Investigation on Nyquist pulse generation using a single dual-parallel Mach-Zehnder modulator

Jian Wu; Jizhao Zang; Yan Li; Deming Kong; Jifang Qiu; Siyuan Zhou; Jindan Shi; Jintong Lin

doi:10.1364/OE.22.020463

1. Introduction

The rapid growth of Internet traffic demands continuing increase in the capacity of the optical transmission systems. Nyquist (orthogonal) optical time-division multiplexing (Nyquist-OTDM) system is a promising candidate to meet such requirement with high spectrum efficiency (SE) [1]. In Nyquist-OTDM systems, the sinc-shaped pulses overlap in time domain but the symbols can be detected at the inter-symbol interference (ISI) free points where periodic zero crossing happens [2]. Recently, a record 1.28 Tbaud Nyquist-OTDM transmission experiment has been reported [3]. Compared with traditional OTDM systems utilizing Gaussian pulses, the bandwidth of Nyquist-OTDM signal can be significantly reduced, which results in an improved tolerance to chromatic dispersion (CD) and polarization mode dispersion (PMD) [4]. In addition, Nyquist-OTDM has the advantage of lower peak-to-average power ratio (PAPR) [5] and higher tolerance to fiber nonlinearity [6]. Furthermore, Nyquist-OTDM signal can be combined with Nyquist wavelength-division multiplexing (Nyquist-WDM) techniques [7–10]. Provided fundamentally minimum bandwidth, the guard band between adjacent wavelength channels can be much narrower, which results in an improved overall spectral efficiency.

The generation of Nyquist pulses with high quality is of significance to enable these systems based on Nyquist pulses. The Nyquist pulses can be generated using digital signal processing [11–13] in electrical domain, or can be obtained by performing pulse shaping with a liquid crystal spatial modulator in optical domain [1, 3, 4]. Optical parametric amplification is also utilized in the generation of Nyquist pulses [14], but the quality of generated Nyquist pulses is limited by the nonlinearity of the RF driver and the phase modulator used for chirp compensation. Since the sinc-shaped waveforms in time domain corresponds to a rectangular spectrum in the frequency domain, the Nyquist pulses can also be obtained directly from the generation of flat frequency comb with electro-optic modulators (EOMs). This kind of schemes features the least number of optical amplifiers, which will improve the quality of generated Nyquist pulses in terms of optical signal-to-noise ratio (OSNR). In addition, it would also be energy-saving and stable due to the elimination of any optical nonlinear process. One reported method uses cascaded EOMs driven by two RF signals which satisfy a certain relationship to generate Nyquist pulses [15, 16]. But the time-delay between the two EOMs would be drifting slowly if no active-feedback control is employed, which is doubtable for long-term stability.

In our previous work, a simple scheme of generating short optical pulses and flat frequency comb with an integrated dual parallel Mach-Zehnder modulator (DPMZM) driven by a single RF source is proposed in [17, 18]. Since the Nyquist pulses in time domain indicate a frequency comb in frequency domain, a similar scheme using DPMZM is employed to generate Nyquist pulses [19–21]. In these papers, the intensity of different sidebands in the generated frequency comb is analyzed, but the phase relationship between these sidebands is not considered. In addition, there is no accurate and complete description about how to adjust the bias voltages applied to the DPMZM.

Compared with our previous work [21], a complete theoretical analysis of the proposed scheme is developed in this paper, which also provides predications of its limitations. The conditions for generating Nyquist pulse are given in detail and a Nyquist pulse train with 5 comb lines can be generated with a single DPMZM. It is proved that both the amplitude and phase of the sidebands in the optical frequency comb are important for generation of Nyquist pulses. Theoretically it is found that it is impossible to generate Nyquist pulses with more than 5 comb lines using a single DPMZM even if 7 flat comb lines are realized. This scheme is then verified by simulation as well as experiment. In the experiment, 40 GHz Nyquist pulses with full-width-at-half-maximum (FWHM) less than 4.65 ps, signal-to-noise ratio (SNR) more than 29.5 dB, normalized root-mean-square error (NRMSE) [16] less than 2.4% are generated. To verify the tunability of this scheme, Nyquist pulses of different repetition rate from 1 GHz to 40 GHz are obtained by tuning the frequency of the RF source. In all cases, the measured SNR is more than 28.4 dB and the calculated NRMSE is less than 6.15%.

