Broadband linearization in photonic time-stretch analog-to-digital converters employing an asymmetrical dual-parallel Mach-Zehnder modulator and a balanced detector

Di Peng; Zhiyao Zhang; Yangxue Ma; Yali Zhang; Shangjian Zhang; Yong Liu

doi:10.1364/OE.24.011546

1. Introduction

Analog-to-digital converters (ADCs) are indispensable components for digital signal processing (DSP) applications including radar system and image processing [1,2]. For broadband applications, simultaneous improvement of input bandwidth, sampling rate and effective number of bits (ENOB) are urgently needed, but highly restrained by timing jitter of the sampling clock, and comparator ambiguity in high-speed electronic ADCs according to the statistic by R. H. Walden [3]. In order to overcome the above-mentioned electronic bottleneck, photonic technologies have been adopted in both sampling and quantization processes during the past years [4–6]. Among the presented photonic ADC schemes, the time-stretch ADC (TS-ADC), which employs optical dispersion to slow down the radio frequency (RF) signal before entering the electronic ADCs [7,8], is a promising technique to enhance the bandwidth and sampling rate of electronic ADCs. The time-stretch preprocessing not only improves the effective bandwidth and sampling rate of the electronic ADCs by N fold (N is the time stretch ratio), but also has the potential to reduce the error owing to the clock jitter of the digitizer, which is beneficial for achieving an ultra-broad bandwidth and an ultra-high speed while maintaining a high ENOB.

In TS-ADCs, it is a critical job to reduce signal distortion in the time-stretch process, which stems from several fields such as spectral non-uniformity, modulation nonlinearity, limited optical bandwidth, higher-order dispersion and nonlinear optical effect [9]. Since RF signal is modulated on the envelope of the linearly-chirped optical pulse (i.e., the pulse spectrum), spectral non-uniformity and its time-varying property contribute mainly to the signal distortion. However, it has been demonstrated that this envelope-introduced distortion can be effectively repaired by differential technique using a chirp-free dual-output Mach-Zehnder modulator (MZM) [8]. Besides, the signal distortion induced by limited optical bandwidth and nonlinear optical effect can be reduced to a negligible level through a smart design of optical-to-electrical bandwidth ratio and an intelligent control of optical power [8,10], respectively. Furthermore, the influence of higher-order dispersion on the signal distortion is generally negligible if the dispersion medium employed is without a sharp dispersion variation in the optical bandwidth [8]. Therefore, the improvement of modulation nonlinearity is important in TS-ADC to enhance the ENOB. For a MZM used in the TS-ADC, it is a contradiction puzzle to set the modulation depth. A large modulation depth is favorable for obtaining a high signal-to-noise ratio (SNR) which is directly relevant to a high ENOB, but it introduces larger harmonics which may instead degrade the ENOB. Although band-pass filtering can be used to remove these nonlinear productions, it is not an effective solution for TS-ADCs aiming at broadband applications. Hence, broadband linearization technologies play a pivotal role in improving the signal-to-noise and distortion ratio (SINAD) and namely the ENOB.

So far, various linearization technologies for TS-ADCs have been proposed, which can be categorized into two groups according to their principles. One group is using a diverse modulator structure with an optimal bias point to realize suppression of harmonics. To date, linearized effectiveness of a dual-parallel MZM (DPMZM) has been demonstrated in RoF systems by several works [11–13]. In a TS-ADC scheme proposed by Zheng et al., a symmetric DPMZM is employed to realize suppression of the third-order harmonic by optimizing three bias voltages, and a spurious-free dynamic range up to 95.15 dB·Hz^2/3 has been achieved [14]. Nevertheless, the reduction of third-order harmonic in [14] is at the expense of increasing the second-order one, which limits the application in a suboctave bandwidth. The other group is employing post-compensation in digital domain, such as differential and arcsine operation employing a dual-output MZM [15–17], optical back propagation (OBP) method based on phase retrieval [18,19]. The differential detection is an online operation which is able to suppress second-order distortions [20], but not efficient for third-order ones. With the assist of arcsine operation, the third-order distortions due to the MZM transfer function can be effectively removed [21]. However, the third-order intermodulation distortions caused by dispersion will remain and restrict the dynamic range, especially in a large modulation depth. In addition, both of the arcsine operation and the OBP method is an offline processing, which implies that it is not able to correct distortions in real time. Therefore, an online broadband linearization technology is urgently required for TS-ADCs specific to broadband applications.

