Parameters of test fibers
1. Introduction
An optical time domain reflectmeter (OTDR) has been developed for detecting the fault location and estimating the average loss of the installed fiber cables. The resolution of the distance has been improved up to a few centimeters. Recently, OTDR has been used for measurements of the transmission characteristics in fiber and optical fiber properties based on the backscattered signal power [1, 2].
As a result of the rapid progress made in the field of optical fiber amplifiers (OFA’s), it has become possible to construct long distance transmission systems without conventional 3R repeaters [3, 4]. However, the use of OFA’s gives rise to the problems of optical nonlinearities such as fourwave mixing (FWM), stimulated Brillouin scattering (SBS), and selfphase modulation (SPM). In OFAbased optical transmissions, both the chromatic dispersion distribution along a fiber and the average chromatic dispersion influence signal performance. Therefore, it has become important to know the longitudinal chromatic dispersion distribution for sophisticated transmission systems such as wavelength multiplexed and optical soliton transmission systems. However, conventional measurement techniques [5, 6] can only determine the average chromatic dispersion of either a short or a long fiber. Recently, there have been some reports on measurement techniques for estimating chromatic dispersion distribution along a fiber [79]. As these measurement techniques are based on optical nonlinear effects, the measurement distance is limited. On the other hand, we have reported the principle of a technique based on bidirectional measurement with OTDR [1].
In this chapter, we describe the measurement techniques for the longitudinal fiber parameters or transmission characteristics along the fiber. The backscattered power contains information on the fiber parameters at the scattered position such as mode field diameter, refractive index, and relativeindex difference. Such information can be obtained by extracting the capture fraction from the backscattered power.
There are two types of techniques based on OTDR for measuring the longitudinal fiber properties by analyzing the backscattered power. One is the way of extracting the required information on the parameter from the capture fraction in the backscattered power just as it is. This technique is called “indirect method” in this section. The other is the way of adding the information into the backscattered power by utilizing the phenomenon between the signal and pump lights and required information can be easily obtained from the additional information in the backscattered power. This method is called “direct method”. By using two types of techniques, the required information can be extracted from the backscattered power in the fiber.
In section 2, the principle of measurement technique for longitudinal fiber parameters such as the mode field diameter and relativeindex difference and the reduction of polarization fluctuation influence in a fiber are described[2,10]. In section 3, the measurement technique for longitudinal transmission characteristics such as chromatic dispersion and the Raman gain efficiency are described. In this section, the direct and the indirect methods are described. In section 4, we summarize the measurement technique based on OTDR.
2. Measurement technique for longitudinal fiber parameters
This section describes the measurement techniques for longitudinal fiber parameters such as mode field diameter and relativeindex difference.
2.1. Mode field diameter distribution
2.1.1. Measurement principle
The backscattered power
where
A reliable way to separate the effects of decay and waveguide imperfections from backscattered signals has already been described [1, 2, 10]. For OTDR signals
where a_{0} is a constant independent of distance z and is expressed as
Therefore, the imperfection contribution
where
With conventional singlemode fibers, the variation in the local scattering coefficient α_{s}(z) is negligible compared to that in the mode field diameter 2
When the mode field diameter 2
However, in a fiber link composed of different kinds of fiber, the local scattering coefficient
Here, we consider the measurement procedure for a fiber link composed of different types of fibers, by taking into account the difference between the scattering coefficients of the composed fibers.
When the scattering coefficient and the refractive index change along the fiber are taken into account, the imperfection contribution
where
Here, we define the first term on the right hand side in (9) as a correction factor
where
where n_{0} is the refractive index of the cladding. Using this relation, the correction factor
Therefore, the mode field diameter 2w(λ, z) distribution can be obtained as
On the contrary, another procedure has been proposed [15]. To circumvent this difficulty, a procedure similar to that introduced in [16], but with an easier implimentation is used. Like [16], two fitting coefficients
Suppose to set a second reference point
From (14) and (15), the MFD becomes
Thus, we need to know the MFD at the two reference points
2.1.2. Reduction of polarization fluctuation influence in a fiber
The polarization state of an optical pulse is continuously changing as the pulse propagates in a fiber, and this polarization fluctuation causes measurement error. This fluctuation must therefore be reduced during the backscattered power accumulation. It is believed that the polarization fluctuation can be reduced by switching the polarization state from 0 to 90 linear polarization during the measurement [2]. Figure 1 shows a block diagram of our experimental setup for measuring the backscattered power.
