Photonic microwave waveforms generation based on time-domain processing

Yang Jiang; Chuang Ma; Guangfu Bai; Xiaosi Qi; Yanlin Tang; Zhenrong Jia; Yuejiao Zi; Fengqin Huang; Tingwei Wu

doi:10.1364/OE.23.019442

1. Introduction

Microwave waveform generation is a widely investigated area in recent years because of its important applications in communication systems, signal processing, instrumentation systems, radar, and so on [1–4]. Photonic technique, which offers many advantages, e.g. reconfigurability, immunity to electromagnetic interference, large bandwidth and low loss is regarded as a promising way for this task.

So far, various photonic approaches for arbitrary waveform generation have been proposed. One popular way is Fourier synthesis method [5], in which an optical frequency comb is used as a coherent broadband source and a tailored optical signal can be achieved by a spatial light modulator (SLM) to manipulate individual spectral comb lines. However, this technique leads to a complicated system and the optical phase is very sensitive to environmental fluctuation. Frequency-to-time mapping (FTTM) technique is another candidate for arbitrary waveform generation [6,7]. In this method, the spectral envelope of an optical frequency comb is modified by the spectral shaper to be a scaled version of the desired waveform. Then the spectral envelope is mapped to the temporal waveform in the photodetector (PD) after a FTTM in a dispersion element. This method may cause relatively low flexibility for the parameters control of the generated signals due to the spectral lines controlled in group.

Photonic generation of arbitrary waveforms can also be implemented through external modulation of a continuous wave (CW). When a CW is modulated by an external modulator, a series of sidebands are generated due to the modulation nonlinearity. Therefore, the desired waveforms are generated by manipulating the phases and amplitudes of these modulation harmonics. For example, triangular and rectangular waveforms can be generated by using a dual-drive Mach-Zehnder modulator [8,9]. In addition, a dual-parallel Mach-Zehnder modulator (DPMZM) can also be employed, in which the power ratio of the modulation sidebands should be carefully controlled by adjusting three biases [10]. To satisfy the phase condition, dispersion devices or an optical bandpass filter has to be employed. Therefore, these approaches have poor operation convenience and high cost. In [11], arbitrary waveforms generation with a configuration of a polarization modulator (PolM) in a Sagnac loop has been reported. Due to the different modulation efficiency for the clockwise and conunter-clockwise light waves in the Sagnac loop, the power of modulation sidebands can be controlled identical to fit the Fourier series expansion of the desired waveforms. However, the polarization sensitivity and the requirement of additional optical spectrum filtering show limited advantages. Triangular waveform generation by using a single-drive MZM has been also reported. According to the proposals, an interleaver [12], a microwave photonic filter (MPF) [13], or stimulated Brillouin scattering (SBS) [14] has to be introduced to select out the first two Fourier series components among the modulation sidebands. Although these schemes have good performance of triangular waveform generation, they have the limitation on generating other waveforms.

Summing up the previous works, the main idea is based on frequency-domain analysis, and the operation process is carried out in frequency domain. Frankly, Fourier method is very effective and successful for arbitrary waveform generation with very high repetition rates [15], but the difficulties and limitations still emerge. For arbitrary waveform generation, the individual spectral line-by-line control has a quite high demand on technical means. However, managing spectral lines in group reduces the flexibility and accuracy, especially when the number of spectral lines is large. It was just because of this that most of the reported works concentrated on triangular waveform generation since only two Fourier series components can make good approximation. As another point of view, a waveform is a specific optical power distribution on time scale. It means that some of waveforms may be more effectively generated by arranging optical power in time domain. By this way, we have recently reported a triangular waveform generation by using time-domain synthesis [16]. It shows that waveform generation can be conveniently realized by overlapping and controlling optical envelopes, which is more stable and avoids the complex manipulation of spectral lines.