2. Principle and simulation

The proposed scheme is based on the generation of a frequency comb with a rectangular shape [15, 16]. As shown in Fig. 1(a), a continuous wave (CW) light is launched into a DPMZM. Only one RF signal with frequency of $f$ is applied to drive MZM1 and push-pull configuration of the child-MZMs is assumed. If $V_{0}$ represents the amplitude of the RF signal applied to MZM1, $V_{D C 1}$ , $V_{D C 2}$ and $V_{D C 3}$ represent the three DC bias voltages respectively, the output field of the DPMZM can be expressed as [17]:

E_{o u t} = \frac{E_{i n} e^{j π}}{2} {\cos [\frac{π V_{0}}{2 V_{π}} \sin (2 π f t) + \frac{π V_{D C 1}}{2 V_{π}}] + \cos (\frac{π V_{D C 2}}{2 V_{π}}) e^{j \frac{π V_{D C 3}}{V_{π}}}}

where

E_{i n}

is the input field,

V_{π}

is the half-wave voltage of the modulators. Based on Jacobi–Anger expansion to the output field, the optical carrier, 1st-order, 2nd-order and 3rd-order sidebands can be expressed as:

E_{0} = \frac{E_{i n} e^{j π}}{2} [\cos A J_{0} (B) + \cos (\frac{π V_{D C 2}}{2 V_{π}}) e^{j \frac{π V_{D C 3}}{V_{π}}}]

E_{+ 1} = \frac{E_{i n} e^{j π}}{2} \sin A J_{1} (B) e^{j (ω t + \frac{π}{2})}

E_{- 1} = \frac{E_{i n} e^{j π}}{2} \sin A J_{1} (B) e^{- j (ω t + \frac{π}{2})}

E_{+ 2} = \frac{E_{i n} e^{j π}}{2} \cos A J_{2} (B) e^{j 2 ω t}

E_{- 2} = \frac{E_{i n} e^{j π}}{2} \cos A J_{2} (B) e^{- j 2 ω t}

E_{+ 3} = \frac{E_{i n} e^{j π}}{2} \sin A J_{3} (B) e^{j (3 ω t + \frac{π}{2})}

E_{- 3} = \frac{E_{i n} e^{j π}}{2} \sin A J_{3} (B) e^{- j (3 ω t + \frac{π}{2})}

where

A = π V_{D C 1} / (2 V_{π})

,

B = π V_{0} / (2 V_{π})

,

ω = 2 π f . J_{n} (x)

represents the n^th-order Bessel function.

Fig. 1 Schematic of the proposed scheme: (a) experimental setup; (b)-(d) spectrums of the optical signal from child-MZM1, child-MZM2, and the DPMZM; (e) intensity (red line) and phase (blue line) of the generated Nyquist pulses.

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The Nyquist pulses can be generated with only one DPMZM by proper adjustment of $V_{0}$ and other applied bias voltages. The key point is the generation of a flat comb with 5 lines. Figures 1(b)-1(d) give a schematic illustration of generating Nyquist pulses using a DPMZM. Firstly, from Eq. (3)-(6), if $V_{0}$ and $V_{D C 1}$ applied on MZM1 satisfy the following equation:

\frac{E_{i n}}{2} \sin A J_{1} (B) = \frac{E_{i n}}{2} \cos A J_{2} (B) = U

or

V_{D C 1} = \frac{2 V_{π}}{π} arc \tan [J_{2} (B) / J_{1} (B)]

where U is the amplitude of the sidebands. Then the 1st-order and 2nd-order sidebands would have the same amplitude and four comb lines with the same amplitude are generated, as shown in Fig. 1(b) with a frequency spacing of 40 GHz as an example. Figure 2(a) shows the optimal value of

V_{D C 1}

as a function of peak-to-peak voltage

(V_{p p} = 2 V_{0})

of the RF driving signal. It can be seen that the optimal

V_{D C 1}

approximately varies with

V_{p p}

linearly when

V_{p p}

is lower than

3 V_{π}

.

