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A self-reference, single-shot characterization technique is proposed and demonstrated for simultaneously measuring the instantaneous frequencies and phases of multi-wavelength optical signals using a single processing and detection platform. The technique enables direct real-time optical sampling of the instantaneous frequencies of amplitude and/or phase modulated signals simultaneously at different wavelengths without requiring the use of any optical reference. Simultaneous real-time instantaneous frequency and phase measurements of a chirped 1 GHz-sinusoid intensity modulation signal and a 3 Gbps-PRBS (pseudo-random binary sequence) phase-modulated signal at two different wavelength channels have been performed for the proof-of-concept demonstration.
©2010 Optical Society of America
1. Introduction
Direct measurement and real-time monitoring of the instantaneous frequency or phase profiles of a high-speed optical signal is of great importance in a wide range of scientific and technical fields. This functionality is particularly important in fiber-optic communication systems, e.g. for diagnosing a variety of optical processes, such as modulation, switching, amplification, wavelength conversion as well as for tracking signal impairments in long-distance data transmission induced by chromatic dispersion, nonlinearities, etc [1–12]. In this context, it is highly desired to implement direct, self-reference, single-shot measurements with a fast update rate in order to be able to track and display the signal impairments and conditions in a fast-reconfigurable real-time mode. Recently, a self-reference single-shot measurement technique for monitoring the instantaneous frequency of single-wavelength arbitrary optical waveforms has been proposed and demonstrated [10]. This technique is based on dual-balanced, all-optical coherent differentiation, originally named as ‘phase reconstruction using optical ultrafast differentiation (PROUD)’ [8]. The dual-balanced PROUD method in Ref [10]. features a non-sequential detection of the intensity waveforms required for instantaneous frequency characterization (original signal intensity and differentiated signal intensity), which in turn enables single-shot and real-time full characterization of arbitrary complex optical waveforms, including direct visualization of the instantaneous frequency profile of phase-modulated signals, a. This previous method has proved useful for characterizing optical signals with arbitrary amplitude and/or phase modulation formats regardless of their data bit rates (only limited by the measurement platform bandwidth).
In this communication, we propose an extension of the basic dual-balanced PROUD scheme [10] to achieve simultaneous, real-time instantaneous frequency and phase characterization of wavelength-division-multiplexed (WDM) signals using a single processing and detection platform. The proposed method can be potentially used for real-time monitoring of the instantaneous frequency and the temporal phase of high-speed signals in a WDM communication scheme. Our proposed measurement system is based on the use of a self-referenced technique, which dramatically simplifies the detection process by avoiding the need for stable optical reference sources. This should be contrasted with optical reference – based methods, such as homodyne or heterodyne schemes using an optical local oscillator [13], which may require the use of multiple reference sources and receivers for the WDM system, determined by the number of wavelength channels to be characterized. The technique proposed here enables simultaneous detection and statistical visualization and monitoring of amplitude and/or phase encoded signals across multiple wavelength channels only requiring the use of a single processing and detection unit. Here, we experimentally demonstrate, for the first time to our knowledge, real-time instantaneous frequency and phase characterization of two simultaneous wavelength channels over a detectable instantaneous frequency bandwidth of more than 15 GHz without using any referenced optical coherent source. To prove the capability of our setup for measuring arbitrary modulations, the signals under test are modulated (i) in phase with a 3 Gbps PRBS (pseudo-random binary sequence with a total number of bits: 215-1) and (ii) in amplitude with a sinusoid at 1 GHz, respectively, and subsequently amplified in a semiconductor optical amplifier (SOA) inducing additional frequency chirp due to the gain modulation.
