Abstract

We demonstrate a single-shot photonic time-stretch digitizer using a dissipative soliton-based passively mode-locked fiber laser. The theoretical analysis and simulation results indicate that the dissipative soliton-based optical source with a flat spectrum relieves the envelope-induced signal distortion, and its high energy spectral density helps to improve the signal-to-noise ratio, both of which are favorable for simplifying the optical front-end architecture of a photonic time-stretch digitizer. By employing a homemade dissipative soliton-based passively mode-locked erbium-doped fiber laser in a single-shot photonic time-stretch digitizer, an effective number of bits of 4.11 bits under an effective sampling rate of 100 GS/s is experimentally obtained without optical amplification in the link and pulse envelope removing process.

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

1. Introduction

Real-time digital oscilloscopes with fast sampling rates and large bandwidths are urgently needed for applications ranging from basic science research to advanced communication and radar systems [1,2]. To date, the sampling rate and the input bandwidth of the most advanced oscilloscopes are limited in the order of a hundred GS/s and multi-tens of GHz, respectively (e.g., Keysight DSOZ634A is with a maximum sampling rate of 160 GS/s and an input bandwidth of 63 GHz). The main constraint factor for the oscilloscope performance is the contradiction between the sampling rate and the conversion accuracy in its core components, i.e., single-chip analog-to-digital converters (ADCs). According to the ADC survey and analysis by Walden, aperture jitter and comparator ambiguity are the two dominated reasons for the effective number of bits (ENOBs) deterioration in the high-frequency (also high-speed sampling rate) range [3]. Although a great effort has been made to enhance the carrier migration rate in the semiconductor, the improvement of sampling rate and bandwidth in electronic ADCs is still relatively slow, which cannot meet the ever-increasing requirement of ultra-high speed digital acquisition of wideband signals in numerous applications [4]. As an alternative, photonic ADCs, which are characterized by large bandwidth and high speed, are recognized as a potential candidate to overcome the electronics bottleneck in recent years [4,5]. Among various photonic ADC schemes, the time-stretch ADC, which employs optical dispersion to slow down the input radio frequency (RF) signal and to compress its bandwidth before digitization, is a promising solution to enhance the sampling rate and the input bandwidth of an electronic ADC or an oscilloscope, and has been intensively researched [6–12]. Based on this technique, a single-shot photonic time-stretch digitizer with an effective sampling rate of 10 TS/s and an ENOB of 4.5 bits is realized by applying a set of Agilent DSO81304B real-time oscilloscope with a sampling rate of 40 GS/s and an input bandwidth of 13 GHz [13].

The photonic time-stretch digitizer generally utilizes a conventional soliton-based passively mode-locked fiber laser as its optical source, which introduces three vital problems. The first one is that the conventional soliton has a hyperbolic-secant-shaped spectrum. After wavelength-to-time mapping by dispersive Fourier transform, the generated optical carrier (i.e., a linearly chirped optical pulse) has a hyperbolic-secant-shaped envelope in the time domain, which will severely distort the stretched signal [14]. Although the non-flatness and the dynamic pulse-to-pulse variation of the carrier envelope can be effectively removed through using a dual-output push-pull Mach-Zehnder electro-optic modulator [15] (e.g., an ENOB of 4.38 bits is obtained without digital filtering process in [16]), both the increasing system complexity and the inevitable offline processing mismatch the demand of a real-time oscilloscope. The second problem is that the time-bandwidth product (i.e., the time aperture multiplied by the effective signal bandwidth) of the photonic ADC is not sufficiently large. The conventional soliton generally has a spectrum width in the order of ten nanometers. In order to enlarge the time aperture (i.e., the width of the chirped optical pulse after the first-stage dispersion medium) to carry a longer signal, a large dispersion is required, which will introduce severe dispersion-induced power penalty, deteriorating the signal-to-noise ratio (SNR) and putting a stringent limit to the effective analog bandwidth. Although this problem can be solved by adopting single-sideband modulation [17] or phase diversity technique [18], the extra offline processing is not attractive for realizing a real-time oscilloscope with the function of online storage and instant display. The third problem is that the energy spectral density of the conventional soliton is low, which is not beneficial for achieving a high SNR. According to the soliton area theorem, the pulse energy of a conventional soliton is limited by the group-velocity dispersion (GVD) and the nonlinearity effect in the optical fiber [19]. When the peak power of the soliton exceeds a critical value, soliton abruption will occur due to the nonlinear phase shift, which limits its pulse energy. In a photonic time-stretch ADC with a large stretch factor, the pulse power sharply decreases during the stretch process. Hence, the application of optical amplifiers is essential to guarantee the signal intensity, which, however, will introduce additional noise and distortion, and inevitably degrade the SNR of the system. Except for conventional soliton-based passively mode-locked fiber lasers, a supercontinuum source is also employed to realize photonic ADCs [20]. Although its flat spectrum and large spectrum width can solve the aforementioned first and second problems, the third one still exists.

In this paper, a single-shot photonic time-stretch digitizer using a dissipative soliton-based passively mode-locked fiber laser is proposed. Compared with the conventional soliton and the supercontinuum source, the dissipative soliton has the following advantages. Firstly, its flat spectrum is benefit for reducing the pulse envelope-induced signal distortion. Secondly, its broadband spectrum is favorable for increasing the time-bandwidth product. Thirdly, its high energy spectral density helps to improve the SNR, and the steep edge of the spectrum can minimize the overlap between the adjacent pulses after time stretch. Actually, the flat-top-spectrum dissipative soliton has been previously adopted to perform time-stretch microscopy, in which its broad spectrum enhances the field of view, and its temporal stability guarantees a high SNR [21,22]. In this work, the flat spectrum and the high energy spectral density of the dissipative soliton are utilized to improve the ENOB of the single-shot photonic time-stretch digitizer. The proposed digitizer scheme is numerically simulated, in which an ENOB of 5.3 bits is obtained without removing the pulse envelope by offline digital processing. Through using a home-made dissipative soliton-based passively mode-locked erbium-doped fiber laser, the proposed scheme is also experimentally demonstrated, in which an ENOB of 4.11 bits is realized without optical amplification in the link and pulse envelope removing process.

2. Operation principle

Figure 1 shows the schematic diagram of the single-shot photonic time-stretch digitizer using a dissipative soliton-based passively mode-locked fiber laser. The mode-locked laser outputs ultra-short dissipative solitons with a rectangular-like spectrum [23,24]. Firstly, the dissipative soliton propagates through the first spool of dispersion compensation fiber (DCF1), after which it transforms to a linearly chirped pulse with a flat envelope over its duration. Then, the RF signal is loaded on the flat envelope of the chirped optical pulse via a push-pull Mach-Zehnder modulator (MZM) biased at its quadrature point, realizing time-to-wavelength mapping. After that, the modulated signal propagates through the second spool of dispersion compensation fiber (DCF2), in which the modulated optical pulse is time stretched and the frequency of the carried RF signal is reduced. Finally, the slowed-down RF signal is converted back to the electrical domain by a photodetector, and digitized by a real-time digital oscilloscope. Since the envelope of the chirped optical pulse is flat over its duration, there is no need to remove the pulse envelope through offline digital processing. Therefore, if the stretch factor is large enough, the RF signal with a frequency beyond the input bandwidth of the oscilloscope can be digitized and directly displayed on the screen with a high fidelity.