In this paper, a novel broadband linearization technique based on an asymmetrical dual-parallel MZM (DPMZM) and a balanced detection scheme is presented for the TS-ADCs. Theoretical model is introduced and linearized parameters are optimized. Numerical simulation results show that the proposed method is efficient for broadband linearization in TS-ADCs even under a large modulation depth.

2. Operation principle

The proposed TS-ADC architecture is shown in Fig. 1, where broadband linearization is realized based on a balanced detection scheme with a carrier-suppressed modulation using an asymmetrical DPMZM in one branch of the Mach-Zehnder intereferometer. The linearly chirped pulses output from the first spool of dispersion compensation fiber (DCF1) are divided into two duplicates by a 3dB directional connector. The DPMZM in the upper branch is used to modulate the input RF signal on the pulse envelope, and the pulse in the lower branch is used as a reference signal that interferes with the modulated one through the second 3dB directional connector. The two optical circulators in parallel are connected by the second spool of dispersion compensation fiber (DCF2), which ensures that the two modulated signals from the second 3dB directional connector have an identical stretch factor. As a result, the complementary distortion components and multiplicative noise in the stretched modulated signals can be eliminated through balanced detection. Particularly, the architecture of the asymmetrical DPMZM is shown in Fig. 2, where the input and output power split ratio of the two branches are $\cos^{2} α : \sin^{2} α$ and $\cos^{2} β : \sin^{2} β$ , respectively. The amplitude split ratio of the RF signal uploaded on the two parallel sub-MZMs is $γ : 1$ , both of which work in push-pull mode with a bias at null point. Additionally, a fixed $π$ phase shift is added between the two parallel branches.

Fig. 1 Architecture of the proposed TS-ADC. MLL: mode-locked laser, DCF: dispersion compensation fiber, DPMZM: dual parallel Mach-Zehnder modulator, OC: optical circulator, PD: photodiode.

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Fig. 2 Architecture of the asymmetrical DPMZM employed in the proposed TS-ADC.

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A mathematical model for the proposed TS-ADC is given as follows. Assuming the output of the mode-locked laser (MLL) is a transform-limited Gaussian pulse whose filed in the frequency domain can be described as

E_{1} (ω) = E_{0} \sqrt{2 π T_{0}^{2}} \exp (- \frac{T_{0}^{2} ω^{2}}{2})

where

E_{0}

is the amplitude of the optical field, and

T_{0}

is the half-width of the pulse at 1/e intensity. After propagating through the DCF1, the field in the frequency domain becomes

E_{2} (ω) = E_{1} (ω) \exp (\frac{j}{2} β_{2} L_{1} ω^{2})

where

β_{2}

and

L_{1}

are the group velocity dispersion (GVD) coefficient and the length of the DCF1, respectively. Supposing the two sub-MZMs in DPMZM are biased at null point and driven by RF signal of

V_{1} (t) = V_{0} \cos (ω_{R F} t)

and

V_{2} (t) = V_{0} γ^{- 1} \cos (ω_{R F} t)

respectively, the field at the output of the DPMZM in the time domain can be described by

E_{3} (T) = \frac{\sqrt{2}}{2} E_{2} (T) {\cos α \cos β \sin [\frac{m}{2} \cos (ω_{R F} t)] - \sin α \sin β \sin [\frac{m}{2 γ} \cos (ω_{R F} t)]}

where

m = π V_{0} / V_{π}

is the modulation index, and

V_{π}

is the half-wave voltage. The two outputs of the second 3dB directional coupler in the time domain can be calculated by

E_{3 -} (T) = \frac{\sqrt{2}}{2} E_{3} (T) - \frac{1}{2} E_{2} (T)

E_{3 +} (T) = j [\frac{\sqrt{2}}{2} E_{3} (T) + \frac{1}{2} E_{2} (T)]

where

E_{3 -} (T)

and

E_{3 +} (T)

correspond to the upper output port and the lower one, respectively. After propagating through the DCF2, the pulse in the frequency domain can be written by

E_{4 \pm} (ω) = E_{3 \pm} (ω) \exp (\frac{j}{2} β_{2} L_{2} ω^{2})

where

L_{2}

is the length of DCF2. Finally, the output current of the two photodetectors (PDs) can be calculated by

I_{\pm} (T) = \frac{1}{2} n c ε_{0} A_{e f f} R_{P D} E_{4 \pm} (T) E_{4 \pm}^{*} (T)

where

E_{4 \pm}

is the optical field after the DCF2.

