Abstract

A new photonic scheme for various waveforms generation has been proposed and demonstrated. In the scheme, two cascaded single-drive LiNbO3 Mach-Zehnder modulators serve as pulse shaper and the polarization-dependent character of the modulators is fully exploited and utilized. By arranging the polarization states of the incident light, two different spectra are achieved on two orthogonal polarization components respectively. Finally, the desired waveforms can be obtained by superimposing the photocurrents of the two orthogonal signals on a photodetector. The detailed theoretical analyses and simulations are given. In the experiment, square-shaped waveform, triangular waveform and sawtooth (or reversed-sawtooth) waveform are obtained successfully. Furthermore, an approach to smoothing the sawtooth waveform with fewer harmonics is suggested and verified.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Radio frequency (RF) arbitrary waveform generation (AWG) has a wide range of applications in wireless communications, radar, measurement systems, and so on [1–3]. AWG using optical technology (optical arbitrary waveform generation, OAWG) provides new access to solving the electronic bottleneck problem in traditional electrical arbitrary waveform generation (EAWG) [3].

Currently, there are many methods to implement OAWG. One of the most popular ways for OAWG is Fourier synthesis. By accurately controlling the amplitudes and phases of optical spectral lines, arbitrary waveform generation can be achieved. Usually, a spatial configuration is employed to implement spectral line control [4], which makes a complex system. Meanwhile, the optical phase is easily affected by the surrounding perturbation. Frequency-to-time mapping (FTTM) is another way to achieve OAWG, in which the desired waveform can be generated by shaping the spectrum of optical pulses and mapping the spectral envelope to the time-domain [5,6]. However, the spectral lines are manipulated in groups, which reduces the flexibility and accuracy of waveform generation.

OAWG can also be achieved by means of time-domain processing [7,8]. In [7], Jiang et al. have confirmed that OAWG can be realized by carving continuous wave (CW) and overlapping the optical envelopes in time domain. In the works, the rectangular waveform, triangular waveform and half duty sawtooth waveform are generated successfully, and the full duty sawtooth waveform is obtained by means of multiplexing technology. The schemes show that the time-domain method is relatively straightforward and can avoid complex spectral line operation. However, in [7] two light sources are required, and the configuration is not compact.

In both Fourier synthesis and time-domain processing, OAWG based on CW modulation is widely used, since it is comparatively simple and efficient. It is reported that dual-parallel Mach-Zehnder modulator (DP-MZM), dual-drive Mach-Zehnder modulator (DD-MZM) and polarization modulator (Pol-M) have been used in many schemes to implement OAWG [9–14]. Recently, a scheme for triangular waveform generation, in which the polarization sensitivity of one single-drive LiNbO3 Mach-Zehnder modulator (MZM) is exploited, has been demonstrated [15]. Although this scheme has the advantages of simple configuration and lower cost, only triangular waveform is obtained.

In this paper, a simple and efficient scheme is proposed for diverse waveforms generation. Two LiNbO3 MZMs are cascaded as pulse shaper, and their polarization sensitivity is used to generate independent sidebands on two orthogonal polarization components of one light field. Simultaneously, the character that the orthogonal components do not beat is fully utilized. Then the desired RF waveform can be achieved by using the time-domain synthesis method. The theoretical analyses and simulations are established, and square-shaped waveform, triangular waveform and sawtooth (or reversed-sawtooth) waveform with the repetition frequency of 3 GHz are obtained experimentally. All the results show good performance.

2. Principle

The experimental setup is schematically illustrated in Fig. 1. A polarization controller (PC) placed in front of either LiNbO3 MZM is used to control the polarization state of the incident light. Due to the fact that MZM is a polarization-dependent device, only the polarization component of the incident light coinciding with the principal axis of the MZM can be modulated. Thus, different spectral properties can be achieved on two orthogonal components. Finally, the desired waveforms can be obtained through the superimposition of the photocurrents of the two orthogonal signals on a photodetector (PD). The polarizing beam splitter (PBS) is placed at the end to separate the signals in two orthogonal directions for observation.

 

Fig. 1 Diagram of the experimental setup. LD: laser diode, PC: polarization controller, MZM: single-drive LiNbO3 Mach-Zehnder modulator, EDFA: erbium-doped fiber amplifier, OC: optical coupler, ODL: optical delay line, ATT: attenuator, PBS: polarizing beam splitter.

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Mathematically, the linearly polarized CW emitted by the laser diode (LD) can be described as

Ein(t)=E0ejω0t
where E0 is the optical field amplitude, and ω0 is the angular frequency of the optical field. Suppose the drive signals applied on the MZMs are
vi=vDCi+vRFicos(ωmt)=εivπ+αivπcos(ωmt),i=1,2
where vDCi are the direct-current (DC) bias voltages, vRFi are the alternating-current (AC) drive voltages, ωm is the angular frequency of the drive signal, and vπ is the half-wave voltage. Moreover, i=1,2 denotes different parameters of the two modulators. εi=vDCi/vπ and αi=vRFi/vπ are the normalized coefficients.

Assuming there is an angle θ between the polarization direction of the incident light and the principal axis (X-axis) of MZM1, the two orthogonal components, E1X(t) and E1Y(t), of the output from MZM1 can be expressed as

E1(t)=[E1X(t)E1Y(t)]=[cosθEin(t){cosϕ1cos[m1cos(ωmt)]sinϕ1sin[m1cos(ωmt)]}sinθEin(t)]
where ϕi=πεi/2 is the bias index and mi=παi/2 is the modulation index (i=1 in the equation above). Suppose Y-axis is the principal axis of MZM2, the output of MZM2 is written as
E2(t)=[E2X(t)E2Y(t)]=[E1X(t)E2Y(t)]=[cosθEin(t){cosϕ1cos[m1cos(ωmt)]sinϕ1sin[m1cos(ωmt)]}sinθEin(t){cosϕ2cos[m2cos(ωmt+φ)]sinϕ2sin[m2cos(ωmt+φ)]}]
where φ is the phase shift introduced by the optical delay line (ODL). By applying the expansion of the Bessel functions of the first kind, Eq. (4) can be approximated by

E2(t)=[E2X(t)E2Y(t)][cosθEin(t)[cosϕ1J0(m1)2sinϕ1J1(m1)cos(ωmt)2cosϕ1J2(m1)cos(2ωmt)+2sinϕ1J3(m1)cos(3ωmt)]sinθEin(t)[cosϕ2J0(m2)2sinϕ2J1(m2)cos(ωmt+φ)2cosϕ2J2(m2)cos(2ωmt+2φ)+2sinϕ2J3(m2)cos(3ωmt+3φ)]].