Fig. 2 (a) The relationship between $V_{D C 1}$ and $V_{p p}$ when the1st-order and 2nd-order sidebands have the same amplitude; (b) intensity difference between1st sidebands and other sidebands when Eq. (9) is satisfied; (c) the suppression ratio of 3rd-order and 4th-order sidebands compared with 1st-order sidebands; (d) $V_{D C 1}$ dependence on $V_{p p}$ of RF driving signal.

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The next step is to generate the flat frequency comb with 5 lines as depicted in Fig. 1(d). This can be realized by properly setting the intensity and phase of the optical carrier using $V_{D C 2}$ and $V_{D C 3}$ (Fig. 1(c)). Figure 2(b) illustrates the intensity difference between the 1st-order sidebands and higher-order sidebands in MZM1 when Eq. (9) or (10) is satisfied, in which the 2nd-order sidebands have the same intensity with 1st-order sidebands. Figure 2(c) shows the suppression ratio of the 3rd-order and 4th-order sidebands compared with 1st-order and 2nd-order sidebands. It can be seen that as the $V_{p p}$ is less than $2 V_{π}$ , the 3rd-order and 4th-order sidebands are suppressed by more than 18 dB and 25 dB respectively, which means that the 3rd-order and higher-order sidebands can be neglected in this case. Therefore, the output signal can be expressed as:

\begin{array}{l} E_{o u t} = \frac{E_{i n} e^{j π}}{2} {[\cos A J_{0} (B) + \cos (\frac{π V_{D C 2}}{2 V_{π}}) e^{j \frac{π V_{D C 3}}{V_{π}}}] + \sin A J_{1} (B) e^{j (ω t + \frac{π}{2})} \\ + \sin A J_{1} (B) e^{- j (ω t + \frac{π}{2})} + \cos A J_{2} (B) e^{j 2 ω t} + \cos A J_{2} (B) e^{- j 2 ω t}} \end{array}

It can be seen from Eq. (11) that if the following conditions are satisfied

\frac{E_{i n}}{2} [\cos A J_{0} (B) + \cos (\frac{π V_{D C 2}}{2 V_{π}}) e^{j \frac{π V_{D C 3}}{V_{π}}}] = - U

where U is defined in Eq. (9). By substituting Eq. (9) and (12) to Eq. (11), the output signal can be expressed as

E_{o u t} = U e^{j π} [- 1 + e^{j (ω t + \frac{π}{2})} + e^{- j (ω t + \frac{π}{2})} + e^{j 2 ω t} + e^{- j 2 ω t}]

which can be further rewritten as

E_{o u t} = 5 U \frac{\sin [5 (π f t + \frac{3 π}{4})]}{5 \sin (π f t + \frac{3 π}{4})}

where f is the frequency of the RF signal. The envelope of the optical field from the DPMZM is periodic sinc-shape and it’s a Nyquist pulse train in time domain [16]. Figure 1(e) shows the waveform (red line) and phase (blue line) of the generated Nyquist pulses. In this case, Eq. (12) can be rewritten as

\cos A J_{0} (B) + \cos (\frac{π V_{D C 2}}{2 V_{π}}) e^{j \frac{π V_{D C 3}}{V_{π}}} = - \sin A J_{1} (B)

Then

V_{D C 3}

and V_DC2 can be determined as:

V_{D C 3} = (2 N + 1) V_{π}, V_{D C 2} = \frac{2 V_{π}}{π} {\pm arc \cos [\sin A J_{1} (B) + \cos A J_{0} (B)]}

or

V_{D C 3} = 2 N V_{π}, V_{D C 2} = \frac{2 V_{π}}{π} {\pm arc \cos [- \sin A J_{1} (B) - \cos A J_{0} (B)]}

where N is an integer. Therefore,

V_{0}

,

V_{D C 1}

,

V_{D C 2}

and

V_{D C 3}

should be set as Eq. (9), (16) and (17) to generate Nyquist pulses with a single DPMZM. Figure 2(d) shows the

V_{D C 2}

dependence on Vpp of RF driving signal when

V_{D C 3}

is set at 0 or

V_{π}

.