 

Fig. 1 Schematic diagram of the single-shot photonic time-stretch digitizer using a dissipative soliton-based passively mode-locked fiber laser. MLL: mode-locked laser; DCF: dispersion compensation fiber; PC: polarization controller; MZM: Mach-Zehnder modulator.

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The dissipative soliton-based passively mode-locked fiber laser employed in the proposed scheme is a ring cavity one, whose architecture is presented in Fig. 2. The polarization-dependent optical integrated component (PD-OIC) involves three devices, i.e., a 980nm/1550nm wavelength division multiplex (WDM), a 1550 nm polarization-dependent isolator (PD-ISO) and a 1550 nm optical coupler (OC) with a splitting ratio of 10:90. The 980 nm pump is injected from the pump port and reflected from the common port to clockwise transmit in the ring cavity. The mode locking is realized by the polarization controller (PC) and the PD-ISO in the PD-OIC, in combination with the Kerr effect in the optical fiber, through nonlinear polarization rotation (NPR) effect [25]. Above the mode locking threshold, ultra-short optical pulses are generated through repeatedly circulating in the clockwise direction of the ring cavity, where 10% of its energy outputs from the tap port. Dissipative solitons are generated by the dynamic balance among several physical mechanisms in the cavity, i.e., the loss, the normal GVD, the self-phase modulation (SPM), the gain saturation, the gain filtering and the ultra-fast saturation absorption effect of the NPR [25]. Therefore, in order to realize dissipative soliton-based mode locking, the GVD in the ring cavity should be net normal dispersion. A section of erbium-doped fiber (EDF) with a large enough normal GVD, which overcompensates the anomalous GVD in the HI 1060F and the SMF-28, is employed as the gain medium.

 

Fig. 2 Architecture of the dissipative soliton-based passively mode-locked erbium-doped fiber laser. PD-OIC: polarization-dependent optical integrated component; PC: polarization controller; EDF: erbium-doped fiber.

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The generation of dissipative soliton in the passively mode-locked fiber laser can be simulated by using the pulse tracking method, in which a random optical field is employed as the original optical field, and the stable dissipative soliton can be obtained by propagating the optical field in the cavity after enough circle number [26]. During the numerical simulation, the output optical field from each discrete optical component is expressed by multiplying its corresponding Jones matrix with its input optical field, and the pulse propagation in the fiber can be described by the Ginzburg-Landau equation (GLE) [19,27], both of which are presented in Appendix. The split-step Fourier transform (SSFT) method is employed to numerically solve the CGLE [28]. After a full circulation in the ring cavity, 90% of the optical field is injected into the cavity through the signal port of the PD-OIC to be the input optical field of the next circulation. Meanwhile, 10% of the optical field outputs from the tap port of the PD-OIC, and is monitored in both time domain and spectrum domain until a stable dissipative soliton-based pulse is acquired.

Once the stable dissipative soliton is obtained, it is used as the input of the photonic time-stretch digitizer. The pulse propagation in the DCFs is described by the generalized nonlinear Schrödinger equation (GNLSE) as [28]

Ax,yz+α2Ax,y+jβ222Ax,yT2β363Ax,yT3=jγ{(|Ax,y|2+23|Ay,x|2)Ax,y+j1ω0[|Ax,y|2Ax,y]TTR[|Ax,y|2]TAx,y}
where Ax and Ay are the amplitude of the optical field along the two principal axes of the fiber. α, β2, β3 and γ are the loss, the GVD, the third-order dispersion and the nonlinearity coefficients of the fiber, respectively. ω0 and TR are the central angular frequency of the optical pulse and the Raman response time of the fiber. Also, the SSFT method is used to numerically solve the GNLSE. The relationship between the input optical field and the output one in the time domain of a MZM biased at its quadrature point and driven by a single-tone RF signal of V(T)=V0(T)cos(ωT) can be written as
Aoutx,y=Ainx,ycos[π4+m2cos(ωT)]
where m = πV0/Vπ is the modulation index. Thereinto, Vπ is the half-wave voltage. The output current of the photodetector can be calculated as
I=12ncε0AeffRPD(|ADCF2x|2+|ADCF2y|2)
where ADCF2-x and ADCF2-y are the two orthogonal optical fields injected into the photodetector, respectively. RPD is the detector responsivity. ε0 is the permittivity in vacuum. n and Aeff are the refractive index and the effective mode area of the fiber, respectively. In addition, the stretch factor M of the photonic time-stretch digitizer is calculated as
M=(L1+L2)/L1
where L1 and L2 are the length of the two spools of the DCF, respectively.

3. Simulation results

In this section, numerical simulation of the photonic time-stretch digitizer using a dissipative soliton is implemented, and the results are compared with those using a conventional soliton. Since the spectral width of the conventional soliton is generally in the order of ten nanometers, a dissipative soliton with a spectral width of 10 nm is generated in the simulation by adopting the fiber parameters given in Table 1. Besides, the parameters of the DCFs used in the time stretch process are presented in Table 2, which correspond to a 14-fold stretch factor.

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Table 1. Fiber parameters for generating dissipative soliton

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Table 2. Parameters of the DCFs in the time stretch process

First of all, the dissipative soliton is obtained by using the pulse tracking method to solve the theoretical model of the mode-locked fiber laser given in Appendix. Figure 3(a) shows the stable output spectrum of the dissipative soliton after 500 circulations in the ring cavity, which has a 3 dB width of 10 nm. As a comparison, Fig. 3(b) exhibits the spectrum of the conventional soliton with an identical 3 dB width. It can be seen from Fig. 3 that the spectrum of the dissipative soliton has a flat top and a sharp rising (falling) edge compared with that of the conventional soliton, which is beneficial for reducing the pulse envelope-induced distortion and minimizing the overlap between the adjacent stretched pulses after time stretch. Additionally, through optimizing the pump power and the net dispersion in the laser cavity, a dissipative soliton with a spectral width up to tens of nm is available, which is favorable for increasing the time-bandwidth product in the time stretch process.

 

Fig. 3 Output spectra of (a) the dissipative soliton and (b) the conventional soliton.