Because only the harmonics with the same polarization state may contribute to beat, when the optical field is detected by a PD, the photocurrent is expressed as

I(t)|E2X(t)|2+|E2Y(t)|2DC+[X1cos(ωmt)+Y1cos(2ωmt)+Z1cos(3ωmt)]i1+[X2cos(ωmt+φ)+Y2cos(2ωmt+2φ)+Z2cos(3ωmt+3φ)]i2
where

[XiYiZi]=[(2BiCi2AiBi2CiDi)[(2i)cos2θ+(i1)sin2θ](Bi22AiCi2BiDi)[(2i)cos2θ+(i1)sin2θ](2AiDi+2BiCi)[(2i)cos2θ+(i1)sin2θ]].

In Eq. (7)

[AiBiCiDi]=[cosϕiJ0(mi)sinϕiJ1(mi)cosϕiJ2(mi)sinϕiJ3(mi)].

It can be perceived from the above equations that the desired harmonics with proper coefficients can be obtained by controlling the parameters of θ, φ, ϕi and mi.

2.1 Square-shaped waveform

Just as described in [7], square-shaped waveform can be simply obtained through the first-stage modulation. The Fourier series expansion of a square-shaped waveform is given by

Tsq(t)=DC+N=1,3,51Nsin(Nωmt).
According to Eq. (3) and Eq. (6), when MZM1 is biased at quadrature bias (QB) point andθ=0, the photocurrent detected at Output 1 is expressed as

I(t)DC+X1cos(ωmt)+Y1cos(2ωmt)+Z1cos(3ωmt)=DC+X1sin(ωmt+π2)+Y1cos(2ωmt)Z1sin(3ωmt+3π2).

Comparing Eq. (10) and Eq. (9), the photocurrent may present a square-shaped envelope in time domain only if X1=3Z1 and Y10. Figure 2(a) shows the calculated values of X1, Y1 and Z1. It can be found that square-shaped waveform can be obtained under the condition that m1=1.142. Figure 2(b) displays the corresponding simulation result.

 

Fig. 2 (a) The calculated coefficients of the first-, second- and third-order harmonics of the photocurrent. (b) Simulation result of square-shaped waveform generation.

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2.2 Triangular waveform

In principle, the Fourier expansion of a periodic triangular waveform is written as

Ttr(t)=DC+N=1,3,51N2cos(Nωmt).

It can be seen that the amplitude of higher order harmonics decreases sharply, and the sum of the first two harmonics can be a good approximation to the whole expansion. Thus, Eq. (11) is simplified as

Ttr(t)=DC+cos(ωmt)+19cos(3ωmt).

According to Fig. 3, two sets of modulation sidebands are carried on the orthogonal components of the optical field respectively. Meanwhile, the photocurrent expressed by Eq. (6) can be rewritten as

 

Fig. 3 Schematic diagram of triangular waveform generation.

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I(t)DC+X2cos(ωmt+φ2)cosφ2+(X1X2)cos(ωmt)+Y2cos(2ωmt+φ)cosφ+(Y1Y2)cos(2ωmt)+Z2cos(3ωmt+3φ2)cos3φ2+(Z1Z2)cos(3ωmt).

When θ=π/4, φ=π/2, ϕ1=ϕ2=π/4 and m1=m2, Eq. (13) is reduced to

I(t)DC+cosπ4[X2cos(ωmt+π4)Z2cos(3ωmt+3π4)].

Obviously, Eq. (14) can be equivalent to Eq. (12) only if X2=9Z2. Figure 4(a) shows the calculated values of X2 and Z2 versus the modulation index. Once m1=m2=0.752, the above condition can be satisfied. As a consequence, triangular waveform can be obtained at Output 2. Figure 4(b) displays the simulation result, in which the two photocurrents, i1 and i2 in Eq. (6) are superimposed for triangular waveform generation.

 

Fig. 4 (a) The calculated coefficients of the first- and third-order harmonics of the photocurrent. (b) Simulation result of triangular waveform synthesis.

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2.3 Sawtooth waveform

The Fourier series expansion of a sawtooth waveform is given by

Tsaw(t)=DC+N=11Nsin(Nωmt).

Considering the third-order approximation, the expansion is approximated by

Tsaw(t)DC+sin(ωmt)+12sin(2ωmt)+13sin(3ωmt).

According to Eq. (6), when φ=π/4, the photocurrent can be obtained as follows.

I(t)DC+[X1cos(ωmt)+Y2cos(2ωmt+π2)+Z1cos(3ωmt)]Saw1+[X2cos(ωmt+π4)+Y1cos(2ωmt)+Z2cos(3ωmt+3π4)]Saw2=DC+[X1sin(ωmt+π2)+Y2sin(2ωmt+π)Z1sin(3ωmt+3π2)]Saw1+[X2sin(ωmt+3π4)Y1sin(2ωmt+6π4)Z2sin(3ωmt+9π4)]Saw2.

Equation (17) can be regarded as the sum of the two terms, Saw1 and Saw2. Compared with Eq. (16), if the conditions that X1=2Y2=3Z1 and Saw20 are met, a sawtooth waveform can be achieved.

Figure 5(a) shows the calculated values of Xi/Zi versus modulation index. When mi=1.142, the ratio of Xi/Zi is −3. For convenience, suppose the power is equally distributed on two orthogonal components (viz. θ=π/4). Figure 5(b) gives the calculated coefficients versus bias index on condition that mi=1.142 and θ=π/4. Although the ratio of X1:Y2:Z1 does not fit that of Eq. (16), it can be further modified by adjusting the polarization of the incident light. If θ=0.684, the expected ratio can be satisfied.

 

Fig. 5 (a) The calculated coefficient ratio of the first-order harmonic to the third-order of the photocurrent versus the modulation index. (b) The calculated coefficients of the first-, second- and third-order harmonics of the photocurrent versus the bias index with the modulation indices of 1.142 and the incident angle of π/4.

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The calculated parameters and coefficients for sawtooth waveform generation are listed in Table 1. The ratio of the coefficients is very close to the ideal ratio of 3:2:1. Figure 6 shows the simulation results of sawtooth (or reversed-sawtooth) waveform synthesis by superposing the two photocurrents.

