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Abstract
Injecting a weak narrow-linewidth CW trigger to control the picosecond pulse pumped supercontinuum (SC) generation in a highly nonlinear dispersion shifted fiber (HNL-DSF), the Raman soliton at 2 μm is experimentally observed. We demonstrate that the cascaded four-wave mixing (FWM) caused by the weak CW trigger accelerates soliton fission and collision, and the large red-shift by the Raman effect in fibers induces obvious Raman soliton occurring in the long wavelength range of SC. A reduced effect on spectral modification on the SC spectrum at higher pump powers is also observed in the experiment. Simulations of the spectral evolution and spectrogram are carried out to verify the experimental observation. Both experiment and simulation results show the SC characteristics in the mid-infrared region can be greatly improved by the triggering effect.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
SC generation in nonlinear fibers has been demonstrated as an effective approach to obtain ultra-broadband light source, which is widely utilized in various fields, such as optical coherence tomography [1], optical frequency metrology [2,3], and environmental monitoring [4]. SC can be efficiently generated by femtosecond (fs), picosecond (ps), nanosecond (ns) or CW pump in highly nonlinear fibers [5]. Compared with the fs pulse pump, the long pulse pump, namely ps, ns, or CW, is relatively easy to be realized and less sensitive to environmental perturbations. In order to achieve a broadband SC spectrum using the minimum length of fiber necessary, the pump wavelength is preferred to be in the slightly anomalous dispersion region of the highly nonlinear fiber, where the required bandwidth is achieved with a fiber length around the characteristic fission length [5]. But the SC pumped by long pulses is generally unstable [6], which does not support some applications such as pulse compression [7,8] and coherent spectroscopy [9,10].
Injecting a weak seed within the modulation instability (MI) gain region can greatly influence the SC generation process, and the resulting SC characteristics can be modified. A weak fs pulse seed was used to modify the bandwidth, stability and rogue soliton statistics of SC, but the experiment was complex which requires precise control on the fs pulse time delay and frequency shift [11]. A low noise SC generation in the ps pulse pumped regime was experimentally demonstrated by coherent seeding with two-color output from a parametric oscillator [12]. The possibility of generating SC in highly nonlinear fibers with improved stability through modulation of the input pulse was also numerically demonstrated [13,14]. but it was relatively difficult to be verified by the experiment. Influences of pump power and Raman gain spectrum on the noise properties, coherence and intensity stability of seeded SC was further discussed by modulating the pump pulse with a seed [15,16]. A weak CW trigger at 10−6 of pump power was used to enhance the SC spectral bandwidth and coherence [17]. Influences of a weak CW trigger on ps or fs pumped SC generation were numerically studied, where modifications of bandwidth, coherence, stability, and rogue waves statistics under different CW triggers were demonstrated [18,19]. Compared with the techniques of a fs pulse seed or a ps pulse seed with THz modulation, adding a weak CW trigger is a simple and handy approach, which only requires adjusting wavelength and power of the CW.
The influence of seeding on SC with a partially phase coherent weak pulse or CW was numerically demonstrated, and a nearly coherent seed pulse was needed to achieve a coherent pulse break-up and low noise SC [16]. An incoherent laser was demonstrated experimentally to control the spectral bandwidth and noise property of MI in the spectral range of 1420 nm - 1680 nm, but the coherence improvement was limited by the incoherent ASE trigger [20]. By adding CW-seeds with phase-modulation frequency from 100 kHz to 10 MHz, the effect of the linewidth of the CW trigger on the temporal coherence of the SC was investigated, but the FWM in triggered SC spectrum was not obvious, and the interference spectra was shown in a relatively narrow wavelength range 1550 nm to 1620 nm [21]. Up to now, for the weak CW trigger, the modification of SC was experimentally investigated in near-infrared region (<1700 nm) [11,12,17,20,21], whereas it might be expected to study the modification of the long wavelength of SC in mid-infrared region, which has various potential applications [22–24]. For different linewidth CW triggers, only the temporal coherence was studied in near-infrared spectrum range [21], and the influence of the CW trigger on the spectral characteristic at 2 μm region has not been experimentally reported.