In this paper, we propose a novel photonic approach to generating a square, triangular, sawtooth (or reversed-sawtooth), and frequency doubling sawtooth (or reversed-sawtooth) waveform through optical pulse shaping in time domain. By using a sinusoidal signal to modulate a CW via a MZM, square-shaped waveforms are directly generated at first, whose shapes or power ratios of their harmonics are able to be modified by changing RF driving voltage. When two identical square-shaped pulses with harmonics power ratio of 9:1 between the 1st- and the 3rd-order components suffer a differential envelope phase shift of π/2, the superposition of these signals contributes to a triangular waveform in a PD. Because a triangular waveform has a linear slope and square waveform has steep rising edge and falling edge, a sawtooth (or reversed-sawtooth) pulse with 50% duty-cycle is obtained by carving a square pulse with a triangular time window. Furthermore, frequency doubling sawtooth waveform with full duty-cycle can be achieved by using multiplexing technique. Both of the simulation and experimental demonstration show good performance. This is a new access to making a microwave waveform generator.

2. Principle

The schematic microwave waveform generator is illustrated by Fig. 1, in which two single-drive MZMs are used for pulse shaping, and different waveforms can be obtained by carving and overlapping the optical field envelopes in time domain. Firstly, let’s consider the general description of a MZM. Assuming that a CW, with angular frequency centered at $ω_{0}$ , is modulated by a sinusoidal signal $V (t) = V_{m} \cos (ω_{m} t)$ via a MZM, where $V_{m}$ is the amplitude, and $ω_{m}$ is the angular frequency of the drive signal. If the MZM is biased with a constant dc voltage, the optical field at the output of a MZM can be approximately expressed by

E_{o u t} (t) = E_{0} \cos [\frac{φ}{2} + \frac{π V (t)}{2 V_{π}}] \cos (ω_{0} t)

where

E_{0}

is the optical field amplitude,

φ = π V_{b i a s} / V_{π}

is the phase shift determined by thedc-bias voltage

V_{b i a s}

, and

V_{π}

is the half-wave voltage of the modulator. The modulation index of the MZM is defined as

β = π V_{m} / V_{π}

, and Eq. (1) can be rewritten as

E_{o u t} (t) = E_{0} \cos \frac{φ}{2} \cos (ω_{0} t) \cos (β \cos ω_{m} t) - E_{0} \sin \frac{φ}{2} \cos (ω_{0} t) \sin (β \cos ω_{m} t)

If the MZM is biased at quadrature point (

V_{b i a s} = V_{π} / 2

), i.e.

φ = π / 2

, applying Jacobi Anger expansion to Eq. (2), we have

\begin{array}{l} E_{o u t} = \frac{\sqrt{2}}{2} E_{0} \cos ω_{0} t [J_{0} (β) + 2 \sum_{n = 1}^{\infty} {(- 1)}^{n} J_{2 n} (β) \cos (2 n ω_{m} t)] \\ - \frac{\sqrt{2}}{2} E_{0} \cos ω_{0} t [- 2 \sum_{n = 1}^{\infty} {(- 1)}^{n} J_{2 n - 1} (β) \cos [(2 n - 1) ω_{m} t]] \end{array}

where

J_{n}

is the Bessel function of the first kind of order

n

. Obviously, the modulation is able to generate many spectral lines with frequency spacing of

ω_{m}

. The amplitude distribution of these spectral lines is governed by the variation of Bessel functions parameterized by

β

. According to the characteristic of Bessel function, the high-order components are negligible. Thus, we consider the frequency components up to the third order. The optical signal can then be approximately expressed as

\begin{array}{l} E_{o u t} \approx \frac{\sqrt{2}}{2} E_{0} \cos ω_{0} t [J_{0} (β) - 2 J_{1} (β) \cos (ω_{m} t) \\ - 2 J_{2} (β) \cos (2 ω_{m} t) + 2 J_{3} (β) \cos (3 ω_{m} t)] \end{array}