2. Operation principle
In the recently introduced dual-balanced optical differentiation technique [10], the differentiation operation consists of two linear-amplitude optical filters, namely frequency-shifted optical differentiators, which provide spectral transfer functions that depend linearly on the frequency variable in such a way that the amplitude variation slopes of the two filters are identical in magnitude but with opposite signs, i.e. the corresponding spectral transfer functions can be mathematically described as jA(ω-Δω) and -jA(ω+Δω), respectively, where Δω is the frequency shift of the signal carrier frequency (ωi) with respect to the filter’s zero transmission frequency, ω is the base-band angular frequency in reference to the signal carrier, and A is a constant factor (slope magnitude). We assume that the signal under test has a temporal complex envelope defined by s(t) = |s(t)|exp[j ϕs(t)]. The signal is launched into the described dual-balanced optical differentiator. Assuming that the available photo-detectors have a bandwidth large enough to accurately capture |s(t)|, then the photo-detected intensity at the output of each of the balanced differentiation filters is proportional to [10]:
These two outputs in Eq. (1) have common terms (amplitude, amplitude differentiation, second-order term of the instantaneous frequency, and common intensity noise) that can be canceled out by a subtraction operation (practically implemented using a balanced photoreceiver) in such a way that only the desired instantaneous frequency information will remain. In other words, balancing the two output intensities followed by a subtraction operation enables a direct detection and visualization of the instantaneous frequency [10], i.e. the balanced photodetected current is proportional to: According to Eq. (2), one can directly obtain the desired instantaneous frequency information by simply dividing the balanced output signal by the input signal intensity. The signal phase can then be reconstructed by numerical cumulative integration of the obtained instantaneous frequency. The linear optical filtering that is required for temporal differentiation can be implemented using different fiber-optic filter technologies, such as a long period fiber gratings [14], fiber Bragg gratings [15], two-arm interferometers [16] etc. A fiber-optics Mach-Zehnder interferometer (MZI) was employed as the dual-balanced optical differentiator in our previous work on balanced PROUD [10]. This implementation is particularly interesting because the desired balanced transfer functions can be directly obtained at the two outputs of the MZI, see discussions below.The key idea in our new proposal here is based on the fact that if the dual-balanced optical differentiator is practically implemented using a two-arm interferometer (e.g. MZI), the optical spectral transfer function for the differentiation process, which extends over a limited (operation) bandwidth, is periodically repeated along the optical frequency domain with a period defined by the interferometer’s free-spectral range (FSR). A schematic of the concept is illustrated in Fig. 1(a) in which the spectral transfer functions corresponding to the two outputs of a MZI are also shown. The frequency operation range, over which each spectral transfer function has a linear-amplitude profile, can be found between the constructive and the destructive spectral interference points at each one of the outputs; as required for dual-balanced differentiation the linear-amplitude transfer functions corresponding to the two outputs around each of the cross-point wavelengths exhibit the same slope but with opposite signs, (see the graphic illustration in the middle of Fig. 1(a)) Hence, the two linear curves around any given cross-point wavelength approximate very nearly the two ideal transfer functions defined above over a frequency range given by a fraction of the FSR. Furthermore, since the respective spectral transfer functions repeat periodically along the optical spectrum with a period defined by FSR= 2πc/l, the same dual-balanced differentiation process can be simultaneously applied over many wavelength channels (equi-spaced in frequency by the interferometer’s FSR) for WDM signal analysis and characterization. Here l is the optical path-length difference between the interferometer arms and c is the speed of light.
Fig. 1 (a) Principle of multi-wavelength balanced differentiation. (b) Experimental diagram for measuring the instantaneous frequencies of two wavelength channels based on the multi-wavelength balanced PROUD technique.
The inset in Fig. 1(a) shows an example of the spectral energy density representing the periodic transfer function of the balanced differentiator with a 41 GHz FSR at two different wavelength channels (ω1 and ω2) where both channels are multiplexed via a WDM filter with 200 GHz channel spacing. As a main advantage, this feature enables the simultaneous implementation of balanced differentiation of multi-wavelength optical signals using a single passive optical filter, which enables simultaneous characterization of the instantaneous frequency profiles of these multi-wavelength signals using a single processing and detection platform. This compares favorably to conventional coherently-referenced signal characterization techniques, in which the demodulation process needs to be implemented separately for different wavelength channels [12].
