A time-domain photonic arbitrary waveform generator

Jinxin Liao; He Wen; Xiaoping Zheng; Hanyi Zhang; Bingkun Zhou

doi:10.1364/OE.20.012631

1. Introduction

High speed arbitrary waveform generation has grown as an important area which finds extensive commercial and military applications, such as testing, large capacity communications, high speed signal processing, and military defense electronics etc. As the optical domain processing technology possesses inherent advantages of large bandwidth, high frequency and immunity to electromagnetic interferences which are difficult for the all-electronic approach to achieve, the photonic arbitrary waveform generator (PAWG) has received significant attention. At present, most of the existing PAWG schemes employ the frequency-domain method known as a fourier-transform based technique. This method allows the amplitude and phase of discrete optical spectral lines to be independently controlled and enables arbitrary waveform to be synthesized in a time aperture [1–8]. In these frequency-domain PAWG apparatus [1–3], a grating followed by a spatial light modulator (SLM) with a large number of spectral controlled elements is usually implemented as an optical pulse shaper. It shows good performance in generating complex radio frequency waveform but with two significant drawbacks. One is that the waveform refreshing time is limited by the response time of the SLM (~10ms). This problem can be released by utilizing the time multiplexing technique [4–7] or replacing the SLM with a much more short response time shaper, such as the electro-optical modulator array [8]. The other one significant drawback is that the maximum time aperture of the output temporal waveform (~2ns) directly associated with the lowest attainable frequency, is determined by the minimum resolution (~1GHz) of the optical pulse shaper employed in the system [9]. The time multiplexing technique can increase the time aperture but only to some extent. The reason is that large numbers of the multiple branches in time-multiplexing based schemes are required to achieve a PAWG capable of fast and flexible waveform refreshing along with infinite waveform time aperture. The number corresponding to the ratio of the waveform refreshing time and the waveform time aperture is tremendous (~10⁵). It is very difficult to expand so many multiple branches to meet the requirement.

However, the PAWG employing the time-domain method which is similar to the traditional electrical AWG does not have these problems [10, 11]. The time-domain PAWG generates samples to approximate the target waveform at each temporal point. The waveform time aperture is determined by the product of the memory depth and the sampling interval, which can be long enough to several milliseconds. It can be much longer with the real-time sequencing technique. Thus, the time-domain method can provide a larger time-bandwidth product compared with the frequency-domain method. Furthermore, the flexibility, the quality and the refreshing rate of the time-domain arbitrary waveform generation are excellent. The time-domain PAWG can be regarded as a photonic digital-to-analog converter (PDAC). But so far, all the proposed PDAC are unipolar, with only positive value [10–16]. From the perspective of dynamic range and noise margin, a bipolar PDAC (BPDAC) may have an advantage over the unipolar PDAC and can achieve higher resolution more easily. This is illustrated by comparing the constellation diagram of the bipolar output against that of the unipolar output [17].

In [18], we have recently put forward a 2N-bit BPDAC based on multi-wavelength optical differential quadrature phase shift keying (ODQPSK) modulation in combination with differential detection. In this paper, this 2N-bit BPDAC is applied to achieve a time domain PAWG with good flexibility, fast waveform refreshing rate and high waveform quality. This PAWG shows three attractive features. The first is that the bipolar output brings about a greater dynamic range and a larger noise margin compared with the unipolar output of other proposed time domain PAWGs or PDACs. The second is that it has good scalabilities both in the sample resolution and the sampling rate. The sample resolution can be increased by using multi-wavelength laser array, and the sampling rate can be increased by using time-multiplexing technique. The third is that it consisting of a multi-wavelength DQPSK transmitter and a DPSK receiver is fully compatible with the mature popular DQPSK system. It can be easily integrated on a chip or constructed with the available photonic integrated circuit (PIC). We set up a proof-of-principle PAWG experiment with 4-bit resolution at 2.5GS/s to demonstrate this scheme. The generated arbitrary waveforms are very close to the ideal waveforms. The average spurious-free dynamic range (SFDR) results of single tone and two tone signals are 31.4dB and 27.9dB, respectively. We also experimentally verify the time-multiplexing PAWG with multiple sampling rates. Furthermore, we stress some specifications of the essential components in this PAWG, and give a summary on this PAWG proposal.