R_{P D}

is the detector responsivity.

c

and

ε_{0}

are the light velocity and the permittivity in vacuum, respectively.

n

and

A_{e f f}

are the refractive index and the effective mode area of the fiber, respectively.

Supposing the optical bandwidth is much larger than the electrical one, the output current after balanced detection can be calculated as

\begin{matrix} I (T) = I_{+} (T) - I_{-} (T) \\ = I_{e n v} (T) {[4 \cos α \cos β J_{1} (\frac{m}{2}) - 4 \sin α \sin β J_{1} (\frac{m}{2 γ})] \cos (φ_{D I P}) \cos (\frac{ω_{R F}}{M} t) \\ - [4 \cos α \cos β J_{3} (\frac{m}{2}) - 4 \sin α \sin β J_{3} (\frac{m}{2 γ})] \cos (9 φ_{D I P}) \cos (\frac{3 ω_{R F}}{M} t) \\ + [4 \cos α \cos β J_{5} (\frac{m}{2}) - 4 \sin α \sin β J_{5} (\frac{m}{2 γ})] \cos (25 φ_{D I P}) \cos (\frac{5 ω_{R F}}{M} t) + \cdot \cdot \cdot} \end{matrix}

where

M = (L_{1} + L_{2}) / L_{1}

is the stretch factor.

φ_{D I P} = β_{2} L_{2} ω_{R F}^{2} / (2 M)

is the phase shift caused by dispersion.

J_{n} (x)

is the Bessel function of the first kind.

I_{e n v} (T)

is the envelope function described by

I_{e n v} (T) = \frac{1}{4} n c ε_{0} A_{e f f} R_{P D} E_{0}^{2} \frac{1}{\sqrt{1 + {(\frac{β_{2} (L_{1} + L_{2})}{T_{0}^{2}})}^{2}}} \exp {- \frac{T^{2}}{T_{0}^{2} [1 + {(\frac{β_{2} (L_{1} + L_{2})}{T_{0}^{2}})}^{2}]}}

Clearly, it can be noted from Eq. (8) that all the even-order harmonics as well as the direct current (DC) are removed thanks to the balanced detection with a carrier-suppressed modulation. By expanding the Bessel function as Taylor series at the point of $x = 0$ according to

J_{n} (x) = {\sum_{m = 0}^{\infty} \frac{{(- 1)}^{m}}{m! (m + n)!} (\frac{x}{2})}^{2 m + n}

the coefficient of the third-order harmonic component can be expressed as

\begin{array}{l} \frac{m^{3}}{4^{2} \times 3!} (\cos α \cos β - \frac{\sin α \sin β}{γ^{3}}) - \frac{m^{5}}{4^{4} \times 4!} (\cos α \cos β - \frac{\sin α \sin β}{γ^{5}}) \\ + \frac{m^{7}}{2 \times 4^{6} \times 5!} (\cos α \cos β - \frac{\sin α \sin β}{γ^{7}}) + \cdot \cdot \cdot \end{array}

Obviously, the first term in Eq. (11) becomes 0 when

\tan α \tan β = γ^{3}

is satisfied, which means that the dominated contribution to the third-order harmonic is cancelled, and the spurious-free dynamic range (SFDR) can be further improved through parameter optimation of the asymmetrical DPMZM. Coincidentally, in the dual-tone modulation case, Eq. (12) is also efficient for suppressing the third-order intermodulation terms (IMD3) due to the identical expansion coefficient. When Eq. (12) is satisfied, the output current of the balance detector as shown in Eq. (8) can be simplified as