If this signal is directly detected by a PD, the photocurrent is given by

i (t) \propto D C + \frac{A}{2} \cos (ω_{m} t) + \frac{B}{2} \cos (2 ω_{m} t) + \frac{C}{2} \cos (3 ω_{m} t)

where the coefficients for each component are

A = 2 J_{1} J_{2} - 2 J_{0} J_{1} - 2 J_{2} J_{3}

,

B = J_{1}^{2} - 2 J_{0} J_{2} - 2 J_{1} J_{3}

, and

C = 2 J_{0} J_{3} + 2 J_{1} J_{2}

. Figure 2(a) shows the coefficient values versus the modulation index, and Fig. 2(b) is the coefficient ratio between

| A |

and C via modulation index. In the following derivation, we only consider the interval of the modulation index from 0.5 to 1.5. Seen in Fig. 2(a), the absolute values of A and C are greatly depended on the modulation index, but

A

is negative and C is positive. Meanwhile, the value of B is always small and closed to zero. Then, we ignore the contribution of the second order harmonic, and the Eq. (5) can be rewritten as

Fig. 1 Schematic diagrams of the proposed microwave waveform generator. LD: laser diode, WDM: wavelength division multiplexer, PC: polarization controller, MZM: Mach-Zehnder modulator, ODL: optical delay line, SMF: single mode fiber, ATT: attenuator.

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Fig. 2 The calculated values of, (a) the coefficients of first-, second- and third-order harmonics of photocurrent, (b) the coefficient ratio between the first-order harmonic and third-order tone versus the modulation index of the MZM, β.

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\begin{array}{l} i (t) \propto D C + \frac{| A |}{2} \cos (ω_{m} t + π) + \frac{C}{2} \cos (3 ω_{m} t) \\ = D C + \frac{| A |}{2} \sin (ω_{m} t + \frac{π}{2}) + \frac{C}{2} \sin (3 ω_{m} t + \frac{3 π}{2}) \end{array}

2.1 Square waveform

It is well known that the Fouier series expansion of a square waveform $T_{s q} (t)$ is given by

T_{s q} (t) = D C + \sum_{n = 1, 3, 5 \dots}^{\infty} \frac{1}{n} \sin (n ω_{m} t)

Comparing Eq. (6) with Eq. (7), we can find that the photocurrent may present a square-shaped envelope in time domain. Figure 3(a) shows the graphic illustration of the transformation from a sinusoidal driving signal to a square wave via a MZM, and Fig. 3(b) is the simulation results when

V_{m}

is set to be 0.4789

V_{π}

, 0.614

V_{π}

and 0.7277

V_{π}

(corresponding to β of 0.752, 0.965 and 1.141), respectively. From the figures, square-shaped waveforms are able to be generated by directly modulating a CW with driving voltage around

V_{π} / 2

. According to the coefficient ratio indicted in Fig. 2(b), the second order approximation of a square waveform can be reached by setting

β = 1.141

.

Fig. 3 (a) Sinusoidally driven MZM as pulse carver for square-shaped waveform generation. (b) The calculated waveforms with β of 0.752 (dot line), 0.965 (solid line) and 1.141 (dash line).

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2.2 Triangular waveform

Now, let’s consider the Fourier series expansion of a triangular waveform

T_{t r} (t) = D C + \sum_{n = 1, 3, 5 \dots}^{\infty} \frac{1}{n^{2}} \cos (n ω_{m} t)

Since triangular waveform contains only odd-order harmonics and the coefficient ratio of the higher-order harmonics decreases dramatically, the first two components can make good approximation. Thus, the expansion can be simplified as

T_{t r} (t) = D C + \cos (ω_{m} t) + \frac{1}{9} \cos (3 ω_{m} t)

To obtain the expression of a photocurrent with the Fourier series expansion of

T_{t r} (t)

