A novel differential mode delay (DMD) measurement technique for a multimode optical fiber based on optical frequency domain reflectometry (OFDR) has been proposed. We have obtained a high-resolution DMD value of 0.054 ps/m for a commercial multimode optical fiber with length of 50 m by using a modified OFDR in a Mach-Zehnder interferometer structure with a tunable external cavity laser and a Mach-Zehnder interferometer instead of Michelson interferometer. We have also compared the OFDR measurement results with those obtained using a traditional time-domain measurement method. DMD resolution with our proposed OFDR technique is more than an order of magnitude better than a result obtainable with a conventional time-domain method.
©2005 Optical Society of America
One of the most important components required for 10 Gb/s next-generation local area network (LAN) transmission system is the development of a multimode optical fiber (MMF) optimized for 850 nm wavelength . In order to develop a high-bandwidth MMF for LAN applications, reliable techniques are required for the bandwidth measurement of an MMF. The concept of a differential mode delay (DMD), and its associated measurement techniques, has been the subject of many recent studies [1, 2] and the time-domain DMD measurement method has already been developed and standardized  for an MMF. In the traditional time-domain DMD measurement method, a short pulse is transmitted to an MMF under test. Pulse spreading or broadening, due to the propagation speed differences between each mode of an MMF, is measured in time domain using a fast time-domain detection technique. The conventional DMD measurement method is both complicated and expensive, because it utilizes ultra-short pulses from a laser source and it requires a fast detection system such as a streak camera or a fast detector combined with a sampling oscilloscope. The resolution of the time domain DMD measurement technique is determined by the temporal pulse width of the laser used for the measurement, and it is typically in the order of few tens of picosecond. When we use a source with a shorter pulse width, the corresponding spectral width of the source becomes wider inevitably. As the pulse width broadening effect due to chromatic dispersion becomes dominant in a fiber when spectral width of a pulse becomes large, the shortest pulse width we can use for the time domain DMD measurement is limited. On the other hand, the minimum length of a fiber for the time-domain DMD measurement is limited by the temporal pulse width used for the measurement; DMD for a fiber cannot be resolved when the length of a fiber under test is short such that the modal delay of a fiber is smaller than or compatible to the input pulse width.
We already have reported the possibility of modal delay measurement for a few-mode fiber (FMF) based on a conventional optical frequency domain reflectometer (OFDR) system operating at 1550 nm wavelength [4, 5]. It was possible to use the reflection-type interferometer since the same core size of an FMF and an SMF as a launching arm can make the higher modes in an FMF couple from and to the fundamental mode of the SMF. However, since a typical MMF used for 10 Gb/s LAN application has larger core than an SMF, it is difficult to make reflected lights from an MMF couple back into an SMF. Here we proposed an optical frequency domain measurement method to analyze the DMD as well as the mode structure of a commercial MMF using a modified transmission-type OFDR based on a tunable laser source and a Mach-Zehnder interferometer for the first time.
2. The principle of DMD measurement for an MMF based on OFDR
In an OFDR system, a Michelson type fiber interferometer is formed with an MMF under test in one arm of the interferometer and a reference SMF in the other arm of the interferometer. When a frequency swept laser source is launched into the interferometer, frequency of beating signal due to temporal modal delay between lights from the reference and the test arms of the fiber interferometer is monitored. Modal delay of an MMF can be obtained by converting frequencies in a beating signal into temporal delays (τ’s) with a simple relation 
where f is the beating frequency and γ is the frequency-sweep rate of a laser, defined by the swept frequency range (Δυ) divided by the swept time (T). Detailed operating principles for an OFDR is explained in detain in Ref. 5.
3. Experiment and results
Figure 1 shows a schematic diagram of our transmission type experimental set-up used for differential mode delay measurements of an MMF based on a modified optical frequency domain reflectometer (OFDR) with the Mach-Zehnder interferometer instead of Michelson interferometer used in traditional OFDR systems. An Agilent TLS 81640A tunable light source (TLS) was used with a tuning range of 5 nm from 1545 to 1550 nm wavelengths. The linear frequency tuning rate of the TLS was set to 5 nm/s (γ = 625 GHz/s) which is 10 times faster than that in the modal delay measurement of a few-mode fiber we have reported before [4, 5]. The optical power of the TLS was kept at 2 mW during the frequency tuning process. Beating signal was acquired by using a data acquisition (DAQ) board, when a trigger signal was generated each time the frequency sweep began.