As shown in Fig. 2(b), when the $V_{p p}$ of the RF signal is set to around 4 $V_{π}$ , the 1st, 2nd and 3rd-order sidebands would have the same amplitude and 7 flat comb lines can be generated if $V_{D C 1}$ , $V_{D C 2}$ and $V_{D C 3}$ are properly set. It can be proved that the higher-order sidebands can be ignored in this case. Therefore, the Eq. (11) can be rewritten as:

\begin{array}{l} E_{o u t} = \frac{E_{i n} e^{j π}}{2} {[\cos A J_{0} (B) + \cos (\frac{π V_{D C 2}}{2 V_{π}}) e^{j \frac{π V_{D C 3}}{V_{π}}}] + \sin A J_{1} (B) e^{j (ω t + \frac{π}{2})} + \sin A J_{1} (B) e^{- j (ω t + \frac{π}{2})} \\ + \cos A J_{2} (B) e^{j 2 ω t} + \cos A J_{2} (B) e^{- j 2 ω t} + \sin A J_{3} (B) e^{j (3 ω t + \frac{π}{2})} + \sin A J_{3} (B) e^{- j (3 ω t + \frac{π}{2})}} \end{array}

If these 7 components have the same amplitude, the following conditions should be satisfied

\frac{E_{i n}}{2} \sin A J_{1} (B) = \frac{E_{i n}}{2} \cos A J_{2} (B) = \frac{E_{i n}}{2} \sin A J_{3} (B) = V

\frac{E_{i n}}{2} [\cos A J_{0} (B) + \cos (\frac{π V_{D C 2}}{2 V_{π}}) e^{j \frac{π V_{D C 3}}{V_{π}}}] = V e^{j φ_{c}}

where

φ_{c}

is the phase of the carrier component, V is the amplitude. For example, it can be easily calculated that as

V_{0} = 1.94 V_{π}

,

V_{D C 1} = 0.63 V_{π}

,

V_{D C 2} = 0.724 V_{π}

and

V_{D C 3} = V_{π}

, a flat comb with 7 lines can be obtained. However, it isn’t a Nyquist pulse train in time domain. The reason can be explained as follows:

Equation (18) can be rewritten with Eq. (19) and (20) as

E_{o u t} = V {e^{j (φ_{c} + π)} + 2 \cos [2 (π f t + \frac{3 π}{4})] + 2 \cos [4 (π f t + \frac{3 π}{4})] - 2 \cos [6 (π f t + \frac{3 π}{4})]}

Finally the output field of the DPMZM can be expressed as:

E_{o u t} = 7 V {\frac{e^{j (φ_{c} + π)} - 1 - 4 \cos [6 (π f t + \frac{3 π}{4})]}{7} + \frac{\sin [7 (π f t + \frac{3 π}{4})]}{7 \sin [(π f t + \frac{3 π}{4})]}}

It can be seen that even the 7 frequency components have the same amplitude, the corresponding waveforms are not sinc-shaped in the time domain. Therefore, it can be concluded that 5 comb lines can be generated at best with a single DPMZM driven by only one RF signal.

A simulation is first made to verify the proposed scheme. The simulation parameters are the same with those in the following practical experiment. In simulation, the frequency $f$ of RF signal is 40 GHz and the $V_{p p}$ of RF signal is coarsely tuned from 0.8 $V_{π}$ to 2 $V_{π}$ with a tuning step of 0.2 $V_{π}$ . At each value of $V_{p p}$ , the Bias 1-3 are also optimized simultaneously according to the above analysis. Figure 3(a) shows the waveforms of the generated Nyquist pulses at different $V_{p p}$ . All the waveforms are similar and the FWHM varies from 4.64 ps to 5.53 ps at the repetition rate of 40 GHz. However, the intensity of the pulses decreases as the decrease of RF driving voltage, indicating the increase of insertion loss (IL) of the DPMZM. For comparison with the Nyquist pulses, all waveforms are normalized and shown in Fig. 3(b). The results show that the generated pulses agree well with the ideal Nyquist pulses. Figure 3(c) shows the optical spectrum of the generated Nyquist pulses when the $V_{p p}$ of RF driving signal is set at $1.4 V_{π}$ . 5 comb lines with nearly the same amplitude are obtained and unwanted mode suppression ratio (UMSR) of 25 dB is achieved.

Fig. 3 The simulation results: (a) waveforms of the generated Nyquist pulses; (b) nomalized waveforms, the ideal Nyquist pulse train is also shown for comparison; (c) optical spectrum of the generated Nyquist pulses when $V_{p p} = 1.4 V_{π}$ .