I (T) = A m \cos (\frac{ω_{R F}}{M} T) + B m^{5} \cos (\frac{3 ω_{R F}}{M} T) + C m^{5} \cos (\frac{5 ω_{R F}}{M} T)

where the coefficients are

A = I_{e n v} (T) \cos α \cos β (1 - γ^{2}) \cos (ω_{R F}^{2} φ_{D I P})

B = \frac{1}{4^{4} \times 4!} I_{e n v} (T) \cos α \cos β (1 - \frac{1}{γ^{2}}) \cos (9 ω_{R F}^{2} φ_{D I P})

C = \frac{1}{4^{4} \times 5!} I_{e n v} (T) \cos α \cos β (1 - \frac{1}{γ^{2}}) \cos (25 ω_{R F}^{2} φ_{D I P})

Through comparing B and C, it is noted that even if the major component of the third-order harmonic has been eliminated, the remainder is still larger than the fifth-order harmonic. Therefore, the SFDR after linearization is still limited by the third-order harmonic, which can be calculated by

S F D R_{3} = {({| \frac{A}{B} |}^{1 / 2} \frac{A^{2} R}{2 N})}^{2 / 3}

where N is the noise power, and R is the load of the photodetector [22]. The noise considered in a real TS-ADC includes quantization noise, shot noise, thermal noise, laser relative intensity noise (RIN) and jitter noise [23]. Generally, the quantization noise or the jitter noise dominates in the ADC with a sampling rate larger than multi-MS/s [5]. Substituting Eqs. (14) and (15) into Eq. (17),

S F D R_{3}

can be expressed as

S F D R_{3} = {(\frac{I_{e n v}^{2} R}{2 N})}^{2 / 3} {(4 {}^{4}\times 4!)}^{1 / 3} {(\cos^{2} α \cos^{2} β)}^{2 / 3} | \frac{{(1 - γ^{2})}^{5 / 3}}{{(1 - 1 / γ^{2})}^{1 / 3}} |

Apparently, there must be an optimizing group of

α

,

β

,

γ

to maximize the

S F D R_{3}

. According to Eq. (12) and the inequation of

\cos^{2} α \cos^{2} β \leq {(1 + \tan α \tan β)}^{- 2}

, Eq. (18) can be written as

S F D R_{3} \leq {(\frac{I_{e n v}^{2} R}{2 N})}^{2 / 3} {(4 {}^{4}\times 4!)}^{1 / 3} | \frac{{(1 - γ^{2})}^{5 / 3}}{{(1 + γ^{3})}^{4 / 3} {(1 - 1 / γ^{2})}^{1 / 3}} |

The equality relationship in the above inequation is satisfied only when the input and output optical power split ratio of two branches in the asymmetrical DPMZM are identical, i.e.,

α = β

. Under this equality relationship, maximum

S F D R_{3}

can be obtained by optimizing the parameter

γ

through derivation. Hence, it can be easily obtained that the optimized value is

γ = 0.382

, which indicates the optimal setting of the power split ratio in the asymmetrical DPMZM should be 0.947:0.053 by substituting the value of

γ

and

α = β

back into Eq. (12).

3. Simulation and discussion

Based on the mathematical analysis in the previous section, numerical simulation is implemented for the proposed linearization scheme to demonstrate its effectiveness. Meanwhile, the results are compared with those for the differential detection based on a dual-output push-pull MZM biased at quadrature point and the differential scheme with assist of arcsine operation, where the arcsine operation is implemented to the ratio of the difference to the sum of two complementary outputs as presented in [15–17]. During the simulation process, the modulation index is set as 0.99 (i.e., modulation depth of 83.6%) to produce the marked distortion productions. The amplitude split ratio of the input RF signal and the power split ratio of the DPMZM input and output ports are set to be 1:2.62 and 0.947:0.053 respectively to maximize the SFDR. An electrical ADC with a quantization level of 16 bits is used to fulfill the digitalization process. In addition, the parameters of the optical source and the DCFs are shown in Table 1, corresponding to a 10-fold stretch factor. A Nyquist Pulse with a rectangular spectrum is used as the optical carrier to eliminate the envelope-induced distortion. The simulation of the optical pulse propagation in the DCFs is implemented through numerically solving the generalized nonlinear Schrödinger equation (GNLSE) [24]. General parameters for a DCF is used in the simulation, and the results show that both the higher-order dispersion and the nonlinear optical effect have a negligible influence on the linearization process.