Tables Icon

Table 1. The calculated parameters and coefficients for sawtooth waveform generation

 

Fig. 6 Simulation results. (a) The sawtooth waveform synthesis. (b) The reversed-sawtooth waveform synthesis.

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Although the above simulation gives an approximate sawtooth waveform, the falling edge is not smooth. Furthermore, a smooth sawtooth waveform can be obtained by setting the appropriate parameters. The coefficient relation is

{X1=X2X1=2Y1=3Z1X2=2Y2=3Z2.

From Eq. (18), the following equation can be derived

{Xi/Zi=3X1/Y1=2X2/Y2=+2

With the conditions above, the two terms (Saw1 and Saw2) of Eq. (17) may present both the saw-toothed envelopes. Figure 7(a) shows the relationship between the bias index and Xi/Yi with the modulation index of 1.142. It is clear that only if the bias indices are the 1.077 and 0.492, the values of Xi/Yi can be very close to −2 and + 2 respectively. According to the results shown in Figs. 5(a) and 7(a), Eq. (19) can be achieved. Figure 7(b) presents the calculated coefficients on condition that mi=1.142 and θ=π/4.

 

Fig. 7 (a) The calculated coefficient ratio of the first-order harmonic to the second-order of the photocurrent versus the bias index with the modulation index of 1.142. (b) The calculated coefficients of the first-, second- and third-order harmonics of the photocurrent versus the bias index with the modulation indices of 1.142 and the incident angle of π/4.

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The calculated parameters and coefficients for smooth sawtooth waveform generation are listed in Table 2. The ratios of coefficients are very close to those in Eq. (18). Thus, the sawtooth waveform can be obtained at Output 2.

Tables Icon

Table 2. The calculated parameters and coefficients for smooth sawtooth waveform generation

Figure 8(a) shows the simulation result of the superposition of the two sawtooth waveforms expressed by Eq. (17). Figure 8(b) presents the comparison of the sawtooth waveform (dash line) and the superimposed waveform (solid line) with a normalized phase and amplitude. Although the superimposed waveform cannot be expressed by Eq. (15), it has a sawtooth-like shape and smooth edge.

 

Fig. 8 (a) Simulation result of the superposition of the two sawtooth waveforms. (b) Comparison of the sawtooth waveform and the superimposed waveform with a normalized phase and amplitude.

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It should be noted that the photocurrents (Saw1 and Saw2) in Eq. (17) are only the mathematical results, which are convenient for finding the parameters but not the actual photocurrents given by Eq. (6). Figure 9 shows the simulation results of the same waveforms generation by superimposing the two actual photocurrents.

 

Fig. 9 Simulation results. (a) The smooth sawtooth waveform synthesis. (b) The smooth reversed-sawtooth waveform synthesis.

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3. Experiments and results

In order to verify the feasibility of the proposed scheme, the experimental demonstration is carried out. Firstly, the polarization-dependent characteristic of MZM is investigated. Here, a sinusoidal drive signal with the frequency of 3 GHz is applied, and an optical carrier suppression (OCS) modulation experiment is performed. As shown in Fig. 10(a), the spectra are detected by an optical spectrum analyzer (OSA, YOKOGAWA AQ6370C), and part of the optical carrier is left if the polarization state of the incident optical field has an angle with the principal axis. Figures 10(b) and 10(c) give the corresponding waveforms measured by an oscilloscope (Agilent 86100D Infiniium DCA-X). By comparing the two waveforms, it can be confirmed that they are both OCS signals, but the one whose polarization state disaccords with the principal axis contains a large DC component. The results indicate that the optical carrier is hardly modulated when its polarization disaccords with the principal axis. Therefore, the polarization-dependent character of MZM can be used to load signals independently on two orthogonal components of one CW source.

 

Fig. 10 Experimental results. (a) The OCS spectra of different incident angles. (b) The corresponding waveform with the polarization of the incident light consistent with the principal axis. (c) The corresponding waveform with the polarization of the incident light inconsistent with the principal axis.

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Next, as illustrated in Fig. 1, the generation of versatile waveforms is shown experimentally. In the experiment, we use two MZMs with the bandwidth of 10 GHz and a photodetector with the 3-dB bandwidth of 50 GHz. The CW light emitted by the LD is sent to MZM1, which is biased at the QB point and driven by a RF signal with the frequency of 3 GHz. By setting the appropriate driving voltage, a square-shaped waveform is obtained. Figure 11(a) shows the square-shaped waveform observed at Output 1. The corresponding electrical spectrum is given by Fig. 11(b), which is measured by an electrical spectrum analyzer (ESA, Agilent N9010A EXA). Here, the power ratio of the first harmonic to the third is 10.17 dBm, which is close to the theoretical value. According to the theoretical analysis, two QB point biased MZMs with the modulation index of 0.752 can be used to achieve triangular waveform generation when PC1 and PC2 are carefully adjusted to distribute the appropriate power ratio on two orthogonal components. Meanwhile, the ODL is adjusted to make the time delay of about 83 ps (corresponding to π/2 envelope phase shift of the modulated signal). Figure 11(c) shows the triangular waveform obtained at Output 2. The corresponding electrical spectrum is given by Fig. 11(d), which also agrees with the theoretical expression.

 

Fig. 11 Measured waveforms and electrical spectra. (a) 3-GHz square-shaped waveform. (b) The corresponding electrical spectrum. (c) 3-GHz triangular waveform with full duty cycle. (d) The corresponding electrical spectrum.

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In order to confirm that the sawtooth waveform can be synthesized by two envelopes carried on two orthogonal components, the waveforms from the PBS are observed firstly as shown by Figs. 12(a) and 12(b). Figures 12(c) and 12(f) show the sawtooth (or reversed-sawtooth) waveform superimposed by these two waveforms, and the waveforms with a smaller time scale are given by Figs. 12(d) and 12(g). It is obvious that the experimental results are consistent with the simulation results. The measured falling time and rising time are 261 ps and 79 ps. It can be calculated that the ratio of the falling time to the rising time stands at about 3:1. Figures 12(e) and 12(h) show the corresponding electrical spectra.

