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Abstract
A sub-100 fs all-fiber broadband optical frequency comb seeded from a 12.5 GHz electro-optic modulated pulse is presented. Combining pulse reshaping, nonlinear mixing with dispersion compensation processes, a frequency comb with the main pulse width of 86 fs was achieved. The frequency comb has a 6 dB spectral bandwidth spanning over 150 nm which corresponding to more than 1500 comb tones. The measured average power of the broadband comb is over 550 mW, and the calculated average power of each comb line is roughly −4 dBm. To illustrate the whole spectral broadening process, a numerical investigation was also brought out, showing a very good match with the experiments. With a delayed self-heterodyne interferometer, the evolutions of the seed comb linewidths and the broadened comb linewidths were measured revealing the same parabolic trend. Specifically, the linewidths of the 20 seed comb lines are less than 10 kHz, while the linewidths of the 400 broadened comb lines are less than 1 MHz. The results also indicate that the nonlinear mixing led to an accumulation of the phase noise with respect to the comb line number, indicating that a low phase noise RF source or phase locking technique is essential to produce ultra-low phase noise broadband electro-optic combs.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical frequency comb (OFC) refers to a series of frequency components with equal intervals and coherent phase, which has revolutionized precise optical frequency measurement by bridging the optical and microwave regions of the electromagnetic spectrum [1,2]. In recent years, OFC has been proved as one of the most powerful tools in many crucial scientific applications such as microwave signals processing [3–5], high-performance waveform synthesis [6–8], high-resolution molecular spectroscopy [9–11], astronomical spectrograph calibration [12,13], optical coherence tomography [14,15] etc. Avoiding the need for multiple laser sources and complicated synchronization techniques, a broadband OFC has also emerged as an attractive approach for wavelength division multiplexing (WDM) in optical communication systems particularly. In the perspective of time domain, OFCs with high peak power and femtosecond durations provide access to ultrafast measurements and quantum states controlling.
With the rapid development of optical technologies, the generation schemes of OFC have been demonstrated in both fiber and chip devices. In general, there are three common methods to generate OFC, namely mode-locked fiber lasers (MLLs) [16–19], micro-resonators [20,21] and electro-optic (EO) modulation [22,23]. To serve as a multi-wavelength source for the application of coherent detection system, OFCs are expected to possess flat comb lines, durable frequency stability, broad spectral coverage and, preferably, adjustable frequency spacing (from several MHz to tens of GHz [24]). Considering the above requirements, EO combs were widely used since it is free from the bondage of the cavity and its repetition frequency is flexible to tune. However, the limited modulation depth of EO modulators restricts the generation of more sideband frequency components. Hence, nonlinear optical broadening such as self-phase modulation (SPM), four-wave mixing (FWM), Raman effects have been utilized in specialty fibers such as highly nonlinear fibers (HNLFs) and dispersion decreasing fibers to enlarge bandwidth instead of increasing the number of modulators. In a previous work [25], Myslivetsan et al. reported an architecture relied on efficient creation of higher-order mixing tones in phase-matched nonlinear fiber stages separated by a linear compressor. However, the use of dual independent carriers may result in the uncorrelated frequency drifts. In 2013, by seeding a directly generated 3.1 ps Gaussian pulse train from an EO comb into a HNLF in the normal dispersion regime, Rui Wu et al. generated a flat-topped OFC covering the whole C-band with 10-GHz repetition rate and ∼365 lines within 3.5 dB power variation [26]. Nevertheless, the flatness of the comb is expected to be further improved. In 2014, Vahid Ataie et al. combined a continuous wave (CW) generation of high-count frequency combs and practical means for ultra-flat spectral equalization for the first time [27]. Since then, a series of signal processing work around the broadband flat EO combs has been carried out [28–31]. Despite of these works, few studies on the features of the EO comb after spectral broadening in the time domain has been reported so far.