Frequency-swept light from the TLS is split using a 30/70 optical coupler. Thirty percent of the optical power goes into an auxiliary interferometer shown as a dashed box in Fig. 1. The auxiliary interferometer is used to measure the nonlinearity of the frequency sweep process. After the nonlinearity in the frequency sweep of the TLS is accurately measured as a function of time, we have rearranged the time axis of obtained data such that time interval between data points varies but the frequency sweeping rate is constant. Based on this data, a new equally spaced beating signal is generated by using a numerical interpolation technique for numerical Fourier transformation .
In the main interferometer, the remaining 70 % of optical power is split once again using a 3 dB fiber coupler. There are two unused fiber arms in our setup, which were submerged into an index matching oil to eliminate the unexpected effect of the reflected light from the both fiber ends. The reference arm of the main interferometer consists of a 49 m SMF whose length is matched to the length of a sample MMF.
A 50 m MMF (InfiniCor SX+ 50/125, Corning Inc.) with a core diameter of 50 μm is put into the test arm of the main interferometer. We have followed a standard launching condition used in a time-domain DMD measurement technique . Light is launched from a cleaved endface of an SMF into the cleaved endface of the MMF. The output beam from the SMF is scanned across the endface of the MMF with 1 μm step size in order to selectively excite all modes of the MMF , while beating signal is measured for each scanning position. The distance between the SMF and the MMF is maintained within 10 μm throughout the entire measurement process. We have used a commercially available fiber fusion splicer for this light launching setup. A fiber polarization controller (PC) is put in the reference arm of the main interferometer to optimize the visibility of the beating signal.
The transmitted light through the SMF in the reference arm of the interferometer is focused at a photo-diode (PD) whose size and bandwidth are 1 mm2 and 125 kHz respectively. The endfaces of the MMF under test and the reference SMF are imaged onto the PD with two lenses. Sizes of the endface images for the SMF and the MMF on the detector were made intentionally different with each other by adjusting the position of optic components in set-up. There was also somewhat offset between the centers of two images on the surface of the PD to obtain nonzero coupling coefficients from the overlap integrals between the fundamental mode from the SMF and odd modes from the MMF. Beating signal in the PD is acquired by using data acquisition board with the bandwidth of 1.2 MHz. A typical beating signal date is shown in Fig. 2(a). The dark region in Fig. 2(a) has high frequency components corresponding to temporal modal delays between the fundamental mode from the SMF and each individual mode from the MMF. Fig. 2(b) shows the beating spectrum obtained by Fourier transformation of the beating signal.
Three peaks in the beating spectrum are matched with three excited modes in the MMF. The frequency scale in x-axis can be converted into the time scale with dividing the frequency by the tuning rate γ, as expressed in Eq.(1). Frequency differences between peaks in the beating signal correspond to the temporal delays associated with the differences in propagation time between modes. The length of the SMF in the reference arm was almost same as the length of an MMF under test, which made the frequency of the beating signal very low. This decreased the phase noise in the measured beating signal . The effect of chromatic dispersion (CD) can be mostly removed from our proposed measurement scheme if we assume that the CDs of SMF and MMF are nearly same .
Figure 3(a) shows the raw data of time-domain DMD measurement results for the same MMF used for our frequency-domain technique. Waveforms of the optical output pulses are measured while scanning the launching position of the probe fiber from one core edge to the other core edge of the MMF end by 1 μm step size. The length of the MMF used for this measurement is about 450 m. A gain-switched laser (OPG-1500, Optune Inc.) was used as the input pulse source operating at λ = 1550 nm, with an FWHM = 39 ps and 10 MHz repetition rate. The optical power was set to 10 mW. And we used a high-speed photo detector with a bandwidth of 10 GHz. It shows that the input pulse is split into eight pulse groups in time-domain. The differential mode delay is about 1.61 ps/m determined by the difference of temporal positions of the leading and trailing edges at 25% of the maximum amplitude of the resulting waveform . In a conventional time domain DMD measurement system with a scanning offset launching method, the resolution bandwidth of the system is defined as the maximum of the full width at half maximums of output pulses for various offset launched input pulses. We define the resolution of our proposed DMD measurement method based on an OFDR as the maximum of the full width at half maximums of output peaks in frequency domain for various offset launching positions. From the full width at half maximum of peaks in Fig. 3(a), we can estimate the temporal resolution of the time-domain measurement method is about 50 ps for 450 m sample length. Therefore the DMD resolution in this case is about 0.11 ps/m (= 50 ps / 450 m).
