Chromatic dispersion measurement based on a high-Q optoelectronic oscillator incorporating cascaded FIR and IIR filters

Yu Tang; Muguang Wang; Beilei Wu; Jing Zhang; Qi Ding; Hongqian Mu; Bin Yin; Jian Sun; Fengping Yan

doi:10.1364/OSAC.1.001205

1. Introduction

Chromatic dispersion is an important parameter in long-haul and high-speed communication system and networking such as wavelength division multiplexing (WDM) systems, radio over fiber (RoF) systems [1] and optical soliton generation in optical time division multiplexing (OTDM) systems. Optical signals get worse and result in deterioration of bit error rate (BER) finally since different frequency components with different transmission speeds due to fiber dispersion cause pulse broadening, inter-symbol interference (ISI), frequency-selective power fading and so on. In order to carry out chromatic dispersion management or compensation of fiber transmission links, chromatic dispersion of optical fibers and components must be evaluated first.

Dispersion measurement has been widely researched and reported based on various methods [2] such as phase shift method [3], interferometric method [4,5] and time of flight method [6,7] in the last decades. These traditional measurement techniques make use of the different times or phases that the light pulses take to travel along a fiber at different wavelengths. In addition, interferometric technique such as the dispersive fringes method is also utilized to characterize the chromatic dispersion of short fiber. However, the setups are bulky and costly because narrow pulse generator and array of lasers are inevitable for phase shift method and time of flight method. The reference fiber in an interferometric method is susceptible to environment influences. Recently, chromatic dispersion measurement based on microwave photonic technique is attracting more and more attention because of the inherent excellent and flexible performance of microwave photonics. In Ref. [8], S. Zhang et al. demonstrated an approach based on a chirped intensity-modulated signal rather than a critical chirp-free operation to realize fiber chromatic dispersion measurement. In this approach, only one notch of the transfer function is needed so the range can be expanded compared to the methods using two notches. The chromatic dispersion can be derived by analyzing the transfer function of the fiber under test measured by a vector network analyzer (VNA). J. Keum-Soo et al. took advantage of a bidirectional modulation of an Mach-Zehnder modulator (MZM) to monitor the chromatic dispersion by measuring the time delay introduced by the device under test (DUT) on different wavelengths which can be obtained by analyzing the radio frequency (RF) interference fringe [9]. Note that the frequency span of the VNA should be properly chosen to avoid aliasing of data. In Refs. [10,11], M. Zhang et al. proposed a dispersion measurement method by modulating an RF signal on two laser diodes (LDs) with different wavelength and scanning the wavelength of one LD. Chromatic dispersion can be calculated from the power value of the microwave signal generated by interfering the two modulated optical light waves and detecting them after a photodetector (PD). However, two LDs including a tunable one are needed in this method, which makes the system costly. Another way to do chromatic dispersion evaluation is to analyze the envelope of electrical spectrum characterized by power fading effect [12]. An expensive tunable microwave source is needed in this experiment. What’s more, the notch frequencies where the envelope vanishes are under the influence of the noise floor in this technique.

An optoelectronic oscillator (OEO) is a versatile positive feedback loop which is usually made up of a laser, an electro-optic modulator (EOM), a PD, an electrical bandpass filter (EBPF) and an electrical amplifier (EA) [13]. The EBPF can be replaced by a broadband microwave photonic filter (MPF) to make the signal generated by the OEO have virtues of ultra-low phase noise, wide tunability and high signal-to-noise ratio. In addition, an MPF embedded in an OEO is also a good candidate to convert various parameters including physical, chemical, biological parameters to microwave frequency information which can be conveniently and precisely detected in the electrical domain. Therefore an OEO has great application prospects in sensing field such as temperature sensing, strain sensing and pressure sensing [14,15].

In this paper, we report an OEO based on a single bandpass MPF consisted of a finite impulse response (FIR) filter cascading with an infinite impulse response (IIR) filter to realize high-speed and high-sensitivity dispersion measurement. To the best of our knowledge, it is the first time that an OEO is applied for chromatic dispersion measurement. Chromatic dispersion can be extracted from the OEO oscillating frequency co-determined by the IIR filter and the FIR filter, whose central frequency dependent on the time delay difference of the two arms of a Mach-Zehnder interferometer (MZI) and the dispersion value of the optical fiber or component under test. A recirculating fiber loop, i.e., the IIR filter, is inserted in the OEO loop to strengthen the oscillation. Both theory analysis and experiment verification are carried out. The single mode fibers (SMFs) under test with lengths ranging from 20 km to 100 km are measured. The measurement result difference between our method and the commercial chromatic dispersion measurement system using time of flight method is less than 3.2%.