In addition to flatness and spectrum width, high coherency is another extremely important criterion for measuring the spectral quality of broadband OFCs, which profoundly affect the accuracy of the combs applied in instantaneous frequency measurement, gas spectrum detection, fiber transmission technology, etc. In [32], the linewidth and phase noise characteristics of 25-GHz-spaced EO comb have been theoretically reckoned and measured. Although a 16-kHz linewidth tunable laser was used to beat with the selected comb mode to be measured, the phase noise cannot be measured at the offset frequency of less than 1 MHz due to the instability of the tunable laser. In [33], the phase noise of 49 EO comb lines was measured simultaneously based on mixing two OFCs with slightly different frequency spacing. However, the phase noise characteristics of the comb after nonlinear broadening were not considered.
In this paper, we demonstrated an efficient generation of a sub-100 fs all-fiber electro-optic optical frequency comb at 1.5 µm with a repetition rate of 12.5 GHz. More than 1500 comb lines over 150 nm bandwidth with a flatness of 6 dB was achieved. The final compressed main pulse width of the frequency comb was ∼86 fs. Numerical simulation showed the spectral and temporal evolutions of the comb broadening in details, which was consistent with the experiments. Besides, we also measured the linewidth characteristics of the comb lines by means of delayed self-heterodyne interferometric (DSHI) technique. The results indicate that linewidth scales quadratically with the comb line number and the process of spectral broadening aggravates the deterioration of the linewidth. Further experiment shows that the phase noise shape of high order comb line matches that of the RF oscillator driving the comb. It is indicated that if RF oscillators with low phase noise and phase locking loops were used, the coherence of broadband EO comb is expected to be further improved.
2. Experiment setup and results
2.1 Experiment setup
The experimental setup of the sub-100 fs all-fiber EO comb with 12.5 GHz repetition rate is depicted in Fig. 1. A CW laser centered at 1550.118 nm was modulated by three phase modulators (PMs) and an intensity modulator (IM). These modulators were driven by a tailored RF oscillator at 12.5 GHz frequency and controlled by a power amplifier and a phase shifter separately (not depicted in Fig. 1). The PMs provided positive chirp necessary for pulse compression, and the nonlinear effect of the IM was used to improve the flatness of OFC. Subsequently, linearly chirped pulse was primally compressed to ∼2 ps in an 850 m single-mode fiber (SMF) with a group-velocity-dispersion (GVD) coefficient of 18 ps/(nm·km). Then the comb pulses experienced two reshaping/compression stages successively. The first reshaping/compression stage was made of an Er-doped fiber amplifier (EDFA), a homemade nonlinear optical loop mirror (NOLM) and a 12 m SMF. While the second one consisted of an EDFA, a homemade NOLM and a 0.5 m SMF. The first NOLM loop was fabricated with a 50 m HNLF a 2×2 optical coupler (split ratio 60:40). And the second NOLM was composed of a 3 m HNLF and a same 2×2 optical coupler. Two polarization controllers were insert into the two NOLMs to achieve the best filtering effect.
Fig. 1. Experimental setup. EDFA: Er-doped fiber amplifier, PM: phase modulator, IM: intensity modulator, SMF: single-mode fiber, HNLF: highly nonlinear fiber, NOLM: nonlinear loop mirror.
Theoretically, an effective nonlinear broadening process could perform in HNLF only if the strict phase matching and sufficient power conditions are met. Nonlinear effect including FWM and SPM is governed by the mixer figure of merit (FoM), defined by the product of nonlinear coefficient ($\gamma $), optical power (P), and effective interaction length (L). Therefore, precise control of the SMF length and efficient nonlinear filtering of the NOLMs are crucial to produce near-ideal pulses with high peak power. Compared with our previous work [34], two NOLMs were adopted instead of one nonlinear amplified optical loop mirror (NALM) in order to avoid the influence of dispersion effect in passive fiber of EDFA on pulses in the loop. Note that the two optical circulators were applied to exclude reflected low power part of the pulses including sidelobes from NOLMs. Afterwards, high peak power pulses accomplished strong nonlinear mixing in the final 30 m HNLF (D < −1.0 ps/(nm·km) at 1550 nm, nonlinear coefficient >10 /W/km). Finally, a 3 m SMF was applied to compensate dispersion for the generation of ultrashort pulses. All the SMFs or HNLFs used in our experimental system belong to the same type.