2. Operation principle

Figure 1(a) shows the architecture of the PAWG with 2N-bit resolution. It is composed of two main parts, the multi-wavelength ODQPSK modulation part and the differential demodulation part. In the multi-wavelength ODQPSK modulation part, N channels of independent light with different wavelengths pass through N dual parallel MZMs (DP-MZM) respectively. Each of the DP-MZM is driven by two channels of non-return-zero (NRZ) digital signal, generating one ODQPSK signal. Combined the N branches together, the multi-wavelength ODQPSK signal is delivered to the demodulation part where a 1-bit delay-time interferometer (DI) acts as a differential demodulator and its two outputs are balanced detected. We first illustrate how the samples with 2-bit resolution are generated by using single wavelength laser, then we detail the implementation of the PAWG with 2N-bit resolution and present the time-multiplexing technique assisted PAWG.

Fig. 1 (a)Architecture of the PAWG with 2N-bit resolution. (b) The changing form of the analog output V_out varies with the phase shift ∆φ in the 2-bit PAWG. When ∆φ≈18.4°, V_out presents bipolar four-equally-spaced discrete values.

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2.1 Principle of PAWG with 2-bit resolution based on ODQPSK modulation in combination with differential detection

In the 2-bit PAWG using a single wavelength, the ODQPSK signal can be expressed as $E (t) e^{i θ}$ , where $θ \in {π / 4, 3 π / 4, 5 π / 4, 7 π / 4}$ . After differential detection, the amplitude of the output sample $V_{o u t}$ is given by:

\begin{array}{l} V_{o u t} \propto {| E_{1} (t - T) e^{i θ_{1}} + E_{2} (t) e^{i θ_{2}} e^{i Δ φ} |}^{2} - {| E_{1} (t - T) e^{i θ_{1}} - E_{2} (t) e^{i θ_{2}} e^{i Δ φ} |}^{2} \\ = 4 | E_{1} (t - T) E_{2}^{*} (t) | \cos (Δ θ + Δ φ), Δ θ = (θ_{2} - θ_{1}) \in {0, π / 2, π, 3 π / 2} \end{array}

where

E_{1} (t - T) e^{i θ_{1}}

is the ODQPSK signal delayed by 1 bit period in the longer arm of DI,

E_{2} (t) e^{i θ_{2}} e^{i Δ φ}

is the ODQPSK signal in the short arm of DI, ∆φ denotes the phase shift between the two arms, and T is the digital bit duration. From Eq. (1), it can be inferred that V_out varies with the phase shift ∆φ in a form of cosine function, where ∆θ determines the initial phase of the function. Figure 1(b) illustrates this phenomenon. As long as the phase shift ∆φ meets the condition

| \cos Δ φ / \sin Δ φ | = 1 / 3 o r 3

, V_out presents bipolar four-equally-spaced discrete values, In Fig. 1(b),

Δ φ \approx 18. 4^{\circ}

is taken for example. As V_out is directly associated with ∆θ which denotes the changing form between the adjacent input digital codes, a precoder is required to map the input digital codes to the bipolar four-equally-spaced discrete values. The coding algorithm of the precoder is given in Eq. (2), and the one-to-one mapping between the input and the output is shown in Table 1 . Thus, a 2-bit PAWG is achieved. Profiting from the optical phase modulation combined with balanced detection, this PAWG generates bipolar samples, and shows advantages of a greater dynamic range and a larger noise margin over the unipolar PAWG or PDAC based on the intensity modulation together with direct detection [12–14]. The reason is that the minimal distance between adjacent two symbols of the phase modulated signal is larger than that of the intensity modulated signal. This advantage is analogous to the 3dB optical signal-to-noise ratio (OSNR) advantage that the phase modulation format owns over the intensity modulation format in optical communication system.

Table 1. The One-To-One Mapping Between the Input and the Output

View Table

{\begin{matrix} I_{n} = \bar{D_{2 n - 1} \oplus D_{2 n}} \cdot (D_{2 n - 1} \oplus I_{n - 1}) + (D_{2 n - 1} \oplus D_{2 n}) \cdot (D_{2 n} \oplus Q_{n - 1}) \\ Q_{n} = \bar{D_{2 n - 1} \oplus D_{2 n}} \cdot (D_{2 n} \oplus Q_{n - 1}) + (D_{2 n - 1} \oplus D_{2 n}) \cdot (D_{2 n - 1} \oplus I_{n - 1}) \end{matrix}