2. Principle

The experimental configuration of the OEO-based chromatic dispersion measurement approach is shown in Fig. 1

Fig. 1 Configuration of the OEO based on a single bandpass microwave photonic filter for dispersion measurement. EDFA: erbium-doped fiber amplifier, OF: optical filter, Pol: polarizer, OC: optical coupler, PC: polarization controller, Att: attenuator, VTDL: variable time delay line, PM: phase modulator, PD: photodetector, EC: electrical coupler, EA: electrical amplifier, ESA: electrical spectrum analyzer.

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. The novel point of the designed approach is to extract chromatic dispersion of the DUT from the oscillating frequency of the OEO with the DUT embedded in the loop. A cost-effective erbium-doped fiber amplifier (EDFA) as a broadband optical source (BOS), an MZI, a DUT, together with a PD make up an FIR-MPF. The FIR filter is established with the variable optical carrier time shift (VOCTS) method [16]. The light waves from the BOS are divided into two branches and time shifted in one branch, so the BOS is sliced without the coherent problem. Finally, a multi-tap filter free from baseband response is formed. Optical-to-electrical conversion is performed by a PD after the light waves go through a DUT and a fiber ring-based IIR filter. By injecting the amplified microwave signal to the RF input port of the phase modulator (PM), the OEO loop is closed. An electrical spectrum analyzer (ESA) is employed to detect the oscillating frequency of the OEO.

Because chromatic dispersion is a wavelength-dependent physical parameter, the central wavelength of an optical filter (OF) is set according to the wavelength at which chromatic dispersion is to be measured. The electrical field at the output of the polarizer (Pol) can be expressed as

e (t) = \frac{1}{2 π} \int E (Ω) \exp (j Ω t) d Ω

and E(Ω) can be written as

E (Ω) = \sqrt{N (Ω)} \exp (j θ (Ω))

where N(Ω) is the power spectral density and θ(Ω) is the phase of the frequency component. The statistical properties of θ(Ω) is given by [17]

< \exp (j θ (Ω)) > = 0

< \exp (j (θ (Ω) - θ (Ω^{'}))) > = 2 π δ (Ω - Ω^{'})

where < > denotes ensemble average. Then the polarized light is injected into an MZI in which a PM and a variable time delay line (VTDL) are incorporated in the two arms respectively. Compared to MZM, the utilization of a PM can avoid the DC bias drift problem and make the measurement system simpler and more stable. Two polarization controllers (PCs) are also embedded into the MZI to adjust the polarization of the light waves paralleling with the principal direction of the PM and make the lights in two arms have the same polarization state. Two 3-dB optical couplers (OCs) and an attenuator (ATT) in the upper arm are used to guarantee the two light branches to combine at the output of the MZI with the same optical power. The VTDL in the upper arm is adopted to control the time delay of the lights in two arms so that the oscillating frequency is within the operating bandwidth of the PD and PM. The light in the upper branch at the output from the VTDL can be described as

E_{u p} (Ω) = E (Ω) \exp (- j Ω Δ τ)

where Δτ is the light travelling time difference between the upper and lower branches determined by the initial arm length difference and the VTDL, which can be expressed by

Δ τ = \frac{n Δ l}{c}

where n is the effective refractive index of the fiber, c is the light speed in vacuum, and Δl is the length difference of the two arms. The free spectrum rang (FSR) of MZI response is as follows:

λ_{F S R} \approx \frac{λ^{2}}{n Δ l} = \frac{λ^{2}}{c Δ τ}

Considering the PM in the lower branch is modulated by a microwave signal given by Acos(ω_mt) where A and ω_m are the amplitude and angular frequency of the microwave signal, respectively, the electrical field at the output of the PM can be expressed as following under small-signal modulation

\begin{array}{l} e_{d o w n} (t) = e (t) \exp (j (γ c o s (ω_{m} t))) \\ = e (t) \sum_{n = - \infty}^{n = \infty} j^{n} J_{n} (γ) e x p (j n ω_{m} t) \\ \approx e (t) [J_{0} (γ) + j J_{1} (γ) e x p (j ω_{m} t) + j J_{1} (γ) e x p (- j ω_{m} t)] \end{array}

where γ = πA/V_π is the modulation index and J_n is the nth-order Bessel function of the first kind. Applying the Fourier transform to both sides of Eq. (8), the electrical field in the frequency domain can be written as