In our investigation, we refer to the positions of the polarization controller shown in Fig. 1 as positions #1 and #2. For simplicity, we defined the Jones matrix of the models shown in Fig. 1 as
where
where
When
The detected power
Using (23) and (24), the total detected power
Equation (25) shows that the obtained power
From (26), it is found that the obtained power depends on
By using the polarization controller, the backscattered power can be suppressed due to the polarization fluctuation.
2.1.3. Experimental results
To confirm the present technique, the mode field diameter distribution along the fiber link composed of the three fibers was measured. OTDR was used to measure the backscattered power of the fiber link. Table I summarizes the fiber parameters in the fiber link.




MFD (μm) at 1310nm at 1550nm 
9.02 10.17 
6.47 7.86 
6.49 7.86 
Cutoff wavelength λ_{c} (nm)  1260  1150  1010 
Relativeindex difference Δ (%)  0.37  0.78  0.77 
Chromatic dispersion D (ps/km/nm) at 1550 nm  16.72  0.29  0.27 
Fiber length (km)  25.0  9.99  20.19 
Figure 2 shows the bidirectional OTDR traces of the fiber link at λ=1550 nm. OTDR (Agilent E6003) with wavelengths of 1550 and 1310 nm was used to measure the backscattered signal powers for the fiber link. In our measurements, the pulse width of the OTDR was 1 μs and the averaging time was 10 minutes.
It is found that three fibers were spliced in the fiber link. The imperfection loss obtained from (2) was shown by using the Fig.1. Figure 3 shows the inperfection loss of the fiber link.
It is found that the losses of Fibers A, B, and C fluctuate along the fiber length. This fluctuation has an effect on the mode field diameter of each fiber. The MFD distribution at λ=1550 nm using Fig. 3 is shown in Fig. 4.
The MFD was estimated by using double reference method. When we measure the MFD distribution of the fiber link, Fibers A and B was used as reference fibers. The MFD was estimated by using (16) and MFDs at the double reference points. The deviations of the MFD for Fiber A, B and C were 0.039 μm, 0.023 μm, and 0.046 μm, respectively. It is clarified that the longitudinal MFD deviation is negligible small for the fibers fabricated by the present fabrication technique.
2.2. Relativeindex difference distribution
2.2.1. Measurement principle
The first term on the right hand side in (9) depends on the variations in the scattering coefficient and refractive index of the core. The local scattering coefficient is proportional to the Rayleigh scattering coefficient. The Rayleigh scattering coefficient R for GeO_{2} doped core fiber is expressed as [14]
where
As the variation in the refractiveindex
Thus, (9) can be rewritten as by using (27) and (28).
Here, if the MFD distribution and the relative index difference
The MFD distribution along the transmission line can be easily estimated by using the double reference method [15]. With this technique, the imperfection loss of each test fiber along the transmission line can be estimated by comparing it with the imperfection losses at two reference points.
Next, the principal estimation error of the proposed method is discussed. The
where
Figure 5 shows the relationship between the correct relative index difference Δ_{R} and the relative Δ estimation error (%) against the refractive index at the 0.35 % and 0.8 % reference points. Here, a k value of 0.62 was used. It is seen that the relative
2.3. Experimental results
To confirm the effectiveness of the present method, I measured the relative index difference distribution
OTDR (Agilent E6003) with wavelengths 1550 and 1310 nm was used to measure the backscattered signal powers for the fiber link. In our measurements, the pulse width of the OTDR was 1 μs and the averaging time was 10 minutes. The spatial resolution of the relative index difference Δ estimation depends on the OTDR pulse width. In the experiments, the spatial resolution was about 200 m.
Figure 6 shows the relative index difference distribution Δ(z) in the fiber link by using the MFD distribution as shown in Fig. 4.