Table 1. Parameters of the optical source and the dispersion compensation fiber.

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In the case of single-tone modulation, a signal with a frequency of 5GHz is loaded on the modulator. Figures 3(a)-3(c) show the output spectrum of the differential detection, the differential scheme with assist of arcsine operation and the proposed one, respectively. Apparently, the RF frequency is down-converted from 5GHz to 500MHz through the 10-fold time stretch process. It can be noted from Fig. 3(a) that, in the differential detection scheme, although the dispersion-induced even-order harmonics can be effectively removed, the third-order harmonic is still large because of the large modulation depth adopted. The carrier to third-order intermodulation ratio (C/IM3) is only 28.24dB in Fig. 3(a), which becomes the primary restriction to the dynamic range. As a comparison, it can be seen from Figs. 3(b) and 3(c) that both the second-order harmonic and the third-order one have been suppressed to a very low scale by using either the arcsine operation or the proposed linearization scheme even under a modulation index of 0.99 (i.e., modulation depth of 83.6%). However, it is noted that the arcsine operation has to be implemented offline which is not efficient for a real time system.

Fig. 3 Output spectrum employing (a) the differential detection, (b) the differential scheme with assist of arcsine operation and (c) the proposed one.

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In order to demonstrate the ability of the proposed linearization scheme in suppressing IMD3, two RF signals with equal amplitude and different frequency of 5GHz and 6GHz are combined to drive the modulator, where the total modulation index is set to be 0.99 as that in the single-tone modulation case. Figures 4(a)-4(c) give the output spectrum of the differential detection, the differential scheme with assist of arcsine operation and the proposed one, respectively. In Fig. 4, the two peaks at frequency of 500MHz ( $f_{1}$ ) and 600MHz ( $f_{2}$ ) are related to the signal frequencies after 10-fold stretching. It can be seen from Fig. 4(b) that all the IMD3s, including the third-order harmonics ( $3 f_{1}$ , $3 f_{2}$ ) and the third-order intermodulation distortions ( $2 f_{1} - f_{2}$ , $2 f_{2} - f_{1}$ , $2 f_{1} + f_{2}$ , $2 f_{2} + f_{1}$ ), are suppressed by more than 20dB compared with those in Fig. 4(a). However, the residual third-order intermodulation distortions of $2 f_{1} - f_{2}$ and $2 f_{2} - f_{1}$ in Fig. 4(b) are still high, which limits the dynamic range. Through using the proposed linearized scheme, it can be noticed from Fig. 4(c) that all the distortion spurs are removed, which is beneficial for enhancing the dynamic range.

Fig. 4 Output spectrum employing (a) the differential detection, (b) the differential scheme with assist of arcsine operation and (c) the proposed one.

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Table 2 presents the comparison of C/IM3 in these three different schemes under various modulation indexes. It can be observed that even though the C/IM3 in these schemes decreases with increasing modulation index, the proposed scheme always has a much better performance compared with the differential detection scheme and the differential scheme with assist of arcsine operation (more than 27.17dB and 9.59 dB, respectively) in suppressing the IMD3. Particularly, when the modulation index is smaller than 0.99, the IMD3 is drowned by the noise floor if the proposed linearization scheme is adopted.

Table 2. Comparison of C/IM3 in the differential detection scheme, the differential scheme with assist of arcsine operation and the proposed one under various modulation indexes.

