## Abstract

We propose a method of testing transmission fiber lines and distributed amplifiers. Multipath interference (MPI) is detected as a beat spectrum between a multipath signal and a direct signal using a synthesized chirped test signal with lightwave frequencies of f_{1} and f_{2} periodically emitted from a distributed feedback laser diode (DFB-LD). This chirped test pulse is generated using a directly modulated DFB-LD with a drive signal calculated using a digital signal processing technique (DSP). A receiver consisting of a photodiode and an electrical spectrum analyzer (ESA) detects a baseband power spectrum peak appearing at the frequency of the test signal frequency deviation (f_{1}-f_{2}) as a beat spectrum of self-heterodyne detection. Multipath interference is converted from the spectrum peak power. This method improved the minimum detectable MPI to as low as −78 dB. We discuss the detailed design and performance of the proposed test method, including a DFB-LD drive signal calculation algorithm with DSP for synthesis of the chirped test signal and experiments on single-mode fibers with discrete reflections.

© 2011 OSA

## 1. Introduction

Rayleigh backscattering due to microscopic refractive index variation of fibers and discrete reflections from poor connectors and poorly spliced points within the transmission line tend to degrade the receiver performance of systems that use distributed amplifiers. This is because forward-scattered and forward-reflected signal light arising from the double scattering and reflection of backward light acts as inband crosstalk or multipath interference (MPI) for receivers. Hence, low MPI is one of the most important factors required for high-performance and reliable distributed amplifier system design and construction [1–6].

We explain the detection of double Rayleigh scattering along a fiber using our synthesized chirped test signal from a directly modulated distributed feedback laser diode (DFB-LD). We also describe the DFB-LD drive signal and calculation algorithm with digital signal processing (DSP) for synthesis of the chirped test signal. We discuss the experimental results using concatenated fiber lines constructed from connectors and single-mode fibers (SMFs).

## 2. System configuration and operation principle

Figure 1
shows the proposed test method, which uses a DFB-LD, a photodiode (PD), and an electrical spectrum analyzer (ESA). The DFB-LD periodically emits a chirped test signal with lightwave frequencies of f_{1} and f_{2} into a distributed amplifier or transmission fiber of several tens to hundreds of kilometers under test. The double-Rayleigh-scattered powers of the pulsed test signal of f_{1} and f_{2} overlap the direct signal of f_{1} and f_{2} at the PD. The direct signal acts as the pulsed local light in a heterodyne receiver. The ESA detects the electrical power of the beat current between the double-Rayleigh-scattered power and the direct signal at the frequency of |f_{1}-f_{2}|.

The detected electrical power of the beat current corresponds to the optical power product of the total forward-scattered signal (${P}_{scattered}^{opttotal}={\displaystyle {\sum}_{i=1}^{n}{P}_{scattered,i}^{opt}}$) and direct signal (${P}_{direct}^{opt}$) as${P}_{\left|{f}_{1}-{f}_{2}\right|}^{ESA}\propto {P}_{direct}^{opt}\cdot {P}_{scattered}^{opttotal}$. Multipath interference is defined as the optical power ratio of the total forward-scattered signal to the direct signal:$MPI\equiv {P}_{scattered}^{opttotal}/{P}_{direct}^{opt}$. Therefore, MPI is simply obtained using these relations as

The advantage of our method is that the beat spectrum ideally concentrates at two frequencies: zero and |f_{1}-f_{2}|. The frequency |f_{1}-f_{2}| can be appropriately determined to be in the frequency band of low noise. Consequently, highly sensitive MPI measurement becomes possible.

## 3. Synthesis of chirped test signal

To obtain the chirped test signal, basic characteristics of the DFB-LD need to be clarified. Chirped characteristics are measured using the self-heterodyne fiber loop interferometer shown in Fig. 2 . A pulsed reference frequency is sampled by SW1 with a 0.2-μs window one time every 5.12 ms (256 times x 20 μs pulse period) from the 50 kHz repetition rate chirped stream and stored in a loss compensated fiber loop with an EDFA. The repetition rate of 50 kHz is selected by the pulse period of nearly twice time of the fiber loop round trip time of 10.1 μs. SW3 selects a pulsed reference frequency of N circuit from the fiber loop outputs. SW2 is used to initialize the loss compensated fiber loop. The beat frequency between the chirped pulse stream and the reference pulse via the fiber loop after circulation is measured using an ESA. The lightwave frequency of the reference pulse into the PDs is shifted by −240 MHz due to acousto-optical modulators used as SW1 and SW3. Because of the time difference between the delay and the half period of the pulse, the temporal beating position (sample timing) in the pulse period shifts according to the number of circuits. By reconstructing the ESA output, the temporal chirp characteristics over a pulse period can be evaluated. This is similar to a sampling oscilloscope operation. Owing to the self-heterodyne configuration and the ESA with a resolution bandwidth of 300 kHz, highly stable chirp evaluation of less than 1 MHz becomes possible.