This study proposed a novel relativeindex difference distribution measurement method for a fiber link based on the use of an OTDR. It was clarified experimentally that the method can be applied to fiber links composed of different kinds of fiber. The relativeindex difference is one of important parameters to estimate the chromatic dispersion. However, there have been no reports on the technique for estimating the relativeindex difference distribution. As far as we know, for the first time, we proposed the novel technique for estimating the relativeindex difference distribution of the fiber link based on the OTDR.
3. Measurement technique for longitudinal transmission characteristics
This section describes the measurement techniques for longitudinal transmission characteristics such as chromatic dispersion and Raman gain efficiency and the experimental results.
3.1. Chromatic dispersion distribution
3.1.1. Measurement principle
The chromatic dispersion is expressed as the sum of the material dispersion
Here,
where c is the light velocity. The material dispersion can be estimated from the dopant concentration in an optical fiber by using Sellmeier’s coefficients [18]. The dopant concentration can be obtained from the relativeindex difference
The empirical relationship between the modefield diameter
where
Here, we approximated the wavelength dependence of the modefield diameter(MFD)
Substituting (36) into (34), the waveguide dispersion can be expressed as
Therefore, the waveguide dispersion
In general, as the coefficient of
In this case, the coefficients
Substituting (38) into (34), the waveguide dispersion can be expressed as
Here, we assume that the MFDs at the two wavelength
The chromatic dispersion can be measured by using the wavelength dependence of the MFD and the relativeindex difference of the core. Both parameters MFD and the relativeindex difference can be easily estimated by using the OTDR. The MFD
3.1.2. Experimental results
The chromatic dispersion measurements were made on the fiber link composed of three different fibers. The parameters of these test fibers are listed in Table 1. The chromatic dispersion is sum of waveguide and material dispersion. The material dispersion can be estimated from the dopant concentration corrssponding to the relativeindex difference. On the contrast, the waveguide dispersion can be obtained by using the wavelength dependence of MFD. The fiber link was measured by bidirectional OTDR with both wavelengths of 1310 and 1550 nm. Figs. 4 and 7 show the MFD distributions at λ=1550 nm and 1310 nm. estimated by using the bidirectional OTDR traces, respectively. To estimate the MFDs, Fibers A and B were used as the reference fibers[15].
The waveguide dispersion can be estimated by using the MFD distributions at both 1310 and 1550 nm and (30). Figure 8 shows the waveguide dispersion of the fiber link at λ=1550 nm.
It is found that the waveguide dispersion of Fiber A (conventional singlemode fiber) was smaller than that of Fiber B and C (dispersionshifted fibers). This is because the zerodispersion wavelength can be shifted to the longer wavelength. On the other hand, the material dispersion can be calculated by using Sellmeire equation when the relativeindex diffence is known. The relativeindex differnce was estimated by using the technique presented in 2.2. Figure 9 shows the material dispersion of the fiber link at λ=1550 nm.
The chromatic dispersion at λ=1550 nm can be estimated by using Figs 9 and 10. Figure 10 shows the chromatic dispersion of the fiber link at λ=1550 nm.
We described a nondestructive technique for measuring the chromatic dispersion distribution along a singlemode fiber based on bidirectional OTDR measurements. This technique was compared with the destructive interferometric technique and found to be in good agreement. We also proposed a measurement procedure for a transmission line composed of different types of singlemode fibers. We confirmed experimentally that our technique can be applied to a transmission line. Our technique for estimating chromatic dispersion distribution will be a powerful tool for designing WDM and FDM transmission systems.
3.2. Raman gain efficiency distribution
The development of various kinds of Internet services has led to a rapidly increase in transmission capacity. With a view to realizing ultrawide band transmission systems, wavelength division multiplexing (WDM) systems have been introduced together with Raman amplification technology [20]. Raman amplification technology is an attractive technology whereby the amplification wavelength region can be adjusted by changing the wavelength of the pump light wavelength. Technologies have been reported for measuring the Raman gain efficiency distribution using pump and signal lasers [21]. In this section, two types of techniques for measuring the Raman gain efficiency is described based on the OTDR. The first one is the direct method using pump lasers. The other is the in direct method without pump lasers.