In this paper, a narrow-linewidth tunable CW trigger is used to trigger the SC generation in HNL-DSF pumped by a ps pulse laser, and the long wavelength extension caused by the Raman soliton is experimentally studied. By changing the CW power and wavelength, this phenomenon is investigated in detail, and the influence of pump power on spectral broadening is also analyzed. The theoretical study of the generalized nonlinear Schrödinger equation (GNLSE) is implemented for the triggered SC generation, and the results are compared with the experimental results. To the best of our knowledge, this is the first experimental observation of 2 μm Raman soliton of SC through injecting a weak narrow-linewidth CW trigger, leading to the improvement of SC characteristics, including bandwidth, coherence and signal-to-noise ratio (SNR).
2. Experimental setup
The experimental setup of SC generation in HNL-DSF triggered by a weak CW is shown in Fig. 1. The pump laser is a multi-stage high-gain Er:Yb co-doped fiber amplifier at a wavelength of 1555 nm (Amonics). The output pulse duration is 50 ps, and the repetition rate is 100 MHz. The maximal average output power of the amplifier is 10.2 W, which corresponds to a peak power of 2.04 kW. A high-performance tunable CW laser (TSL-710, Santec) with 100-kHz linewidth, is used as a trigger, and the tuning range is from 1480 nm to 1640 nm. The CW laser has a high SNR of over 90 dB/0.1 nm, and the maximum power can be up to 30 mW. Two isolators are employed to protect the pump and trigger from damaging by the back-reflected light. The polarization controllers (PCs) located before the coupler are utilized to match the polarization of the pump and trigger light. The pump laser and tunable trigger are combined by a 10/90% high power fiber coupler, and then launched into an 82.5-meter HNL-DSF (YOFC, NL-1550-Zero) with zero-dispersion wavelength at around 1550 nm, where the dispersion slope is 0.017 ps/nm2/km [25]. The nonlinear coefficient γ is calculated by use of the mode field diameter (4.05 μm @ 1550 nm) as an estimate of the effective area Aeff, and γ = 2πn2/(λAeff) ~9.4 /W/km, where n2 is assumed to be ~3 × 10−20 m2/W. The output SC spectrum is measured by an optical spectrum analyzer (AQ6375B & AQ6370D, Yokogawa). The output power is monitored by a power meter (S148C, Thorlabs) with a power range from 1 μW to 1 W for the wavelength range from 1200 nm to 2500 nm.
In order to study the spectrum modification of SC triggered by an incoherent light, a narrow bandwidth amplified spontaneous emission (ASE) source is also used as a trigger for comparison. A versatile manually optical tunable filter that allows both wavelength tuning (1530 nm - 1610 nm) and passband width tuning (0.1 nm - 15 nm) (TF-350, Santec) is used in our experiment. A low power ASE source covering wavelength from 1500 nm to 1650 nm is filtered by the tunable bandpass filter (TBF). The filtered broadband source is then used as a seed and amplified by an erbium-doped fiber amplifier (EDFA) with the output power up to 45 mW.
3. Results and discussion
We start our detailed analysis of SC with CW trigger at different position with respect to the MI gain spectrum. When the CW trigger locates in the MI gain band, the CW trigger plays a leading role in MI process instead of random noise for SC generation. The pump peak power in our experiment is 38 W measured by the power meter. The MI gain band extends from zero detuning up to a maximum frequency of (1/2π) (4γP0/|β2|)1/2 = 6.56 THz, which corresponds to wavelengths at 1502.1 nm and 1607.9 nm. The maximum trigger power injected in HNL-DSF is 24.3 mW, which has considered the insertion losses of fiber coupler and mode field adaptor. Sweeping the trigger wavelength from 1500 nm to 1610 nm, obvious spectrum broadening happens for CW trigger at 1544 nm or 1566 nm. Since 1544 nm and 1566 nm CW triggers have similar spectra, we only focus on the results with 1544 nm CW trigger in the following discussions.