 

Fig. 12 Measured waveforms and electrical spectra. (a),(b) The waveforms on the two orthogonal components. (c),(d) 3-GHz sawtooth waveform. (e) The corresponding electrical spectrum. (f),(g) 3-GHz reversed-sawtooth waveform. (h) The corresponding electrical spectrum.

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Finally, based on the theoretical analysis, the sawtooth waveform with smooth edges can be obtained at Output 2 by adjusting the bias voltages of the MZMs and the two PCs. Figures 13(a) and 13(b) present the waveforms on the two orthogonal components. Figures 13(c), 13(d), 13(f) and 13(g) show the smooth sawtooth (or reversed-sawtooth) waveform corresponding to the simulation results shown by Fig. (9). The falling time is 232 ps and the rising time 108 ps with the corresponding ratio of about 2:1. By comparing the waveforms shown in Fig. 12 and those in Fig. 13, it can be found that the latter are smoother. The corresponding electrical spectra are given by Figs. 13(e) and 13(h).

 

Fig. 13 Measured waveforms and electrical spectra. (a),(b) The waveforms on the two orthogonal components. (c),(d) 3-GHz smooth sawtooth waveform. (e) The corresponding electrical spectrum. (f),(g) 3-GHz smooth reversed-sawtooth waveform. (h) The corresponding electrical spectrum.

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From the experimental verification above, it can be seen that the results are consistent with the theoretical analyses and that the proposed scheme is efficient. By using one light source and two single-drive Mach-Zehnder modulators, various waveforms can be generated conveniently without using any dispersive elements or optical filters. In addition, complex spectral line manipulation is not required. Taking into account the bandwidth limitation of our measuring instrument (ESA with the maximum measurement frequency of 26.5 GHz), we only carry out the experiment of 3-GHz waveforms generation. Actually, the proposed system can offer potential for larger operation bandwidth, which is mainly subject to the bandwidth of the MZMs and PD, especially the latter, because PD must have the bandwidth larger than the highest order tone. In 2005, a PIN photodetector with the bandwidth of 120 GHz was reported [16], which means that it is possible to achieve more than 10-order harmonic tones of 10-GHz sawtooth waveform (or higher frequency triangular waveform) in our scheme.

4. Conclusion

A simple and efficient scheme for generating various waveforms is proposed, and the theoretical analysis and the experimental verification are carried out. Two cascaded MZMs are used to carve the CW light emitted by the LD. Due to the polarization-dependent character of MZM, the two PCs in front of the MZMs can be used to control the polarization of the incident light to achieve different spectral characteristics on the orthogonal components. In the experiment, by using sinusoidal drive signal at the frequency of 3 GHz we have successfully obtained square-shaped waveform, triangular waveform and sawtooth (or reversed-sawtooth) waveform with the repetition frequency of 3 GHz. Furthermore, an approach to generating the sawtooth waveform with smooth edges has been validated.

Funding

National Natural Science Foundation of China (NSFC) (61465002, 61751102); High Level Innovation Talent Program of Guizhou Province, China (2015-4010); the College Innovation Talent Team of Guizhou Province, China (2014-32).

References and links

1. J. P. Yao, “Microwave Photonics,” J. Lightwave Technol. 27(3), 314–335 (2009). [CrossRef]  

2. J. P. Yao, “Photonic Generation of Microwave Arbitrary Waveforms,” Opt. Commun. 284(15), 3723–3736 (2011). [CrossRef]  

3. S. T. Cundiff and A. M. Weiner, “Optical arbitrary waveform generation,” Nat. Photonics 4(11), 760–766 (2010). [CrossRef]  

4. 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]  

5. A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, “United time-frequency spectroscopy for dynamics and global structure,” Science 306(5704), 2063–2068 (2004). [CrossRef]   [PubMed]  

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. Y. Jiang, C. Ma, G. Bai, X. Qi, Y. Tang, Z. Jia, Y. Zi, F. Huang, and T. Wu, “Photonic microwave waveforms generation based on time-domain processing,” Opt. Express 23(15), 19442–19452 (2015). [CrossRef]   [PubMed]  

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

9. G. F. Bai, L. Hu, Y. Jiang, J. Tian, Y. J. Zi, T. W. Wu, and F. Q. Huang, “Versatile photonic microwave waveforms generation using a dual-parallel Mach–Zehnder modulator without other dispersive elements,” Opt. Commun. 396, 134–140 (2017). [CrossRef]  

10. W. Li, W. T. Wang, and N. H. Zhu, “Photonic Generation of Radio-Frequency Waveforms Based on Dual-Parallel Mach–Zehnder Modulator,” IEEE Photonics J. 6(3), 1–8 (2014).

11. 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]  

12. J. Wu, J. Zang, Y. Li, D. Kong, J. Qiu, S. Zhou, J. Shi, and J. Lin, “Investigation on Nyquist pulse generation using a single dual-parallel Mach-Zehnder modulator,” Opt. Express 22(17), 20463–20472 (2014). [CrossRef]   [PubMed]  

13. B. Dai, Z. S. Gao, X. Wang, H. W. 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 (2012). [CrossRef]  

14. W. L. Liu and J. P. Yao, “Photonic Generation of Microwave Waveforms Based on a Polarization Modulator in a Sagnac Loop,” J. Lightwave Technol. 32(20), 3637–3644 (2014). [CrossRef]  

15. C. Ma, Y. Jiang, G. F. Bai, Y. L. Tang, X. S. Qi, Z. R. Jia, Y. J. Zi, and J. L. Yu, “Photonic generation of microwave triangular waveform based on polarization-dependent modulation efficiency of a single-drive Mach–Zehnder modulator,” Opt. Commun. 363, 207–210 (2016). [CrossRef]  

16. A. Beling, H. G. Bach, G. G. Mekonnen, R. Kunkel, and D. Schmidt, “Miniaturized Waveguide-Integrated p-i-n Photodetector With 120-GHz Bandwidth and High Responsivity,” IEEE Photonics Technol. Lett. 17(10), 2152–2154 (2005). [CrossRef]  