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Then, the simulation of the photonic time-stretch digitizers using both the dissipative soliton and the conventional one are implemented. In the simulation, an RF signal with a frequency of 8.434 GHz is used as the input signal, and the modulation index of the MZM is set to be 0.6 (i.e., modulation depth of 56.46%). An electronic digitizer with a sampling rate of 10 GS/s and a quantization level of 6 bits is adopted to fulfill the digitization process. Figures 4(a) and 4(b) exhibit the digitized signal using the dissipative soliton and the conventional one, respectively, in which the points represent the digitized data and the solid lines are the sine fitted curves using the digitized data. The corresponding Fourier spectra of the digitized signals are also shown in Figs. 5(a) and 5(b), respectively. Apparently, the signal frequency has been down-converted from 8.434 GHz to 0.602 GHz through 14-fold time stretch, which on the other hand indicates that the effective sampling rate of the digitizer is increased from 10 GS/s to 140 GS/s. In order to evaluate the conversion accuracy of the photonic time-stretch digitizer, the digitized data within the spectral range of 7 nm near the center wavelength are extracted and sine fitted in the time domain, where the calculated ENOBs are 5.2 bits and 2.9 bits for the digitizers using the dissipative soliton and the conventional one, respectively. Since an ENOB above 5 bits is sufficient for signal observation and rough measurement in the high-speed oscilloscope application, the photonic time-stretch digitizer using dissipative solitons can meet this requirement even without removing the pulse envelope through offline digital processing. This characteristic not only simplifies the optical front-end structure but also makes the real-time display of the signal on the screen available. Further simulation shows that through increasing the quantization level of the electronic digitizer, the ENOB of the photonic time-stretch digitizer stops rising (e.g., the ENOBs are 5.3 bits and 2.9 bits for the photonic time-stretch digitizers using the dissipative soliton and the conventional one, respectively, under a quantization level of 8 bits). This is because the ENOB of the dissipative soliton-based photonic time-stretch ADC is eventually restrained by the second harmonic suppression ratio as shown in Fig. 5(a). In the conventional soliton-based photonic time-stretch ADC, although the performance of the harmonic suppression ratio and the noise floor level is resemble to the dissipative soliton-based one, there is a strong unwanted low frequency component (close to DC) induced by the slowly varying envelope as shown in Fig. 5(b), which will degrade the signal-to-noise and distortion ratio (SINAD), and restrict the ENOB.

 

Fig. 4 Digitized signals from the photonic time-stretch digitizers employing (a) the dissipative soliton and (b) the conventional soliton.

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Fig. 5 Fourier spectra of the digitized signal from the photonic time-stretch digitizers employing (a) the dissipative soliton and (b) the conventional soliton.

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Figure 6 presents the digitized signal from the photonic time-stretch digitizers after removing the pulse envelope by adopting a dual-output push-pull MZM and the corresponding digital correction algorithm [15], where Figs. 6(a) and 6(b) are the results by employing the dissipative soliton and the conventional one, respectively (the frequency of the input RF signal is 8.434 GHz, and the modulation index is set to be 1). Meanwhile, Figs. 7(a) and 7(b) exhibit the corresponding Fourier spectra. Clearly, the DC component, the envelope-induce distortion and the even-order harmonics are all suppressed thanks to the complementary structure and the digital post-processing. The ENOB is calculated to be 5.4 bits for the dissipative soliton-based digitizer, which is still 0.1 bits higher than that using the conventional soliton. This is attributed to that, compared with the conventional soliton with a hyperbolic-secant-shaped envelope, the dissipative soliton with a flat-top envelope can assist the stretched signal in utilizing the dynamic range of the digital oscilloscope more efficiently over the pulse duration.

 

Fig. 6 Digitized signals from the photonic time-stretch digitizers employing (a) the dissipative soliton and (b) the conventional soliton after removing the pulse envelope by adopting a dual-output push-pull MZM and the corresponding digital correction algorithm.

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Fig. 7 Fourier spectra of the digitized signal from the photonic time-stretch digitizers employing (a) the dissipative soliton and (b) the conventional soliton after removing the pulse envelope by adopting a dual-output push-pull MZM and the corresponding digital correction algorithm.

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4. Experiment results

In order to experimentally evaluate the performance of the proposed scheme, a dissipative soliton-based passively mode-locked erbium-doped fiber laser is constructed with its spectrum presented in Fig. 8(a), according to the fiber parameters given in Table 3. The net dispersion in the ring cavity is calculated to be 0.205 ps2, and the pump power is 196 mW. For comparison, a conventional soliton-based passively mode-locked erbium-doped fiber laser is also produced with its spectrum shown in Fig. 8(b). It should be pointed out that the power spectral intensity seems higher in Fig. 8(b) than that in Fig. 8(a), which attributes to the different loss of the tunable optical attenuator at the output of the optical sources in the measurement. Table 4 lists the output parameters of the two optical sources without the tunable optical attenuator, which indicates that the dissipative soliton has an energy spectral density 50 times higher than that of the conventional one. It can be seen from Fig. 8(a) that the beneficial performance of the dissipative soliton, such as the flatness, the broadband and the steep edge of the spectrum, is manifested. Especially, the spectrum flatness in the wavelength range of 1572.0 nm to 1577.6 nm is 0.2 dB, which is favorable for reducing the pulse envelope-induced signal distortion in the time stretch process. This flat spectrum range can be further enhanced through managing the dispersion, optimizing the pump power and finely adjusting the PC status in the cavity [23].

 

Fig. 8 Output spectra of (a) the dissipative soliton and (b) the conventional soliton.

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Tables Icon

Table 3. Fiber parameters in the dissipative soliton-based passively mode-locked fiber laser

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Table 4. Output parameters of the two optical sources

Then, the two optical sources are separately employed to realize a photonic time-stretch digitizer whose architecture is shown in Fig. 1. The parameters of the DCFs used in the time stretch process are listed in Table 5, which correspond to a 10-fold stretch factor. In the experiment, a single-tone RF signal from a microwave source (R&S SMB100A) with a frequency of 5 GHz and a power of 13 dBm is modulated on the envelope of the linearly chirped pulse from DCF1 via a push-pull MZM (EOSPACE) biased at its quadrature point. After propagating through DCF2, the stretched signal is detected by a photodetector (HP 11982A), and digitized by a real-time digital oscilloscope (R&S RTO1024) with a sampling rate of 10 GS/s and an input bandwidth of 2 GHz. Figures 9(a) and 9(b) show the extracted output waveform of the dissipative soliton-based photonic time-stretch digitizer within the 0.2 dB bandwidth of the dissipative soliton (1572.5 nm to 1577.2 nm) and its Fourier spectrum, respectively, where the points represent the digitized data and the solid line is the sine fitted curve. Thanks to the flatness of the spectrum, the ENOB is calculated to be 4.11 bits. There are two main reasons for that the ENOB in the experiment is 1.2 bits lower than the simulation result. Firstly, the modulation depth is not large enough to beat the system noise in the experiment, which can be seen from the lower signal power level and the higher second harmonic suppression ratio in Fig. 9(b) compared with those exhibited in Fig. 5(a). Secondly, the signal does not fully fill the vertical scale of the oscilloscope, and thus does not make full use of the quantization levels (the ENOB is tested to be 6.07 bits when a microwave signal with a frequency of 595 MHz from the microwave source fully fills the vertical scale of the oscilloscope). As a comparison, Figs. 10(a) and 10(b) present the output waveform of the conventional soliton-based photonic time-stretch digitizer and its Fourier spectrum, respectively. It should be pointed out that, considering the high repetition frequency of the conventional soliton-based optical source (up to 136.6 MHz), an optical passband filter (Santec OTF-350) with a bandwidth of 4.7 nm is used to avoid the overlap between the adjacent pulses. Obviously, the digitized signal is seriously distorted due to the non-flatness of the pulse envelope, which can be seen from the non-uniform of signal amplitude in the time domain, and also the strong low frequency component (close to DC) in the frequency domain.