2.2 Implementation of PAWG with 2N-bit resolution

The resolution of this PAWG can be scaled from 2-bit to 2N-bit by using N channels of incoherent light with different wavelengths, where the optical power ratio is set as $1 : 4 : \dots : 4^{N - 1}$ . Similar weighted and summing methods have been reported in [12–14]. For multi-wavelength laser array, there are some requirements on the frequency difference ∆f between any two light waves that should be specified. First, ∆f should be an integral multiple of the free spectral range (FSR) of DI which is equal to 1/T, to ensure that each wavelength light wave obtains the same phase shift of ∆φ in DI, since the transmission function of the DI is periodic and the phase shift ∆φ is directly associated with the lightwave frequency [17]. Second, ∆f should be greater than the detector’s bandwidth to ensure that the beating noise of any two light waves is removed. Figure 2 illustrates these requirements. The optical power ratio of different wavelengths can also be realized by using a multi-wavelength laser array with equal optical power of each wavelength followed by a special weighted coupler with split ratio of $1 : 4 : \dots : 4^{N - 1}$ .

Fig. 2 Requirements on the multi-wavelength laser array.

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2.3 Time multiplexing PAWG with 2N-bit resolution

With the optical domain time passive multiplexing method which has advantages of low loss, stable delay time, and immunity to electromagnetic interferences etc, the multi-level optical short pulse can be easily temporal interleaved to increase the sampling rate of this PAWG. The architecture of the 2N-bit PAWG with m multiple expanded sampling rate is presented in Fig. 3 . In the apparatus, the multi-wavelength time-interleaved short pulse generator with very small time jitter (<300fs) is based on phase modulating the multi-wavelength pulse source and subsequent compressing the pulse in the dispersive medium [7]. The generated optical short pulse trains with different wavelengths are delivered to a wavelength demultiplexer. The separated single wavelength short pulse train with repetition of Fs-GS/s enters the time multiplexing unit (TMU) array, respectively. In the TMU, the single wavelength short pulse train is spilt into m parallel DPMZMs and is DQPSK modulated, respectively. The bit duration T of the NRZ digital driving signal is equal to 1/Fs. By setting the corresponding time delay of the m channels as $τ, 2 τ, \dots, m τ (m τ = T)$ , the repetition of the output DQPSK modulated pulse train is increased to m∙Fs-GS/s, which means that the sampling rate is m multiple expanded. Then, by synchronizing and summing all the N channels of DQPSK modulated short pulse with different wavelengths together and setting the corresponding optical power ratio as $1 : 4 : \dots : 4^{N - 1}$ , the sample resolution is scaled to 2N-bit. Thus, a 2N-bit PAWG with m multiple expanded sampling rate is built. It can be seen that in this m∙Fs-GS/s 2N-bit PAWG, 2∙m∙N channels of NRZ digital driving signal with a lower bit rate of Fs-GS/s, m∙N DPMZMs are required.

Fig. 3 Architecture of the time multiplexing PAWG with 2N-bit resolution.

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3. Results and discussions

Limited by only one independent channel of 10Gbit/s signal, we just set up a 4-bit 2.5-GS/s PAWG experiment as shown in Fig. 4 to verify the proposed 2N-bit PAWG. In the experiment, two continuous wave (CW) lights with different wavelengths enter into two DP-MZMs and are quadrature modulated respectively. The 2.5Gbit/s non-return-zero driven digital signals are obtained by demultiplexing a 10Gbit/s digital signal from a pulse pattern generator (PPG). The generated dual-wavelength ODQPSK signal is directed into a 1-bit DI followed by a BD after being amplified. The DI is welded by two 2 × 2 couplers where the delay time difference between the two arms is 400 ps. Its two output ports are balanced detected, and the detected output electrical signal is sent to an oscilloscope for measuring. Then, the entire system is calibrated as follows. First, switch one laser on only and regulate ∆φ around 18.4° to build a 2-bit PAWG. Second, switch the other laser on only and tune its wavelength to accommodate the built 2-bit subsystem. Third, synchronize the two ODQPSK signals with a tunable optical time delay (TTD) module and adjust the optical power ratio between the two ODQPSK signals as 1:4 with a variable optical attenuator (VOA). After this, the 4-bit PAWG at 2.5GS/s is built.

Fig. 4 Experiment setup of a PAWG with 4-bit resolution at 2.5GS/s.