3.2.1. Measurement principle
Direct method
Figure 11 shows the schematic diagram for measuring the Raman gain efficiency distribution in the optical fibers by using an OTDR.
The pulsed signal and the continuous wave pump lights are launched into the test fiber through the WDM coupler. These lights copropagate through the test optical fiber. An optical filter is inserted between the OTDR and the WDM coupler to eliminate the Rayleigh backscattering of the pump light.
Here, we derive the signal power at the distance of
where
where
In particular, when the field distribution is Gaussian, the effective area
where
From (43), the pump power
Substituting (46) into (42), the signal power
The signal power
where
On the contrary, when the pump light is off, the backscattered power
The backscattered power of OTDR,
The backscattered power at
The following equation can be derived from (50) and (51).
On the contrary, when
From the definition of
Therefore, the Raman gain efficiency
Here,
Therefore, the Raman gain efficiency distribution can be estimated from the length dependence of the pump power and the derivative of
Indirect method
The Raman gain coefficient
where
The Raman gain efficiency can be expressed as
From (59), we can approximate the Raman gain coefficient by using the relativeindex difference
If we know the Raman gain efficiency (
Here, if we assume that the wavelength dependence of MFD is negligible, (60) can be approximated as
The Raman gain efficiency can be estimated by measuring both the MFD and the relativeindex difference distributions of the test fiber. Thus, the Raman gain efficiency can be obtained indirectly by using OTDR without pump lasers. This technique is a relative measurement method, so the measurement accuracy depends on the Raman gain efficiency of the reference fiber.
3.2.2. Experimental results
Direct method
The Raman gain efficiencies for a conventional singlemode fiber with a length of 25 km and a fibre link installed in the field with a length of 11km composed of 22 conventional singlemode fibers with a piece length of 500 m were measured to confirm the effectiveness of our technique.
Figure 12 shows the backscattered powers with and without pumping for the conventional singlemode fiber. OTDR (Anritsu) with a wavelength of 1550 nm was used to measure the backscattered power. The OTDR pulse width was 1μs and the averaging time was 5 min. The pump laser with a wavelength of 1475 nm was used. It is found that the signal power is amplified by the pump power.
Figure 13 shows the backscattered power difference S_{d} defined in (14) plotted as a function of fiber length.
S_{d}(z) was best fitted to the polynomial function as to calculate its derivative.
The attenuation coefficient of the test fiber at λ=1475 nm was 0.217 dB/km. The pump power P_{p}(0) was 88 mW. The Raman gain efficiency distribution along the fiber length can be estimated by using (56) and (62). Figure 14 shows the Raman gain efficiency distribution estimated by our technique.
It is seen that Raman gain efficiency along the fiber length is almost the same as 0.3 W^{1}km^{1}.
Next, the Raman gain efficiency for the fiber link composed of 22 conventional singlemode fibers was measured. Figure 15 shows the backscattered powers with and without pumping and the backscattered power difference S_{d} plotted as a function of fiber length.
The attenuation coefficient α_{p} was measured by the OTDR with a wavelength of 1450 nm. The length dependence of the pump power
It is found that the Raman gain efficiency distribution in the fiber link varies from 0.22 to 0.32 W^{1}km^{1}. The Raman gain efficiency distribution of the fiber link installed in the field shows the appropriate value. As a result, it is confirmed that our technique can be applied to the fiber link.
Indirect method
The Raman gain efficiency of the concatenated fiber link as shown in Fig. 17 was measured to confirm the effectiveness of our technique.
The fibers Ref#1 and Ref#2 were used as reference fibers for estimating the MFD and the relativeindex difference



MFD (μm) at 1550nm  7.86  10.2 
Cutoff wavelength λ_{c} (nm)  1150  1130 
Relativeindex difference Δ (%)  0.78   
Fiber length L (km)  10.0  3.0 
Loss (dB/km)  0.20  0.19 
Figure 18 shows the MFD distribution at λ=1550 nm in the concatenated fiber link estimated by [4]. In this measurement, the OTDR pulse width was 1 μs and the averaging time was 3 min. The parameters of test fibers #1 to #3 are listed in Table 3.