Figure 3(b) shows the modal delay of the same MMF with a length of 50 m measured using our modified OFDR method for the same offset conditions. Note that the length of the fiber used for our proposed method is about 1/10 of the sample fiber used for the time-domain measurement method.
Polarization dependent visibility change in our measurement was minimized by using a linear polarizer (LP) placed just in front of the PD. Its principle is equal to well-known polarization diversity detection in an optical low coherence reflectometer (OLCR) using a polarization beam splitter . For a given offset launching position, amplitudes of two beating signals were measured at two orthogonal linear polarization states by rotating the LP by 90 degrees. These amplitudes of the two beating signals were added to find the polarization state independent amplitude of a beating signal. The intensity of each waveform was normalized to the maximum peak intensity. Normalized time in the lower x-axis scale in the figure was obtained by dividing the measured modal delay with the sample length, which is 450 m for the time-domain measurement result and 50 m for the frequency-domain measurement result. From the full width at half maximum of peaks in Fig. 3(b), we can estimate the temporal resolution of our proposed modified OFDR measurement method is about 2.7 ps for 50 m sample length. The minimum measurable DMD value is then about 0.054 ps/m (= 2.7 ps / 50 m).
Same temporal resolution can be obtained in time-domain measurement method with a short pulse whose pulse width is less than 2.7 ps together with a picosecond resolution detection system such as a streak camera. The spectral bandwidth of a pulse is increased when the pulse width is decreased due to the time-bandwidth product of a laser pulse. Therefore, there is a limitation in DMD measurement resolution for a given input pulse width, and reducing the temporal pulse width of a laser source may not help to improve the DMD resolution after a certain extent in time-domain DMD measurement method. For example, the minimum wavelength spectrum for a 2.7 ps pulse is about 0.39 nm for a Gaussian pulse at 850 nm center wavelength. If we use a standard chromatic dispersion coefficient of D = 107 ps/km-nm for a silica fiber, the pulse broadening due to chromatic dispersion of a fiber is about 2.1 ps (= 50 m × 0.39 nm × 0.107 ps/m-nm) resulting in 4.8 ps output pulse width after propagating 50 m length of a fiber without the effect of DMD. Assuming that the minimum measurable modal delay of an MMF is about the output pulse width without DMD effect, the resolution of DMD becomes 0.096 ps/m in this case. If the pulse width of the laser source is further reduced to 1.5 ps, the pulse broadening due to chromatic dispersion of a fiber is about 3.7 ps (= 50 m × 0.076 ps/m) resulting in 5.2 ps output pulse. The minimum DMD resolution in this case becomes 0.104 ps/m.
The frequency domain DMD measurement result determined from the waveform data shown in Fig. 3(b) is about 1.67 ps/m, which is about 3.7 % off from the time-domain measurement result shown in Fig. 4(a). Both measurements show eight peaks in raw data, which indicates that there exist eight transverse mode groups in the MMF corresponding to these eight different modal propagation speeds. This modal delay measurement can be used to calculate the propagation constant for each transverse mode group of the MMF. The peak positions of the waveforms shown in Fig. 3(a) and 3(b) are almost consistent with each other, except for few peaks. Unlike the time-domain measurement results, the waveforms in the frequency-domain measurement are not perfectly symmetric around the center of the core. The 3rd, 4th and the 6th peaks from the right side in Fig. 3(b) show low amplitudes compared to the corresponding amplitude peaks shown in Fig. 3(a). These mismatches are basically coming from the differences of overlap integrals between the fundamental mode profile of the SMF and the higher order mode profiles in the MMF at the detecting PD.