Figure 3 shows the chirp characteristics of the output emitted from a directly modulated 1558- nm DFB-LD at a repetition rate of 50 kHz by a rectangular pulse stream. The threshold current of the DFB-LD was 13.4 mA and the optical power at an operating current of 40 mA was 6.5 mW. The temporal chirp response was clearly obtained from the beat frequency in the Fig. 3 (b).

Chirped characteristics arise from the temperature and carrier density change of the LD active layer caused by the electrical modulation signal [7-8]. This process is modeled using the following equation:

*Δf(t)*is the frequency shift from the average ($\overline{f(t)}$): $\Delta f\left(t\right)\equiv f(t)-\overline{f(t)}$,

*ΔJ*is the heat generated from the modulation current

_{Q}*ΔI*,

_{LD}*z(f)*is the frequency domain thermal impedance,

*F*is the inverse Fourier transform, and

^{−1}*k*is a coefficient.

_{f}The parameters in Eq. (2) are extracted by measuring the temporal response as a function of the bias current and pulse amplitude. From the peak-to-peak chirp response, an empirical formula for *ΔJ _{Q}* and

*ΔI*relation is expressed as

_{LD}*a*and

*b*are coefficients, and

*I*is the bias current. Thermal impedance of the analytical expression obtained from a two-dimensional diffusion equation of a cylindrical coordinate is used:

_{bias}*ω*is the angular frequency,

*j*is $\sqrt{-1}$,

*K*and

_{0}*K*are modified Bessel functions. The time constant

_{1}*τ*is extracted by fitting the slope of the temporal chirp response. The coefficient

_{d}*k*is obtained from the peak-to-peak chirp response and the time constant. The coefficient

_{z}*k*in the second term of Eq. (2) is extracted from the frequency jump observed at the alternate instant of the modulation rectangular pulse polarity. The experimentally obtained parameters in Eqs. (2)–(4) are summarized as

_{f}*a*, 353 (MHz/mA);

*b*, 3 (MHz/mA);

*k*, 26 (MHz/mA);

_{f}*k*, –0.58; and

_{z}*τ*, 5(μs).

_{d}The first and second terms of Eq. (2) are the dominant and fractional roles in determining the chirp characteristics, respectively. To periodically synthesize the appropriate chirped test signal with lightwave frequencies of f_{1} and f_{2}, the DFB-LD modulation current *ΔI _{LD}* is calculated from Eq. (2) according to the calculation algorithm for DSP shown in Fig. 4
. Analytical calculation is difficult due to chirp model nonlinearity. An iterative process of about five steps is used. In blocks 2 and 4, calculation with the chirp model is carried out. First, inverse calculation from tentative target pattern to drive current is carried out with the dominant term only at block 2. Second, the effect of the fractional term is taken into account at block 4. Blocks 1, 3, and 5 are pre and post calculation blocks for the iterative process. In block 3, low pass filters and a limiter block, the operating range of the drive current is restricted appropriately. By monitoring the convergence, the driving signal is obtained from block 3. For convergence of the iterative process, an appropriate cutoff frequency is important. In our case, about 5MHz was used.

The tentative target chirp patterns for the first n = 1 and successive n_{th} iterations are expressed as

The inverse calculation in block 2 is carried out using fast Fourier transform (*FFT*) and inverse FFT (*IFFT*) as follows:

The conversion of *ΔJ _{Q}* to

*ΔI*is carried out by solving Eq. (3).