References

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  1. J. P. Yao, “Microwave Photonics,” J. Lightwave Technol. 27(3), 314–335 (2009).
    [Crossref]
  2. J. P. Yao, “Photonic Generation of Microwave Arbitrary Waveforms,” Opt. Commun. 284(15), 3723–3736 (2011).
    [Crossref]
  3. S. T. Cundiff and A. M. Weiner, “Optical arbitrary waveform generation,” Nat. Photonics 4(11), 760–766 (2010).
    [Crossref]
  4. 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]
  5. A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, “United time-frequency spectroscopy for dynamics and global structure,” Science 306(5704), 2063–2068 (2004).
    [Crossref] [PubMed]
  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. Y. Jiang, C. Ma, G. Bai, X. Qi, Y. Tang, Z. Jia, Y. Zi, F. Huang, and T. Wu, “Photonic microwave waveforms generation based on time-domain processing,” Opt. Express 23(15), 19442–19452 (2015).
    [Crossref] [PubMed]
  8. Y. Jiang, C. Ma, G. F. Bai, Z. R. Jia, Y. J. Zi, S. H. Cai, T. W. Wu, and F. Q. Huang, “Photonic generation of triangular waveform by utilizing time-domain synthesis,” IEEE Photonics Technol. Lett. 27(16), 1725–1728 (2015).
    [Crossref]
  9. G. F. Bai, L. Hu, Y. Jiang, J. Tian, Y. J. Zi, T. W. Wu, and F. Q. Huang, “Versatile photonic microwave waveforms generation using a dual-parallel Mach–Zehnder modulator without other dispersive elements,” Opt. Commun. 396, 134–140 (2017).
    [Crossref]
  10. W. Li, W. T. Wang, and N. H. Zhu, “Photonic Generation of Radio-Frequency Waveforms Based on Dual-Parallel Mach–Zehnder Modulator,” IEEE Photonics J. 6(3), 1–8 (2014).
  11. 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]
  12. J. Wu, J. Zang, Y. Li, D. Kong, J. Qiu, S. Zhou, J. Shi, and J. Lin, “Investigation on Nyquist pulse generation using a single dual-parallel Mach-Zehnder modulator,” Opt. Express 22(17), 20463–20472 (2014).
    [Crossref] [PubMed]
  13. B. Dai, Z. S. Gao, X. Wang, H. W. 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 (2012).
    [Crossref]
  14. W. L. Liu and J. P. Yao, “Photonic Generation of Microwave Waveforms Based on a Polarization Modulator in a Sagnac Loop,” J. Lightwave Technol. 32(20), 3637–3644 (2014).
    [Crossref]
  15. C. Ma, Y. Jiang, G. F. Bai, Y. L. Tang, X. S. Qi, Z. R. Jia, Y. J. Zi, and J. L. Yu, “Photonic generation of microwave triangular waveform based on polarization-dependent modulation efficiency of a single-drive Mach–Zehnder modulator,” Opt. Commun. 363, 207–210 (2016).
    [Crossref]
  16. A. Beling, H. G. Bach, G. G. Mekonnen, R. Kunkel, and D. Schmidt, “Miniaturized Waveguide-Integrated p-i-n Photodetector With 120-GHz Bandwidth and High Responsivity,” IEEE Photonics Technol. Lett. 17(10), 2152–2154 (2005).
    [Crossref]

2017 (1)

G. F. Bai, L. Hu, Y. Jiang, J. Tian, Y. J. Zi, T. W. Wu, and F. Q. Huang, “Versatile photonic microwave waveforms generation using a dual-parallel Mach–Zehnder modulator without other dispersive elements,” Opt. Commun. 396, 134–140 (2017).
[Crossref]

2016 (1)

C. Ma, Y. Jiang, G. F. Bai, Y. L. Tang, X. S. Qi, Z. R. Jia, Y. J. Zi, and J. L. Yu, “Photonic generation of microwave triangular waveform based on polarization-dependent modulation efficiency of a single-drive Mach–Zehnder modulator,” Opt. Commun. 363, 207–210 (2016).
[Crossref]

2015 (2)

Y. Jiang, C. Ma, G. Bai, X. Qi, Y. Tang, Z. Jia, Y. Zi, F. Huang, and T. Wu, “Photonic microwave waveforms generation based on time-domain processing,” Opt. Express 23(15), 19442–19452 (2015).
[Crossref] [PubMed]

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

2014 (3)

2013 (1)

2012 (1)

2011 (2)

2010 (1)

S. T. Cundiff and A. M. Weiner, “Optical arbitrary waveform generation,” Nat. Photonics 4(11), 760–766 (2010).
[Crossref]

2009 (1)

2007 (1)

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]

2005 (1)

A. Beling, H. G. Bach, G. G. Mekonnen, R. Kunkel, and D. Schmidt, “Miniaturized Waveguide-Integrated p-i-n Photodetector With 120-GHz Bandwidth and High Responsivity,” IEEE Photonics Technol. Lett. 17(10), 2152–2154 (2005).
[Crossref]

2004 (1)

A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, “United time-frequency spectroscopy for dynamics and global structure,” Science 306(5704), 2063–2068 (2004).
[Crossref] [PubMed]

Bach, H. G.

A. Beling, H. G. Bach, G. G. Mekonnen, R. Kunkel, and D. Schmidt, “Miniaturized Waveguide-Integrated p-i-n Photodetector With 120-GHz Bandwidth and High Responsivity,” IEEE Photonics Technol. Lett. 17(10), 2152–2154 (2005).
[Crossref]

Bai, G.

Bai, G. F.

G. F. Bai, L. Hu, Y. Jiang, J. Tian, Y. J. Zi, T. W. Wu, and F. Q. Huang, “Versatile photonic microwave waveforms generation using a dual-parallel Mach–Zehnder modulator without other dispersive elements,” Opt. Commun. 396, 134–140 (2017).
[Crossref]

C. Ma, Y. Jiang, G. F. Bai, Y. L. Tang, X. S. Qi, Z. R. Jia, Y. J. Zi, and J. L. Yu, “Photonic generation of microwave triangular waveform based on polarization-dependent modulation efficiency of a single-drive Mach–Zehnder modulator,” Opt. Commun. 363, 207–210 (2016).
[Crossref]

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

Beling, A.

A. Beling, H. G. Bach, G. G. Mekonnen, R. Kunkel, and D. Schmidt, “Miniaturized Waveguide-Integrated p-i-n Photodetector With 120-GHz Bandwidth and High Responsivity,” IEEE Photonics Technol. Lett. 17(10), 2152–2154 (2005).
[Crossref]

Cai, S. H.

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

Chen, H. W.

Cundiff, S. T.

S. T. Cundiff and A. M. Weiner, “Optical arbitrary waveform generation,” Nat. Photonics 4(11), 760–766 (2010).
[Crossref]

Dai, B.