3. Experiments
a. Proof-of-concept experiments
Figure 1(b) shows the schematic for the proof-of-concept experimental setup aimed to demonstrate simultaneous instantaneous frequency detection of two-wavelength multiplexed signals. To illustrate the capability of detecting two different modulation characteristics, one signal centered at 1550.9 nm (ω1= 2π×193.4 THz) was modulated using a high-speed phase modulator with a 3-dB bandwidth of 30 GHz. Its modulation format was a pseudo-random binary sequence, PRBS, having a bit-length period of 215-1 at 3 Gb/s. The rising time of the phase modulation was shorter than 300 ps. The other signal, centered at 1549.3 nm (ω2=2π×193.6 THz,200 GHz off the phase modulated signal), was modulated using a intensity modulator driven by a 1 GHz sinusoid continuous waveform and was subsequently amplified in a semiconductor optical amplifier (SOA) to add a strong frequency chirp induced by the SOA intensity-dependent gain modulation. After the modulations and amplifications, the two wavelength-multiplexed signals were combined through a WDM filter (not shown in the diagram). The qualitatively expected intensity and phase profiles are illustrated in Fig. 1(b). To be able to display the two characterized results using a single oscilloscope channel, the signals were first temporally gated, each over a time duration of ~42 ns, using a 2.5 GHz Mach-Zehnder modulator (JDSU Inc.) and subsequently time delayed with respect to each other using a paired WDM filter system with a 10-meter delay line at ω2, corresponding to a relative time delay between the two signals (~50ns) longer than the gate duration. The signal isolation was around 20 dB determined by the on/off extinction ratio of the modulator. The gated-and-delayed multi-wavelength signal was split into two paths through a fiber coupler with 50/50 split ratio. One was differentiated in the balanced optical differentiator which consisted of a fiber-optic MZI with a relative length difference of ~4.8 mm, in which the fiber arms were tightly fixed on a package.
For long-term monitoring with a reasonable stability, an appropriate feedback control may be necessary for maintaining the temperature in the MZI-based differentiation device. The spectral interference pattern, whose phase slowly drifts depending on the environment temperature, was stable enough to observe the targeted results (i.e. the instantaneous frequencies) in real time for more than a minute. The corresponding FSR of the interferometer was 41 GHz (spectral transmission at the output of the differentiator was measured with a broadband source and is shown in the inset of Fig. 1(a)). The two differentiated outputs were sent to a 23-GHz (3-dB bandwidth) balanced photoreceiver (DSC-R410, Discovery Semiconductor inc.) and sampled at 25 GS/s using a real-time oscilloscope (DPO70804, Tektronix) with a 3-dB bandwidth of 8-GHz. The input signal intensity waveforms were detected and sampled through the other fiber-coupler output using a 2.8-GHz single-ended photodetector (Series F InGaAs-2 Mod 42A, MFA optics). The use of a detector with a bandwidth smaller than the oscilloscope bandwidth (8GHz) ultimately limited the detectable bandwidth of the amplitude-modulated signal because the complete reconstruction of its instantaneous frequency requires the intensity profile of the input signal (this measurement is however not required in the case of the phase-only modulated signal).
Figure 2 shows persistent-mode acquisitions of the two acquired intensity waveforms, i.e. the balanced differentiation output and the original signal intensity. The phase modulation and the chirped amplitude modulation at different wavelength channels were simultaneously acquired along two different, sequential time intervals as defined by the gating process. The persistent time was 50 ms and the full measurement time window was 100 ns. Due to the random nature of the PRBS phase modulation, the up-shift and the down-shift of the instantaneous frequency pattern could be visualized within the same time frame (see Fig. 2(b)). The instantaneous frequency of the chirped amplitude modulation varied depending on the modulator bias condition and the state of polarization of the signal in the SOA [17]. One of the acquired waveforms is shown in Fig. 2(c). A single-shot measurement is also shown in Fig. 3 with properly calibrated instantaneous frequency scales. Figure 3(a) shows the directly acquired waveforms from the balanced differentiation output (brown color) and the original signal intensity (orange color) at 25 GS/s. To obtain each instantaneous frequency profile, the corresponding balanced differentiation output was divided by the original intensity waveform and multiplied by the calibration factors of 21.0 GHz/V and 18.2 GHz/V for the phase modulation signal and the chirped amplitude modulation signal, respectively. It is worth noting that this calibration factor is proportional to the slope of the linear spectral amplitude (transfer function of the temporal differentiator) with respect to frequency and the input signal average power [8]. In our experiment, the coefficients have been directly determined by the following procedure: (1) The input driving electric signal was first acquired using the oscilloscope and this measured profile was then numerically converted into the corresponding phase profile by assuming that the π phase shift is obtained at Vπ = 6 V (nominal value of the used EO modulator) ; (2) A numerical derivative of the phase profile was subsequently performed to estimate the maximum frequency shift induced by the electro-optic modulation; (3) Finally, the estimated maximum frequency shift was compared to the direct optical instantaneous frequency detected by the photoreceiver (scaled in Voltage). The different calibration factors for the two different modulations are attributed to the difference in the corresponding signal powers. In Fig. 3, a dynamic movie with an update rate of 3 frames-per-second (fps) is shown (Media 1) demonstrating that the two independent instantaneous frequency profiles were simultaneously reconstructed in real time. Every loop of acquisition and calculation took approximately 250ms. One can observe the dynamic behavior of the instantaneous frequency of the random signal in Fig. 3(b) whereas as expected, the instantaneous frequency for the case of intensity modulation with a sinusoid was static.