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Table 5. Parameters of the DCFs

 

Fig. 9 Output of the dissipative soliton-based photonic time-stretch digitizer. (a) Output waveform and (b) Fourier spectrum.

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Fig. 10 Output of the conventional soliton-based photonic time-stretch digitizer. (a) Output waveform and (b) Fourier spectrum.

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Additionally, due to the high energy spectral density of the dissipative soliton, no optical amplifier is employed in the photonic time-stretch digitizer experiment using the dissipative soliton-based optical source. Nevertheless, the output optical power in the experiment using the conventional soliton-based optical source is too low to be detected by the photodetector (−25 dBm). Therefore, an erbium-doped fiber amplifier (EDFA) is inevitable to boost the optical power, which introduces additional noise and increases the noise floor as shown in Fig. 10(b).

Finally, it can be seen from Fig. 8 that, the dissipative soliton has a much wider spectrum than the conventional soliton, which is favorable for yielding a large time-bandwidth product as pointed out in [6]. Nevertheless, only a small part of the dissipative soliton spectrum is used to achieve time-stretch digitization in the experiment, since the spectrum of our home-maded dissipative soliton source is not sufficiently flat in its full range. If the complementary structure and the digital post-processing as presented in [15] are employed to maintain a high enough ENOB, the superiority of the wide spectrum in enhancing the time-bandwidth product can be utilized. Moreover, it is feasible to improve the spectrum flatness of the dissipative soliton through optimizing the optical source. Hence, the dissipative soliton is a potential candidate to simultaneously achieve a large time-bandwidth product and simplify the post processing of the time-stretch digitizer.

5. Conclusion

In summary, we demonstrate a single-shot photonic time-stretch digitizer using a dissipative soliton-based passively mode-locked fiber laser. In the simulation, an ENOB of 5.3 bits is obtained without removing the pulse envelope by offline digital processing, which is 2.4 bits higher than that adopting the conventional soliton. A dissipative soliton-based passively mode-locked erbium-doped fiber laser is produced, which has a relatively flat spectrum and an energy spectral density 50 times higher than that of the conventional one. By employing this home-made dissipative soliton-based optical source in a single-shot photonic time-stretch digitizer, an ENOB of 4.11 bits under an effective sampling rate of 100 GS/s is experimentally achieved without removing the pulse envelope and adding optical amplifiers in the link. The results indicate that the dissipative soliton helps to largely simplify the optical front-end structure of a photonic time stretch digitizer.

Appendix

The Jones matrix of the PD-ISO and the PC are

JPD-ISO=(cos2θsinθcosθcosθsinθsin2θ)
JPC=(100exp(iφPC))
where θ is the angle between the x-axis of the fiber and the polarization orientation of the PD-ISO, and φPC is the phase difference of the polarized components between x-axis and y-axis of the fiber produced by the PC.

The Ginzburg-Landau equation (GLE) can be written as

Axz+αAx+δAxT+iβ222AxT2β363AxT3=iγ(|Ax|2+23|Ay|2)Ax+iγ3Ay2Ax*exp(i2Δβz)+g2Ax+g2Ωg22AxT2
Ayz+αAyδAyT+iβ222AyT2β363AyT3=iγ(|Ay|2+23|Ax|2)Ay+iγ3Ax2Ay*exp(i2Δβz)+g2Ay+g2Ωg22AyT2
where Ax and Ay are the amplitude of the optical field along the two principal axes of the fiber. α, β2, β3 and γ are the loss, the GVD, the third-order dispersion and the nonlinearity coefficients of the fiber, respectively. Ωg is the gain bandwidth of the EDF. Δβ=2π/LB is the wave-number difference between the two orthogonal optical field. LB is the beat-length of the fiber birefringence. 2δ=Δβλ/(2πc), in which λ and c are the wavelength and the velocity of the light in vacuum, respectively. g is the saturated gain of the EDF, which can be calculated as
g=g0exp[1Psat(|Ax|2+|Ay|2)dT]
where g0 and Psat are the small-signal gain coefficient and the saturation energy of the EDF, respectively. For the non-doped fiber (i.e., HI 1060F and SMF-28), g0 is set to be zero.

Funding

National Natural Science Foundation of China (Grant Nos. 61575037, 61421002, 11574070); Leading Talents of Guangdong Province Program; China Scholarship Council (Grant No. 201606075076).

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19. D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, “Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers,” Phys. Rev. A 72(4), 043816 (2005). [CrossRef]  

20. J. H. Wong, H. Q. Lam, K. E. K. Lee, V. Wong, P. H. Lim, S. Aditya, and P. P. Shum, “Generation of flat supercontinuum for time-stretched analog-to-digital converters,” in Proceedings of International Quantum Electronics Conference and Conference on Lasers and Electro-optics Pacific Rim (IEEE, 2011), pp. C409. [CrossRef]  

21. X. Wei, J. Xu, Y. Xu, L. Yu, J. Xu, B. Li, A. K. S. Lau, X. Wang, C. Zhang, K. K. Tsia, and K. K. Y. Wong, “Breathing laser as an inertia-free swept source for high-quality ultrafast optical bioimaging,” Opt. Lett. 39(23), 6593–6596 (2014). [CrossRef]   [PubMed]  

22. X. Wei, A. K. S. Lau, Y. Xu, K. K. Tsia, and K. K. Y. Wong, “28 MHz swept source at 1.0 μm for ultrafast quantitative phase imaging,” Biomed. Opt. Express 6(10), 3855–3864 (2015). [CrossRef]   [PubMed]  

23. F. W. Wise, A. Chong, and W. H. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photonics Rev. 2(1), 58–73 (2008). [CrossRef]  

24. H. D. Xia, H. P. Li, X. X. Zhang, S. J. Zhang, X. G. Tang, and Y. Liu, “Characteristics of dissipative solitons in an all-fiber thulium-doped fiber ring laser,” Opt. Eng. 52(5), 054201 (2013). [CrossRef]  

25. V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Selfstarting passively mode-locked fibre ring soliton laser exploiting nonlinear polarisation rotation,” Electron. Lett. 28(15), 1391–1393 (1992). [CrossRef]  

26. X. Liu, “Numerical and experimental investigation of dissipative solitons in passively mode-locked fiber lasers with large net-normal-dispersion and high nonlinearity,” Opt. Express 17(25), 22401–22416 (2009). [CrossRef]   [PubMed]  

27. L. M. Zhao, D. Y. Tang, H. Y. Tam, and C. Lu, “Pulse breaking recovery in fiber lasers,” Opt. Express 16(16), 12102–12107 (2008). [CrossRef]   [PubMed]  

28. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007), Chap. 2.