Figure 2(a) illustrates the output spectra measured by AQ6375B from the HNL-DSF with untriggered SC (blue curve) and triggered SC (red curve). The generated SC shows spectral bandwidth and intensity enhancement on both blue-shifted and red-shifted sides when the narrow-linewidth CW is injected. The spectral ranges of untriggered and triggered SC are 1333.1 nm - 2040.2 nm and 1233 nm - 2115.5 nm in −30 dB level of intensity, and the spectral bandwidth is broadened by 175.4 nm for the triggered SC. Owning to the large MI gain of 1544 nm CW trigger, strong cascaded FWM is observed in the wavelength range from 1425 nm to 1635 nm, which are shown in the inset of Fig. 2(a). The induced Raman soliton at 2 μm region is experimentally observed in long wavelength of generated SC, and typical Raman spectrum has been shown in Fig. 2(a). In the short wavelength range, we can also observe the corresponding dispersion waves in the spectrum. The strong cascaded FWM can cause the transfer of energy in the SC spectrum. In order to investigate the transfer of energy in the red-shifted side, the spectral power density is measured by the OSA and shown in Fig. 2(b). The spectral power density in above 1800 nm region descends rapidly in untriggered SC, while the spectral power density of the CW triggered SC is enhanced tremendously and a strong spectral envelope is observed at 2 μm. This result conforms to the Raman spectrum in Fig. 2(a), and it suggests that the energy of the SC spectrum is transferred to red-shifted side, hence the spectral width is enhanced.
Fig. 2 The output spectra of SC in untriggered and CW triggered at 1544 nm: (a) the output spectral on logarithmic scale; (b) the output average spectral power density linear scale in above 1800 nm region.
The spectrum broadening can be attributed to the cascaded FWM in the triggered SC generation. This process can be described by the MI gain spectrum gMI and Raman gain spectrum gR, and the expressions of gMI [15] and gR [26] are:
where ωp is the pump frequency. P0 is the pump power. Ω = ω-ωp is the angular frequency offset relative to the pump. Δko and Δke are sums over odd and even order derivatives of the propagation constant β. and hR(Ω) are the nonlinear response of silica fiber and Raman response function in frequency domain. Figure 3 shows the spectra of untriggered and triggered SC in MI and Raman gain region of HNL-DSF. Compared with the untriggered SC, the multiple FWM spectral sidebands are generated when the weak 1544 nm CW trigger is added, and the cascaded FWM can be clearly seen in MI and Raman gain spectrum. In addition, the intensity of SC in Raman gain spectrum is improved by the weak CW trigger, which is much stronger than the untriggered SC. This phenomenon indicates that more energy in SC is transferred to the Raman gain region. When the SC spectrum covers the Raman gain spectrum, the Raman-induced soliton self-frequency shift dominates the long wavelength of SC. The explicit process is that the cascaded FWM in triggered SC results in a faster soliton fission, and the stronger soliton collision lead to a higher intensity fundamental soliton subsequently. The generated solitons experience a larger red-shift by the Raman effect, and a significant red-shifted spectral component can be shown in long wavelength of SC. Hence, the triggered SC spectrum is broadened, and the obvious Raman soliton is observed in the experiment.Fig. 3 The MI and Raman gain curves of HNL-DSF under 38 W pump power, and output spectra of untriggered and triggered SC are shown in this region.