MFD(μm) at 1550 nm  10.4  10.2  10.4 
Cutoff wavelength λ_{c} (nm)    1250   
Fiber length L (km)  3.0  3.0  3.0 
Loss (dB/km) at 1550 nm  0.18  0.19  0.19 
Raman gain efficiency* (1/W/km)  0.66  0.75  0.64 
Figure 19 shows the relativeindex difference
The Raman gain efficiency normalized by that of Ref#2 was estimated from Figs. 18 and 19 by using (61), which is shown in Fig. 20. The Raman gain efficiency of Ref#2 was estimated to be 0.75 by the direct measurement technique. It is seen that the Raman gain efficiency of Ref#1 is the largest among the test fibers because the relativeindex difference
Next, we measured the Raman gain efficiency of the test fibers directly by using a pump laser. The experimental results are summarized in Table 3. We found that each group fiber has almost the same the Raman gain efficiency. We also found that the ratio of the Raman gain efficiency of group B to that of group A is about 1.2, which is in good agreement with the results obtained with the present technique.
We described a new technique for measuring Raman gain efficiency distribution using a conventional OTDR. The Raman gain efficiency in the 25km long singlemode fiber and the fiber link installed in the field with a length of 11 km composed of 22 conventional singlemode fibers were successfully estimated experimentally.
4. Conclusion
We described the measurement techniques for the longitudinal fiber parameters or transmission characteristics along the fiber based on the OTDR.
We described two types of techniques based on OTDR for measuring the longitudinal fiber properties by analyzing the backscattered power. One was the way of extracting the required information on the parameter from the capture fraction in the backscattered power just as it is. This technique is called “indirect method”. As the backscattered capture fraction contains the information on the fiber parameters, the fiber parameters distibution can be obtained by analizing the backscattered capture fraction. The other was the way of adding the information into the backscattered power by utilizing the phenomenon between the signal and pump lights and required information can be easily from the additional power in the backscattered power. This method is called “direct method”. By using two types of techniques, the required information can be extracted from the backscattered power in the fiber.
OTDR based measurement techniques will be powerful to estimate the various kinds of properties in the fibers or the optical transmission lines.
Acknowledgments
The author would like to express sincere thank to Prof. Tateda M. and Dr. Nakajima K. for their fruitful discussions. He would like to also thank Dr. Yamashita I., Dr. Tsutsumi Y. and Mr. Hatada H. for their helps during measurements.References
 1.
Ohashi M. and Tateda M., ”Novel technique for measuring longitudinal chromatic dispersion distribution in singlemode fibres,” Electron Lett. , vol. 29, pp. 426427, 1993.  2.
Nakajima K., Ohashi M. and Tateda M., “Chromatic dispersion distribution measurement along a singlemode optical fiber,” J. Lightwave Technol ., vol. 15, pp. 10951101, 1997.  3.
Hagimoto K., Iwatsuki K., Takada A., Nakazawa M., Saruwatari M., Aida K., and Nakagawa K., “250 km nonrepeated transmission experiment at 1.8 Gb/s using LD pumped Er_{3+}doped fiber amplifiers in IM/direct detection system,” Electron. Lett. , vol. 25, no. 10, pp. 662–664, 1989.  4.
Nakazawa M., Kimura Y., Suzuki K., Kubota H., Komukai T., Yamada E., Sugawa T., Yoshida E., Yamamoto T., Imai T., Sahara A., Nakazawa H., Yamauchi O., and Umezawa M., “Field demonstration of soliton transmission at 10 Gbit/s over 2000 km in Tokyo metropolitan optical loop network,” Electron. Lett. , vol. 31, no. 12, pp. 992–994, 1995.  5.
Tateda M., Shibata N., and Seikai S., “Interferometric method for chromatic dispersion measurement in a singlemode optical fiber,” J. Quantum Electron. , vol. QE17, pp. 404–407, Mar. 1981.  6.
Daikoku K. and Sugimura A., “Direct measurement of wavelength dispersion in optical fibers  Difference method,” Electron. Lett. , vol.14, no. 5, pp. 149–151, 1978.  7.