Felinto, D.

A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, “United time-frequency spectroscopy for dynamics and global structure,” Science 306(5704), 2063–2068 (2004).
[Crossref] [PubMed]

Gao, Z. S.

Ge, X.

Hu, L.

G. F. Bai, L. Hu, Y. Jiang, J. Tian, Y. J. Zi, T. W. Wu, and F. Q. Huang, “Versatile photonic microwave waveforms generation using a dual-parallel Mach–Zehnder modulator without other dispersive elements,” Opt. Commun. 396, 134–140 (2017).
[Crossref]

Huang, C. B.

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]

Huang, F.

Huang, F. Q.

G. F. Bai, L. Hu, Y. Jiang, J. Tian, Y. J. Zi, T. W. Wu, and F. Q. Huang, “Versatile photonic microwave waveforms generation using a dual-parallel Mach–Zehnder modulator without other dispersive elements,” Opt. Commun. 396, 134–140 (2017).
[Crossref]

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

Jia, Z.

Jia, Z. R.

C. Ma, Y. Jiang, G. F. Bai, Y. L. Tang, X. S. Qi, Z. R. Jia, Y. J. Zi, and J. L. Yu, “Photonic generation of microwave triangular waveform based on polarization-dependent modulation efficiency of a single-drive Mach–Zehnder modulator,” Opt. Commun. 363, 207–210 (2016).
[Crossref]

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

Jiang, Y.

G. F. Bai, L. Hu, Y. Jiang, J. Tian, Y. J. Zi, T. W. Wu, and F. Q. Huang, “Versatile photonic microwave waveforms generation using a dual-parallel Mach–Zehnder modulator without other dispersive elements,” Opt. Commun. 396, 134–140 (2017).
[Crossref]

C. Ma, Y. Jiang, G. F. Bai, Y. L. Tang, X. S. Qi, Z. R. Jia, Y. J. Zi, and J. L. Yu, “Photonic generation of microwave triangular waveform based on polarization-dependent modulation efficiency of a single-drive Mach–Zehnder modulator,” Opt. Commun. 363, 207–210 (2016).
[Crossref]

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

Y. Jiang, C. Ma, G. Bai, X. Qi, Y. Tang, Z. Jia, Y. Zi, F. Huang, and T. Wu, “Photonic microwave waveforms generation based on time-domain processing,” Opt. Express 23(15), 19442–19452 (2015).
[Crossref] [PubMed]

Jiang, Z.

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]

Kataoka, N.

Kong, D.

Kunkel, R.

A. Beling, H. G. Bach, G. G. Mekonnen, R. Kunkel, and D. Schmidt, “Miniaturized Waveguide-Integrated p-i-n Photodetector With 120-GHz Bandwidth and High Responsivity,” IEEE Photonics Technol. Lett. 17(10), 2152–2154 (2005).
[Crossref]

Lawall, J. R.

A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, “United time-frequency spectroscopy for dynamics and global structure,” Science 306(5704), 2063–2068 (2004).
[Crossref] [PubMed]

Leaird, D. E.

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]

Li, W.

W. Li, W. T. Wang, and N. H. Zhu, “Photonic Generation of Radio-Frequency Waveforms Based on Dual-Parallel Mach–Zehnder Modulator,” IEEE Photonics J. 6(3), 1–8 (2014).

Li, Y.

Lin, J.

Liu, W. L.

Luo, B.

Ma, C.

C. Ma, Y. Jiang, G. F. Bai, Y. L. Tang, X. S. Qi, Z. R. Jia, Y. J. Zi, and J. L. Yu, “Photonic generation of microwave triangular waveform based on polarization-dependent modulation efficiency of a single-drive Mach–Zehnder modulator,” Opt. Commun. 363, 207–210 (2016).
[Crossref]

Y. Jiang, C. Ma, G. Bai, X. Qi, Y. Tang, Z. Jia, Y. Zi, F. Huang, and T. Wu, “Photonic microwave waveforms generation based on time-domain processing,” Opt. Express 23(15), 19442–19452 (2015).
[Crossref] [PubMed]

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

Marian, A.

A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, “United time-frequency spectroscopy for dynamics and global structure,” Science 306(5704), 2063–2068 (2004).
[Crossref] [PubMed]

Mekonnen, G. G.

A. Beling, H. G. Bach, G. G. Mekonnen, R. Kunkel, and D. Schmidt, “Miniaturized Waveguide-Integrated p-i-n Photodetector With 120-GHz Bandwidth and High Responsivity,” IEEE Photonics Technol. Lett. 17(10), 2152–2154 (2005).
[Crossref]

Pan, S.

Pan, W.

Qi, X.

Qi, X. S.

C. Ma, Y. Jiang, G. F. Bai, Y. L. Tang, X. S. Qi, Z. R. Jia, Y. J. Zi, and J. L. Yu, “Photonic generation of microwave triangular waveform based on polarization-dependent modulation efficiency of a single-drive Mach–Zehnder modulator,” Opt. Commun. 363, 207–210 (2016).
[Crossref]

Qiu, J.

Schmidt, D.

A. Beling, H. G. Bach, G. G. Mekonnen, R. Kunkel, and D. Schmidt, “Miniaturized Waveguide-Integrated p-i-n Photodetector With 120-GHz Bandwidth and High Responsivity,” IEEE Photonics Technol. Lett. 17(10), 2152–2154 (2005).
[Crossref]

Shi, J.

Stowe, M. C.

A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, “United time-frequency spectroscopy for dynamics and global structure,” Science 306(5704), 2063–2068 (2004).
[Crossref] [PubMed]

Tang, Y.

Tang, Y. L.

C. Ma, Y. Jiang, G. F. Bai, Y. L. Tang, X. S. Qi, Z. R. Jia, Y. J. Zi, and J. L. Yu, “Photonic generation of microwave triangular waveform based on polarization-dependent modulation efficiency of a single-drive Mach–Zehnder modulator,” Opt. Commun. 363, 207–210 (2016).
[Crossref]

Tian, J.

G. F. Bai, L. Hu, Y. Jiang, J. Tian, Y. J. Zi, T. W. Wu, and F. Q. Huang, “Versatile photonic microwave waveforms generation using a dual-parallel Mach–Zehnder modulator without other dispersive elements,” Opt. Commun. 396, 134–140 (2017).
[Crossref]

Wada, N.