In spite of this drawback, the frequency domain DMD measurement has many advantages. One of the major advantages of our proposed measurement method is that our method has a very high resolution and a high sensitivity in DMD measurement compared to the conventional time-domain technique. As shown in Fig. 3(b), the excited modes were separated precisely even when the fiber length was only 50 m. By using a conventional time-domain measurement method it is very hard to measure DMD for an MMF whose length is less than 500 m. Meanwhile fiber or cabling companies have yet to measure the DMD value of a short length MMF in 10 Gb/s LAN applications. As the temporal resolution in our frequency domain DMD measurement method is about 2.7 ps for 50 m sample length, we can obtain a DMD resolution of 0.11 ps/m, which is a DMD resolution obtainable with at least 450 m length of an MMF for a conventional time-domain measurement method. In addition, the time domain measurement requires high power pulse source due to low sensitivity of the highspeed detector. Therefore, it is difficult to measure the DMD of a long length MMF by using this method. On the other hand, the DMD measurement based on interferometers can obtain easily high sensitivity of over − 60 dB [7, 8]. It is possible that the temporal mode distribution for a long length of an MMF can be obtained precisely by using our modified OFDR method. Our proposed frequency domain measurement method also solves the resolution degradation problem due to pulse broadening by the chromatic dispersion of a MMF, which is a major limiting factor in a traditional time-domain DMD measurement method. An SMF whose length is almost same as that of an MMF under test is put in the reference arm of the Mach-Zehnder interferometer setup. Assuming that the chromatic dispersion of a sample fiber is approximately same as that of an SMF, the effect of the chromatic dispersion can be removed in our frequency domain DMD measurement method. Therefore, modal delay becomes the most dominant factor for dispersion of a light propagating through the MMF in our frequency domain measurement scheme. Our proposed DMD measurement method is only affected by the chromatic dispersion of the length difference between the two arms of a Mach-Zehnder interferometer, which is 1 m since we use an SMF whose length is 1 m shorter than that of the sample fiber . By using an SMF in the reference arm of our setup we can improve the measurable length of an MMF by reducing the temporal mismatch between the lights from the reference and the sample arms. Another advantage of using a reference SMF fiber in our setup is improvement in the resolution of our DMD measurement method by eliminating the effect of chromatic dispersion. The frequency-tuning rate of a tunable laser and the difference in chromatic dispersion between the sample and the reference arms of our setup are two major factors which determines the resolution of our measurement method. When the SMF length in the measurement system is very different form the MMF under test the resolution of our measurement method will be degraded, and this degradation in our measurement resolution can be readily monitored by the broadening of full width at half maximums in the peaks of our data.
Finally, our proposed measurement scheme is very economical compared to the conventional time-domain DMD measurement method which requires a high-speed detector combined with a sampling oscilloscope, or a streak camera. We propose that modified OFDR system is a very powerful alternative solution for DMD measurements in multimode fibers. However, a modified OFDR combined with a tunable coherent light source operating at λ = 1310 or 850 nm is required as we have demonstrated our proposed measurement method at 1550 nm wavelength region in order to measure the modal delay of a commercially available MMF for real gigabit Ethernet applications. In the future, we expect that a portable version of our proposed DMD measurement system can be available soon in the field just like the case of an optical time domain reflectometer (OTDR).
A new very high-resolution DMD measurement technique for an MMF using a modified OFDR system has been proposed. We have demonstrated our proposed method by measuring the DMD of a commercially available multimode optical fiber by using a high speed TLS and transmission-type interferometer. Measured results of our proposed frequency-domain technique were compared with the results of a conventional time-domain measurement method. Our measured DMD value of 1.67 ps/m in frequency-domain measurement at 1550 nm wavelength is consistent with the DMD of 1.61 ps/m in time domain measurement. Its temporal resolution of 2.7 ps is also fourteen times better than that of time domain measurement. We have demonstrated the frequency-domain DMD measurement method with high resolution based on an OFDR as a powerful tool for analyzing an MMF.
This research was partially supported by KOSEF through UFON, an ERC program of GIST, by KISTEP through the Critical Technology 21 programs, and by the BK-21 IT Project, MOE, Korea. The authors are thankful to God for all valuable results in the paper.
References and links
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