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Normally, SFDR is a crucial specification represents the dynamic performance, which is defined as the scale of the input RF signal when the distortions are below the noise floor while the signal is above it [25]. In the following simulation, SFDR is employed to evaluate the performance of the proposed linearization scheme. The noise floor is about −75 dBm for a resolution bandwidth of 16.7MHz (i.e., the normalized noise floor is around −147.23dBm/Hz). Figures 5(a)-5(c) exhibit the scale of SFDR employing the differential detection scheme, the differential scheme with assist of arcsine operation and the proposed one, respectively. In Fig. 5, the hollow triangle and the solid rectangle represent the normalized output RF power of the fundamental signal and the IMD3, respectively. It can be seen from Fig. 5(a) that the fundamental signal and the IMD3 increase with input RF power in a slope of about one and three respectively, which follows the theoretical performance of a normal analog system. In Figs. 5(b) and 5(c), the curve slope of the fundamental signal is resemble to the regularity in Fig. 5(a). However, the scale of IMD3 in Fig. 5(c) increases with input RF power in a slope of about five rather than three as shown in Fig. 5(a). The reason is that the main contribution to the IMD3 is the fifth power term instead of the third power one in Eq. (11) when the linearity condition Eq. (12) is satisfied. This IMD3 slope increasing in the proposed linearization scheme is favorable for improving the SFDR. The calculated SFDRs in Figs. 5(a) and 5(c) are 97.1 and 116.2 dB@1Hz respectively, indicating that the proposed scheme wins a ~19dB SFDR improvement compared with the differential detection scheme. In Fig. 5(b), the output power of the IMD3 increases with input RF power in an increasing slope due to the nonlinear algorithm of the arcsine operation, and the slope is certainly larger than three based on the essence of taylor series expansion. As can be seen from Fig. 5, the SFDR in Fig. 5(c) is also predicted to be larger than that in Fig. 5(b). In addition, another prominent superiority of the proposed scheme can be found in the large input RF power region (i.e., the large modulation index or depth region), where a much higher IMD3 suppression ratio (defined as the power ratio of the fundamental signal and the IMD3) can be obtained through the proposed scheme. This characteristic is favorable for TS-ADC which generally need a large modulation depth to enhance SNR.

Fig. 5 Output RF power vs input RF power in (a) the differential detection, (b) the differential scheme with assist of arcsine operation and (c) the proposed one.

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Additionally, it can be found from Figs. 5(a) and 5(b) that the output RF power of the fundamental signal in these schemes will not further increase in the large modulation index case. Nevertheless, this saturation behavior can be removed by using the proposed scheme. This can be explained by the Taylor series expansion of the fundamental output signal, which can be simplify as

\frac{m}{4} - \frac{m^{3}}{2 \times 4^{3}} + \frac{m^{5}}{12 \times 4^{5}} \dots \dots

\cos^{2} α (1 - γ^{2}) \frac{m}{4} + \cos^{2} α (1 - \frac{1}{γ^{2}}) \frac{m^{5}}{12 \times 4^{5}} \dots \dots

where Eq. (20) and (21) are relevant to the differential detection and the proposed linearization scheme, respectively. The power saturation effect in the conventional scheme attributes to the third power term in Eq. (20), while it is completely eliminated in Eq. (21). Therefore, it can be concluded that the proposed linearization scheme will be markedly superior to those conventional schemes under a large modulation depth, as it not only effectively suppresses the IMD3, but also eliminates the saturation of the fundamental signal.

It should also be pointed out that, although the proposed asymmetric DPMZM scheme looks more complicated than the conventional single MZM one, the extra RF power loss induced by the diversity of modulation fashion is only 1.85dB, which can be obtained through comparing the output RF signals between these two schemes. In addition, the typical value of the insertion loss in an optical circulator is 0.6dB. Therefore, the extra power penalty is acceptable in the proposed scheme, which will not destroy the profit brought by the linearization process.

4. Analysis of parameter deviation

In the previous section, it has been presented that SFDR can be greatly improved by employing the proposed linearization scheme with a group of optimal parameters. However, some imperfection of the optical power splitter is inevitable in practical applications, which may lead to parameter deviation from the optimal values. Normally, the RF power split ratio is tunable. Hence, the influence of optical split ratio deviation on the ADC performance is analyzed when Eq. (12) is satisfied. ENOB, an important figure of merit, is used to characterize the quantization accuracy of an ADC, which is relevant to SINAD in decibels according to $E N O B = (S I N A D - 1.76) / 6.02$ [2]. In the simulation, an electronic ADC with a quantization level of 8 bits is used, and the modulation index is set as 1.5. Figure 6 presents the ENOB under various deviations of sin²α and sin²β. It is noted from the theoretical analysis that the optimal setting of the power split ratio in the input and output ports of the asymmetrical DPMZM is 0.947:0.053, i.e., $\sin^{2} α = \sin^{2} β = 0.053$ . In Fig. 6, the ENOB remains high even when the input and output split ratio of the lower branch has a large positive deviation, which implies that the optical power split ratio deviation can be compensated by adjusting the RF power split ratio $γ$ . Also, a negative deviation up to 50% can be corrected through tunable $γ$ . Therefore, the feasibility of the optimal parameters in the proposed linearized scheme is testified.