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Programming the four channels of input digital bit sequences, we can synthesize arbitrary waveform in the time domain. Figure 5(a) shows the generated raw waveforms of the sawtooth wave (with 16 ramp), the triangle wave (with 16 ramp), the sinusoidal wave (f = 99.82MHz), and the two-tone wave (f₁ = 399.22MHz / f₂ = 439.14MHz). The burr of waveform is a fundamental issue which is the result of the phase modulation together with differential detection. More specifically, from Eq. (1), we know that only when ∆θ = 0 which means that both the two channels of digital bits keep continuous in transition time, would the $| E_{1} (t - T) E_{2}^{*} (t) |$ and the output analog amplitude remains unchanged in transition time. In other three changing forms where at least one digital bit changes, the $| E_{1} (t - T) E_{2}^{*} (t) |$ would depress in transition time, and the burr of waveform emerges. The lowpass filtering operation can remove the burr but pay a cost of lowering the highest attainable frequency of the output analog signal, as the 3dB cut-off frequency should be smaller than half of the sampling rate. Fig. 5(b) shows the comparison between the corresponding waveforms after being filtered by a software filter (3 order Bessel lowpass filter, f_{3dB cut-off}≈1GHz) and the ideal waveforms. The corresponding cross correlation coefficients are 0.9987, 0.9962, 0.9905, and 0.9982. It can be seen that the generated waveforms are very close to the ideal waveforms.

Fig. 5 (a)Generated raw waveforms of the sawtooth wave (with 16 ramp), the triangle wave (with 16 ramp), the sinusoidal wave (f = 99.82MHz), and the two-tone wave (f₁ = 399.22MHz / f₂ = 439.14MHz). (b)Comparison between the corresponding filtered waveforms (blue line) and the ideal waveforms (red line).

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To further evaluate the performance of this 4-bit PAWG, we sweep synthesize single-tone signals and use the spectrum analyzer to measure the corresponding SFDR. Normal detector without average operation is used. We also employed signal-to-noise and distortion ratio (SINAD) test method shown in [19] along with (SINAD-6.02)/1.76 to compute the effective number of bits (ENOB). The SFDR and ENOB results are shown in Fig. 6(a) and the average SFDR value is 31.4dB. We also synthesize two-tone signals at three groups of frequency (f₁ = 598.82MHz / f₂ = 658.72MHz; f₁ = 608.72MHz / f₂ = 648.80MHz; f₁ = 399.22MHz / f₂ = 439.14MHz). The spectrums are shown in Fig. 6(b) and the corresponding SFDR are 28.1dB, 27.3dB and 28.3dB with an average of 27.9dB. The spurious spectrum and the loss of the ENOB mainly come from two aspects, the burr between samples and the fluctuation of samples. The burr mainly brings the high frequency interference that can be relieved by lowpass filtering. The fluctuation of samples originates from the nonideal characteristic (e.g. drifting or distortion) of the amplified driven signal, which is concerned with the programmed data pattern because of the AC coupled characteristic of the driver. By relieving the nonideal characteristic of the amplified driven signal, the SFDR and ENOB results can be improved.

Fig. 6 (a) SFDR and ENOB results. (b) Spectrum of two-tone signals at three groups of frequency.

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Adding an optical short pulse generator, we can transform the built 4-bit PAWG to a time-multiplexing 20-GS/s 2-bit PAWG. The two parallel DP-MZMs can be regarded as a TMU( × 2). In the optical short pulse generator, the CW light is modulated by an amplitude modulator (AM), generating a pulse train with a full width of half maximum (FWHM) of 30ps and a repetition rate of 10GHz. The pulse train is put into a phase modulator (PM) followed by a tunable dispersion compensation module (TDCM). With high power phase modulation and appropriate dispersion, the pulse train is compressed with FWHM of 12ps. Then the short pulse train enters into the TMU( × 2). The entire experiment needs recalibration, including regulating the TTD module to multiplex the pulse trains and adjusting the VOA to make the two channels have the same optical power. When only one channel is used, the sampling rate of the generated pulse train is 10GHz, as shown in Fig. 0.7(a). When both channels are used, the sampling rate of the generated pulse train turns into 20GHz, as shown in Fig. 7(b) . It can be seen that the peaks of the pulse train appear bipolar four-equally-spaced values. Since the bandwidth of commercial DP-MZM has achieved more than 40GHz, this PAWG can easily realize 40GS/s by using higher speed driving digital signals, and surpass 80GS/s assisted by the optical domain time multiplexing technique. Such a high speed is very difficult for the current electronic AWG or DAC to achieve [20].