, at first, the modulation index should be equal to 0.752 (corresponding to coefficient ratio of 9:1) as indicted in Fig. 2(b). Then, if two of such signals with envelope phase difference of π/2 are overlapped in a PD, the photocurrent is given by

\begin{array}{l} i (t) = i_{1} (t) + i_{2} (t) \propto D C + \frac{| A |}{2} [\cos (ω_{m} t + π) + \frac{1}{9} \cos (3 ω_{m} t)] \\ + \frac{| A |}{2} [\cos (ω_{m} t + π + \frac{π}{2}) + \frac{1}{9} \cos (3 ω_{m} t + \frac{3 π}{2})] \\ = D C + \frac{\sqrt{2} | A |}{4} [\cos (ω_{m} t + \frac{5 π}{4}) + \frac{1}{9} \cos (3 ω_{m} t + \frac{15 π}{4})] \end{array}

It is clear that Eq. (10) gives a triangular waveform, and the calculated result is shown by Fig. 4. It is worth noting that the power ratio and the phase relationship have a tolerance range, which means the current parameters of this second order approximation may not be the best choice. By properly adjusting the parameters, even better triangular waveform can be achieved [17].

Fig. 4 Simulation result of a triangular waveform generation by the superimposition of two square-shaped waveforms with π/2 phase shift. The modulation index of a MZM is 0.752.

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2.3 Sawtooth waveform

The Fourier series expansion of a sawthooth waveform $T_{s a} (t)$ is written as

T_{s a} (t) = D C + \sum_{n = 1}^{\infty} \frac{1}{n} \sin (n ω_{m} t)

From Eq. (11), a sawtooth waveform has both odd- and even-order harmonics with gradually decreasing coefficients. It is a great challenge to directly generate modulation harmonics satisfied with Eq. (11), even for finite number of Fourier series components. However, the solution can be found in time domain. It is known that a square pulse has a steep rising edge and falling edge, and a triangular pulse has a linear rising and falling edge. Assuming that a square pulse stream is synchronized with a triangular pulse stream, they can be expressed by piecewise functions as

T_{s q} (t) = {\begin{matrix} 1, t \in [k T, k T + \frac{T}{2}) \\ 0, t \in [k T + \frac{T}{2}, k T + T) \end{matrix}

T_{t r} (t) = {\begin{matrix} (2 k + 1) - (\frac{2}{T}) t, t \in [k T, k T + \frac{T}{2}) \\ (\frac{2}{T}) t - (2 k + 1), t \in [k T + \frac{T}{2}, k T + T) \end{matrix}

where

k

is an integer,

T

is the period of the signals, and their amplitudes are normalized. If the triangular signal is applied on a MZM to carve the square pulse, the envelope of the output can be mathematically expressed as

T_{s q} (t) \times T_{t r} (t) = {\begin{matrix} (2 k + 1) - (\frac{2}{T}) t, t \in [k T, k T + \frac{T}{2}) \\ 0, t \in [k T + \frac{T}{2}, k T + T) \end{matrix}

The equation above presents a signal with linear falling edge in the first half period and keeping zero in the second half period. Obviously, this is a sawtooth waveform with 50% duty cycle. If the modulation window shifts half period, a reversed-sawtooth waveform is obtained. In addition, by taking multiplexing technique, a frequency doubling sawtooth waveform with full duty cycle can be achieved. The graphic illustration of this process is shown by Fig. 5.

Fig. 5 The graphic illustration of a sawtooth (or reversed-sawtooth) waveform generation by carving a square pulse with a triangular time window. The frequency doubling sawtooth (or reversed-sawtooth) waveform can be further generated by multiplexing technique.

