1. Introduction

Chromatic-dispersion is a critical parameter in optical fibers because it limits the data-rate of long-haul telecommunication systems and the efficiency of nonlinear four-wave mixing through pulse-broadening, walk-off, and phase mismatch. There are several approaches for the measurement of chromatic-dispersion in kilometers-long optical fibers such as the pulse-delay method [1], the modulation phase-shift method [2], and the Sagnac interferometer based method [3,4]. Chromatic-dispersion in fibers with lengths on the order of one meter is measured using methods based on Mach–Zehnder and Michelson interferometers [5, 6].

The modulation phase-shift method has been widely used because it enables the measurement of chromatic-dispersion at picosecond-level precision. This method measures the shift in the phase of a sinusoidal optical signal induced by propagation in a fiber under-test (FUT) as the laser wavelength is varied allowing for the determination of the relative groups-delay Δt_d (λ) = t_d (λ) − t_d(λ^ref) as a function of wavelength λ. Chromatic-dispersion is then obtained using D (λ) = (1/L)d{Δt_d} /dλ, where L is the length of the fiber under-test, and λ^ref is a reference wavelength. Current implementations of this method are bandwidth-limited because they utilize electronic signal-processing for phase-shift acquisition. A novel implementation that utilized all-optical signal processing for phase-shift acquisition can be achieved using a Kerr phase-interrogator [7, 8]. The Kerr phase-interrogator converts phase variation of a sinusoidal optical signals into power variation by ultrafast all-optical signal processing based on the Kerr nonlinear effect [7, 8]. The ultrafast response of the Kerr phase-interrogator opens the way for real-time monitoring of chromatic-dispersion and novel sensing devices.

In this paper, we present a novel approach for chromatic-dispersion measurement in long optical fibers by a modulation phase-shift method based on a Kerr phase-interrogator. The Kerr phase-interrogator setup is configured for chromatic-dispersion characterization by measurement of relative and absolute group-delays of a sinusoidal optical signal as a function of laser carrier wavelength. Theoretical analysis shows that the variation of the sideband power generated by nonlinear Kerr effect determines the relative group-delay when the laser wavelength is varied, and determines the absolute group-delay when the frequency of the sinusoidal optical signal is varied. Chromatic-dispersion measurement in standard single-mode silica fibers (SMF-28) and other commercially available fibers is experimentally demonstrated.

2. Experimental setup

Figure 1(a) shows the Kerr phase-interrogator configured for chromatic-dispersion measurement. Similar to the setup presented in [7], a continuous-wave (CW) laser (Agilent 81980A) with a wavelength λ_l is amplitude-modulated using a sinusoidal electrical signal generator (HP 83752A) to obtain a sinusoidal optical signal oscillating at a frequency f_s with an optical spectrum composed of two distinct peaks separated by $\mathrm{\Delta }\lambda =\left|\left(-{\lambda }_l^2/c\right)f_s\right|$, as illustrated in Fig. 1(b). A fiber-coupled polarization beam splitter splits the power of the sinusoidal signal into a FUT path and a reference path, and a circulator connects a FUT that is terminated with a mirror to the FUT path. A fiber-coupled polarization beam combiner recombines the signals from the FUT and the reference paths, and the combined signal at the output of the fiber polarization combiner is amplified using an Erbium-doped fiber amplifier (Amonics AEDFA-33-B-FA) and is launched into a nonlinear Kerr medium comprised of a 2 km long single-mode silica fiber (SMF-28e).

 

Fig. 1 Schematic of (a) the dispersion measurement setup based on a Kerr phase-interrogator, and illustrations of the spectral evolution with the variation of (b) the laser wavelength λ_s and (c) sinusoidal optical signal frequency f_s; dotted line indicates the variation of the power of the side-band as λ_l and f_s are varied. RF: radio-frequency; CW: continuous-wave; EOM: electro-optic modulator; PC: polarization controller; FUT: fiber under test; FPS: fiber polarization splitter; FPC: fiber polarization combiner; EDFA: Erbium-doped fiber amplifier; and PD: photodiode.