_{LD}Figure 5(a)
shows a temporal target chirp pattern for synthesis. The peak-to-peak frequency deviation |f_{1}-f_{2}| was 300 MHz, the transition time from f_{1} to f_{2} was 0.9 μs, and the repetition rate was 50 kHz. We selected the repetition rate of 50 kHz for the following two reasons. First, the systematic error caused by the low repetition rate test pulse in the MPI measurement is expected to be less than 0.5 dB for a test fiber length that exceeds 2km by the 50 kHz repetition rate test signal [6]. Second, the self-heterodyne fiber loop interferometer for measuring chirp characteristics can operate around 50 kHz. Figure 5(b) shows a synthesized drive signal at a 40-mA bias current attained after iterations of five loops. The frequency variation from a temporal target chirp pattern is expected to be less than 0.2 MHz, except the transition time from the simulation. At the transition time, large frequencies over shoots by 10 MHz are anticipated. Figure 5(c) shows the measured optical power waveform emitted from the DFB-LD modulated by the synthesized drive signal, and Fig. 5(d) shows the measured temporal chirp pattern obtained by the synthesized drive signal. The peak-to-peak frequency deviation of 300 MHz was attained as expected. The frequencies, f_{1} and f_{2}, exhibited variations of about +/− 1 MHz, which were larger than those in the simulation(0.2MHz), except the transition time of 1 μs. This discrepancy may be due to parameters errors used in the simulation. To overcome the frequency variation of about +/−1 MHz, the resolution bandwidth (RBW) of the ESA is adjusted to the widest value of 3 MHz for detecting the beat power with the frequency variation around |f_{1}-f_{2}|, although the minimum ESA RBW is 300 kHz. Then the frequency variations are less than the ESA RBW. Figure 5(e) shows that the beat spectrum can be easily detected with the ESA for the test signal passing through a 25.3-km SMF/DS. A large spectrum peak was observed at 300 MHz. Thus, the drive signal was successfully synthesized for enabling highly sensitive MPI measurement.

## 4. MPI measurements of single-mode fibers

The transmitter and receiver pair calibration for the MPI measurement was carried out using a Mach-Zehnder interferometer of two paths, which was described by Aida et al. [6]. One path contained an attenuator for adjusting the direct signal power to the receiver. The other path contained a Rayleigh backscattered light generator consisted of a three-port circulator and a far-end-terminated 25.3-km SMF/DS, and provided sufficient optical power to compensate the insertion loss of the optical components. The light from each path can be measured using an optical power meter and can be adjusted. Using this procedure, a calibrated MPI test signal is generated in the desired value. Precise calibrations can be carried out in the receiver saturated power region as well as liner operation. In Fig. 6 , the MPI values are calibrated at several reference points in the range of −74 to −40 dB.

Multipath interference measurements were carried out using various lengths of a standard SMF and SMF/DS. The coupled power into the photodiode of the receiver was adjusted between −7 and −3 dBm, appropriately. Figure 6 shows the relationship between MPI and fiber length, plotted for the SMF (●) and SMF/DS (▲). The solid lines in Fig. 6 are theoretical MPIs for both fibers, calculated from the following equation:

The parameters in Eq. (7) for the fiber under test were obtained from the backscattering and loss measurements as follows:

The measured MPI values agreed well with the theoretical ones for both fibers of over 10 km in length. The discrepancies between the measured MPI values and the theoretical ones over 10 km length were less than +/− 0.3 dB. A relatively large discrepancy of 1.4 dB was observed for the SMF of 3 km length. The discrete reflections from connectors at the fiber both ends were arisen, although SPC (about −50 dB) connectors were used. Because the inherent MPI of the 3-km fiber was calculated to be as small as −79.2 dB, discrete reflections strongly affected MPI measurement. This test method improved the minimum detectable MPI to as low as −78 dB, compared with that of −50 dB with conventional test methods [1, 3] and −70 dB with a method that uses an analog equalizing circuit for emitting a chirped test signal from a DFB-LD [6].

The proposed method can estimate the MPI value in the rage of −78 to −57 dB as shown in Fig. 6, because of the synthesized chirped test signal with the self-heterodyne detection and their calibrations. The estimated MPI values agreed well with the theoretical ones calculated by Eq. (7) for both fibers of over 10 km in length. This means that a fiber itself can be used as a reference MPI generator for low range of MPI value. But the proposed method is more effective to measure the wide range of MPI value.

Figure 7 shows the relationship between the MPI of fiber lines containing discrete reflections at both ends plotted for 3.0- and 40.1-km SMFs. The reflection coefficient at the far end of the fiber varied from −47 to −26.5 dB. The near end reflection coefficient was fixed at −46 dB. The solid lines in Fig. 7 are theoretical MPIs calculated from the following equation:

The measured MPI values agreed well with the theoretical ones for both fiber lines with discrete reflections.

## 5. Conclusions

We proposed an MPI test method with self-heterodyne detection that periodically inputs a synthesized chirped test signal of lightwave frequencies f_{1} and f_{2} emitted from a directly modulated DFB-LD to a distributed amplifier or transmission fiber under test. The advantage of our method is that the beat spectrum, which corresponds to a beat spectrum between the multipath signals and the direct signal, ideally concentrates at two frequencies: zero and |f_{1}-f_{2}|; the frequency |f_{1}-f_{2}| can be appropriately determined to be in the frequency band of low noise. Consequently, highly sensitive MPI measurement becomes possible. We evaluated the synthesized test signal chirp characteristics and the sensitivity of the proposed MPI test method. We found this test method improved the minimum detectable MPI to as low as −78 dB.

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