The CW trigger power can also influence the SC generation. In the experiment, the trigger power is tuned from 0 to 24.3 mW, and the output spectra with different trigger powers are illustrated in Fig. 4(a). The trigger wavelength is fixed at 1544 nm. It can be clearly observed that the effective spectral bandwidth is vastly broadened as the trigger power increases, and the cascaded FWM becomes stronger at a higher trigger power. An obvious Raman soliton in long wavelength of SC can be observed at trigger power of 24.3 mW, which is 6.3 × 10−4 of the pump power. To further study the influence of trigger wavelength on SC generation, we tune the CW trigger wavelength in MI gain region, and the trigger power is fixed at ~24.3 mW. We select six different wavelength positions of 1535 nm, 1540 nm, 1542 nm, 1544 nm, 1546 nm, 1548 nm in MI gain spectrum, the output spectra triggered by each selected wavelength are measured and shown in Fig. 4(b). Compared with the untriggered SC spectrum, the spectral broadening is obvious when the trigger locates in 1542 nm, 1544 nm and 1546 nm, and the corresponding trigger induced bandwidth broadening are 158.6 nm, 175.2 nm and 140.3 nm. Additionally, we found that little spectra broadening happens when the trigger locates in a lower or higher gain region such as 1540 nm and 1548 nm, and the trigger induced bandwidth broadening are only 38.2 nm and 52.6 nm. It can be explained that the CW trigger which is placed in the lower MI gain region, cannot support the significant beating effect because of a short interaction length with the pump pulse [15]. While the trigger locates in the higher MI gain region such as 1535 nm in Fig. 4(b), a stronger FWM in SC can be observed, but this process consumes a rather portion of pump power and the resulting SC is narrowed by 44.6 nm. It can also be noted that the MI gain spectrum has a symmetrical lobe, and the trigger which locates in short wavelength or long wavelength region of gain spectrum can provide similar effects for the SC generation. We also measured the output spectra when the trigger locates in long wavelength of MI gain spectrum which is from 1555 nm to 1610 nm, and obviously spectral broadening can be observed at trigger wavelength of 1566 nm.
Fig. 4 (a) Output SC spectra triggered by 1544 nm CW with different powers: no trigger (black curve), 4.1 mW (red curve), 12.1 mW (blue curve) and 24.3 mW (purple curve); (b)The measured output spectra of untriggered and triggered by six different CW wavelengths.
To demonstrate the power dependency of the CW triggering, we measured the output spectra in different pump powers when the trigger is 23.4 mW at 1544 nm. Figures 5(a)-5(c) show the comparison between the output spectra with the pump powers of 32 W, 44 W and 56 W. Output spectra for pump power below 32 W are not considered here because there is no obvious bandwidth broadening for pump power under 32 W. At the pump power of 44 W, an effective spectral broadening can be observed in the long and short wavelength of SC. While the pump power further increases to 56 W, the spectra of untriggered and triggered SC nearly overlap as shown in Fig. 5(c), which means that the triggering effect is weakened at a relatively high pump power. Figure 5(d) shows the induced spectral bandwidth broadening for CW triggered SC at −30 dB level as the pump power increases, where dots and solid line represent the experiment data and its polynomial fitting. At lower pump powers, the spectral width increases rapidly. After reaching a maximum bandwidth broadening of 175.2 nm at the pump power of 38 W, the broadening spectral width gradually decreases when the pump power increases. When the pump power is beyond 56 W, the trigger induced bandwidth broadening is almost negligible.
Fig. 5 The output spectra in different pump powers: (a)-(c) the output spectra at pump power of 32 W, 44 W and 56 W; (d) the induced spectral bandwidth broadening at −30 dB versus the pump power, and the red solid line is a fitting curve.
Comparison of the SC modification between ASE and narrow-linewidth CW trigger is also carried out in our experiment, and the corresponding output spectra are measured. As illustrated in Fig. 1, the broadband source is filtered by TBF with a 0.8 nm bandwidth and the central wavelength is 1544 nm, which is the same as the narrow-linewidth CW trigger. The filtered broadband source is then injected to the EDFA as a seed, and the output power is maintained at 24.3 mW by adjusting the pump current. When the filter bandwidth is below 0.8 nm, the filtered ASE source cannot be amplified by the EDFA since the spontaneous emission noise restrains the amplification. The output spectra of narrow-linewidth CW and filtered ASE source are shown in Fig. 6(a). The ASE source is added to the SC generation in HNL-DSF, and the output spectrum is shown in Fig. 6(b). It can be observed that the SC spectrum is also broadened by the ASE source with observable Raman soliton. However, compared with the narrow-linewidth CW trigger, the spectral width enhancement is insufficient. The cascaded FWM caused by the ASE source is weak with lower intensity and the spectral width is narrower than that caused by the narrow-linewidth CW trigger. The reason can be analyzed as following. The coherence time of the trigger is described by τc = λ02/(c∆λ), where ∆λ represents the trigger bandwidth and c is the speed of light in fiber. For the 0.8 nm bandwidth incoherent ASE source centered at 1544 nm, the coherence time 9.9 ps is significantly less than the 50 ps pump pulse duration, which means a weak modulation effect by the incoherent ASE source across the pump pulse.