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3. Experiment and results

In order to confirm the operation principle described above, the experiment demonstration is carried out. At first, square-shaped waveforms are experimentally generated by directly modulating a CW with different modulation index, where one of the LDs in Fig. 1 is disconnected. A distributed-feedback semiconductor laser diode (DFB-LD) outputs a CW with wavelength of 1549.2 nm, which is modulated by the MZM with a 3-GHz sinusoidal drive signal and the MZM is biased at quadrature point. By changing the driving voltage, three typical outputs corresponding to the simulation results in Fig. 3 are obtained. Figure 6(a) and 6(b) show the generated square-shaped waveform and its electrical spectrum under the modulation index of 0.752. In this case, the power ratio between 1st- and 3rd-order harmonics presents a good approximation with the Fourier series expansion of a triangular waveform, but the phase relationship determines a square-shaped (or trapezoidal) envelope with rising and falling time of 69 ps. When the modulation index increases, i.e. 0.92, as shown by Fig. 6(c) and 6(d), a square pulse with flat top and bottom is obtained, where the measured rising and falling time are 31 ps. However, the power relationship among the harmonics is not accurately satisfied with an ideal square waveform at this time. If the modulation index is set to be 1.141, a good approximation of a square waveform with rising and falling time of 29 ps is achieved (seen in Fig. 6(e) and 6(f)), where the power ratio between first two harmonics is closed to the Fourier series expansion of an ideal square waveform. In the three cases, all of them have duty cycles of 50%.

Fig. 6 Measured (a), (c), (e) square-shaped waveform and (b), (d), (f) the corresponding electrical spectra when the MZM is biased at the quadrature point with modulation index of 0.752, 0.965 and 1.141, respectively.

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Next, we show the triangular waveform and sawtooth waveforms generation based upon the experimental setup shown in Fig. 1. Two CWs with wavelengths of 1549.2 nm and 1546.78 nm from two DFB-LDs are combined by a WDM coupler and sent to the MZM 1, where the MZM is biased at quadrature point with modulation index of 0.752. This is the same as the situation shown in Fig. 6(a) and 6(b), and the two identical signals on two wavelengths have harmonic coefficient ratio of 9:1 between their first- and third-order components. Through a 3-dB optical coupler, the signals are power split into two branches. In the lower branch, a 2-km single mode fiber (SMF) is used as a time delay element, which introduces a differential delay on two optical envelopes. Here, the delay is proportional to the wavelength shift multiplied by the group-velocity dispersion (GVD) of the dispersive fiber, which is about 82.5 ps (corresponding to an envelope phase shift of π/2 for a 3-GHz pulse stream) in our case. Of course, the delay can be tuned by either adjusting the wavelength difference between two signals or changing the accumulation of the dispersion. Although the wavelength difference has very large tuning range, the minimum value must be larger than the bandwidth of the PD to prevent beat noise between two optical carriers. However, if an optical sampling oscilloscope is used, the beat noise may still be detected. When these two optical envelopes are overlapped in a high speed PIN photodetector, a triangular envelope is responded, whose waveform and electrical spectrum is given by Fig. 7(a) and 7(b). It can be seen that the experimental results are well agreed with the theoretical predication and the spectrum shows a good approximation of the Fourier series expansion. It is worth noting that the usage of two light sources in conjugation with a dispersion element is not the only choice, which can be implemented by using a single light source, and the function of phase shift and superimposition can be carried out by a pair of polarization beam splitter (PBS) and polarization beam combiner (PBC) with proper optical path difference between two arms. In addition, a wideband electrical delay lines can also be used after a photodetection for this kind of phase shift.

Fig. 7 Experiment results. (a) Generated triangular waveform with repetition frequency of 3 GHz. (b) The corresponding electrical spectrum.

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For sawtooth waveform generation, the obtained triangular signal is applied on the second MZM (MZM 2) as drive signal, which provides a triangular time window to carve the square-shaped pulse on the upper branch. By adjusting the tunable optical delay line (ODL 1), the phase of the square envelopes on two wavelengths can be simultaneously controlled and a sawtooth waveform or reversed-sawtooth waveform with 50% duty cycle is generated on each wavelength. As shown in Fig. 8(a), a clean and stable sawtooth waveform is experimentally generated. The measured rising time and falling time are 27 ps and 93 ps, respectively. It can be seen from Fig. 8(b) that the corresponding electrical spectrum is close to the Fourier series expansion of a sawtooth waveform. It has at least eight harmonic tunes because the used electrical spectrum analyzer (ESA, Agilent N9010A EXA) has only operation bandwidth of 26.5 GHz. Similarly, the reversed-sawtooth waveform is achieved when the optical signal in the upper branch gets another half-period delay. The measurements are given by Fig. 8(c) and 8(d).