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Nonlinear Kerr-effect in the Kerr medium leads to the formation of distinct sidebands P_i with i = 1,2,... [7, 9, 10], as illustrated in Fig. 1(b), and the power of the first side-band is given by [7]

The relative phase Δϕ(λ_l) = ϕ(λ_l) − ϕ_ref is obtained from P₁ (λ_l) using the relation

Measurement of the relative group-delay presented above does not specify whether Δt_d increases or decreases with λ_l, and hence, does not determine whether chromatic-dispersion is normal with D_c < 0 or anomalous with D_c > 0. The absolute group-delay t_d must be measured at two consecutive wavelengths to specify the actual sign of D_c (λ_l). The Kerr phase-interrogator setup in Fig. 1(a) is modified for the measurement of t_d by replacing the optical spectrum analyzer with a 3 GHz band-pass filter (TeraXion TFC) followed by a photo-detector (New-Focus 1811) that is connected to an oscilloscope (Agilent DSO81204B). In the modified setup, the laser wavelength λ_l is fixed and the sinusoidal optical signal frequency f_s is varied which, according to Eq. (1), leads to the variation of the side-band power P₁, as illustrated by the dotted red line in Fig. 1(c). The relative phase Δϕ(f_s) = ϕ(f_s) − ϕ_init is obtained from P₁ (f_s) using

3. Experimental results

We proof-test this approach by characterization of a standard single-mode SMF-28 with L = 2.04 km. The CW laser wavelength λ_l is varied in steps of 0.1 nm and the measured spectrum at the optical spectrum analyzer is recorded for each λ_l. Figure 2(a) presents several measured spectra clearly showing the variation of the sideband power as λ_l is increased. Figure 2(b) presents the measured values of P₁ as a function of λ_l for the wavelength range between λ_l = 1545 nm and λ_l = 1555 nm. Also presented in Fig. 2(b) is the measured value of P₁ (λ_l) when the FUT is removed showing that the variation of P₁ arises only from chromatic-dispersion in the FUT. Figure 2(c) presents the measured relative phase-difference Δϕ_meas (λ_l) obtained from P₁ (λ_l) using Eq. (2), and the polynomial fit Δϕ(λ_l) obtained by fitting Δϕ_meas (λ_l) to a third degree polynomial. The value of Δt_d (λ_l) is calculated from Δϕ(λ_l) using Eq. (3) and then D_c (λ_l) is obtained by using Eq. (4). Figure 2(d) presents the resulting D_c (λ_l) showing close agreement with the results obtained using the standard modulation phase-shift method [2].

 

Fig. 2 Experimental results for chromatic-dispersion characterization of a single-mode fiber SMF-28 with L = 2.04 km showing (a) spectra at the output of the Kerr medium for several laser wavelengths λ_l, (b) side-band power P₁ as a function of λ_l, (c) phase-difference Δϕ as a function of λ_l, and (d) chromatic-dispersion D_c as a function of λ_l along with values obtained using the standard modulation phase-shift method.

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The laser wavelength is fixed at λ_l = 1545 nm and f_s is varied slowly at a rate of r = 10MHz/s from an initial value $f_s^{\mathit{init}}=20.000$ GHz to a final value $f_s^{\mathit{fin}}=20.001$ GHz and the side-band power P₁ (t) is measured using an oscilloscope. The average of 16 traces of P₁ (t) is acquired using the oscilloscope and the time variable t is replaced by the sinusoidal signal frequency f_s = rt leading to P₁ as a function of f_s. Figure 3(a) presents a section of the measurement results for P₁ (f_s) showing a sinusoidal variation of P₁ as f_s increases in agreement with Eq. (1). The phase-difference Δϕ(f_s) is obtained by applying Eq. (5) to P₁ (f_s) and the results are presented in Fig. 3(b). Application of Eq. (6) to Δϕ(f_s) results in an absolute group-delay of t_d = 20204.21458 ns at λ_l = 1545 nm. Similarly, a value of t_d = 20204.24123 ns is measured at λ_l = 1555 nm indicating that t_d decreases as λ_l increases and that chromatic-dispersion is anomalous. The chromatic-dispersion measurement process is repeated for a low-dispersion fiber with L = 5.96 km and a bend-insensitive fiber with L = 4.37 km, and the results are presented in Fig 4.

 

Fig. 3 (a) Measured side-band power P₁ and (b) the measured phase-difference as a function of $f_s-f_s^{\mathit{init}}$ with $f_s^{\mathit{init}}=20\hspace{0.17em}\text{GHz}$.

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Fig. 4 Measured chromatic-dispersion D (λ_l) for several fibers. SMF-28: standard single-mode fiber with L = 2.04 km; BIF: bend-insensitive fiber with L = 5.96 km; LDF: low-dispersion fiber with L = 4.37 km.