E_{d o w n} (Ω) = J_{0} (γ) E (Ω) + j J_{1} (γ) E (Ω - ω_{m}) + j J_{1} (γ) E (Ω + ω_{m})

Afterwards the light waves in two branches are combined to a beam of light by the OC₂. The electrical field at the output of MZI can be expressed as

E_{M Z I} (Ω) = E_{u p} (Ω) + E_{d o w n} (Ω)

Note that the losses all are omitted for simplification in the above derivations. Then the light wave goes through a dispersive device to be measured such as dispersion compensating fiber (DCF) or SMF. The DUT can be regarded as a phase filter, whose transfer function can be expressed as

T (Ω) = | T (Ω) | \exp [- j Φ (Ω)]

where |T(Ω)| = 1 and Φ(Ω) can be given by the Taylor expansion

Φ (Ω) \approx Φ (Ω_{0}) + τ_{0} (Ω - Ω_{0}) + \frac{1}{2} β_{2} {(Ω - Ω_{0})}^{2}

where τ₀ and β₂ are the group delay and the total dispersion centered at Ω₀, separately. After the DUT, the signal can be expressed as

E_{D U T} (Ω) = E_{M Z I} (Ω) T (Ω)

According to the square-law detection of the PD, the spectrum of the photocurrent can be written as

\begin{array}{l} I (ω) = r < \frac{1}{2 π} E_{D U T} (ω) \otimes E^{*}_{D U T} (- ω) > \\ = \frac{r}{2 π} \int < E_{M Z I} (Ω) E^{*}_{M Z I} (Ω - ω) > T (Ω) T^{*} (Ω - ω) d Ω \end{array}

where ω is the angular frequency of the microwave signal and r is the responsivity of the PD. Recall that frequency-domain expression of the input signal is πA[δ(ω-ω_m) + δ(ω-ω_m)], therefore the transfer function of the FIR-MPF can be described by

H (ω) = I (ω) / {π A [δ (ω - ω_{m}) + δ (ω + ω_{m})]} = H_{0} (ω) + H_{1} (ω)

where

H_{0} (ω) = \frac{2 r J_{0} (γ) J_{1} (γ)}{π A} \exp (- j ω τ_{0}) \sin (β_{2} ω^{2} / 2) H_{b} (ω)

\begin{array}{l} H_{1} (ω) = \frac{r J_{1} (γ)}{π A} \exp (j π / 2 - ω τ_{0} - β_{2} ω^{2} / 2 + Δ τ Ω_{0}) H_{b} (ω - \frac{Δ τ}{β_{2}}) \\ + \frac{r J_{1} (γ)}{π A} \exp (- j π / 2 - ω τ_{0} + β_{2} ω^{2} / 2 - Δ τ Ω_{0}) H_{b} (ω + \frac{Δ τ}{β_{2}}) \end{array}

where H_b(ω) = ∫N(Ω)exp[-jωβ₂(Ω-Ω₀)]dΩ is the baseband response.

As can be seen in Eq. (17), the MPF has a single passband. The central frequency of the passband satisfies

- Δ τ + ω_{0} β_{2} = 0

It can be seen that the central frequency of the single bandpass MPF, as well as the oscillating frequency of the OEO, depends on Δτ and β₂. Hereto, by measuring the oscillating frequency of the OEO, we can obtain the chromatic dispersion of the DUT.