2.2 Temporal and spectral characterization
Figure 2 indicates autocorrelation traces illustrating pulse evolution after different stages corresponding to these numbered points in Fig. 1. After compression in the 850 m SMF, the pulse width was 2.32 ps. Through two reshaping/ compression stages, a near-ideal Gaussian pulse was obtained with 117 fs width, which signified the favorable suppression of the parasitic sidelobes. The output power of the EDFA2 was ∼1.4 W, prior to the second NOLM, while after the second reshaping /compression stage, the obtained peak power leading up to mixing stage was over 350 W. Due to a certain amount of dispersion effect in the last 30 m HNLF, the pulse width was stretched to 4.6 ps. Nonetheless, after the last section of 3 m SMF, the pulse was compressed by more than 50 times to generate 86 fs pulse with 12.5 GHz repetition. Such high–repetition rate source of few-cycle pulses with sub 100 fs pulse width could be valuable for applications like optically controlled electronics [35], where both fast switching speeds and peak intensity are important. It can be observed that there is a pedestal in the last autocorrelation plot. This was attributed to a long train of shock waves following the pulse front caused by high-order dispersion. Hence, our fitting was only performed on the main pulse in the center part of the autocorrelation trace instead of the low-power pedestal data.
Fig. 2. Autocorrelation traces at different positions. (1) After the 850 m SMF; (2) after the 12 m SMF; (3) after the 0.5 m SMF; (4) after the 3 m SMF.
Meanwhile, the spectral evolution of the OFC at these numbered points measured with an optical spectrum analyzer (OSA) with a resolution bandwidth of 1 nm. is shown in Fig. 3. Besides, the insets show partial spectral details measured at a resolution of 0.02 nm. According to these results observed from the OSA, the initial number of comb lines was 23 within 5 dB after modulated by EO modulators. In contrast, 1500 tones over 100 nm bandwidth within 6 dB flatness was achieved in the end. Although limited by the resolution of OSA, a 50 dB optical signal to noise ratio (OSNR) can be reckoned from noise floor. The final spectrum also reveals that OSNR of the comb lines decreased with respect to the offset with the center frequencies. Since the zero-dispersion wavelength of HNLF is near 1680 nm, the OSNR in the shortwave direction attenuate faster. In addition, broadening process was not spectrally equalized, especially in the central regions, which also enhanced noise in the wings of the spectrum. This is primarily due to substantial generation of dispersive waves that are not part of the soliton spectrum and result in spectral nonuniformities [36]. Even so, a more detailed inspection into the spectrum (see Fig. 4) demonstrates that broadband OFC providing more than 350 tones in C-band within 5 dB flatness and 600 tones in L-band within 3 dB flatness could be well served as a multi-wavelength source for coherent channel transmitters. The measured average power of the broadband comb is over 550 mW, and the calculated power of each comb line is around −4 dBm.
Fig. 3. Spectral evolution at different positions. (1) The seed comb; (2) After NOLM1; (3) After NOLM2; (4) After the mixing stage.
2.3 Numerical simulation and analysis
In order to illustrate the whole spectral broadening process, the spectral and temporal evolutions of the EO comb as a function of the propagation distance are examined in Fig. 5 by solving the nonlinear Schrodinger equation. The original EO seed comb which occupied 4 nm bandwidth had same shape envelope as that produced by the experiment, corresponding to the total phase reversal of modulators over 10 $\pi $. The evolution of the spectrum shown in Fig. 5(e) clearly depicts the spectral evolution of EO comb in the two reshaping/compression stages and the final mixing process. As can be seen, the spectrum gradually expanded from the initial 23 comb lines to more than a thousand of comb lines. While performing pulse shaping, the two NOLM loops slightly broadened the spectrum due to the existence of HNLF. When compressed pulses with high peak power were injected into the last 30 m HNLF, the spectrum was rapidly broadened under the strong frequency mixing effect. The simulated output spectrum covering 100 nm within a 3 dB flatness is displayed in Fig. 5(b). Since the parameters used in the simulation were optimized, the simulated spectral flatness is even better than the experimental results. It is noted that the fluctuation in the center of the spectrum caused by the residual low-power signal light in the experiments could also be verified by the simulation as depicted in Fig. 5(b).
