, respectively. In order to acquire proper spectra of the BDG reflection for each pair of the pump-probe, our time-domain measurements were carried out with following steps:
- All the PC’s (pump1, 2 and probe) are controlled to maximize the BDG reflection (i.e. time trace) at the high frequency region of Δν and the BDG spectrum of LP01x-LP11y is measured.
- The probe PC is controlled (while the pump PC’s fixed) to minimize the BDG reflection at the high frequency region of Δν, and the BDG spectrum of LP01x-LP11x is measured at the middle frequency region of Δν.
- The pump PC’s are controlled (while the probe PC fixed) to maximize the BDG reflection at the low frequency region of Δν, and the BDG spectrum of LP01y-LP11x is measured.
- The probe PC is controlled (while the pump PC’s fixed) to minimize the BDG reflection at the low frequency region of Δν and the BDG spectrum of LP01y-LP11y is measured at the middle frequency region of Δν.
In the above steps the sweep ranges of Δν were 442.76 – 446.96 GHz (for the low), 447.16 – 451.36 GHz (for the middle), and 451.08 – 455.48 GHz (for the high), respectively. The accuracy of the optical frequency was about 1 GHz for the absolute value of Δν limited by the resolution of the OSA, and about 10 MHz for the relative value between the sweep ranges by the frequency drift of the LDs.
Figures 4(a)-4(d) show the measured distributions of the BDG spectra along the FUT for different pump-probe pairs. As seen in the examples of local BDG spectra (at z = 9.1, 37.2, 67.2 m in the case of LP01y-LP11x) of the insets the BDG reflection appeared in broad spectral range (~2 GHz) with several side peaks. The BDG can be viewed as a weak Bragg grating , so the reflection spectrum is sensitive to the uniformity of the BDG. Considering that the BDG frequency of current scheme is determined by the local ERI difference of two modes in Eq. (5) and that the spectral widths (< 100 MHz) of the pump1 and the probe pulses are much narrower than 2 GHz, we think it is reasonable to attribute the broad spectrum by several side peaks to the non-uniformity of the fiber within the spatial resolution (~1.5 m) of the measurement. The width of the BDG spectrum is measured to be ~60 MHz in Gaussian fitting when side peaks are suppressed (such as the position z = 37.2 m in Fig. 4). It is also notable that similar spectral shapes and widths of the BDG signal are obtained for different pair of pump-probe modes at the same position of the FUT. In addition, a gradual increase (~3 GHz) of the center frequency is observed along the FUT which was loosely wound without intentional strain or temperature gradient. Since the variation of 3 GHz in the νD corresponds to the change of only about 0.67% in Δn or LB, we think the gradual change shows the long-range non-uniformity of the FUT occurred in the fabrication process of the preform or the drawing process of the fiber. It is also notable that the overall distributions of the BDG spectra of different pump-probe pairs appear to be quite similar to one another except difference center frequencies.
Distributed maps of νD and corresponding LB obtained by the peak search (spectral centroid) of the measured BDG spectra are plotted in Fig. 5(a) for the pump-probe pairs of different polarizations. The LB’s are calculated from Eq. (4) assuming ng11 = 1.45. The polarization dependence of ng11 is thought to be negligible considering the amount of birefringence (~3 x 10−5) of the FUT. The νD ranges from 443.3 GHz to 454.5 GHz in the FUT according to the polarization states of the pump-probe pairs and the positions, and local fluctuations with a gradual increase of νD are commonly seen for all the cases. It is also notable that the vB is almost uniform within 2 MHz along the FUT while the BDG frequency changes as much as ~3 GHz. Figure 5(b) depicts the frequency difference (ΔνD) between the νD’s of different pump-probe pairs with respect to the position acquired by the cross-correlation of the local BDG spectra which is useful in calculating the spectral shift of multi-peak spectrum . It is remarkable that the differences are quite uniform along the fiber compared to the strong fluctuations seen in the map of νD. This feature confirms that the variations of the BDG spectra are almost uniform along the fiber for different pump-probe pairs, and their origin is not the noise of the measurement but the structural variation of the FUT itself.
Another important result obtained from the relative difference of νD is the amount of birefringence Δnxy ( = nx – ny) of each spatial mode. For example, Δnxy of the LP01 mode is calculated from Eq. (5) as follows:Fig. 6 which are calculated from the result of Fig. 5(b). It is seen that the birefringence of the LP11 mode is slightly (~4%) larger than that of the LP01 mode in this e-core TMF, with a similar shape of local fluctuations.
Temperature (CT) and strain (Cε) coefficients of the νD are useful parameters for high-sensitivity and discriminative sensing based on a PMF [22, 23]. We measured the CT and the Cε of the νD’s for different pump-probe pairs as a feasibility study of distributed sensing by the BDG in the e-core TMF. The measurements were conducted by applying temperature and strain variations to short sections of the FUT (5 m for temperature, 2 m for strain). The results are shown in Figs. 7 and 8 for the temperature and the strain, respectively. As seen in Fig. 7 the CT’s are measured to be −0.16, 2.3, 2.9, and 4.9 (MHz/°C) for νDxy, νDyy, νDxx, and νDyx, respectively. It is remarkable that not only the amplitude but also the sign of CT’s are different according to the polarization states of the pump and the probe, and the CT appears to be smaller for the cases with larger νD. Such different CT’s for different polarization pairs of modes indicate that the temperature dependence of the birefringence is different for each mode. We think further investigation is needed on this point for clear understanding. It is also interesting that the maximum value of 4.9 MHz/°C is about 5 times larger than that of the νB of ordinary SMF’s (~1 MHz/°C), and about 10 times smaller than that of the BDG based on a PANDA PMF .
The strain coefficient Cε’s are measured to be −0.018, −0.012, −0.089, and −0.081 (MHz/με) for νDxy, νDyy, νDxx, and νDyx, respectively, as depicted in Fig. 8. The maximum strain coefficient is observed in the case of νDxx, not νDyx like the case of CT, and the maximum value is about twice that of the νB of ordinary SMF’s (~0.05 MHz/με) with opposite sign. We think the large differences shown in the CT and the Cε of the νD in the e-core TMF could be applied to discriminative sensing of temperature and strain.
In conclusion we have demonstrated the optical time domain measurement and the characterization of the intermodal beat length in an e-core TMF based on the analysis of the BDG spectra. It was shown that the BDG operations are possible with four different pairs of the spatial and polarization modes and that the modal structure in the e-core TMF can be investigated using the distribution maps of the BDG frequencies. Additionally, the BDG frequencies of different polarization pairs show large differences in the temperature and the strain coefficients, which could be applied for distributed fiber sensors.
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2012R1A1A2009103).
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