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We also measure chromatic-dispersion of a dispersion-shifted fiber with L = 2.27 km for which the phase-difference Δϕ does not vary monotonically with λ_l. Figure 5(a) presents the measured P₁ as λ_l is varied in steps of 0.5 nm within the wavelength range between λ_l = 1535 nm and λ_l = 1565 nm. Figure 5(b) presents the measured relative phase-difference Δϕ_meas (λ_l) and a polynomial fit Δϕ(λ_l). Figure 5(c) presents the resulting D_c (λ_l) showing a value of 0 ps/nm-km at λ_l = 1552 nm in close agreement with the value obtained using the standard modulation phase-shift method. The measured absolute group-delay t_d is 22298.17251 ns at λ_l = 1535 nm, 22298.13254 ns at λ_l = 1550 nm, and 22298.17712 ns at λ_l = 1565 nm indicating that chromatic-dispersion is normal for λ_l < 1552 nm and anomalous for λ_l > 1552 nm.

 

Fig. 5 Experimental results for chromatic-dispersion characterization of a dispersion-shifted fiber with L = 2.27 km showing (a) the measured P₁ (λ_l), (b) measured phase-difference Δϕ(λ_l), and (c) measured chromatic-dispersion D_c (λ_l) along with the standard modulation phase-shift method measurement results.

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The precision of this method is obtained from the minimum detectable phase-difference $\mathrm{\Delta }{\varphi }^{\mathit{min}}=\pi f_s\mathrm{\Delta }{t}_d^{\mathit{min}}=\alpha$ [7]. Using f_s = 20 GHz and α = 10⁻² leads to a minimum detectable relative group-delay of $\mathrm{\Delta }{t}_d^{\mathit{min}}=159\hspace{0.17em}\text{fs}$. It is possible to achieve f_s = 100 GHz by using commercially available 50 GHz electro-optic modulators [7] leading to $\mathrm{\Delta }{t}_d^{\mathit{min}}=32\hspace{0.17em}\text{fs}$. Furthermore, the limits of chromatic-dispersion measurement approach are estimated from the group-delay variation rate ρ = D × L = Δt_d/Δλ [4, 11]. The minimum measurable chromatic-dispersion is ${\rho }^{\mathit{min}}=\mathrm{\Delta }{t}_d^{\mathit{min}}/\mathrm{\Delta }{\lambda }_l^{\mathit{max}}=\alpha /\pi f_s\mathrm{\Delta }{\lambda }_l^{\mathit{max}}$ with $\mathrm{\Delta }{\lambda }_l^{\mathit{max}}$ being the maximum laser scanning range. In our experimental setup, $\mathrm{\Delta }{\lambda }_l^{\mathit{max}}=30\hspace{0.17em}\text{nm}$ is limited by the gain region of the Erbium-doped fiber amplifier, f_s = 20 GHz, and α = 10⁻² leading to ρ^min = 5.3 fs/nm. The maximum measurable chromatic-dispersion is ${\rho }^{\mathit{max}}=\mathrm{\Delta }{t}_d^{\mathit{max}}/\mathrm{\Delta }{\lambda }_l^{\mathit{min}}$ where Δλ_min is the minimum laser step. Requiring N sampling points within a cycle of P₁ (λ_l) leads to Δϕ^max = π/N which corresponds to $\mathrm{\Delta }{t}_d^{\mathit{max}}=1/N{f}_s$ and ${\rho }^{\mathit{max}}=1/N{f}_s\mathrm{\Delta }{\lambda }_l^{\mathit{min}}$. Using the minimum wavelength step of our tunable laser Δλ_min = 0.001 nm, f_s = 20 GHz, and N = 15 leads to ρ^max = 3.33 ns/nm.

4. Conclusion

We present a novel approach for chromatic-dispersion measurement based on a Kerr phase-interrogator. Chromatic-dispersion in four commercially available fibers has been characterized. Unlike conventional modulation phase-shift implementations, the novel approach acquires the phase-shift of a sinusoidal optical signal by ultrafast all-optical signal-processing rather than electronic signal-processing. Utilization of ultrafast all-optical signal-processing in the implementation of the phase-shift method allows for real-time chromatic-dispersion monitoring and novel sensing devices as will presented in future work.