Deriving from Eq. (6), Eq. (7) and Eq. (18), the central frequency of the passband of the FIR filter can be written as

ω_{0} = \frac{Δ τ}{β_{2}} = \frac{2 π}{D \cdot λ_{F S R}}

where D is the total dispersion and β₂ and D have the relationship of D = - 2πcβ₂ /λ².The mode spacing of the OEO is expressed as f _FSR1 = 1/τ₁, where τ₁ is the time delay caused by the OEO delay line. The long fiber under test also offers a long delay line so the OEO is a high-Q one. For a fiber with a length of 20 km, the mode spacing of the OEO is about 10 kHz. According to Eq. (17), the 3-dB bandwidth of the FIR filter is tens of MHz to several hundred MHz. However, the 3-dB bandwidth of the FIR filter could be slightly enlarged because of dispersion slope. Considering the small mode spacing of the OEO, to suppress the side mode and make the oscillation more stable, an additional IIR filter is employed [18]. A recirculating fiber loop which is made of a 2 × 2 3-dB OC and a section of SMF is cascaded with the FIR filter. One output of the OC is fed back to one input of the OC, producing an impulse response of infinite duration. The transfer function of the fiber ring resonator can be expressed as [19]

H (ω) = \frac{η + (1 - 2 η) e x p (- j ω τ_{2})}{1 - η e x p (- j ω τ_{2})}

where η is the coupling ratio. The FSR of the IIR filter meets

f_{F S R 2} = \frac{1}{τ_{2}} = \frac{c}{n L_{2}}

where L₂ is the length of the fiber ring. In the pass band of the FIR filter, small pass bands are selected by the IIR filter. The total response of the bandpass filter is the superposition of the responses of both the FIR and IIR filters. Thus, it has a high-Q value.

Note that the oscillating frequency mainly depends on the central frequency of the FIR filter, while the resolution of the measurement is decided by the FSR of the IIR filter. When the OEO oscillation is established, the dispersion of the DUT can be mapped to the oscillating frequency. The measurement utilizes the Vernier effect [20], where the main scale is dominated by the FIR filter and Vernier scale is determined by the IIR filter. The mode spacing of the OEO has a very slight influence to the measurement compared to the IIR filter.

3. Experimental results and discussion

An experiment as a proof of concept is performed based on the setup in Fig. 1. First the light emitted by a home-made EDFA used as a BOS is tailored by an OF (Finisar, 1000S) and polarized by a Pol. The 3-dB bandwidth of the OF is set to be about 5 nm, and the central wavelength of the OF ie, λ₀ is first set at 1540 nm to measure the dispersion of DUT at this wavelength. Afterwards the light is coupled into an MZI by the 3-dB OC₁. The 3-dB bandwidth and the half-wave voltage of the PM (EOSPACE) in the lower arm is 10 GHz and 3V, respectively. The ATT is set to 6 dB insertion loss to harmonize the optical powers of the upper arm and the lower arm. The PD has a 3-dB bandwidth of 10 GHz. To make sure that the oscillation signal can be detected by the PD, the time delay of the two arms is adjusted to be 13.1 ps by using a VODL (General Photonics, 0~350 ps) embedding in the upper arm of MZI in our experiment, corresponding to an FSR of 0.612 nm, which can be seen from Fig. 2

Fig. 2 The optical spectrum at the output of the OC₂ when the central wavelength of the OF is set to be 1540 nm.

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by monitoring the optical spectrum at the output from OC₂ using an optical spectrum analyzer (OSA, Ando AQ 6317C) with a wavelength resolution of 0.01 nm. In order to narrow the bandwidth of the MPF, an IIR based on a recirculating fiber loop structure with length of 6 m is employed. An EA (SHF, 806E) is used to amplify the electrical signal in order to provide enough gain for the oscillation. An ESA (Agilent N9010A) is used to monitor the oscillating microwave signal of the OEO.

Firstly, the measurement at the wavelength of 1540 nm is performed. The DUT in the experiment are eight spools of fibers with different chromatic dispersion and the fiber lengths range from 20 km to 100 km. The oscillating frequencies that change with the dispersion of the eight spools of fibers are shown in Fig. 3

Fig. 3 Experimentally measured frequency spectra of the generated microwave signals when different fibers with different dispersion are inserted into the OEO loop (The central wavelength of the OF is 1540 nm).

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. More than 37-dB side-mode suppression ratio is achieved. Also some small higher harmonics of the oscillating frequencies which are caused by the nonlinearity of the loop are also detected. The chromatic dispersion of the DUT measured by a chromatic dispersion measurement system (CD400, PE. Fiberoptics Ltd) [21] which utilizes the time of flight method and our OEO are compared in Fig. 4

Fig. 4 Chromatic dispersion at the wavelength of 1540 nm measured by CD400 and our OEO, respectively.

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. As can be seen, there is a good agreement between the two results. The measurement result difference between the two methods is less than 2.9%.