Fig. 2 Persistent-mode acquisition of the instantaneous frequencies of phase (b) and amplitude (c) modulated signals. (a) A full-scale view of the direct simultaneous acquisition of the instantaneous frequencies at two different wavelength channels. Magnified images of the instantaneous frequencies of the phase-modulated (b) and the amplitude modulated and amplified (c) signals.
Fig. 3 Direct single-shot measurements of the instantaneous frequency profiles with properly scaled frequency axex are shown in real time at 3 fps. (a) a full-scale view of the direct simultaneous acquisition of the instantaneous frequencies at two different wavelength channels. (b) instantaneous frequency of the phase modulated signal. (c) instantaneous frequency of the amplitude modulated and amplified signal. (Media 1)
The instantaneous phase profiles of the modulated signals were also directly calculated from the measured instantaneous frequencies. To reconstruct the phase profile from the given instantaneous frequency, a numerical cumulative summation (CS) was applied. It is important to note that the reconstructed phase profiles actually represent relative phases without an absolute phase reference. A high-pass numerical filter was applied before the CS as low-frequency noises induce otherwise significant phase errors. Figures 4(a) and (b) show the directly recovered instantaneous frequency profiles for the phase modulated (a) and the amplitude modulated (b) signals with properly calibrated scales. The phase profiles directly calculated by the CS with the mentioned high-pass filtering are shown in Figs. 4 (c) and (d), respectively. A dynamic movie showing the real-time visualization of these recovered profiles is also shown in this figure (Media 2). Even though the low frequency noises were suppressed by the high-pass filtering, the results presented in the dynamic movie of Fig. 4(c) shows that the phase profiles with long ones or zeros were distorted due to the absence of the low frequency component.
Fig. 4 Direct single-shot measurement of the instantaneous frequency and phase profiles is shown in real time at 3 fps: Direct simultaneous acquisition of the calibrated instantaneous frequencies at two different wavelength channels for (a) the phase modulation and (b) the amplitude modulation. Instantaneous phases directly calculated from the instantaneous frequencies for the phase modulation (c) and the amplitude modulation (d), respectively. (Media 2)
b. Numerical analysis of the measurement accuracy tolerance to carrier frequency shifts
In this section we analyze the tolerance of the dual-balance differentiation technique to shifts of the signal carrier frequency. In the experiment described in the previous section, the dual-balanced differentiation technique was implemented with the signal under test centered at a carrier frequency coinciding with the crossing point of the spectral transfer functions of the two MZI output arms. At this wavelength point the transfer functions corresponding to the two interferometer outputs are linear and with the same slope magnitude. In this condition, the ratio between the balanced photodetector output (iBD) and the photodetected signal under test (iout) is proportional to the time derivative of the instantaneous phase [10]:
where k is a constant that depends on the photodetectors responsivity, A is the slope of the MZI transfer functions at the signal carrier frequency, l is the optical path-length difference between the MZI arms, c is the speed of light, and·ϕs is the signal instantaneous phase. The instantaneous frequency can thus be obtained as If a frequency drift, Δω, exists between the cross-point and the signal carrier frequency, the ratio (iBD / iout) in Eq. (3) can be rewritten as Therefore, from Eq. (4) and (5), it can be easily inferred that the instantaneous frequency becomes This simple theoretical analysis shows that if the system is calibrated to work at the crossing point of the MZI transfer functions, the calculated instantaneous frequency is affected linearly by an error equal to the value of the carrier frequency shift. As a result, once the carrier frequency shift is known or monitored, the correct value of the instantaneous frequency can be precisely recovered.Nevertheless the MZI transfer function is linear only over a limited frequency range (see Fig. 1 (a)). If the spectrum of the signal under test extends close to the maximum transmission frequency, then the recovered instantaneous frequency temporal profile will be distorted and the measurement will be affected by errors that cannot be compensated for in a straightforward fashion.