Wang, W. T.

W. Li, W. T. Wang, and N. H. Zhu, “Photonic Generation of Radio-Frequency Waveforms Based on Dual-Parallel Mach–Zehnder Modulator,” IEEE Photonics J. 6(3), 1–8 (2014).

Wang, X.

Weiner, A. M.

S. T. Cundiff and A. M. Weiner, “Optical arbitrary waveform generation,” Nat. Photonics 4(11), 760–766 (2010).
[Crossref]

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]

Wu, J.

Wu, T.

Wu, T. W.

G. F. Bai, L. Hu, Y. Jiang, J. Tian, Y. J. Zi, T. W. Wu, and F. Q. Huang, “Versatile photonic microwave waveforms generation using a dual-parallel Mach–Zehnder modulator without other dispersive elements,” Opt. Commun. 396, 134–140 (2017).
[Crossref]

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

Yan, L.

Yao, J. P.

Yao, S.

Ye, J.

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]

A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, “United time-frequency spectroscopy for dynamics and global structure,” Science 306(5704), 2063–2068 (2004).
[Crossref] [PubMed]

Yi, A.

Yu, J. L.

C. Ma, Y. Jiang, G. F. Bai, Y. L. Tang, X. S. Qi, Z. R. Jia, Y. J. Zi, and J. L. Yu, “Photonic generation of microwave triangular waveform based on polarization-dependent modulation efficiency of a single-drive Mach–Zehnder modulator,” Opt. Commun. 363, 207–210 (2016).
[Crossref]

Zang, J.

Zhang, F.

Zhou, S.

Zhu, N. H.

W. Li, W. T. Wang, and N. H. Zhu, “Photonic Generation of Radio-Frequency Waveforms Based on Dual-Parallel Mach–Zehnder Modulator,” IEEE Photonics J. 6(3), 1–8 (2014).

Zi, Y.

Zi, Y. J.

G. F. Bai, L. Hu, Y. Jiang, J. Tian, Y. J. Zi, T. W. Wu, and F. Q. Huang, “Versatile photonic microwave waveforms generation using a dual-parallel Mach–Zehnder modulator without other dispersive elements,” Opt. Commun. 396, 134–140 (2017).
[Crossref]

C. Ma, Y. Jiang, G. F. Bai, Y. L. Tang, X. S. Qi, Z. R. Jia, Y. J. Zi, and J. L. Yu, “Photonic generation of microwave triangular waveform based on polarization-dependent modulation efficiency of a single-drive Mach–Zehnder modulator,” Opt. Commun. 363, 207–210 (2016).
[Crossref]

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

Zou, X.

IEEE Photonics J. (1)

W. Li, W. T. Wang, and N. H. Zhu, “Photonic Generation of Radio-Frequency Waveforms Based on Dual-Parallel Mach–Zehnder Modulator,” IEEE Photonics J. 6(3), 1–8 (2014).

IEEE Photonics Technol. Lett. (2)

A. Beling, H. G. Bach, G. G. Mekonnen, R. Kunkel, and D. Schmidt, “Miniaturized Waveguide-Integrated p-i-n Photodetector With 120-GHz Bandwidth and High Responsivity,” IEEE Photonics Technol. Lett. 17(10), 2152–2154 (2005).
[Crossref]

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

J. Lightwave Technol. (3)

Nat. Photonics (2)

S. T. Cundiff and A. M. Weiner, “Optical arbitrary waveform generation,” Nat. Photonics 4(11), 760–766 (2010).
[Crossref]

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]

Opt. Commun. (3)

J. P. Yao, “Photonic Generation of Microwave Arbitrary Waveforms,” Opt. Commun. 284(15), 3723–3736 (2011).
[Crossref]

G. F. Bai, L. Hu, Y. Jiang, J. Tian, Y. J. Zi, T. W. Wu, and F. Q. Huang, “Versatile photonic microwave waveforms generation using a dual-parallel Mach–Zehnder modulator without other dispersive elements,” Opt. Commun. 396, 134–140 (2017).
[Crossref]

C. Ma, Y. Jiang, G. F. Bai, Y. L. Tang, X. S. Qi, Z. R. Jia, Y. J. Zi, and J. L. Yu, “Photonic generation of microwave triangular waveform based on polarization-dependent modulation efficiency of a single-drive Mach–Zehnder modulator,” Opt. Commun. 363, 207–210 (2016).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Science (1)

A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, “United time-frequency spectroscopy for dynamics and global structure,” Science 306(5704), 2063–2068 (2004).
[Crossref] [PubMed]

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Figures (13)

Fig. 1
Fig. 1 Diagram of the experimental setup. LD: laser diode, PC: polarization controller, MZM: single-drive LiNbO3 Mach-Zehnder modulator, EDFA: erbium-doped fiber amplifier, OC: optical coupler, ODL: optical delay line, ATT: attenuator, PBS: polarizing beam splitter.
Fig. 2
Fig. 2 (a) The calculated coefficients of the first-, second- and third-order harmonics of the photocurrent. (b) Simulation result of square-shaped waveform generation.
Fig. 3
Fig. 3 Schematic diagram of triangular waveform generation.
Fig. 4
Fig. 4 (a) The calculated coefficients of the first- and third-order harmonics of the photocurrent. (b) Simulation result of triangular waveform synthesis.
Fig. 5
Fig. 5 (a) The calculated coefficient ratio of the first-order harmonic to the third-order of the photocurrent versus the modulation index. (b) The calculated coefficients of the first-, second- and third-order harmonics of the photocurrent versus the bias index with the modulation indices of 1.142 and the incident angle of π/4.
Fig. 6
Fig. 6 Simulation results. (a) The sawtooth waveform synthesis. (b) The reversed-sawtooth waveform synthesis.
Fig. 7
Fig. 7 (a) The calculated coefficient ratio of the first-order harmonic to the second-order of the photocurrent versus the bias index with the modulation index of 1.142. (b) The calculated coefficients of the first-, second- and third-order harmonics of the photocurrent versus the bias index with the modulation indices of 1.142 and the incident angle of π/4.
Fig. 8
Fig. 8 (a) Simulation result of the superposition of the two sawtooth waveforms. (b) Comparison of the sawtooth waveform and the superimposed waveform with a normalized phase and amplitude.
Fig. 9
Fig. 9 Simulation results. (a) The smooth sawtooth waveform synthesis. (b) The smooth reversed-sawtooth waveform synthesis.
Fig. 10
Fig. 10 Experimental results. (a) The OCS spectra of different incident angles. (b) The corresponding waveform with the polarization of the incident light consistent with the principal axis. (c) The corresponding waveform with the polarization of the incident light inconsistent with the principal axis.
Fig. 11
Fig. 11 Measured waveforms and electrical spectra. (a) 3-GHz square-shaped waveform. (b) The corresponding electrical spectrum. (c) 3-GHz triangular waveform with full duty cycle. (d) The corresponding electrical spectrum.
Fig. 12
Fig. 12 Measured waveforms and electrical spectra. (a),(b) The waveforms on the two orthogonal components. (c),(d) 3-GHz sawtooth waveform. (e) The corresponding electrical spectrum. (f),(g) 3-GHz reversed-sawtooth waveform. (h) The corresponding electrical spectrum.
Fig. 13
Fig. 13 Measured waveforms and electrical spectra. (a),(b) The waveforms on the two orthogonal components. (c),(d) 3-GHz smooth sawtooth waveform. (e) The corresponding electrical spectrum. (f),(g) 3-GHz smooth reversed-sawtooth waveform. (h) The corresponding electrical spectrum.