Fig. 5. NLSES based simulation of spectral and temporal evolution. (a) spectrum of the seed comb; (b) spectrum after the last section of HNLF; (c) pulse after the 850 m SMF; (d) pulse after the last section of SMF; (e) spectral evolution from the first NOLM to the last SMF; (f) temporal evolution from the first NOLM to the last SMF.
As shown in Fig. 5(c), a pulse with a width of nearly 2 ps was obtained after compression by 850 m SMF. The temporal evolution of the EO comb is shown in Fig. 5(f). As can be seen, the EDFAs not only amplified the compressed pulse signal, but also amplified the low-power sidelobes. Thanks to the two NOLM loops, pulse sidelobes could be effectively suppressed. Besides, three pulse narrowing stages caused by effective dispersion compensation can be detected, corresponding to three sections of SMF. Eventually, the EO comb had an asymmetric pulse shape comprised with a ∼90 fs main pulse and a ∼1.3 ps pulse tail as shown in Fig. 5(d). Through simulations, it is very easy to know that the pulse tail originated from uncompensated high-order dispersions in the fiber chain [37]. And the pulse tail corresponds to the picosecond pedestal measured in the autocorrelation trace as shown in Fig. 2(4). Generally speaking, the numerical simulation agrees very well with the experimental results, indicating that it could be used to design EO comb systems with more diverse parameters.
2.4 Comb linewidth characterization
The spectral shape of an EO comb is expected to be sets of ideal Dirac structures in terms of theory. Indeed, an EO comb is the result of the interaction between the microwave signal and the CW laser. Moreover, nonlinear broadening process also bring about the interaction between pulses. Thus, noises caused by different sources are inevitably incorporated and it will widen the linewidth of the comb lines even disrupt comb coherent structure, which seriously limits the application of combs in coherent detection and communication. Besides, undesirable decreased optical signal-to-noise ratio (SNR) of the lines may occur.
In order to characterize the coherence between the comb lines, we applied the DSHI technique to measure the linewidth of the comb lines before and after the spectral broadening. As shown in Fig. 6, in order to measure the linewidth of each line of the generated parametric OFC, a tunable narrowband filter was used in the experiment to filter out the selected comb line, and then the DSHI method was applied. Specifically, the light of the selected comb line was split into two paths, one of which was delayed by a 50 km SMF and the other light experience frequency shift through an acousto-optic modulator (AOM) driven by a 40 MHz RF oscillator. In final, the resulting beat response was measured. It is worth noting that in this case the 3 dB spectral spread is twice the original value [38].
Figure 7 shows the dependence of the linewidth on comb line number as well as the measured linewidth characteristics of the tenth comb before and after broadening, respectively. Limited by the tuning range of the filter, we discretely selected dozens of comb lines within the 1530–1570 nm bandwidth for measurement after broadening, namely, the ±1st, ±2nd, ±3rd, ±4th, ±5th, ±6th, ±7th, ±8th, ±9th, ±10th, ±20th, ±30th, ±40th, ±50th, ±100th, ±150th and ±200th comb lines. The linewidths of the 20 seed comb lines are less than 10 kHz initially, while the linewidths of the 400 broadened comb lines are less than 1 MHz after broadening. From the results, we can get two conclusions: First, on both sides of the central comb, the linewidth changed almost symmetrically. This was because that the EO modulation was centered on the frequency of CW and expanded symmetrically on both sides, and so was the nonlinear frequency broadening process. Second, the relationship between the linewidth and the number of comb lines was parabolic, no matter before or after broadening. This can be attributed to the accumulation of noise from the RF source. As mentioned in [32], the linewidth difference $\Delta {f_k}$ between the zeroth mode and the kth mode before broadening can be expressed as
Fig. 7. (a) Dependence of the linewidth on comb line number before and after broadening. (b)The linewidth characteristics of the tenth comb before and after broadening.