Jopson R. M., Eiselt M., Stolen R. H., Derosier R. M., Vengsarkar A. M., and Koren U., “Nondestructive dispersionzero measurements along an optical fiber,” Electron. Lett. , vol. 31, no. 24, pp. 2115–2117, 1995.  8.
Nishi S. and Saruwatari M., “Technique for measuring the distributed zero dispersion wavelength of optical fibers using pulse amplification caused by modulation instability,” Electron. Lett. , vol. 31, no. 3, pp. 225–226, 1995.  9.
Onaka H., Otsuka K., Miyata H., and Chikama T., “Measuring the longitudinal distribution of fourwave mixing efficiency in dispersionshifted fibers,” Photon. Technol. Lett. , vol. 6, pp. 1454–1456, Dec. 1994.  10.
Ohashi M.,“Novel OTDR technique for measuring relativeindex difference of fiber links“, IEEE Photon. Technol. Lett. , vol. 18, pp. 25842586, 2006.  11.
Vita P. Di. and Rossi U., “Backscattering measurements in optical fibers: Separation of power decay from imperfection contribution,” Electron. Lett. , vol. 15, pp. 467–469, 1979.  12.
Brinkmeyer E., “Analysis of the backscattering method for singlemode optical fibers,” J. Opt. Soc. Amer. , vol. 70, pp. 1010–1012, 1980.  13.
O’Sullivan M. S. and Ferner J., “Interpretation of SM fiber OTDR signatures,” in Proc. SPIE’86 Optic. Testing Metrology , vol. 661, pp. 171–176, 1986.  14.
Tsujikawa K., Ohashi M., Shiraki K., and Tateda M., “Scattering property of F and GeO_{2} codoped silica glasses,” Electron. Lett. , vol.30, pp. 351–352, 1994.  15.
Rossaro A., Schiano M., Tambosso T. and D’Alessandro D., “Spatially resolved chromatic dispersion measurement by a bidirectional OTDR technique,” I EEE J. Select. Topics Quantum Electron ., vol. 7, pp. 475483, 2001.  16.
ITUT Recommendation COM1555E, Dec. 1997.  17.
Pask C., “Physical interpretation of Peterman’s strange spot size for singlemode fibers,” Electron. Lett. , vol. 20, pp. 144–145, 1984.  18.
Shibata N., Kawachi M., and Edahira T., “Optical loss characteristics of highGeO_{2} content silica fibers,” IECE(J) Trans. , vol. E63, pp. 837841, 1980.  19.
Marcuse D., “Loss analysis of single mode fiber splice,” Bell Syst. Tech. J. , vol. 56, pp. 703–718, 1977.  20.
Takachio N., Suzuki H., Masuda H., and Koga M., “32x10 Gb/s distributed Raman amplification transmission with 50GHz channel spacing in the zerodispersion region over 640 km of 1.55μm dispersion shifted fiber,” presented at the Optical Fiber Communication Conf. and Int. Conf. Integrated Optics Optical Fiber Communication (OFC/IOOC’99) , Postdeadline Paper PD9.1, 1999.  21.
Nissov M., Davidson C. R., Rottwitt K., Menges R., Corbett P. C., Innis D., and Bergano N. S., “100 Gb/s (10x10 Gb/s) WDM transmission over 7200 km using distributed Raman amplification,” in Proc. Eur. Conf. Opt. Commun. (ECOC) , Edinburgh, Scotland, pp. 9–12, 1997.  22.
Agrawal G. P., Nonlinear Fiber Optics , 3rd ed. New York: Academic Press, 1995.  23.
Shibata N., Horiguchi M., and Edahiro T., “Raman spectra of binary highsilica glasses and fibers containing GeO_{2}, P_{2}O_{5} and B_{2}O_{3}, ” J. NonCryst. Solids , vol. 45, pp. 115126, 1981.  24.
Nakashima T., Seikai S., and Nakazawa M., “Dependence of Raman gain on relative index difference for GeO_{2}doped singlemode fibers,” Opt. Lett. , vol. 10, pp. 420422, 1985.