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3. Experimental setup, results and discussions

The experimental setup is shown in Fig. 1(a). The CW light at 1550 nm with optical power of 13.5 dBm is launched into a DPMZM (Fujitsu FTM7961EX, $V_{π}$ is 3.5V and extinction ratio of child MZMs is more than 20 dB) via a polarization controller (PC). The microwave signal at 40 GHz from a RF source (Agilent E8257D) is first amplified by a broad-band electrical amplifier (SHF 806E) and then fed to the DPMZM to drive the child-MZM1. The insertion loss of the DPMZM is compensated by a low noise optical amplifier (EDFA). After amplified to 10 dBm, the optical signal is measured with a 500 GHz optical sampling oscilloscope (OSO, EXFO PSO-102) and an optical spectrum analyzer (OSA, Yokogawa AQ6370B).

The experimental results are shown in Fig. 4. Figures 4(a)-4(c) are the waveforms and corresponding optical spectrums (measured with resolution of 0.02 nm) of the generated Nyquist pulses when the $V_{p p}$ of RF driving signal is set at 0.8 $V_{π}$ , 1.4 $V_{π}$ and 2.0 $V_{π}$ respectively. The measured FWHM of these Nyquist pulses are 4.53 ps, 4.77 ps and 5.05 ps. In the optical spectrums, 5 comb lines are achieved. The higher-order sidebands are also observed, but they are suppressed by more than 30 dB, 24 dB and 17.5 dB respectively. Figure 4(d) depicts the measured SNR and FWHM of the generated Nyquist pulses. It should be noted that, SNR in this paper is refer to the electrical SNR measured by the OSO, which can be used to characterize the quality of the generated Nyquist pulses [16]. As RF driving voltage is tuned from 0.8 $V_{π}$ to 2.0 $V_{π}$ , the SNR increases from 23.8 dB to 32.2 dB while the FWHM varies from 4.53 ps to 5.05 ps. As mentioned above, the insertion loss of DPMZM increase as the $V_{p p}$ decreases, which leads to low SNR of the pulses due to the relative large amplified spontaneous emission (ASE) noise induced by EDFA. Therefore, the generated Nyquist pulses at low RF driving voltages have a lower SNR.

Fig. 4 The experimental results: the generated waveforms and corresponding spectrums when the RF voltage is set at 0.8 $V_{π}$ (a), 1.4 $V_{π}$ (b), and 2.0 $V_{π}$ (c) respectively; (d) the OSO-measured SNR and FWHM at different RF driving voltages.

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Figure 5(a) shows the two-time averaged waveforms of the generated Nyquist pulses at different RF driving voltages, which have been normalized for comparison with the ideal Nyquist pulses, also shown in the Figure. The generated waveforms agree very well with that of ideal Nyquist pulses. The symmetry of generated Nyquist pulses in our experiment is not as perfect as in the simulation, which is mainly caused by the non-ideal push-pull operation of the MZM1 in Fig. 1(a).

Fig. 5 (a) the normalized waveforms of the generated pulses and ideal Nyquist one; (b) the NRMSE of the generated Nyquist pulses and insertion loss of DPMZM.

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To quantify the deviation between the generated pulses and ideals Nyquist ones, the NRMSE of the waveforms obtained from the experiment and simulation are calculated. Figure 5(b) illustrates the calculated NRMSE of generated Nyquist pulses and insertion loss of the DPMZM. Both experimental and simulated results are shown together for comparison. The experimental waveforms used in the calculation are two-time averaged. For the experimental results, when the voltage of RF driven signal is tuned from 0.8 $V_{π}$ to 2 $V_{π}$ , the NRMSE increases from 1.25% to 4.15%. The minimum NRMSE is achieved at the lowest RF driving voltage. It can also be seen from the spectrums in Figs. 4(a)-4(c). Since the higher-order sidebands should be suppressed as effectively as possible, a maximum UMSR of 30 dB is achieved in Fig. 4(a), which means the waveform in time domain is closest to ideal Nyquist pulses. However, the insertion loss of the DPMZM is the largest in this case, which is about 31.5 dB. Therefore, there is a tradeoff between the insertion loss of DPMZM and the deviation between generated pulses and ideal Nyquist ones.