Fig. 8 Measured waveforms and electrical spectra. (a) 3-GHz sawtooth waveform with 50% duty cycle. (b) The corresponding electrical spectrum. (c) 3-GHz reversed-sawtooth waveform with 50% duty cycle. (d) The corresponding electrical spectrum.

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Finally, the multiplexing technique is employed to obtain frequency doubling sawtooth waveforms with full duty cycle. Here, the outputs from MZM 2 are separated into two wavelength channels by a WDM. After power equalization by a tuning optical attenuator (ATT) and time shift by adjusting ODL 2, the signals are recombined by the followed WDM and mixed in a PD. Figure 9(a) and 9(b) show the sawtooth waveform with time scale of 100 ps/div and 20 ps/div, and the corresponding spectrum is shown in Fig. 9(c). Both of the waveform and electrical spectrum indicate that it is a sawtooth pulse stream with repetition frequency of 6 GHz. Again, the reversed-sawtooth waveform can also be obtained, as shown in Fig. 9(d) and 9(e), and the corresponding spectrum is given by Fig. 9(f).

Fig. 9 Measured waveforms and electrical spectra. (a), (b) 6-GHz sawtooth waveform with full duty cycle. (c) The corresponding electrical spectrum. (d), (e) 6-GHz reversed-sawtooth waveform with full duty cycle. (f) The corresponding electrical spectrum.

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From the above experimental verification, the practicality and the significances of this approach are well exhibited. Obviously, this is a simple and flexible scheme for generating several basic microwave waveforms. The key point is that the required spectral line manipulating in Fourier synthesis method is substituted for signal envelope control. It can also be regarded as an intuitive way to manage spectral lines in group. Although only the modulation frequency of 3 GHz is demonstrated, the tunability of the proposed scheme is reliable. One deficiency of the current configuration is the bandwidth limitation of the second MZM. However, the second-stage pulse carving can be performed by using nonlinear effects in optical fiber, e.g. four wave mixing (FWM). In this case, the proposed scheme has a very large bandwidth, and the operation bandwidth is only determined by the first modulator and the bandwidth of the used PD.

4. Conclusion

We have theoretically and experimentally demonstrated a novel approach to generating microwave waveforms based on optical pulse carving and overlapping in time domain. A single-drive MZM biased at quadrature point is severed as pulse carver, which is able to generate square-shaped waveforms with different harmonic power ratio between the first-order and the third-order components. When the modulation index is set to be 0.752, a triangular waveform with full duty cycle is obtained by the superimposition of the modulated signal and its copy with π/2 phase shift. If this square pulse is further carved via the second MZM with a triangular modulation signal, sawtooth (or reversed-sawtooth) waveform with 50% duty cycle is generated. Furthermore, the frequency doubling sawtooth (or reversed-sawtooth) waveform with full duty cycle can be consequently achieved through multiplexing technique. The key significance is that the waveforms generation is performed mainly by means of time-domain synthesis, which manages signals envelopes in stead of spectral line manipulation. Therefore, we don’t need to take much account of the phase and amplitude relationship among the harmonic components, and the desired waveforms can be generated by a more intuitive and convenient way.

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 61061004, 61465002), High Level Innovation Talent Program of Guizhou Province, China (Grant No. 2015(4010)), and the College Innovation Talent Team of Guizhou Province, China (Grant No. [2014]32).

References and links

1. A. I. Latkin, S. Boscolo, R. S. Bhamber, and S. K. Turitsyn, “Optical frequency conversion, pulse compression and signal copying using triangular pulses,” in ECOC, Brussels, Belgium (2008), paper Mo.3.F.4.