Fig. 6 (a) The output spectra of an ASE source and a narrow-linewidth CW; (b) The output spectra of SC untriggered and triggered by two different CW triggers.
4. Numerical simulation
To get an insight into the dynamics of the SC generation triggered by a weak CW, the GNLSE including the third-order dispersion (TOD), Raman effects, self-steepening and optical shock formation, is used to simulate the SC generation [4,27]:
where A(z,t) is the slowly varying electric field envelope as a function of propagation distance z and time t along the fiber. The nonlinear response function R(t) = (1−fR) δ(t) + fR hR(t) accounts for the instantaneous and Raman responses, where fR = 0.18, and hR is the fused silica Raman responses function. τshock = τ0 = 1/ω0 is associated with the self-steepening effect and optical shocking. The dispersion parameters at pump wavelength 1555 nm are β2 = −0.832 ps2/km and β3 = 0.0442 ps3/km. α is the fiber propagation loss, and the measured value is 0.935 dB/km. The pump pulse in simulation is chirp-free Gaussian with FWHM of 50 ps, peak power 38 W, and central wavelength 1555 nm. The CW power Ptrigger is 24.3 mW, and the expressions of pump laser and CW trigger are described in [18]. The input random phase noise is included in the frequency domain using one photon per mode spectral density on each spectral discretization bin, and the noise amplitude is assumed to be 10−4 of the pump amplitude. The other parameters used in the simulation are the same as the experiment. Equation (3) is solved using the well-known split-step Fourier method [26].Figure 7 shows the simulation and experiment results of spectral evolution along the fiber span in untriggered and SC triggered at selected wavelengths of 1544 nm, 1535 nm, and 1548 nm. In the absence of CW trigger, the spectral broadening is initiated by MI, which spontaneously grows from the noise, and is followed by the onset of solitons, TOD, and interaction between different solitons. When a weak 1544 nm CW trigger is added as shown in Fig. 7(b), the spectra broadening is initiated by the CW trigger rather than the noise, and the spectral width is enhanced in around 20 m, which is shorter than the 25 m in Fig. 8(a). The cascaded FWM is also clearly observed in Fig. 7(b), which causes a coherent broadening, consequently the spectral coherence, SNR and stability of SC are greatly improved in the CW-triggered SC. It can be noted that a large soliton is formed in around 52 m, the spectral width and intensity are enhanced in red-shifted sides, and it is consistent with the experimental result in Fig. 2(a). When the CW trigger is 1535 nm which has a higher MI gain in Fig. 7(c), the stronger cascaded FWM can be observed, and the spectrum is broadened in a shorter fiber length. However, this process will consume massive pump power, and results in the output SC spectrum being narrowed. Figure 7(d) shows the spectral evolution of SC triggered at 1548 nm, and the spectral broadening is inconspicuous because of the lower MI gain. The averaged spectrum is an ensemble of 150 numerical realizations, and the simulation results are in a good agreement with experimental results. We have also numerically studied the temporal coherence and SNR of the CW-triggered SC. The spectrally averaged coherence [28] and the overall SNR [15] can be used to quantify the temporal coherence and the intensity stability of the SC spectrum, and in our examples they are calculated from an ensemble of 150 realizations in the 1200 nm - 2200 nm wavelength range. In the absence of the CW trigger, the average coherence and overall SNR are 0.12 and 1.31. Considering the 1544 nm CW trigger, the average coherence and overall SNR can be improved to 0.27 and 1.89 respectively. In particular, when the 1535 nm CW trigger is added, the average coherence and overall SNR are improved obviously, and the values are 0.54 and 6.79. The results indicate that the CW trigger with a higher MI gain is beneficial to the modification of the coherence and SNR. The average coherence and overall SNR of SC triggered by 1548 nm CW are also calculated, but the modification is not obvious because of the lower MI gain.