References

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  1. R. H. Walden, “Analog-to-digital converter in the early twenty-first century,” in Wiley Encyclopedia of Computer Science and Engineering, B. W. Wah, ed. (Wiley,2008).
  2. Y. Han and B. Jalali, “One tera-sample/sec real-time transient digitizer,” in Proceedings of the IEEE Instrumentation and Measurement Technology Conference (IEEE, 2005), pp. 507–509.
    [Crossref]
  3. R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Comm. 17(4), 539–550 (1999).
    [Crossref]
  4. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
    [Crossref]
  5. G. C. Valley, “Photonic analog-to-digital converters,” Opt. Express 15(5), 1955–1982 (2007).
    [Crossref] [PubMed]
  6. Y. Han and B. Jalali, “Photonic time-stretched analog-to-digital converter: fundamental concepts and practical considerations,” J. Lightwave Technol. 21(12), 3085–3103 (2003).
    [Crossref]
  7. J. Chou, J. A. Conway, G. A. Sefler, G. C. Valley, and B. Jalali, “Photonic bandwidth compression front end for digital oscilloscopes,” J. Lightwave Technol. 27(22), 5073–5077 (2009).
    [Crossref]
  8. J. H. Wong, H. Q. Lam, R. M. Li, K. E. K. Lee, V. Wong, P. H. Lim, S. Aditya, P. P. Shum, S. H. Xu, K. Wu, and C. Ouyang, “Photonic time-stretched analog-to-digital converter amenable to continuous-time operation based on polarization modulation with balanced detection scheme,” J. Lightwave Technol. 29(20), 3099–3106 (2011).
    [Crossref]
  9. S. Weber, C. Reinheimer, and G. V. Freymann, “Magnification dependent dispersion penalty studied with resonator-based time-stretch oscilloscope,” J. Lightwave Technol. 32(20), 3618–3622 (2014).
    [Crossref]
  10. A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11(6), 341–351 (2017).
    [Crossref]
  11. A. M. Fard, S. Gupta, and B. Jalali, “Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging,” Laser Photonics Rev. 7(2), 207–263 (2013).
    [Crossref]
  12. K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
    [Crossref]
  13. J. Chou, O. Boyraz, D. Solli, and B. Jalali, “Femtosecond real-time single-shot digitizer,” Appl. Phys. Lett. 91(16), 161105 (2007).
    [Crossref]
  14. T. Jannson, “Real-time Fourier transformation in dispersive optical fibers,” Opt. Lett. 8(4), 232–234 (1983).
    [Crossref] [PubMed]
  15. S. Gupta, G. C. Valley, and B. Jalali, “Distortion cancellation in time-stretch analog-to-digital converter,” J. Lightwave Technol. 25(12), 3716–3721 (2007).
    [Crossref]
  16. W. Ng, T. D. Rockwood, G. A. Sefler, and G. C. Valley, “Demonstration of a large stretch-ratio (M=41) photonic analog-to-digital converter with 8 ENOB for an input signal bandwidth of 10 GHz,” IEEE Photonics Technol. Lett. 24(14), 1185–1187 (2012).
    [Crossref]
  17. Y. Han and B. Jalali, “Time-bandwidth product of the photonic time-stretched analog-to-digital converter,” IEEE T. Microw. Theory 51(7), 1886–1892 (2003).
    [Crossref]
  18. Y. Han, O. Boyraz, and B. Jalali, “Ultrawide-band photonic time-stretch A/D converter Employing phase diversity,” IEEE T. Microw. Theory 53(4), 1404–1408 (2005).
    [Crossref]
  19. D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, “Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers,” Phys. Rev. A 72(4), 043816 (2005).
    [Crossref]
  20. J. H. Wong, H. Q. Lam, K. E. K. Lee, V. Wong, P. H. Lim, S. Aditya, and P. P. Shum, “Generation of flat supercontinuum for time-stretched analog-to-digital converters,” in Proceedings of International Quantum Electronics Conference and Conference on Lasers and Electro-optics Pacific Rim (IEEE, 2011), pp. C409.
    [Crossref]
  21. X. Wei, J. Xu, Y. Xu, L. Yu, J. Xu, B. Li, A. K. S. Lau, X. Wang, C. Zhang, K. K. Tsia, and K. K. Y. Wong, “Breathing laser as an inertia-free swept source for high-quality ultrafast optical bioimaging,” Opt. Lett. 39(23), 6593–6596 (2014).
    [Crossref] [PubMed]
  22. X. Wei, A. K. S. Lau, Y. Xu, K. K. Tsia, and K. K. Y. Wong, “28 MHz swept source at 1.0 μm for ultrafast quantitative phase imaging,” Biomed. Opt. Express 6(10), 3855–3864 (2015).
    [Crossref] [PubMed]
  23. F. W. Wise, A. Chong, and W. H. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photonics Rev. 2(1), 58–73 (2008).
    [Crossref]
  24. H. D. Xia, H. P. Li, X. X. Zhang, S. J. Zhang, X. G. Tang, and Y. Liu, “Characteristics of dissipative solitons in an all-fiber thulium-doped fiber ring laser,” Opt. Eng. 52(5), 054201 (2013).
    [Crossref]
  25. V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Selfstarting passively mode-locked fibre ring soliton laser exploiting nonlinear polarisation rotation,” Electron. Lett. 28(15), 1391–1393 (1992).
    [Crossref]
  26. X. Liu, “Numerical and experimental investigation of dissipative solitons in passively mode-locked fiber lasers with large net-normal-dispersion and high nonlinearity,” Opt. Express 17(25), 22401–22416 (2009).
    [Crossref] [PubMed]
  27. L. M. Zhao, D. Y. Tang, H. Y. Tam, and C. Lu, “Pulse breaking recovery in fiber lasers,” Opt. Express 16(16), 12102–12107 (2008).
    [Crossref] [PubMed]
  28. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007), Chap. 2.