2. A. I. Latkin, S. Boscolo, R. S. Bhamber, and S. K. Turitsyn, “Doubling of optical signals using triangularpulses,” J. Opt. Soc. Am. B 26(8), 1492–1496 (2009). [CrossRef]

3. R. S. Bhamber, A. I. Latkin, S. Boscolo, and S. K. Turitsyn, “All-optical TDM to WDM signal conversion and partial regeneration using XPM with triangular pulses,” in ECOC, Brussels, Belgium (2008), paper Th.1.B.2.

4. J. P. Yao, “Photonic generation of microwave arbitrary waveforms,” Opt. Commun. 284(15), 3723–3736 (2011). [CrossRef]

5. Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007). [CrossRef]

6. J. Ye, L. Yan, W. Pan, B. Luo, X. Zou, A. Yi, and S. Yao, “Photonic generation of triangular-shaped pulses based on frequency-to-time conversion,” Opt. Lett. 36(8), 1458–1460 (2011). [CrossRef] [PubMed]

7. H.-Y. Jiang, L.-S. Yan, Y.-F. Sun, J. Ye, W. Pan, B. Luo, and X.-H. Zou, “Photonic arbitrary waveform generation based on crossed frequency to time mapping,” Opt. Express 21(5), 6488–6496 (2013). [CrossRef] [PubMed]

8. B. Dai, Z. Gao, X. Wang, H. Chen, N. Kataoka, and N. Wada, “Generation of versatile waveforms from CW light using a dual-drive Mach–Zehnder modulator and employing chromatic dispersion,” J. Lightwave Technol. 31(1), 145–151 (2013). [CrossRef]

9. J. Li, X. Zhang, B. Hraimel, T. Ning, L. Pei, and K. Wu, “Performance analysis of a photonic-assisted periodic triangular-shaped pulses generator,” J. Lightwave Technol. 30(11), 1617–1624 (2012). [CrossRef]

10. F. Zhang, X. Ge, and S. Pan, “Triangular pulse generation using a dual-parallel Mach-Zehnder modulator driven by a single-frequency radio frequency signal,” Opt. Lett. 38(21), 4491–4493 (2013). [CrossRef] [PubMed]

11. W. Liu and J. Yao, “Photonic generation of microwave waveforms based on a polarization modulator in a Sagnac loop,” J. Lightwave Technol. 32(20), 3637–3644 (2014). [CrossRef]

12. J. Li, T. G. Ning, L. Pei, W. Jian, H. D. You, H. Y. Chen, and C. Zhang, “Photonic-assisted periodic triangular-shaped pulses generation with tunable repetition rate,” IEEE Photonics Technol. Lett. 25(10), 952–954 (2013). [CrossRef]

13. W. Li, W. T. Wang, W. H. Sun, W. Y. Wang, and N. H. Zhu, “Generation of triangular waveforms based on a microwave photonic filter with negative coefficient,” Opt. Express 22(12), 14993–15001 (2014). [CrossRef] [PubMed]

14. X. Liu, W. Pan, X. Zou, D. Zheng, L. Yan, B. Luo, and B. Lu, “Photonic generation of triangular-shaped Microwave pulses using SBS-based optical carrier processing,” J. Lightwave Technol. 32(20), 3797–3802 (2014). [CrossRef]

15. D. S. Wu, D. J. Richardson, and R. Slavik, “Optical Fourier synthesis of high-repetition-rate pulses,” Optica 2(1), 18–26 (2015). [CrossRef]

16. Y. Jiang, C. Ma, G. Bai, Z. Jia, Y. Zi, S. Cai, T. Wu, and F. Huang, “Photonic generation of triangular waveform by utilizing time-domain synthesis,” IEEE Photonics Technol. Lett. 27(16), 1725–1728 (2015). [CrossRef]

17. C. Finot, “40-GHz photonic waveform generator by linear shaping of four spectral sidebands,” Opt. Lett. 40(7), 1422–1425 (2015). [CrossRef] [PubMed]

Photonic microwave waveforms generation based on time-domain processing

Abstract

1. Introduction

2. Principle

2.1 Square waveform

2.2 Triangular waveform

2.3 Sawtooth waveform

3. Experiment and results

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (9)

Equations (14)

Optics Express