The repetition rate of the generated Nyquist pulses can be tuned by changing the frequency of RF signal. The waveforms and spectrums of the pulses at different repetition rate are shown in Fig. 6, where the frequency $f$ of the RF driving signal is set at 1 GHz, 5 GHz, 10 GHz and 20 GHz, 30 GHz and 40 GHz respectively. Table 1 gives the measured SNR, calculated NRMSE, UMSR and FWHM of these Nyquist pulses. From the results, it can be seen that the generated Nyquist pulses have high performance of a minimum SNR of 28.4 dB, a maximum NRMSE of 6.15% and the minimum UMSR of 18 dB. According to the above analysis, for a fixed optical input power of DPMZM, there is a tradeoff between SNR and UMSR and these parameters are highly dependent on the RF driving voltage $V_{p p}$ , which makes it difficult to determine the optimal value of $V_{p p}$ . For the results shown in Fig. 6, the RF driving voltages and bias of DPMZM are just properly adjusted to ensure SNR of about 30 dB and UMSR of about 20 dB for different repetition rate. Because the resolution of the OSA is limited (about 2.5 GHz), the sidebands in case of f = 1 GHz and 5 GHz cannot be distinguished clearly, as shown in Figs. 6(a) and 6(b). As a result, the UMSR can’t be measured. Actually, it is also the reason of relative large NRMSE at f = 1 GHz and 5 GHz, because the optimizing of the $V_{p p}$ and DC bias voltages needs the distinguished comb spectrum as a reference. The NRMSE can be reduced if OSA with higher resolution is employed during the optimizing procedure.

Fig. 6 The spectrums and waveforms of the generated Nyquist pulses at repetition rate of 1 GHz (a), 5 GHz (b), 10 GHz (c), 20 GHz (d), 30 GHz (e) and 40 GHz (f) respectively.

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Table 1. SNR, NRMSE, UMSR, FWHM of the generated Nyquist pulses at different repetition rate

View Table

For the proposed scheme, the generated waveforms are sensitive to the bias drift of DPMZM, especially at low driving voltage. This problem can be solved with an offset bias control circuit using electronic feedback. In addition, cascaded DPMZMs can be used to generate more comb lines [18–20], which results in Nyquist pulses with narrower pulse width and enables multiplexing of more sub-channels in a fixed time slot.

4. Conclusions

In this paper, the generation of Nyquist pulses using a DPMZM is proposed and demonstrated. The proposed scheme is investigated both theoretically and experimentally. It is theoretically proved that Nyquist pulses with a spectrum of 5 flat comb lines can be generated using a single DPMZM. 7 flat comb lines in frequency domain can also be obtained if a large RF driving voltage is applied to DPMZM but the generated waveforms won’t present a sinc-shape. 40 GHz Nyquist pulses with FWHM less than 4.65 ps, SNR more than 29.5 dB, NRMSE below 2.4% are generated experimentally. A good agreement between the experimental results and simulated ones is reached. The tunability of this scheme is verified by generating Nyquist pulses with different repetition rate. 1 GHz to 40 GHz Nyquist pulses with SNR more than 28.4 dB and NRMSE below 6.15% are achieved experimentally. Featuring simple structure and flexibility in repetition rate as well as central wavelength, this scheme may find good application in future Nyquist-pulse-based communication systems.

Acknowledgment

This work was partly supported by 863 program 2013AA014202, 2012AA011303, 973 program 2014CB340100, 2011CB301700, NSFC program 61331008, 61205031, 61307055, fund of State Key Laboratory of Information Photonics and Optical Communications (BUPT), and the fundamental research funds for the central universities.

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Repetition Rate (GHz)	1	5	10	20	30	40
SNR (dB)	34.3	31.7	31.2	28.7	28.4	29.5
NRMSE (%)	6.15	5.74	1.10	2.37	2.31	2.40
UMSR (dB)			25.1	18	19.5	25.9
FWHM (ps)	212.3	41.33	18.17	9.57	6.21	4.65

Investigation on Nyquist pulse generation using a single dual-parallel Mach-Zehnder modulator

Abstract

1. Introduction

2. Principle and simulation

3. Experimental setup, results and discussions

4. Conclusions

Acknowledgment

References and links

Cited By

Figures (6)

Tables (1)

Equations (22)

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