Fig. 7 The single-shot simulations of spectral evolution of SC in untriggered and triggered SC at 1544 nm, 1535 nm, 1548 nm, top rows show the averaged output spectra (red curve) and the experimental results (blue curve).
Fig. 8 The spectrogram of SC in untriggered and triggered at 1544 nm, top rows show the temporal pulse (brown curve) and right rows show the output spectrum (red curve).
Figure 8 shows the spectrogram of SC generation at fiber output corresponding to the results of Figs. 7(a) and 7(b) in untriggered and SC triggered at 1544 nm. In the untriggered SC, the pulse is slowly broken up into solitons, which is caused by the spontaneous MI in fiber. It can be seen the solitons are mainly generated in central region of pulse where the pump power is highest, but the amplitude and phase of the generated solitons are in a random fashion. The redshift to longer wavelength side is generated by the soliton fission and collision, therefore the dynamics is relatively turbulent. When the 1544 nm CW trigger is added, the temporal pulse is rapidly broken up, and can be attributed to the large MI gain at 1544 nm. Compared with Fig. 8(a), the solitons are deterministically generated, and they have high coherence and SNR because of the coherent nature of CW trigger as shown in Fig. 8(b). It should be pointed out that the cascaded FWM caused by the CW trigger lead to a faster soliton fission occurs in this condition. The energetic soliton fission facilitates the Raman-induced self-frequency shift in SC generation, and the red-shifted of the Raman soliton and the blue-shifted of the dispersive waves can be seen in Fig. 8(b), and the spectral bandwidth is drastically broadened. The simulation shows the process of the induced Raman soliton formation. Adding a weak narrow-linewidth CW trigger modifies the transition between MI gain and soliton fission, and the spectral characteristics are enhanced. In addition, the evidence of soliton collision can also be found in Fig. 8(b). When the spectral of two solitons are close enough for the Raman process to occur, the inelastic collision happens through the Raman process occurred, and the transfer of energy between low frequency solitons and high frequency solitons through this process.
5. Summary
In conclusion, we have experimentally observed the induced Raman soliton at 2 μm in the ps pulse pumped SC triggered by a narrow-linewidth tunable CW laser. Sweeping the CW wavelength in MI gain region, the strong induced Raman soliton occurs at 1544 nm and 1566 nm, and the spectral power density in red-shifted side is measured. The cascaded FWM caused by the weak CW trigger accelerates soliton fission and collision, the generated solitons experience a larger red-shift by the Raman effect in fiber, and the obvious Raman soliton is observed in SC. When the long wavelength of SC is spanned to 2 μm region, a higher trigger power is needed to generate stronger cascaded FWM in fiber, and the obvious spectrum modification happens at power of 23.4 mW, which is 6.3 × 10−4 as compared to the pump peak power. The spectral evolution and spectrogram of the untriggered and triggered SC generation are numerically studied, the simulation results are in good agreement with the experiment. To the best of our knowledge, this is the first demonstration of 2 μm Raman soliton of ps pulse pumped SC generation triggered by a 100-kHz linewidth CW trigger, and this work is expected to pave the way for obtaining an SC light source with high coherence, SNR, and stability in mid-infrared region.
Funding
National Natural Science Foundation of China (61675008, 61805281), Shenzhen Science and Technology Innovation Commission (KQJSCX20170727163424873), Tsinghua-Berkeley Shenzhen Institute (TBSI) Faculty Start-up Fund.
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