2017 (1)

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11(6), 341–351 (2017).
[Crossref]

2015 (1)

2014 (2)

2013 (3)

A. M. Fard, S. Gupta, and B. Jalali, “Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging,” Laser Photonics Rev. 7(2), 207–263 (2013).
[Crossref]

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
[Crossref]

H. D. Xia, H. P. Li, X. X. Zhang, S. J. Zhang, X. G. Tang, and Y. Liu, “Characteristics of dissipative solitons in an all-fiber thulium-doped fiber ring laser,” Opt. Eng. 52(5), 054201 (2013).
[Crossref]

2012 (1)

W. Ng, T. D. Rockwood, G. A. Sefler, and G. C. Valley, “Demonstration of a large stretch-ratio (M=41) photonic analog-to-digital converter with 8 ENOB for an input signal bandwidth of 10 GHz,” IEEE Photonics Technol. Lett. 24(14), 1185–1187 (2012).
[Crossref]

2011 (1)

2009 (2)

2008 (2)

L. M. Zhao, D. Y. Tang, H. Y. Tam, and C. Lu, “Pulse breaking recovery in fiber lasers,” Opt. Express 16(16), 12102–12107 (2008).
[Crossref] [PubMed]

F. W. Wise, A. Chong, and W. H. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photonics Rev. 2(1), 58–73 (2008).
[Crossref]

2007 (4)

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

G. C. Valley, “Photonic analog-to-digital converters,” Opt. Express 15(5), 1955–1982 (2007).
[Crossref] [PubMed]

J. Chou, O. Boyraz, D. Solli, and B. Jalali, “Femtosecond real-time single-shot digitizer,” Appl. Phys. Lett. 91(16), 161105 (2007).
[Crossref]

S. Gupta, G. C. Valley, and B. Jalali, “Distortion cancellation in time-stretch analog-to-digital converter,” J. Lightwave Technol. 25(12), 3716–3721 (2007).
[Crossref]

2005 (2)

Y. Han, O. Boyraz, and B. Jalali, “Ultrawide-band photonic time-stretch A/D converter Employing phase diversity,” IEEE T. Microw. Theory 53(4), 1404–1408 (2005).
[Crossref]

D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, “Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers,” Phys. Rev. A 72(4), 043816 (2005).
[Crossref]

2003 (2)

Y. Han and B. Jalali, “Time-bandwidth product of the photonic time-stretched analog-to-digital converter,” IEEE T. Microw. Theory 51(7), 1886–1892 (2003).
[Crossref]

Y. Han and B. Jalali, “Photonic time-stretched analog-to-digital converter: fundamental concepts and practical considerations,” J. Lightwave Technol. 21(12), 3085–3103 (2003).
[Crossref]

1999 (1)

R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Comm. 17(4), 539–550 (1999).
[Crossref]

1992 (1)

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Selfstarting passively mode-locked fibre ring soliton laser exploiting nonlinear polarisation rotation,” Electron. Lett. 28(15), 1391–1393 (1992).
[Crossref]

1983 (1)

Aditya, S.

J. H. Wong, H. Q. Lam, R. M. Li, K. E. K. Lee, V. Wong, P. H. Lim, S. Aditya, P. P. Shum, S. H. Xu, K. Wu, and C. Ouyang, “Photonic time-stretched analog-to-digital converter amenable to continuous-time operation based on polarization modulation with balanced detection scheme,” J. Lightwave Technol. 29(20), 3099–3106 (2011).
[Crossref]

J. H. Wong, H. Q. Lam, K. E. K. Lee, V. Wong, P. H. Lim, S. Aditya, and P. P. Shum, “Generation of flat supercontinuum for time-stretched analog-to-digital converters,” in Proceedings of International Quantum Electronics Conference and Conference on Lasers and Electro-optics Pacific Rim (IEEE, 2011), pp. C409.
[Crossref]

Barland, S.

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11(6), 341–351 (2017).
[Crossref]

Boyraz, O.

J. Chou, O. Boyraz, D. Solli, and B. Jalali, “Femtosecond real-time single-shot digitizer,” Appl. Phys. Lett. 91(16), 161105 (2007).
[Crossref]

Y. Han, O. Boyraz, and B. Jalali, “Ultrawide-band photonic time-stretch A/D converter Employing phase diversity,” IEEE T. Microw. Theory 53(4), 1404–1408 (2005).
[Crossref]

Broderick, N.

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11(6), 341–351 (2017).
[Crossref]

Capmany, J.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

Chong, A.

F. W. Wise, A. Chong, and W. H. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photonics Rev. 2(1), 58–73 (2008).
[Crossref]

Chou, J.

Churkin, D. V.

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11(6), 341–351 (2017).
[Crossref]

Conway, J. A.

Fard, A. M.

A. M. Fard, S. Gupta, and B. Jalali, “Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging,” Laser Photonics Rev. 7(2), 207–263 (2013).
[Crossref]

Freymann, G. V.

Goda, K.

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
[Crossref]

Gupta, S.

A. M. Fard, S. Gupta, and B. Jalali, “Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging,” Laser Photonics Rev. 7(2), 207–263 (2013).
[Crossref]

S. Gupta, G. C. Valley, and B. Jalali, “Distortion cancellation in time-stretch analog-to-digital converter,” J. Lightwave Technol. 25(12), 3716–3721 (2007).
[Crossref]

Han, Y.

Y. Han, O. Boyraz, and B. Jalali, “Ultrawide-band photonic time-stretch A/D converter Employing phase diversity,” IEEE T. Microw. Theory 53(4), 1404–1408 (2005).
[Crossref]

Y. Han and B. Jalali, “Time-bandwidth product of the photonic time-stretched analog-to-digital converter,” IEEE T. Microw. Theory 51(7), 1886–1892 (2003).
[Crossref]

Y. Han and B. Jalali, “Photonic time-stretched analog-to-digital converter: fundamental concepts and practical considerations,” J. Lightwave Technol. 21(12), 3085–3103 (2003).
[Crossref]

Y. Han and B. Jalali, “One tera-sample/sec real-time transient digitizer,” in Proceedings of the IEEE Instrumentation and Measurement Technology Conference (IEEE, 2005), pp. 507–509.
[Crossref]

Jalali, B.

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11(6), 341–351 (2017).
[Crossref]

A. M. Fard, S. Gupta, and B. Jalali, “Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging,” Laser Photonics Rev. 7(2), 207–263 (2013).
[Crossref]

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
[Crossref]

J. Chou, J. A. Conway, G. A. Sefler, G. C. Valley, and B. Jalali, “Photonic bandwidth compression front end for digital oscilloscopes,” J. Lightwave Technol. 27(22), 5073–5077 (2009).
[Crossref]

J. Chou, O. Boyraz, D. Solli, and B. Jalali, “Femtosecond real-time single-shot digitizer,” Appl. Phys. Lett. 91(16), 161105 (2007).
[Crossref]

S. Gupta, G. C. Valley, and B. Jalali, “Distortion cancellation in time-stretch analog-to-digital converter,” J. Lightwave Technol. 25(12), 3716–3721 (2007).
[Crossref]

Y. Han, O. Boyraz, and B. Jalali, “Ultrawide-band photonic time-stretch A/D converter Employing phase diversity,” IEEE T. Microw. Theory 53(4), 1404–1408 (2005).
[Crossref]

Y. Han and B. Jalali, “Time-bandwidth product of the photonic time-stretched analog-to-digital converter,” IEEE T. Microw. Theory 51(7), 1886–1892 (2003).
[Crossref]

Y. Han and B. Jalali, “Photonic time-stretched analog-to-digital converter: fundamental concepts and practical considerations,” J. Lightwave Technol. 21(12), 3085–3103 (2003).
[Crossref]

Y. Han and B. Jalali, “One tera-sample/sec real-time transient digitizer,” in Proceedings of the IEEE Instrumentation and Measurement Technology Conference (IEEE, 2005), pp. 507–509.
[Crossref]

Jannson, T.