Fig. 6 ENOB under various deviations of sin²α and sin²β.

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Additionally, the optical source employed in a TS-ADC is a broadband one, which may induce some deviation from the optimal situation. Firstly, the half-wave voltage of the MZM varies with optical wavelength, which leads to a shift of bias point and a change of modulation index through the chirped optical pulse duration. The bias point and modulation index deviation may produce additional spurs in the spectrum. Secondly, for the same reason, it is difficult to maintain a fixed phase shift of $π$ as shown in Fig. 2 through the chirped optical pulse duration. This phase shift deviation may also induce extra spurs. Thirdly, the split ratio variation of the 3dB directional connector for different optical wavelength alters the interference situation, which may introduce accessional spurs. Therefore, in order to minish these linearization deteriorations caused by the limited spectrum response of the device, the optical bandwidth employed in the time stretch process should be carefully considered for an experimental setup.

5. Conclusions

In conclusion, a novel broadband linearization scheme for TS-ADC based on an asymmetrical DPMZM and a balanced detector is proposed. Linearized parameters are optimized and numerical simulations are performed. Both theoretical analysis and simulation results demonstrate that the proposed scheme with linearized parameters has a superior performance on suppressing the even-order distortions and the third-order spurs even under a large modulation depth. The SFDR of the proposed scheme is also largely enhanced in comparison with the differential detection scheme and the differential scheme with assist of arcsine operation. Therefore, it can be concluded that the proposed scheme is effective for linearizing a broadband TS-ADC in real time.

Acknowledgments

This work was supported by the 973 Program of China (Grant No. 2012CB315702), the National Nature Science Foundation of China (Grant Nos. 61205109, 61575037, 61307031), Fund for Creative Research Groups (Grant No. 61421002), and by the Innovation Funds of Collaboration Innovation Center of Electronic Materials and Devices (Grant No. ICEM2015-2001).

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Physical Quantity	Values and Units
Central wavelength of the optical pulse	1555 nm
Full width at half maximum (FWHM) of the optical pulse	210 fs
Peak power of the optical pulse	973 W
GVD coefficient of the DCF	−130ps/km/nm
Length of the DCF1	1.3 km
Length of the DCF2	11.7 km

modulation index	C/IM3 of the differential detection	C/IM3 after the arcsine operation	C/IM3 of the proposed scheme
0.99	30.22 dB	52.44 dB	Suppress to the noise floor
1.12	27.96 dB	49.09 dB	58.68 dB
1.25	25.93 dB	45.64 dB	55.63 dB
1.40	23.80 dB	41.11 dB	52.75 dB
1.57	21.60 dB	34.58 dB	48.77 dB

Physical Quantity	Values and Units
Central wavelength of the optical pulse	1555 nm
Full width at half maximum (FWHM) of the optical pulse	210 fs
Peak power of the optical pulse	973 W
GVD coefficient of the DCF	−130ps/km/nm
Length of the DCF1	1.3 km
Length of the DCF2	11.7 km

modulation index	C/IM3 of the differential detection	C/IM3 after the arcsine operation	C/IM3 of the proposed scheme
0.99	30.22 dB	52.44 dB	Suppress to the noise floor
1.12	27.96 dB	49.09 dB	58.68 dB
1.25	25.93 dB	45.64 dB	55.63 dB
1.40	23.80 dB	41.11 dB	52.75 dB
1.57	21.60 dB	34.58 dB	48.77 dB

Broadband linearization in photonic time-stretch analog-to-digital converters employing an asymmetrical dual-parallel Mach-Zehnder modulator and a balanced detector

Abstract

1. Introduction

2. Operation principle

3. Simulation and discussion

4. Analysis of parameter deviation

5. Conclusions

Acknowledgments

References and links

Cited By

Figures (6)

Tables (2)

Equations (21)

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