The linewidth of the CW laser source in our experiment was around 3 kHz, but the linewidth of the comb lines deteriorated to several hundred kHz after broadening. In order to further confirm the influence of the phase noise of the RF oscillator, we carefully performed the phase-noise characterization using a laser source with a narrow linewidth (<100 Hz) and high stability at 1537.4 nm to beat with the 168th comb line to it. The photodetector mixed the optical fields of the two lasers to produce an electrical RF tone at the frequency difference between the two optical frequencies.
The phase of the seed comb line after EO modulation can be expressed as:
where ${\theta _L}$ is the phase of the CW laser and ${\theta _{RF}}$ is the phase of the RF oscillator. The cascade of FWM leads to the scaling of phase in the higher-order FWM components as follows [39]:If the m-th order comb line and the n-th order comb line were regarded as pump seeds, the phase of the N-th order comb line can be expressed as:
According to the above equation, we can conclude that the phase noise of the RF oscillator is multiplied to the high-order comb line. Figure 8 shows the phase noise of beat note and the 12.5 GHz RF oscillator. At the offset frequencies from 100 Hz to 10 kHz, the phase noise of the corresponding comb line reflected by the beat note was the integration of the CW laser source and the RF oscillator. At the same time, the near-end phase noise of the comb lines was also affected by other factors such as link disturbance, environmental vibration and temperature changes. The length of the optical fiber link required by our experiment is about 960 m. Hence, the near-end phase noise of the 168th comb line was obviously raised after broadening due to these factors. At the offset frequencies from 10 kHz to 100 MHz, the phase noise of the comb line was an approximate reproduction of the RF oscillator. It is precisely because the phase noise of the RF oscillator is not effectively suppressed, the linewidth of the comb line is broadened the nearly 40 dBc/Hz increase in vertical axis was due to the accumulation of phase noise as the number of comb line increase to 168. Under the influence of the RF oscillator, the linewidth of the EO comb lines was continuously expanded, and this characteristic deteriorated during the mixing process. In [35,40,41], phase noise reduction and coherence improvement can be achieved by adopting RF oscillator phase-locked to the CW pump source via f-2f stabilization of the carrier–envelope offset, or locking the corresponding comb line to the ultra-stable laser as the reference frequency standard.
3. Conclusions
In summary, we presented a sub 100 fs all-fiber broadband optical frequency comb seeded from an EO modulated CW laser seed with 12.5-GHz repetition rate at 1.5 µm in this paper. Combining experimental research and numerical analysis, an 86-fs pulse with a 6 dB spectral bandwidth of >150 nm and over 1500 comb lines was achieved. The width of the output pulse was close to the high-order dispersion limit, and the calculated power of a single comb line was ∼ −4 dB, which could be utilized in frequency conversion, optical comb spectroscopy, absolute distance measurement, etc. In addition, the linewidth characteristics of the comb lines before and after the spectral broadening were measured. Specifically, the linewidths of the 20 seed comb lines were less than 10 kHz, while the linewidths of the 400 broadened comb lines deteriorated to several hundred kHz after broadening, which indicates that a low phase noise RF source or phase locking technology should be used for the generation of ultrahigh coherent combs. In the following work, we will carry out research on the application of dual optical comb interleaved spectroscopy, and adopt methods such as phase locking and environmental noise isolation to further improve its stability.
Funding
National Natural Science Foundation of China (Grant Nos. 11804387, 11802339, 11805276, 11902358, 61805282, 61801498, and 62075240); the Scientific Researches Foundation of National University of Defense Technology (Grant Nos. ZK18-03-22, ZK18-01-03, and ZK18-03-36); the National Science Fund for Distinguished Young Scholars of Hunan Province (Grant No. 2020JJ2036).
Acknowledgement
The authors would like to thank Dr. GuoChao Wang for providing the special optical fiber fusion splicer and Dr. Mo Chen for helpful discussions on the phase noise measurement method.
Disclosures
The authors declare no conflicts of interest.
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