Lam, H. Q.

J. H. Wong, H. Q. Lam, R. M. Li, K. E. K. Lee, V. Wong, P. H. Lim, S. Aditya, P. P. Shum, S. H. Xu, K. Wu, and C. Ouyang, “Photonic time-stretched analog-to-digital converter amenable to continuous-time operation based on polarization modulation with balanced detection scheme,” J. Lightwave Technol. 29(20), 3099–3106 (2011).
[Crossref]

J. H. Wong, H. Q. Lam, K. E. K. Lee, V. Wong, P. H. Lim, S. Aditya, and P. P. Shum, “Generation of flat supercontinuum for time-stretched analog-to-digital converters,” in Proceedings of International Quantum Electronics Conference and Conference on Lasers and Electro-optics Pacific Rim (IEEE, 2011), pp. C409.
[Crossref]

Lau, A. K. S.

Lee, K. E. K.

J. H. Wong, H. Q. Lam, R. M. Li, K. E. K. Lee, V. Wong, P. H. Lim, S. Aditya, P. P. Shum, S. H. Xu, K. Wu, and C. Ouyang, “Photonic time-stretched analog-to-digital converter amenable to continuous-time operation based on polarization modulation with balanced detection scheme,” J. Lightwave Technol. 29(20), 3099–3106 (2011).
[Crossref]

J. H. Wong, H. Q. Lam, K. E. K. Lee, V. Wong, P. H. Lim, S. Aditya, and P. P. Shum, “Generation of flat supercontinuum for time-stretched analog-to-digital converters,” in Proceedings of International Quantum Electronics Conference and Conference on Lasers and Electro-optics Pacific Rim (IEEE, 2011), pp. C409.
[Crossref]

Li, B.

Li, H. P.

H. D. Xia, H. P. Li, X. X. Zhang, S. J. Zhang, X. G. Tang, and Y. Liu, “Characteristics of dissipative solitons in an all-fiber thulium-doped fiber ring laser,” Opt. Eng. 52(5), 054201 (2013).
[Crossref]

Li, R. M.

Lim, P. H.

J. H. Wong, H. Q. Lam, R. M. Li, K. E. K. Lee, V. Wong, P. H. Lim, S. Aditya, P. P. Shum, S. H. Xu, K. Wu, and C. Ouyang, “Photonic time-stretched analog-to-digital converter amenable to continuous-time operation based on polarization modulation with balanced detection scheme,” J. Lightwave Technol. 29(20), 3099–3106 (2011).
[Crossref]

J. H. Wong, H. Q. Lam, K. E. K. Lee, V. Wong, P. H. Lim, S. Aditya, and P. P. Shum, “Generation of flat supercontinuum for time-stretched analog-to-digital converters,” in Proceedings of International Quantum Electronics Conference and Conference on Lasers and Electro-optics Pacific Rim (IEEE, 2011), pp. C409.
[Crossref]

Liu, A. Q.

D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, “Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers,” Phys. Rev. A 72(4), 043816 (2005).
[Crossref]

Liu, X.

Liu, Y.

H. D. Xia, H. P. Li, X. X. Zhang, S. J. Zhang, X. G. Tang, and Y. Liu, “Characteristics of dissipative solitons in an all-fiber thulium-doped fiber ring laser,” Opt. Eng. 52(5), 054201 (2013).
[Crossref]

Lu, C.

Mahjoubfar, A.

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11(6), 341–351 (2017).
[Crossref]

Matsas, V. J.

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Selfstarting passively mode-locked fibre ring soliton laser exploiting nonlinear polarisation rotation,” Electron. Lett. 28(15), 1391–1393 (1992).
[Crossref]

Newson, T. P.

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Selfstarting passively mode-locked fibre ring soliton laser exploiting nonlinear polarisation rotation,” Electron. Lett. 28(15), 1391–1393 (1992).
[Crossref]

Ng, W.

W. Ng, T. D. Rockwood, G. A. Sefler, and G. C. Valley, “Demonstration of a large stretch-ratio (M=41) photonic analog-to-digital converter with 8 ENOB for an input signal bandwidth of 10 GHz,” IEEE Photonics Technol. Lett. 24(14), 1185–1187 (2012).
[Crossref]

Novak, D.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

Ouyang, C.

Payne, D. N.

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Selfstarting passively mode-locked fibre ring soliton laser exploiting nonlinear polarisation rotation,” Electron. Lett. 28(15), 1391–1393 (1992).
[Crossref]

Reinheimer, C.

Renninger, W. H.

F. W. Wise, A. Chong, and W. H. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photonics Rev. 2(1), 58–73 (2008).
[Crossref]

Richardson, D. J.

V. J. Matsas, T. P. Newson, D. J. Richardson, and D. N. Payne, “Selfstarting passively mode-locked fibre ring soliton laser exploiting nonlinear polarisation rotation,” Electron. Lett. 28(15), 1391–1393 (1992).
[Crossref]

Rockwood, T. D.

W. Ng, T. D. Rockwood, G. A. Sefler, and G. C. Valley, “Demonstration of a large stretch-ratio (M=41) photonic analog-to-digital converter with 8 ENOB for an input signal bandwidth of 10 GHz,” IEEE Photonics Technol. Lett. 24(14), 1185–1187 (2012).
[Crossref]

Sefler, G. A.

W. Ng, T. D. Rockwood, G. A. Sefler, and G. C. Valley, “Demonstration of a large stretch-ratio (M=41) photonic analog-to-digital converter with 8 ENOB for an input signal bandwidth of 10 GHz,” IEEE Photonics Technol. Lett. 24(14), 1185–1187 (2012).
[Crossref]

J. Chou, J. A. Conway, G. A. Sefler, G. C. Valley, and B. Jalali, “Photonic bandwidth compression front end for digital oscilloscopes,” J. Lightwave Technol. 27(22), 5073–5077 (2009).
[Crossref]

Shum, P. P.

J. H. Wong, H. Q. Lam, R. M. Li, K. E. K. Lee, V. Wong, P. H. Lim, S. Aditya, P. P. Shum, S. H. Xu, K. Wu, and C. Ouyang, “Photonic time-stretched analog-to-digital converter amenable to continuous-time operation based on polarization modulation with balanced detection scheme,” J. Lightwave Technol. 29(20), 3099–3106 (2011).
[Crossref]

J. H. Wong, H. Q. Lam, K. E. K. Lee, V. Wong, P. H. Lim, S. Aditya, and P. P. Shum, “Generation of flat supercontinuum for time-stretched analog-to-digital converters,” in Proceedings of International Quantum Electronics Conference and Conference on Lasers and Electro-optics Pacific Rim (IEEE, 2011), pp. C409.
[Crossref]

Solli, D.

J. Chou, O. Boyraz, D. Solli, and B. Jalali, “Femtosecond real-time single-shot digitizer,” Appl. Phys. Lett. 91(16), 161105 (2007).
[Crossref]

Tam, H. Y.