Tables (2)

Tables Icon

Table 1 The calculated parameters and coefficients for sawtooth waveform generation

Tables Icon

Table 2 The calculated parameters and coefficients for smooth sawtooth waveform generation

Equations (19)

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E in (t)= E 0 e j ω 0 t
v i = v DC i + v RF i cos( ω m t)= ε i v π + α i v π cos( ω m t), i=1,2
E 1 (t)=[ E 1 X (t) E 1 Y (t) ] =[ cosθ E in (t){cos ϕ 1 cos[ m 1 cos( ω m t)]sin ϕ 1 sin[ m 1 cos( ω m t)]} sinθ E in (t) ]
E 2 (t)=[ E 2 X (t) E 2 Y (t) ]=[ E 1 X (t) E 2 Y (t) ] =[ cosθ E in (t){cos ϕ 1 cos[ m 1 cos( ω m t)]sin ϕ 1 sin[ m 1 cos( ω m t)]} sinθ E in (t){cos ϕ 2 cos[ m 2 cos( ω m t+φ)]sin ϕ 2 sin[ m 2 cos( ω m t+φ)]} ]
E 2 (t)=[ E 2 X (t) E 2 Y (t) ] [ cosθ E in (t)[cos ϕ 1 J 0 ( m 1 )2sin ϕ 1 J 1 ( m 1 )cos( ω m t) 2cos ϕ 1 J 2 ( m 1 )cos(2 ω m t)+2sin ϕ 1 J 3 ( m 1 )cos(3 ω m t)] sinθ E in (t)[cos ϕ 2 J 0 ( m 2 )2sin ϕ 2 J 1 ( m 2 )cos( ω m t+φ) 2cos ϕ 2 J 2 ( m 2 )cos(2 ω m t+2φ)+2sin ϕ 2 J 3 ( m 2 )cos(3 ω m t+3φ)] ].
I(t) | E 2 X (t) | 2 + | E 2 Y (t) | 2 DC+ [ X 1 cos( ω m t)+ Y 1 cos(2 ω m t)+ Z 1 cos(3 ω m t) ] i 1 + [ X 2 cos( ω m t+φ)+ Y 2 cos(2 ω m t+2φ)+ Z 2 cos(3 ω m t+3φ) ] i 2
[ X i Y i Z i ]=[ (2 B i C i 2 A i B i 2 C i D i )[(2i) cos 2 θ+(i1) sin 2 θ] ( B i 2 2 A i C i 2 B i D i )[(2i) cos 2 θ+(i1) sin 2 θ] (2 A i D i +2 B i C i )[(2i) cos 2 θ+(i1) sin 2 θ] ].
[ A i B i C i D i ]=[ cos ϕ i J 0 ( m i ) sin ϕ i J 1 ( m i ) cos ϕ i J 2 ( m i ) sin ϕ i J 3 ( m i ) ].
T sq (t)=DC+ N=1,3,5 1 N sin(N ω m t).
I(t)DC+ X 1 cos( ω m t)+ Y 1 cos(2 ω m t)+ Z 1 cos(3 ω m t) =DC+ X 1 sin( ω m t+ π 2 )+ Y 1 cos(2 ω m t) Z 1 sin(3 ω m t+ 3π 2 ).
T tr (t)=DC+ N=1,3,5 1 N 2 cos(N ω m t).
T tr (t)=DC+cos( ω m t)+ 1 9 cos(3 ω m t).
I(t)DC+ X 2 cos( ω m t+ φ 2 )cos φ 2 +( X 1 X 2 )cos( ω m t) + Y 2 cos(2 ω m t+φ)cosφ+( Y 1 Y 2 )cos(2 ω m t) + Z 2 cos(3 ω m t+ 3φ 2 )cos 3φ 2 +( Z 1 Z 2 )cos(3 ω m t).
I(t)DC+cos π 4 [ X 2 cos( ω m t+ π 4 ) Z 2 cos(3 ω m t+ 3π 4 ) ].
T saw (t)=DC+ N=1 1 N sin(N ω m t).
T saw (t)DC+sin( ω m t)+ 1 2 sin(2 ω m t)+ 1 3 sin(3 ω m t).
I(t)DC+ [ X 1 cos( ω m t)+ Y 2 cos(2 ω m t+ π 2 )+ Z 1 cos(3 ω m t) ] Saw1 + [ X 2 cos( ω m t+ π 4 )+ Y 1 cos(2 ω m t)+ Z 2 cos(3 ω m t+ 3π 4 ) ] Saw2 =DC+ [ X 1 sin( ω m t+ π 2 )+ Y 2 sin(2 ω m t+π) Z 1 sin(3 ω m t+ 3π 2 ) ] Saw1 + [ X 2 sin( ω m t+ 3π 4 ) Y 1 sin(2 ω m t+ 6π 4 ) Z 2 sin(3 ω m t+ 9π 4 ) ] Saw2 .
{ X 1 = X 2 X 1 =2 Y 1 =3 Z 1 X 2 =2 Y 2 =3 Z 2 .
{ X i / Z i =3 X 1 / Y 1 =2 X 2 / Y 2 =+2

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