Fig. 7 (a) Generated pulse train at 10GHz when only one channel is used. (b) Generated pulse train at 20GHz when two channels are used.

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For this PAWG proposal, the performance depends on the stabilization of (∆θ + ∆φ). Therefore, to meet this requirement, some specifications of the essential components should be specified. Seen from Fig. 1(b), we know that the condition of $| \cos Δ φ / \sin Δ φ | = 1 / 3 o r 3$ guarantees the perfect linearity of the digital-to-analog conversion, and a small phase detuning of ∆φ in DI significantly affects the linearity since the inner sample value and the outer sample value move in opposite direction with different rates of change. From Eq. (1), we obtain the amplitude deviation ratio of discrete sample values as

d V_{o u t} / V_{o u t} = - \tan (Δ θ + Δ φ) \cdot d Δ φ |_{Δ φ = {18.4}^{\circ}}

It can be inferred that the inner sample value (∆φ = π/2 or 3π/2) is more vulnerable to the phase detuning. We calculate that if the required amplitude deviation ratio is less than 5%, the tolerable phase detuning is about ± 1°. Such a stringent requirement on phase shift stabilization requires the application of DI have precise temperature control and athermal package. Besides, the disturbance of ∆θ mainly resulting from the phase noise of the laser sCource and the chirp occurred in the modulation process brings an undesirable affect on the signal-to-noise ratio (SNR) of the analog output. However, the chirp can be reduced distinctly by using common push-pull type MZMs. The impact of the phase noise related to the laser linewidth can also be neglected by using narrow linewidth lasers, especially at much higher sampling rate [21].

As discussed before, it can be seen that this PAWG is fully compatible with the mature popular DQPSK system. This feature brings many benefits. A main one is that the greatly developed photonic integrated circuit (PIC) technologies on the mature ODQPSK system enable this PAWG to be integrated on a chip or constructed with available PICs. As reported in [22] and [23], a differential detection receiver and a large-scale transmitter PIC consisting of 10 tunable distributed-feed-back (DFB) lasers followed by 10 DP-MZMs corresponding to the two main parts of this PAWG were implemented. The integration of this PAWG would make it more stable and more practical.

4. Conclusion

We have put forward a time domain PAWG scheme based on multi-wavelength ODQPSK modulation in combination with differential detection. Proof-of-principle experiments of 4-bit PAWG at 2.5GS/s and 2-bit time-multiplexing PAWG at 20GS/s are set up to demonstrate this PAWG scheme. The generated arbitrary waveform is very close to the ideal waveform. The measured average SFDR of single-tone signals and two-tone signals are 31.4db and 27.9db, respectively. Compared with the frequency domain PAWG, this time domain PAWG shows advantages of large time-domain product, good flexibility, fast waveform refreshing rate and high waveform quality. In contrast with other proposed time domain PAWGs or PDACs, this PAWG shows a greater dynamic range and a larger noise margin due to its bipolar output, and has good scalabilities both in resolution and sampling rate. Furthermore, the PIC technology has allowed this PAWG consisting of a multi-wavelength DQPSK transmitter and a DPSK receiver to be integrated on a chip, and presents a good prospect of this PAWG’s wide practical applications in future.

Acknowledgments

This work was supported in part by National Nature Science Foundation of China (NSFC) under grant No. 60736003, 61025004, and 61032005; National Basic Research Program of China under the grant No 2012CB315603-04; Foundation of the Key State Lab of Integrated Optoelectronics under grant No. 2010KFB007; the Ph.D. Programs Foundation of Ministry of Education of China under grant No. 20100002110039, and the Postdoctoral Science Foundation of China under grant No. 2012M510442.

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A time-domain photonic arbitrary waveform generator

Abstract

1. Introduction

2. Operation principle

2.1 Principle of PAWG with 2-bit resolution based on ODQPSK modulation in combination with differential detection

2.2 Implementation of PAWG with 2N-bit resolution

2.3 Time multiplexing PAWG with 2N-bit resolution

3. Results and discussions

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (7)

Tables (1)

Equations (3)

Optics Express