Tang, D. Y.

L. M. Zhao, D. Y. Tang, H. Y. Tam, and C. Lu, “Pulse breaking recovery in fiber lasers,” Opt. Express 16(16), 12102–12107 (2008).
[Crossref] [PubMed]

D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, “Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers,” Phys. Rev. A 72(4), 043816 (2005).
[Crossref]

Tang, X. G.

H. D. Xia, H. P. Li, X. X. Zhang, S. J. Zhang, X. G. Tang, and Y. Liu, “Characteristics of dissipative solitons in an all-fiber thulium-doped fiber ring laser,” Opt. Eng. 52(5), 054201 (2013).
[Crossref]

Tsia, K. K.

Turitsyn, S. K.

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F. W. Wise, A. Chong, and W. H. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photonics Rev. 2(1), 58–73 (2008).
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J. H. Wong, H. Q. Lam, R. M. Li, K. E. K. Lee, V. Wong, P. H. Lim, S. Aditya, P. P. Shum, S. H. Xu, K. Wu, and C. Ouyang, “Photonic time-stretched analog-to-digital converter amenable to continuous-time operation based on polarization modulation with balanced detection scheme,” J. Lightwave Technol. 29(20), 3099–3106 (2011).
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J. H. Wong, H. Q. Lam, K. E. K. Lee, V. Wong, P. H. Lim, S. Aditya, and P. P. Shum, “Generation of flat supercontinuum for time-stretched analog-to-digital converters,” in Proceedings of International Quantum Electronics Conference and Conference on Lasers and Electro-optics Pacific Rim (IEEE, 2011), pp. C409.
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Wong, V.

J. H. Wong, H. Q. Lam, R. M. Li, K. E. K. Lee, V. Wong, P. H. Lim, S. Aditya, P. P. Shum, S. H. Xu, K. Wu, and C. Ouyang, “Photonic time-stretched analog-to-digital converter amenable to continuous-time operation based on polarization modulation with balanced detection scheme,” J. Lightwave Technol. 29(20), 3099–3106 (2011).
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J. H. Wong, H. Q. Lam, K. E. K. Lee, V. Wong, P. H. Lim, S. Aditya, and P. P. Shum, “Generation of flat supercontinuum for time-stretched analog-to-digital converters,” in Proceedings of International Quantum Electronics Conference and Conference on Lasers and Electro-optics Pacific Rim (IEEE, 2011), pp. C409.
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Opt. Lett. (2)

Phys. Rev. A (1)

D. Y. Tang, L. M. Zhao, B. Zhao, and A. Q. Liu, “Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers,” Phys. Rev. A 72(4), 043816 (2005).
[Crossref]

Other (4)

J. H. Wong, H. Q. Lam, K. E. K. Lee, V. Wong, P. H. Lim, S. Aditya, and P. P. Shum, “Generation of flat supercontinuum for time-stretched analog-to-digital converters,” in Proceedings of International Quantum Electronics Conference and Conference on Lasers and Electro-optics Pacific Rim (IEEE, 2011), pp. C409.
[Crossref]

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Y. Han and B. Jalali, “One tera-sample/sec real-time transient digitizer,” in Proceedings of the IEEE Instrumentation and Measurement Technology Conference (IEEE, 2005), pp. 507–509.
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G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007), Chap. 2.

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Figures (10)

Fig. 1
Fig. 1 Schematic diagram of the single-shot photonic time-stretch digitizer using a dissipative soliton-based passively mode-locked fiber laser. MLL: mode-locked laser; DCF: dispersion compensation fiber; PC: polarization controller; MZM: Mach-Zehnder modulator.
Fig. 2
Fig. 2 Architecture of the dissipative soliton-based passively mode-locked erbium-doped fiber laser. PD-OIC: polarization-dependent optical integrated component; PC: polarization controller; EDF: erbium-doped fiber.
Fig. 3
Fig. 3 Output spectra of (a) the dissipative soliton and (b) the conventional soliton.
Fig. 4
Fig. 4 Digitized signals from the photonic time-stretch digitizers employing (a) the dissipative soliton and (b) the conventional soliton.
Fig. 5
Fig. 5 Fourier spectra of the digitized signal from the photonic time-stretch digitizers employing (a) the dissipative soliton and (b) the conventional soliton.
Fig. 6
Fig. 6 Digitized signals from the photonic time-stretch digitizers employing (a) the dissipative soliton and (b) the conventional soliton after removing the pulse envelope by adopting a dual-output push-pull MZM and the corresponding digital correction algorithm.
Fig. 7
Fig. 7 Fourier spectra of the digitized signal from the photonic time-stretch digitizers employing (a) the dissipative soliton and (b) the conventional soliton after removing the pulse envelope by adopting a dual-output push-pull MZM and the corresponding digital correction algorithm.
Fig. 8
Fig. 8 Output spectra of (a) the dissipative soliton and (b) the conventional soliton.
Fig. 9
Fig. 9 Output of the dissipative soliton-based photonic time-stretch digitizer. (a) Output waveform and (b) Fourier spectrum.
Fig. 10
Fig. 10 Output of the conventional soliton-based photonic time-stretch digitizer. (a) Output waveform and (b) Fourier spectrum.

Tables (5)

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Table 1 Fiber parameters for generating dissipative soliton

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Table 2 Parameters of the DCFs in the time stretch process

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Table 3 Fiber parameters in the dissipative soliton-based passively mode-locked fiber laser

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Table 4 Output parameters of the two optical sources

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Table 5 Parameters of the DCFs

Equations (9)

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A x,y z + α 2 A x,y +j β 2 2 2 A x,y T 2 β 3 6 3 A x,y T 3 =jγ{ ( | A x,y | 2 + 2 3 | A y,x | 2 ) A x,y +j 1 ω 0 [ | A x,y | 2 A x,y ] T T R [ | A x,y | 2 ] T A x,y }
A outx,y = A inx,y cos[ π 4 + m 2 cos( ωT ) ]
I= 1 2 nc ε 0 A eff R PD ( | A DCF2x | 2 + | A DCF2y | 2 )
M= ( L 1 + L 2 )/ L 1
J PD-ISO =( cos 2 θ sinθcosθ cosθsinθ sin 2 θ )
J PC =( 1 0 0 exp( i φ PC ) )
A x z +α A x +δ A x T + i β 2 2 2 A x T 2 β 3 6 3 A x T 3 =iγ( | A x | 2 + 2 3 | A y | 2 ) A x + iγ 3 A y 2 A x * exp( i2Δβz )+ g 2 A x + g 2 Ω g 2 2 A x T 2
A y z +α A y δ A y T + i β 2 2 2 A y T 2 β 3 6 3 A y T 3 =iγ( | A y | 2 + 2 3 | A x | 2 ) A y + iγ 3 A x 2 A y * exp( i2Δβz )+ g 2 A y + g 2 Ω g 2 2 A y T 2
g= g 0 exp[ 1 P sat ( | A x | 2 + | A y | 2 ) dT ]

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