Then the measurement at the wavelength of 1550 nm is conducted as well. The 3-dB bandwidth of the OF is set to be about 5.2 nm. The FSR of the MZI is about 0.68 nm. The experimental results of optical spectrum and electrical spectrum are shown in Fig. 5

Fig. 5 The optical spectrum at the output of the OC₂ with a central wavelength of 1550 nm.

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and Fig. 6

Fig. 6 Experimental measured frequency spectra of the generated microwave signals when different fibers with different dispersion are embedded to the OEO (The central wavelength of the OF is 1550 nm).

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, separately. The side-mode suppression ratio is about 35 dB. As can be seen in Fig. 7

Fig. 7 Chromatic dispersion at the wavelength of 1550 nm measured by CD400 and our OEO, respectively.

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, the measurement results of the two methods match well. The measurement result difference between the two methods is less than 3.2%.

As mentioned above, the chromatic dispersion of several spools of fibers at the wavelength of 1540 nm and 1550 nm are measured by testing the oscillating frequencies of the OEO, respectively. We assume the chromatic dispersion measurement by CD400 is the reference value whose measurement uncertainty is less than 1.5% according to the datasheet. The measured results by OEO match well with the results by using CD400. Totally speaking, the measurement error gets larger when the oscillating frequency gets smaller, as can be seen from Fig. 4 and Fig. 7. It can be explained according to Eq. (19) that the same frequency error will lead to a larger chromatic dispersion error when the oscillating frequency is small. The sensitivity is dependent on the dispersion value. Higher sensitivity is obtained when the dispersion value gets smaller.

In the above discussion, dispersion slope is neglected in order to simplify the analysis, which also is in line with the actual situation. For example, in a condition where the bandwidth of the OF is 5 nm, the DUT is a 20-km SMF and the oscillating frequency is 5 GHz, the frequency shift Δω/ω₀ caused by the dispersion slope is around 0.004375% corresponding to 0.22 MHz according to Ref. [22]. The FSR of the IIR filter is about 30 MHz, so the maximum measurement error caused by the IIR is about 15 MHz, with equivalent chromatic dispersion of 0.05 ps/(nm∙km). Table 1

Table 1. Comparison of Dispersion Measurement Techniques

View Table

compares different measurement techniques including the traditional ones and the ones based on microwave photonic methods. The lengths of fibers under test and measurement error are listed. Compared to the result in [8] (with a relative error of 3.46%), [9] (with a measurement difference of 0.19 ps/nm/km) and [11] (with a measurement difference of 0.21 ps/nm/km), our method has a better performance.

4. Conclusion

In conclusion, a novel approach to realize chromatic dispersion measurement has been proposed and experimentally demonstrated. The novelty lies in that the chromatic dispersion is estimated by measuring the oscillating frequency of the OEO so the measurement is high-speed and high-resolution. Because neither VNA nor extra microwave source is needed, the method is also simple and cost-effective. Additionally, the application of a PM can avoid bias drift problem. An experiment has been carried out to verify the approach and chromatic dispersion measurement result difference between our method and the time of flight method by a commercial CD400 is less than 3.2%.

Funding

Fundamental Research Funds for the Central Universities (2018JBZ109); National Natural Science Foundation of China (61475015, 61775015, 61827818 and 61671047).

References

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Type		Range (Length of fiber under test)	Performance
Traditional techniques	Phase-shift technique [3]	101.9 km	0.02 ps/nm/km accuracy
	Interferometric technique [2,4,5]	<0.005 km	0.1 ps resolution
	Time of flight [2,6,7]	>0.5 km	2 ps/nm/km accuracy
Microwave photonic techniques	Chirped intensity modulation [8]	6.1 km −81.5 km	3.46% relative error
	Bidirectional modulation [9]	2.235 km	0.19 ps/nm/km accuracy
	Microwave interference [11]	25 km	0.21 ps/nm/km accuracy
	Proposed OEO-based method	20 km-100 km	3.2% relative error

Chromatic dispersion measurement based on a high-Q optoelectronic oscillator incorporating cascaded FIR and IIR filters

Abstract

1. Introduction

2. Principle

3. Experimental results and discussion

4. Conclusion

Funding

References

Cited By

Figures (7)

Tables (1)

Equations (21)

OSA Continuum