The tolerance of the measurement technique has been investigated by carrying out simulations of the dual-balanced PROUD as a function of the input carrier frequency shift with respect to the crossing point of the MZI transfer functions. The maximum total error (total error) and the maximum distortion (maximum_distortion) have been calculated. The total error is defined as the maximum error on the instantaneous frequency calculated as the maximum absolute difference between the measured instantaneous frequency in the actual case and the instantaneous frequency that is recovered when the signal under test is exactly centered at the transfer functions’ crossing point. maximum_distortion is defined as |maximum_error|2/|maximum_IF|2. Here maximum_error is the maximum difference between the actual instantaneous frequency with the offset introduced by the frequency shift subtracted and the instantaneous frequency measured when the signal under test is at the transfer functions crossing point. maximum_IF is the maximum value of the instantaneous frequency when the signal under test is at the transfer functions crossing point. The simulations are carried out for a signal with a constant envelope and a 3 GHz sinusoidal temporal phase modulation. The FSR of the MZI transfer functions is 41 GHz, according to the experimental condition. Figure 5 reports the simulation results for the total error (Fig. 5 (a)) and the maximum_distortion (Fig. 5 (b)). Figure 5 (a) shows a linear behavior for moderate frequency shifts (up to 5 GHz), in good agreement with the above theoretical analysis. In this range of carrier frequency shifts the actual value of the instantaneous frequency can be recovered with a maximum_distortion below 0.1, as shown in Fig. 5 (b). For frequency shifts higher than 5 GHz the slope of the maximum_distortion curve increases rapidly and the measured instantaneous frequency is affected by a higher imprecision. Commercial tunable CW lasers for DWDM applications have a wavelength stability of ± 2.5 GHz [18]. For these values, the maximum_distortion in the recovered instantaneous frequency profile using a setup similar to our experimental platform would be <0.01.
Fig. 5 Numerical evaluation of the dual-balanced differentiation technique as a function of the carrier frequency shift with respect to the crossing point of the MZI transfer functions. (a) total_error. (b) maximum_distortion.
4. Conclusions
We have proposed and experimentally demonstrated simultaneous, real-time instantaneous frequency characterization of wavelength-division-multiplexed (WDM) signals using a single processing and detection platform. The instantaneous frequency profiles of two different GHz-bandwidth signal modulations (one was phase-modulated with a PRBS (215-1) format and the other was amplitude-modulated by a sinusoid and frequency chirped in a SOA) were successfully acquired simultaneously, directly visualized in persistent mode and characterized in real-time. Instantaneous frequencies higher than 15 GHz were precisely detected for two channels with a frequency spacing of 200 GHz.
The theoretical analysis and the numerical simulations on the measurement accuracy tolerance, depending on the signal carrier frequency drifts, show that the dual-balanced differentiation technique is fairly robust to signal carrier frequency shifts.
It should be relatively straightforward to scale up the demonstrated approach over many WDM channels, each one having an operation bandwidth in the tens of GHz range (limited by the bandwidth of available real-time digitizers) using a single measurement platform. Hence, this newly proposed technique should prove particularly useful for real-time complex-field (amplitude and phase) monitoring of signals in a WDM communication system.
Acknowledgments
The authors would like to thank Prof. Serioja Tatu (INRS-EMT) for lending us the pulse pattern generator. This work was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada and the Fonds Québécois de la Recherche sur la Nature et les Technologies (FQRNT).
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